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Laureηt 2023-06-10 20:56:24 +02:00
commit 1fe10f27ff
Signed by: Laurent
SSH key fingerprint: SHA256:kZEpW8cMJ54PDeCvOhzreNr4FSh6R13CMGH/POoO8DI
87 changed files with 6840 additions and 0 deletions
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69
BE2019/.Naturelle.aux Executable file
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@ -0,0 +1,69 @@
COQAUX1 b99e0673e480d281145bd0be828a8006 /home/lfainsin/1A/Modé/BE2019/Naturelle.v
383 387 proof_build_time "0.000"
0 0 E_imp_th "0.000"
383 387 context_used ""
383 387 proof_check_time "0.000"
0 0 VernacProof "tac:no using:no"
916 920 proof_build_time "0.000"
0 0 E_forall_th "0.000"
916 920 context_used ""
916 920 proof_check_time "0.000"
1291 1295 proof_build_time "0.001"
0 0 E_et_g_th "0.001"
1291 1295 context_used ""
1291 1295 proof_check_time "0.000"
1601 1605 proof_build_time "0.001"
0 0 E_et_d_th "0.001"
1601 1605 context_used ""
1601 1605 proof_check_time "0.000"
1983 1987 proof_build_time "0.001"
0 0 E_ou_th "0.001"
1983 1987 context_used ""
1983 1987 proof_check_time "0.000"
0 0 VernacProof "tac:no using:no"
2806 2810 proof_build_time "0.001"
0 0 E_exists_th "0.001"
2806 2810 context_used ""
2806 2810 proof_check_time "0.000"
3280 3284 proof_build_time "0.000"
0 0 E_antiT_th "0.000"
3280 3284 context_used ""
3280 3284 proof_check_time "0.000"
3502 3506 proof_build_time "0.001"
0 0 I_antiT_th "0.001"
3502 3506 context_used ""
3502 3506 proof_check_time "0.000"
3683 3687 proof_build_time "0.000"
0 0 I_non_th "0.000"
3683 3687 context_used ""
3683 3687 proof_check_time "0.000"
4135 4158 context_used ""
4135 4158 context_used ""
4135 4158 context_used ""
0 0 VernacProof "tac:no using:no"
4398 4402 proof_build_time "0.003"
0 0 Yoga "0.003"
4398 4402 context_used ""
4398 4402 proof_check_time "0.000"
4404 4428 context_used ""
4404 4428 context_used ""
4557 4561 proof_build_time "0.001"
0 0 contra "0.001"
4557 4561 context_used ""
4557 4561 proof_check_time "0.000"
4642 4646 proof_build_time "0.001"
0 0 P2nnP "0.001"
4642 4646 context_used ""
4642 4646 proof_check_time "0.000"
4731 4735 proof_build_time "0.001"
0 0 nnP2P "0.001"
4731 4735 context_used ""
4731 4735 proof_check_time "0.000"
4737 4755 context_used ""
4756 4786 context_used ""
0 0 VernacProof "tac:no using:no"
4984 4988 proof_build_time "0.002"
0 0 Swap "0.002"
4984 4988 context_used ""
4984 4988 proof_check_time "0.000"
0 0 vo_compile_time "0.617"

254
BE2019/Naturelle.glob Executable file
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DIGEST b99e0673e480d281145bd0be828a8006
FNaturelle
R15:23 Coq.Logic.Classical <> <> lib
R97:100 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R97:100 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R218:221 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R218:221 Coq.Init.Logic <> ::type_scope:x_'->'_x not
prf 278:285 <> E_imp_th
R314:314 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R325:329 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R333:336 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R337:339 Naturelle <> psi var
R330:332 Naturelle <> phi var
R318:321 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R322:324 Naturelle <> psi var
R315:317 Naturelle <> phi var
R443:450 Naturelle <> E_imp_th thm
R521:528 Naturelle <> E_imp_th thm
prf 816:826 <> E_forall_th
R856:859 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R855:855 Naturelle <> A var
R869:869 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R885:889 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R890:892 Naturelle <> phi var
R894:894 Naturelle <> a var
R880:882 Naturelle <> phi var
R884:884 Naturelle <> x var
R996:1006 Naturelle <> E_forall_th thm
R1086:1089 Coq.Init.Logic <> ::type_scope:x_'/\'_x not
R1086:1089 Coq.Init.Logic <> ::type_scope:x_'/\'_x not
R1105:1108 Coq.Init.Logic <> conj constr
prf 1157:1165 <> E_et_g_th
R1194:1194 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R1205:1209 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R1210:1212 Naturelle <> phi var
R1198:1201 Coq.Init.Logic <> ::type_scope:x_'/\'_x not
R1195:1197 Naturelle <> phi var
R1202:1204 Naturelle <> psi var
R1352:1360 Naturelle <> E_et_g_th thm
R1432:1440 Naturelle <> E_et_g_th thm
prf 1465:1473 <> E_et_d_th
R1502:1502 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R1513:1517 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R1518:1520 Naturelle <> psi var
R1506:1509 Coq.Init.Logic <> ::type_scope:x_'/\'_x not
R1503:1505 Naturelle <> phi var
R1510:1512 Naturelle <> psi var
R1662:1670 Naturelle <> E_et_d_th thm
R1743:1751 Naturelle <> E_et_d_th thm
prf 1776:1782 <> E_ou_th
R1815:1815 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R1826:1830 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R1831:1831 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R1842:1846 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R1847:1847 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R1858:1862 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R1863:1865 Naturelle <> chi var
R1851:1854 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R1855:1857 Naturelle <> chi var
R1848:1850 Naturelle <> psi var
R1835:1838 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R1839:1841 Naturelle <> chi var
R1832:1834 Naturelle <> phi var
R1819:1822 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
R1816:1818 Naturelle <> phi var
R1823:1825 Naturelle <> psi var
R2042:2048 Naturelle <> E_ou_th thm
R2124:2130 Naturelle <> E_ou_th thm
R2194:2197 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
R2194:2197 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
R2213:2221 Coq.Init.Logic <> or_introl constr
R2305:2308 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
R2305:2308 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
R2324:2332 Coq.Init.Logic <> or_intror constr
R2416:2423 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R2430:2433 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R2439:2439 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R2438:2438 Naturelle <> x var
R2416:2423 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R2430:2433 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R2439:2439 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R2438:2438 Naturelle <> x var
R2453:2460 Coq.Init.Logic <> ex_intro constr
R2561:2568 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R2575:2578 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R2584:2584 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R2583:2583 Naturelle <> x var
R2561:2568 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R2575:2578 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R2584:2584 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R2583:2583 Naturelle <> x var
R2597:2604 Coq.Init.Logic <> ex_intro constr
prf 2669:2679 <> E_exists_th
R2709:2712 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R2708:2708 Naturelle <> A var
R2733:2733 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R2749:2753 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R2754:2754 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R2777:2781 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R2782:2784 Naturelle <> chi var
R2770:2773 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R2774:2776 Naturelle <> chi var
R2765:2767 Naturelle <> phi var
R2769:2769 Naturelle <> a var
R2734:2740 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R2742:2743 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R2744:2746 Naturelle <> phi var
R2748:2748 Naturelle <> x var
R2963:2973 Naturelle <> E_exists_th thm
R3083:3085 Coq.Init.Logic <> not def
R3116:3120 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
R3132:3132 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
R3123:3126 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R3127:3131 Coq.Init.Logic <> False ind
R3116:3120 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
R3132:3132 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
R3123:3126 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R3127:3131 Coq.Init.Logic <> False ind
R3145:3151 Coq.Logic.Classical_Prop <> classic prfax
prf 3209:3218 <> E_antiT_th
R3248:3251 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R3252:3254 Naturelle <> phi var
R3243:3247 Coq.Init.Logic <> False ind
R3340:3349 Naturelle <> E_antiT_th thm
prf 3370:3379 <> I_antiT_th
R3407:3410 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R3411:3411 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R3416:3420 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R3421:3425 Coq.Init.Logic <> False ind
R3412:3412 Coq.Init.Logic <> ::type_scope:'~'_x not
R3413:3415 Naturelle <> phi var
R3404:3406 Naturelle <> phi var
R3435:3437 Coq.Init.Logic <> not def
R3551:3555 Coq.Init.Logic <> False ind
R3551:3555 Coq.Init.Logic <> False ind
R3567:3576 Naturelle <> I_antiT_th thm
prf 3598:3605 <> I_non_th
R3630:3630 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R3643:3647 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R3648:3648 Coq.Init.Logic <> ::type_scope:'~'_x not
R3649:3651 Naturelle <> phi var
R3634:3637 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R3638:3642 Coq.Init.Logic <> False ind
R3631:3633 Naturelle <> phi var
R3669:3671 Coq.Init.Logic <> not def
R3730:3731 Coq.Init.Logic <> ::type_scope:'~'_x not
R3730:3731 Coq.Init.Logic <> ::type_scope:'~'_x not
R3745:3752 Naturelle <> I_non_th thm
R3801:3810 Naturelle <> I_antiT_th thm
R3875:3878 Coq.Logic.Classical_Prop <> NNPP thm
var 4144:4144 <> E
var 4146:4146 <> Y
var 4148:4148 <> R
prf 4168:4171 <> Yoga
R4175:4175 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R4203:4207 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R4210:4213 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R4214:4214 Coq.Init.Logic <> ::type_scope:'~'_x not
R4215:4215 Naturelle <> E defax
R4208:4208 Coq.Init.Logic <> ::type_scope:'~'_x not
R4209:4209 Naturelle <> R defax
R4176:4176 Coq.Init.Logic <> ::type_scope:x_'/\'_x not
R4190:4195 Coq.Init.Logic <> ::type_scope:x_'/\'_x not
R4202:4202 Coq.Init.Logic <> ::type_scope:x_'/\'_x not
R4178:4182 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R4189:4189 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R4184:4187 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
R4183:4183 Naturelle <> Y defax
R4188:4188 Naturelle <> R defax
R4177:4177 Naturelle <> E defax
R4197:4200 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R4201:4201 Naturelle <> R defax
R4196:4196 Naturelle <> Y defax
R4263:4263 Naturelle <> R defax
R4272:4272 Naturelle <> Y defax
R4274:4274 Naturelle <> R defax
R4285:4285 Naturelle <> E defax
R4300:4303 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R4304:4304 Naturelle <> R defax
R4299:4299 Naturelle <> Y defax
R4300:4303 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R4304:4304 Naturelle <> R defax
R4299:4299 Naturelle <> Y defax
R4343:4346 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R4348:4351 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
R4347:4347 Naturelle <> Y defax
R4352:4352 Naturelle <> R defax
R4342:4342 Naturelle <> E defax
R4343:4346 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R4348:4351 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
R4347:4347 Naturelle <> Y defax
R4352:4352 Naturelle <> R defax
R4342:4342 Naturelle <> E defax
var 4413:4415 <> phi
var 4417:4419 <> psi
prf 4438:4443 <> contra
R4447:4447 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R4458:4463 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R4476:4476 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R4468:4471 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R4472:4472 Coq.Init.Logic <> ::type_scope:'~'_x not
R4473:4475 Naturelle <> phi defax
R4464:4464 Coq.Init.Logic <> ::type_scope:'~'_x not
R4465:4467 Naturelle <> psi defax
R4451:4454 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R4455:4457 Naturelle <> psi defax
R4448:4450 Naturelle <> phi defax
R4517:4519 Naturelle <> psi defax
R4528:4530 Naturelle <> phi defax
prf 4571:4575 <> P2nnP
R4582:4585 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R4586:4586 Coq.Init.Logic <> ::type_scope:'~'_x not
R4587:4587 Coq.Init.Logic <> ::type_scope:'~'_x not
R4588:4590 Naturelle <> phi defax
R4579:4581 Naturelle <> phi defax
R4621:4623 Naturelle <> phi defax
prf 4656:4660 <> nnP2P
R4670:4673 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R4674:4676 Naturelle <> phi defax
R4664:4664 Coq.Init.Logic <> ::type_scope:'~'_x not
R4665:4666 Coq.Init.Logic <> ::type_scope:'~'_x not
R4667:4669 Naturelle <> phi defax
R4708:4708 Coq.Init.Logic <> ::type_scope:'~'_x not
R4709:4711 Naturelle <> phi defax
R4708:4708 Coq.Init.Logic <> ::type_scope:'~'_x not
R4709:4711 Naturelle <> phi defax
var 4746:4746 <> A
var 4765:4767 <> chi
R4772:4775 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R4777:4780 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R4776:4776 Naturelle <> A defax
R4771:4771 Naturelle <> A defax
prf 4796:4799 <> Swap
R4803:4803 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R4831:4836 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R4864:4864 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R4847:4853 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R4855:4856 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R4857:4859 Naturelle <> chi defax
R4863:4863 Naturelle <> y var
R4861:4861 Naturelle <> x var
R4804:4810 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R4812:4813 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R4824:4826 Naturelle <> chi defax
R4830:4830 Naturelle <> y var
R4828:4828 Naturelle <> x var
R4926:4926 Naturelle <> A defax
R4929:4931 Naturelle <> chi defax
R4935:4935 Naturelle <> y var
R4933:4933 Naturelle <> x var
R4926:4926 Naturelle <> A defax
R4929:4931 Naturelle <> chi defax
R4935:4935 Naturelle <> y var
R4933:4933 Naturelle <> x var

292
BE2019/Naturelle.v Executable file
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Require Export Classical.
Ltac Hyp Nom := exact Nom.
Ltac I_imp' :=
match goal with
| |- ?A -> ?B => let hyp := fresh "H" in intro hyp
| _ => fail
end.
Ltac I_imp Nom :=
match goal with
| |- ?A -> ?B => intro Nom
| _ => fail
end.
Theorem E_imp_th : forall (phi psi : Prop), (phi -> psi) -> phi -> psi.
intros Pphi Ppsi Hphi2psi.
Hyp Hphi2psi.
Qed.
Ltac E_imp' :=
match goal with
| |- ?P => eapply (E_imp_th _ P)
end.
Ltac E_imp phi :=
match goal with
| |- ?P => apply (E_imp_th phi P)
end.
Ltac I_forall' :=
match goal with
| |- forall (x : ?A), ?P => let hyp := fresh x in intro hyp
| _ => fail
end.
Ltac I_forall Nom :=
match goal with
| |- forall (x : ?A), ?P => intro Nom
| _ => fail
end.
Theorem E_forall_th : forall (A : Type) (phi : A -> Prop) a, (forall x, phi x) -> phi a.
Proof.
firstorder.
Qed.
Ltac E_forall x :=
pattern x;
match goal with
| |- (?P x) => apply (E_forall_th _ P x)
| _ => fail
end.
Ltac I_et :=
match goal with
| |- (?A /\ ?B) => apply (@conj A B)
| _ => fail
end.
Theorem E_et_g_th : forall (phi psi : Prop), (phi /\ psi) -> phi.
intros Pphi Ppsi Hphi_et_psi.
elim Hphi_et_psi.
intros Hphi Hpsi.
Hyp Hphi.
Qed.
Ltac E_et_g' :=
match goal with
| |- ?P => eapply (E_et_g_th P _)
end.
Ltac E_et_g psi :=
match goal with
| |- ?P => apply (E_et_g_th P psi)
end.
Theorem E_et_d_th : forall (phi psi : Prop), (phi /\ psi) -> psi.
intros Pphi Ppsi H_phi_et_psi.
elim H_phi_et_psi.
intros Hphi Hpsi.
Hyp Hpsi.
Qed.
Ltac E_et_d' :=
match goal with
| |- ?P => eapply (E_et_d_th _ P)
end.
Ltac E_et_d phi :=
match goal with
| |- ?P => eapply (E_et_d_th phi P)
end.
Theorem E_ou_th : forall (phi psi chi : Prop), (phi \/ psi) -> (phi -> chi) -> (psi -> chi) -> chi.
intros Pphi Ppsi Pchi Hphi_ou_psi Hphi_imp_chi Hpsi_imp_chi.
elim Hphi_ou_psi.
Hyp Hphi_imp_chi.
Hyp Hpsi_imp_chi.
Qed.
Ltac E_ou' :=
match goal with
| |- ?P => eapply (E_ou_th _ _ P)
end.
Ltac E_ou phi psi :=
match goal with
| |- ?P => apply (E_ou_th phi psi P)
end.
Ltac I_ou_g :=
match goal with
| |- (?A \/ ?B) => apply (@or_introl A B)
| _ => fail
end.
Ltac I_ou_d :=
match goal with
| |- (?A \/ ?B) => apply (@or_intror A B)
| _ => fail
end.
Ltac I_exists' :=
match goal with
| |- exists (x : ?A), (@?P x) => eapply (@ex_intro A P _)
| _ => fail
end.
Ltac I_exists t :=
match goal with
| |- exists (x : ?A), (@?P x) => apply (@ex_intro _ P t)
| _ => fail
end.
Theorem E_exists_th : forall (A : Type) (phi : A -> Prop) (chi : Prop), (exists x, phi x) -> (forall a, phi a -> chi) -> chi.
Proof.
firstorder.
Qed.
(*
Ltac E_exists phi :=
match goal with
| |- ?P => apply (E_exists_th _ phi P)
end.
*)
Ltac E_exists phi :=
match goal with
| |- ?P => apply (E_exists_th _ phi P); [ idtac | let t := fresh "t" in let ht := fresh "Ht" in intros t ht ]
end.
Ltac TE :=
unfold not;
match goal with
| |- (?P \/ (?P -> False)) => exact (classic P)
| _ => fail
end.
Theorem E_antiT_th : forall (phi : Prop), False -> phi.
intros Pphi F.
elim F.
Qed.
Ltac E_antiT :=
match goal with
| |- ?P => apply (E_antiT_th P)
end.
Theorem I_antiT_th : forall (phi : Prop), phi -> (~phi) -> False.
unfold not.
intro Pphi.
intros Hphi Hnphi.
cut Pphi.
Hyp Hnphi.
Hyp Hphi.
Qed.
Ltac I_antiT phi :=
match goal with
| |- False => apply (I_antiT_th phi)
end.
Theorem I_non_th : forall (phi : Prop), (phi -> False) -> ~phi.
intros.
unfold not.
exact H.
Qed.
Ltac I_non Nom :=
match goal with
| |- ~ ?P => apply (I_non_th P); intro Nom
end.
Ltac E_non phi :=
apply (I_antiT_th phi).
Ltac absurde Nom :=
match goal with
| |- ?P => apply (NNPP P); intro Nom
end.
(*
Ltac I_antiT phi := apply (I_antiT_th phi).
Ltac absurde Nom phi :=
match goal with
| |- phi =>
cut (phi \/ ~phi);
[
intros L;
elim L;
[
auto
|
clear L;
intro Nom;
apply (E_antiT_th)
]
|
apply (classic phi)
]
| _ => fail
end.
*)
Variable E Y R : Prop.
Theorem Yoga : ((E -> (Y \/ R)) /\ (Y -> R)) -> ~R -> ~E.
Proof.
I_imp H1.
I_imp H2.
I_non H3.
I_antiT R.
E_ou Y R.
E_imp E.
E_et_g (Y -> R).
Hyp H1.
Hyp H3.
E_et_d (E -> Y \/ R).
Hyp H1.
I_imp H4.
Hyp H4.
Hyp H2.
Qed.
Variable phi psi : Prop.
Theorem contra : (phi -> psi) -> (~psi -> ~phi).
I_imp H1.
I_imp H2.
I_non H3.
I_antiT psi.
E_imp phi.
Hyp H1.
Hyp H3.
Hyp H2.
Qed.
Theorem P2nnP : phi -> ~~phi.
I_imp H1.
I_non H2.
I_antiT phi.
Hyp H1.
Hyp H2.
Qed.
Theorem nnP2P : ~~ phi -> phi.
I_imp H1.
absurde H2.
E_non (~phi).
Hyp H2.
Hyp H1.
Qed.
Variable A : Type.
Variable chi : A -> A -> Prop.
Theorem Swap : (exists y, forall x, chi x y) -> (forall x, exists y, chi x y).
Proof.
I_imp H1.
I_forall x.
E_exists (fun y => forall x : A, chi x y).
Hyp H1.
I_exists t.
E_forall x.
Hyp Ht.
Qed.

23
BE2019/coq-exercice-1.v Executable file
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Require Import Naturelle.
Section Session1_2019_Logique_Exercice_1.
Variable A B C : Prop.
Theorem Exercice_1_Coq : (A -> B -> C) -> ((A /\ B) -> C).
intros.
cut B.
cut A.
exact H.
destruct H0.
exact H0.
destruct H0.
exact H1.
Qed.
Theorem Exercice_1_Naturelle : (A -> B -> C) -> ((A /\ B) -> C).
Proof.
(* A COMPLETER *)
Qed.
End Session1_2019_Logique_Exercice_1.

19
BE2019/coq-exercice-2.v Executable file
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Require Import Naturelle.
Section Session1_2019_Logique_Exercice_2.
Variable A B : Prop.
Theorem Exercice_2_Coq : (~A) \/ B -> (~A) \/ (A /\ B).
intros.
right.
split.
Qed.
Theorem Exercice_2_Naturelle : (~A) \/ B -> (~A) \/ (A /\ B).
Proof.
(* A COMPLETER *)
Qed.
End Session1_2019_Logique_Exercice_2.

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BE2019/coq-exercice-3.v Executable file
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Section Session1_2019_Induction_Exercice_3.
(* Déclaration d’un domaine pour les éléments des listes *)
Variable A : Set.
(* Déclaration d'un type liste générique d'éléments de type E *)
Inductive liste (E : Set) : Set :=
Nil
: liste E
| Cons : E -> liste E -> liste E.
(* Déclaration du nom de la fonction append *)
Variable append_spec : forall E : Set, liste E -> liste E -> liste E.
(* Spécification du comportement de append pour Nil en premier paramètre *)
Axiom append_Nil : forall E : Set, forall (l : liste E), append_spec E (Nil E) l = l.
(* Spécification du comportement de append pour Cons en premier paramètre *)
Axiom append_Cons : forall E : Set, forall (t : E), forall (q l : liste E),
append_spec E ((Cons E) t q) l = (Cons E) t (append_spec E q l).
(* Spécification du comportement de append pour Nil en second paramètre *)
Axiom append_Nil_right : forall E : Set, forall (l : liste E), (append_spec E l (Nil E)) = l.
(* append est associative à gauche et à droite *)
Axiom append_associative : forall E : Set, forall (l1 l2 l3 : liste E),
(append_spec E l1 (append_spec E l2 l3)) = (append_spec E (append_spec E l1 l2) l3).
(* Déclaration du nom de la fonction flatten *)
Variable flatten_spec : forall E : Set, liste (liste E) -> liste E.
(* Spécification du comportement de flatten pour Nil *)
Axiom flatten_Nil : forall E : Set, flatten_spec E (Nil (liste E)) = (Nil E).
(* Spécification du comportement de flatten pour Cons *)
Axiom flatten_Cons : forall E : Set, forall (t : liste E), forall (q : liste (liste E)),
flatten_spec E (Cons (liste E) t q) = append_spec E t (flatten_spec E q).
(* Déclaration du nom de la fonction split *)
Variable split_spec : forall E : Set, liste E -> liste (liste E).
(* Spécification du comportement de split pour Nil *)
Axiom split_Nil : forall E : Set, split_spec E (Nil E) = (Nil (liste E)).
(* Spécification du comportement de split pour Cons *)
Axiom split_Cons : forall E : Set, forall (t : E), forall (q : liste E),
split_spec E (Cons E t q) = Cons (liste E) (Cons E t (Nil E)) (split_spec E q).
(* Cohérence de flatten et de split : flatten(split(l)) = l*)
Theorem flatten_split_consistency : forall E : Set, forall (l : liste E),
flatten_spec E (split_spec E l) = l.
intros.
induction l.
rewrite split_Nil.
rewrite flatten_Nil.
reflexivity.
rewrite split_Cons.
rewrite flatten_Cons.
rewrite IHl.
rewrite append_Cons.
rewrite append_Nil.
reflexivity.
Qed.
(* Implantation de la fonction append *)
Fixpoint append_impl (E : Set) (l1 l2 : liste E) {struct l1} : liste E :=
match l1 with
Nil _ => l2
| (Cons _ t1 q1) => (Cons E t1 (append_impl E q1 l2))
end.
Theorem append_correctness : forall E : Set, forall (l1 l2 : liste E),
(append_spec E l1 l2) = (append_impl E l1 l2).
intro TE.
induction l1.
intro Hl2.
rewrite append_Nil.
simpl.
reflexivity.
intro Hl2.
rewrite append_Cons.
simpl.
rewrite IHl1.
reflexivity.
Qed.
(* Implantation de la fonction flatten *)
Fixpoint flatten_impl (E : Set) (l : liste (liste E)) {struct l} : liste E :=
match l with
Nil => Nil
| (Cons t1 q1) => (Cons t1 (flatten_impl q1 l2))
end.
(* Correction de l'implantation de flatten par rapport à sa spécification *)
Theorem flatten_correctness : forall E : Set, forall (l : liste (liste E)),
(flatten_spec E l) = (flatten_impl E l).
Proof.
(* A COMPLETER *)
Qed.
End Session1_2019_Induction_Exercice_3.

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BE2019/why3-exercice-4.mlw Executable file
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(* BE : Session 1 2019 *)
(* Implémentation de la fonction somme des premiers entiers par un algorithme ascendant *)
module Somme
use int.Int
use int.ComputerDivision
use ref.Refint
let somme (n: int) : int
requires { n >= 0 }
ensures { 2*result = n*(n+1) }
=
let i = ref 0 in
let r = ref 0 in
while (!i < n) do
invariant { 2*!r = !i*(!i+1) }
variant { n - !i }
i := (!i) + 1;
r := (!r) + (!i)
done;
!r
end

44
BE2019/why3-exercice-4/why3mnexercicemn4_Somme_VC_somme_1.v Executable file
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(* This file is generated by Why3's Coq driver *)
(* Beware! Only edit allowed sections below *)
Require Import BuiltIn.
Require BuiltIn.
Require int.Int.
Require int.Abs.
Require int.ComputerDivision.
(* Why3 assumption *)
Inductive ref (a:Type) :=
| mk_ref : a -> ref a.
Axiom ref_WhyType : forall (a:Type) {a_WT:WhyType a}, WhyType (ref a).
Existing Instance ref_WhyType.
Arguments mk_ref {a}.
(* Why3 assumption *)
Definition contents {a:Type} {a_WT:WhyType a} (v:ref a) : a :=
match v with
| mk_ref x => x
end.
Parameter n: Z.
Parameter r: Z.
Parameter i: Z.
Axiom H : (i < n)%Z.
Parameter i1: Z.
Axiom H1 : (i1 = (i + 1%Z)%Z).
Parameter r1: Z.
Axiom H2 : (r1 = (r + i1)%Z).
(* Why3 goal *)
Theorem VC_somme : False.
Proof.
Qed.

44
BE2019/why3-exercice-4/why3mnexercicemn4_Somme_VC_somme_2.v Executable file
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(* This file is generated by Why3's Coq driver *)
(* Beware! Only edit allowed sections below *)
Require Import BuiltIn.
Require BuiltIn.
Require int.Int.
Require int.Abs.
Require int.ComputerDivision.
(* Why3 assumption *)
Inductive ref (a:Type) :=
| mk_ref : a -> ref a.
Axiom ref_WhyType : forall (a:Type) {a_WT:WhyType a}, WhyType (ref a).
Existing Instance ref_WhyType.
Arguments mk_ref {a}.
(* Why3 assumption *)
Definition contents {a:Type} {a_WT:WhyType a} (v:ref a) : a :=
match v with
| mk_ref x => x
end.
Parameter n: Z.
Parameter r: Z.
Parameter i: Z.
Axiom H : (i < n)%Z.
Parameter i1: Z.
Axiom H1 : (i1 = (i + 1%Z)%Z).
Parameter r1: Z.
Axiom H2 : (r1 = (r + i1)%Z).
(* Why3 goal *)
Theorem VC_somme : False.
Proof.
Qed.

39
BE2019/why3-exercice-4/why3session.xml Executable file
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<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
"http://why3.lri.fr/why3session.dtd">
<why3session shape_version="5">
<prover id="0" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="1" name="Alt-Ergo" version="2.0.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="2" name="Z3" version="4.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="3" name="CVC4" version="1.5" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="4" name="Coq" version="8.9.1" timelimit="0" steplimit="0" memlimit="0"/>
<prover id="5" name="Z3" version="4.4.1" alternative="noBV" timelimit="5" steplimit="0" memlimit="1000"/>
<file>
<path name=".."/>
<path name="why3-exercice-4.mlw"/>
<theory name="Somme">
<goal name="VC somme" expl="VC for somme">
<proof prover="1"><result status="unknown" time="0.05"/></proof>
<transf name="split_vc" >
<goal name="VC somme.0" expl="loop invariant init" proved="true">
<proof prover="1"><result status="valid" time="0.00" steps="1"/></proof>
</goal>
<goal name="VC somme.1" expl="loop variant decrease">
<proof prover="0"><result status="unknown" time="0.07"/></proof>
<proof prover="1"><result status="unknown" time="0.04"/></proof>
<proof prover="2"><result status="timeout" time="5.00"/></proof>
<proof prover="3"><result status="unknown" time="0.01"/></proof>
<proof prover="4" obsolete="true" edited="why3mnexercicemn4_Somme_VC_somme_2.v"><result status="unknown" time="0.00" steps="0"/></proof>
<proof prover="5"><result status="timeout" time="5.00"/></proof>
</goal>
<goal name="VC somme.2" expl="loop invariant preservation" proved="true">
<proof prover="1"><result status="valid" time="0.00" steps="4"/></proof>
</goal>
<goal name="VC somme.3" expl="postcondition" proved="true">
<proof prover="1"><result status="valid" time="0.00" steps="2"/></proof>
</goal>
</transf>
</goal>
</theory>
</file>
</why3session>

40
BE2020/.Naturelle.aux Executable file
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COQAUX1 3e03a7b5b5c26232f0f3e8f10219c975 /home/lfainsin/1A/Modé/BE2020/Naturelle.v
383 387 proof_build_time "0.000"
0 0 E_imp_th "0.000"
383 387 context_used ""
383 387 proof_check_time "0.000"
0 0 VernacProof "tac:no using:no"
916 920 proof_build_time "0.000"
0 0 E_forall_th "0.000"
916 920 context_used ""
916 920 proof_check_time "0.000"
1291 1295 proof_build_time "0.001"
0 0 E_et_g_th "0.001"
1291 1295 context_used ""
1291 1295 proof_check_time "0.000"
1601 1605 proof_build_time "0.000"
0 0 E_et_d_th "0.000"
1601 1605 context_used ""
1601 1605 proof_check_time "0.000"
1983 1987 proof_build_time "0.001"
0 0 E_ou_th "0.001"
1983 1987 context_used ""
1983 1987 proof_check_time "0.000"
0 0 VernacProof "tac:no using:no"
2806 2810 proof_build_time "0.001"
0 0 E_exists_th "0.001"
2806 2810 context_used ""
2806 2810 proof_check_time "0.000"
3280 3284 proof_build_time "0.000"
0 0 E_antiT_th "0.000"
3280 3284 context_used ""
3280 3284 proof_check_time "0.000"
3502 3506 proof_build_time "0.001"
0 0 I_antiT_th "0.001"
3502 3506 context_used ""
3502 3506 proof_check_time "0.000"
3683 3687 proof_build_time "0.000"
0 0 I_non_th "0.000"
3683 3687 context_used ""
3683 3687 proof_check_time "0.000"
0 0 vo_compile_time "0.107"

150
BE2020/Naturelle.glob Executable file
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DIGEST 3e03a7b5b5c26232f0f3e8f10219c975
FNaturelle
R15:23 Coq.Logic.Classical <> <> lib
R97:100 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R97:100 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R218:221 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R218:221 Coq.Init.Logic <> ::type_scope:x_'->'_x not
prf 278:285 <> E_imp_th
R314:314 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R325:329 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R333:336 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R337:339 Naturelle <> psi var
R330:332 Naturelle <> phi var
R318:321 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R322:324 Naturelle <> psi var
R315:317 Naturelle <> phi var
R443:450 Naturelle <> E_imp_th thm
R521:528 Naturelle <> E_imp_th thm
prf 816:826 <> E_forall_th
R856:859 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R855:855 Naturelle <> A var
R869:869 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R885:889 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R890:892 Naturelle <> phi var
R894:894 Naturelle <> a var
R880:882 Naturelle <> phi var
R884:884 Naturelle <> x var
R996:1006 Naturelle <> E_forall_th thm
R1086:1089 Coq.Init.Logic <> ::type_scope:x_'/\'_x not
R1086:1089 Coq.Init.Logic <> ::type_scope:x_'/\'_x not
R1105:1108 Coq.Init.Logic <> conj constr
prf 1157:1165 <> E_et_g_th
R1194:1194 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R1205:1209 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R1210:1212 Naturelle <> phi var
R1198:1201 Coq.Init.Logic <> ::type_scope:x_'/\'_x not
R1195:1197 Naturelle <> phi var
R1202:1204 Naturelle <> psi var
R1352:1360 Naturelle <> E_et_g_th thm
R1432:1440 Naturelle <> E_et_g_th thm
prf 1465:1473 <> E_et_d_th
R1502:1502 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R1513:1517 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R1518:1520 Naturelle <> psi var
R1506:1509 Coq.Init.Logic <> ::type_scope:x_'/\'_x not
R1503:1505 Naturelle <> phi var
R1510:1512 Naturelle <> psi var
R1662:1670 Naturelle <> E_et_d_th thm
R1743:1751 Naturelle <> E_et_d_th thm
prf 1776:1782 <> E_ou_th
R1815:1815 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R1826:1830 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R1831:1831 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R1842:1846 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R1847:1847 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R1858:1862 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R1863:1865 Naturelle <> chi var
R1851:1854 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R1855:1857 Naturelle <> chi var
R1848:1850 Naturelle <> psi var
R1835:1838 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R1839:1841 Naturelle <> chi var
R1832:1834 Naturelle <> phi var
R1819:1822 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
R1816:1818 Naturelle <> phi var
R1823:1825 Naturelle <> psi var
R2042:2048 Naturelle <> E_ou_th thm
R2124:2130 Naturelle <> E_ou_th thm
R2194:2197 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
R2194:2197 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
R2213:2221 Coq.Init.Logic <> or_introl constr
R2305:2308 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
R2305:2308 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
R2324:2332 Coq.Init.Logic <> or_intror constr
R2416:2423 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R2430:2433 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R2439:2439 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R2438:2438 Naturelle <> x var
R2416:2423 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R2430:2433 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R2439:2439 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R2438:2438 Naturelle <> x var
R2453:2460 Coq.Init.Logic <> ex_intro constr
R2561:2568 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R2575:2578 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R2584:2584 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R2583:2583 Naturelle <> x var
R2561:2568 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R2575:2578 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R2584:2584 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R2583:2583 Naturelle <> x var
R2597:2604 Coq.Init.Logic <> ex_intro constr
prf 2669:2679 <> E_exists_th
R2709:2712 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R2708:2708 Naturelle <> A var
R2733:2733 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R2749:2753 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R2754:2754 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R2777:2781 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R2782:2784 Naturelle <> chi var
R2770:2773 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R2774:2776 Naturelle <> chi var
R2765:2767 Naturelle <> phi var
R2769:2769 Naturelle <> a var
R2734:2740 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R2742:2743 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R2744:2746 Naturelle <> phi var
R2748:2748 Naturelle <> x var
R2963:2973 Naturelle <> E_exists_th thm
R3083:3085 Coq.Init.Logic <> not def
R3116:3120 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
R3132:3132 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
R3123:3126 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R3127:3131 Coq.Init.Logic <> False ind
R3116:3120 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
R3132:3132 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
R3123:3126 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R3127:3131 Coq.Init.Logic <> False ind
R3145:3151 Coq.Logic.Classical_Prop <> classic prfax
prf 3209:3218 <> E_antiT_th
R3248:3251 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R3252:3254 Naturelle <> phi var
R3243:3247 Coq.Init.Logic <> False ind
R3340:3349 Naturelle <> E_antiT_th thm
prf 3370:3379 <> I_antiT_th
R3407:3410 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R3411:3411 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R3416:3420 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R3421:3425 Coq.Init.Logic <> False ind
R3412:3412 Coq.Init.Logic <> ::type_scope:'~'_x not
R3413:3415 Naturelle <> phi var
R3404:3406 Naturelle <> phi var
R3435:3437 Coq.Init.Logic <> not def
R3551:3555 Coq.Init.Logic <> False ind
R3551:3555 Coq.Init.Logic <> False ind
R3567:3576 Naturelle <> I_antiT_th thm
prf 3598:3605 <> I_non_th
R3630:3630 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R3643:3647 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R3648:3648 Coq.Init.Logic <> ::type_scope:'~'_x not
R3649:3651 Naturelle <> phi var
R3634:3637 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R3638:3642 Coq.Init.Logic <> False ind
R3631:3633 Naturelle <> phi var
R3669:3671 Coq.Init.Logic <> not def
R3730:3731 Coq.Init.Logic <> ::type_scope:'~'_x not
R3730:3731 Coq.Init.Logic <> ::type_scope:'~'_x not
R3745:3752 Naturelle <> I_non_th thm
R3801:3810 Naturelle <> I_antiT_th thm
R3875:3878 Coq.Logic.Classical_Prop <> NNPP thm

224
BE2020/Naturelle.v Executable file
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Require Export Classical.
Ltac Hyp Nom := exact Nom.
Ltac I_imp' :=
match goal with
| |- ?A -> ?B => let hyp := fresh "H" in intro hyp
| _ => fail
end.
Ltac I_imp Nom :=
match goal with
| |- ?A -> ?B => intro Nom
| _ => fail
end.
Theorem E_imp_th : forall (phi psi : Prop), (phi -> psi) -> phi -> psi.
intros Pphi Ppsi Hphi2psi.
Hyp Hphi2psi.
Qed.
Ltac E_imp' :=
match goal with
| |- ?P => eapply (E_imp_th _ P)
end.
Ltac E_imp phi :=
match goal with
| |- ?P => apply (E_imp_th phi P)
end.
Ltac I_forall' :=
match goal with
| |- forall (x : ?A), ?P => let hyp := fresh x in intro hyp
| _ => fail
end.
Ltac I_forall Nom :=
match goal with
| |- forall (x : ?A), ?P => intro Nom
| _ => fail
end.
Theorem E_forall_th : forall (A : Type) (phi : A -> Prop) a, (forall x, phi x) -> phi a.
Proof.
firstorder.
Qed.
Ltac E_forall x :=
pattern x;
match goal with
| |- (?P x) => apply (E_forall_th _ P x)
| _ => fail
end.
Ltac I_et :=
match goal with
| |- (?A /\ ?B) => apply (@conj A B)
| _ => fail
end.
Theorem E_et_g_th : forall (phi psi : Prop), (phi /\ psi) -> phi.
intros Pphi Ppsi Hphi_et_psi.
elim Hphi_et_psi.
intros Hphi Hpsi.
Hyp Hphi.
Qed.
Ltac E_et_g' :=
match goal with
| |- ?P => eapply (E_et_g_th P _)
end.
Ltac E_et_g psi :=
match goal with
| |- ?P => apply (E_et_g_th P psi)
end.
Theorem E_et_d_th : forall (phi psi : Prop), (phi /\ psi) -> psi.
intros Pphi Ppsi H_phi_et_psi.
elim H_phi_et_psi.
intros Hphi Hpsi.
Hyp Hpsi.
Qed.
Ltac E_et_d' :=
match goal with
| |- ?P => eapply (E_et_d_th _ P)
end.
Ltac E_et_d phi :=
match goal with
| |- ?P => eapply (E_et_d_th phi P)
end.
Theorem E_ou_th : forall (phi psi chi : Prop), (phi \/ psi) -> (phi -> chi) -> (psi -> chi) -> chi.
intros Pphi Ppsi Pchi Hphi_ou_psi Hphi_imp_chi Hpsi_imp_chi.
elim Hphi_ou_psi.
Hyp Hphi_imp_chi.
Hyp Hpsi_imp_chi.
Qed.
Ltac E_ou' :=
match goal with
| |- ?P => eapply (E_ou_th _ _ P)
end.
Ltac E_ou phi psi :=
match goal with
| |- ?P => apply (E_ou_th phi psi P)
end.
Ltac I_ou_g :=
match goal with
| |- (?A \/ ?B) => apply (@or_introl A B)
| _ => fail
end.
Ltac I_ou_d :=
match goal with
| |- (?A \/ ?B) => apply (@or_intror A B)
| _ => fail
end.
Ltac I_exists' :=
match goal with
| |- exists (x : ?A), (@?P x) => eapply (@ex_intro A P _)
| _ => fail
end.
Ltac I_exists t :=
match goal with
| |- exists (x : ?A), (@?P x) => apply (@ex_intro _ P t)
| _ => fail
end.
Theorem E_exists_th : forall (A : Type) (phi : A -> Prop) (chi : Prop), (exists x, phi x) -> (forall a, phi a -> chi) -> chi.
Proof.
firstorder.
Qed.
(*
Ltac E_exists phi :=
match goal with
| |- ?P => apply (E_exists_th _ phi P)
end.
*)
Ltac E_exists phi :=
match goal with
| |- ?P => apply (E_exists_th _ phi P); [ idtac | let t := fresh "t" in let ht := fresh "Ht" in intros t ht ]
end.
Ltac TE :=
unfold not;
match goal with
| |- (?P \/ (?P -> False)) => exact (classic P)
| _ => fail
end.
Theorem E_antiT_th : forall (phi : Prop), False -> phi.
intros Pphi F.
elim F.
Qed.
Ltac E_antiT :=
match goal with
| |- ?P => apply (E_antiT_th P)
end.
Theorem I_antiT_th : forall (phi : Prop), phi -> (~phi) -> False.
unfold not.
intro Pphi.
intros Hphi Hnphi.
cut Pphi.
Hyp Hnphi.
Hyp Hphi.
Qed.
Ltac I_antiT phi :=
match goal with
| |- False => apply (I_antiT_th phi)
end.
Theorem I_non_th : forall (phi : Prop), (phi -> False) -> ~phi.
intros.
unfold not.
exact H.
Qed.
Ltac I_non Nom :=
match goal with
| |- ~ ?P => apply (I_non_th P); intro Nom
end.
Ltac E_non phi :=
apply (I_antiT_th phi).
Ltac absurde Nom :=
match goal with
| |- ?P => apply (NNPP P); intro Nom
end.
(*
Ltac I_antiT phi := apply (I_antiT_th phi).
Ltac absurde Nom phi :=
match goal with
| |- phi =>
cut (phi \/ ~phi);
[
intros L;
elim L;
[
auto
|
clear L;
intro Nom;
apply (E_antiT_th)
]
|
apply (classic phi)
]
| _ => fail
end.
*)

41
BE2020/coq_exercice_1.v Executable file
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Require Import Naturelle.
Section Session1_2020_Logique_Exercice_1.
Variable A B C : Prop.
Theorem Exercice_1_Naturelle : ((A -> C) \/ (B -> C)) -> ((A /\ B) -> C).
I_imp H1.
I_imp H2.
E_imp A.
E_ou (A -> C) (B -> C).
Hyp H1.
trivial.
I_imp H3.
I_imp H4.
E_imp B.
Hyp H3.
E_et_d A.
Hyp H2.
E_et_g B.
Hyp H2.
Qed.
Theorem Exercice_1_Coq : ((A -> C) \/ (B -> C)) -> ((A /\ B) -> C).
intros.
destruct H.
destruct H0.
cut A.
exact H.
exact H0.
cut B.
exact H.
cut (A /\ B).
intro H2.
elim H2.
intros HA HB.
exact HB.
exact H0.
Qed.
End Session1_2020_Logique_Exercice_1.

17
BE2020/coq_exercice_2.v Executable file
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Require Import Naturelle.
Section Session1_2020_Logique_Exercice_2.
Variable A B : Prop.
Theorem Exercice_2_Naturelle : (A -> B) -> ((~A) \/ B).
Proof.
(* A COMPLETER *)
Qed.
Theorem Exercice_2_Coq : (A -> B) -> ((~A) \/ B).
Proof.
(* A COMPLETER *)
Qed.
End Session1_2020_Logique_Exercice_2.

91
BE2020/coq_exercice_3.v Executable file
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Section Session1_2020_Induction_Exercice_3.
(* Déclaration d’un domaine pour les éléments des listes *)
Variable A : Set.
Inductive entier : Set :=
Zero : entier
| Succ : entier -> entier.
(* Déclaration du nom de la fonction somme *)
Variable somme_spec : entier -> entier -> entier.
(* Spécification du comportement de somme pour Zero en premier paramètre *)
Axiom somme_Zero : forall (n : entier), somme_spec Zero n = n.
(* Spécification du comportement de somme pour Succ en premier paramètre *)
Axiom somme_Succ : forall (n m : entier),
somme_spec (Succ n) m = Succ (somme_spec n m).
(* somme est associative à gauche et à droite *)
Axiom somme_associative : forall (n1 n2 n3 : entier),
(somme_spec n1 (somme_spec n2 n3)) = (somme_spec (somme_spec n1 n2) n3).
Inductive liste : Set :=
Nil
: liste
| Cons : A -> liste -> liste.
(* Déclaration du nom de la fonction append *)
Variable append_spec : liste -> liste -> liste.
(* Spécification du comportement de append pour Nil en premier paramètre *)
Axiom append_Nil : forall (l : liste), append_spec Nil l = l.
(* Spécification du comportement de append pour Cons en premier paramètre *)
Axiom append_Cons : forall (t : A), forall (q l : liste),
append_spec (Cons t q) l = Cons t (append_spec q l).
(* append est associative à gauche et à droite *)
Axiom append_associative : forall (l1 l2 l3 : liste),
(append_spec l1 (append_spec l2 l3)) = (append_spec (append_spec l1 l2) l3).
(* Déclaration du nom de la fonction taille *)
Variable taille_spec : liste -> entier.
(* Spécification du comportement de taille pour Nil en paramètre *)
Axiom taille_Nil : taille_spec Nil = Zero .
(* Spécification du comportement de taille pour Cons en paramètre *)
Axiom taille_Cons : forall (t : A), forall (q : liste),
taille_spec (Cons t q) = Succ (taille_spec q) .
(* taille commute avec append *)
Theorem taille_append : forall (l1 l2 : liste),
(taille_spec (append_spec l1 l2)) = (somme_spec (taille_spec l1) (taille_spec l2)).
intros.
induction l1.
rewrite append_Nil.
rewrite taille_Nil.
rewrite somme_Zero.
reflexivity.
rewrite append_Cons.
rewrite taille_Cons.
rewrite taille_Cons.
rewrite somme_Succ.
rewrite IHl1.
reflexivity.
Qed.
(* Implantation de la fonction taille *)
Fixpoint taille_impl (l : liste) {struct l} : entier :=
match l with
Nil => Zero
| (Cons t q) => (Succ (taille_impl q))
end.
Theorem taille_correctness : forall (l : liste),
(taille_spec l) = (taille_impl l).
intros.
induction l.
simpl taille_impl.
rewrite taille_Nil.
reflexivity.
simpl taille_impl.
rewrite taille_Cons.
rewrite IHl.
reflexivity.
Qed.
End Session1_2020_Induction_Exercice_3.

23
BE2020/why3_exercice_4.mlw Executable file
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(* BE : Session 1 2020 *)
(* Implémentation de la fonction carre d'un entier naturel par un algorithme inspiré des identités remarquables *)
module Carre
use int.Int
use ref.Refint
let carre (n: int) : int
requires { 0 <= n }
ensures { !r = n*n }
=
let x = ref n in
let r = ref 0 in
while (!x <> 0) do
invariant { !r + (!x)*(!x) = n*n && 0 <= !x }
variant { !x }
r := (!r) + 2 * (!x) - 1;
x := (!x) - 1
done;
!r
end

36
BE2020/why3_exercice_4/why3session.xml Executable file
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<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
"http://why3.lri.fr/why3session.dtd">
<why3session shape_version="5">
<prover id="0" name="Alt-Ergo" version="2.0.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="1" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="2" name="Z3" version="4.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="3" name="CVC4" version="1.5" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="4" name="Z3" version="4.4.1" alternative="noBV" timelimit="5" steplimit="0" memlimit="1000"/>
<file>
<path name=".."/>
<path name="why3_exercice_4.mlw"/>
<theory name="Carre">
<goal name="VC carre" expl="VC for carre">
<transf name="split_vc" >
<goal name="VC carre.0" expl="loop invariant init" proved="true">
<proof prover="0"><result status="valid" time="0.00" steps="1"/></proof>
</goal>
<goal name="VC carre.1" expl="loop variant decrease">
<proof prover="0"><result status="unknown" time="0.01"/></proof>
<proof prover="1"><result status="unknown" time="0.12"/></proof>
<proof prover="2"><result status="timeout" time="5.00"/></proof>
<proof prover="3"><result status="unknown" time="0.02"/></proof>
<proof prover="4"><result status="timeout" time="5.00"/></proof>
</goal>
<goal name="VC carre.2" expl="loop invariant preservation" proved="true">
<proof prover="0"><result status="valid" time="0.00" steps="4"/></proof>
</goal>
<goal name="VC carre.3" expl="postcondition" proved="true">
<proof prover="0"><result status="valid" time="0.00" steps="2"/></proof>
</goal>
</transf>
</goal>
</theory>
</file>
</why3session>

40
TP1/.Naturelle.aux Executable file
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COQAUX1 f13e540aa0997388dd1408b0662438d6 /home/lfainsin/1A/Modé/TP1/Naturelle.v
383 387 proof_build_time "0.001"
0 0 E_imp_th "0.001"
383 387 context_used ""
383 387 proof_check_time "0.000"
0 0 VernacProof "tac:no using:no"
916 920 proof_build_time "0.001"
0 0 E_forall_th "0.001"
916 920 context_used ""
916 920 proof_check_time "0.000"
1291 1295 proof_build_time "0.001"
0 0 E_et_g_th "0.001"
1291 1295 context_used ""
1291 1295 proof_check_time "0.000"
1601 1605 proof_build_time "0.001"
0 0 E_et_d_th "0.001"
1601 1605 context_used ""
1601 1605 proof_check_time "0.000"
1983 1987 proof_build_time "0.001"
0 0 E_ou_th "0.001"
1983 1987 context_used ""
1983 1987 proof_check_time "0.000"
0 0 VernacProof "tac:no using:no"
2806 2810 proof_build_time "0.001"
0 0 E_exists_th "0.001"
2806 2810 context_used ""
2806 2810 proof_check_time "0.000"
3280 3284 proof_build_time "0.000"
0 0 E_antiT_th "0.000"
3280 3284 context_used ""
3280 3284 proof_check_time "0.000"
3502 3506 proof_build_time "0.001"
0 0 I_antiT_th "0.001"
3502 3506 context_used ""
3502 3506 proof_check_time "0.000"
3683 3687 proof_build_time "0.000"
0 0 I_non_th "0.000"
3683 3687 context_used ""
3683 3687 proof_check_time "0.000"
0 0 vo_compile_time "0.713"

150
TP1/Naturelle.glob Executable file
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DIGEST f13e540aa0997388dd1408b0662438d6
FNaturelle
R15:23 Coq.Logic.Classical <> <> lib
R97:100 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R97:100 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R218:221 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R218:221 Coq.Init.Logic <> ::type_scope:x_'->'_x not
prf 278:285 <> E_imp_th
R314:314 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R325:329 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R333:336 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R337:339 Naturelle <> psi var
R330:332 Naturelle <> phi var
R318:321 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R322:324 Naturelle <> psi var
R315:317 Naturelle <> phi var
R443:450 Naturelle <> E_imp_th thm
R521:528 Naturelle <> E_imp_th thm
prf 816:826 <> E_forall_th
R856:859 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R855:855 Naturelle <> A var
R869:869 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R885:889 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R890:892 Naturelle <> phi var
R894:894 Naturelle <> a var
R880:882 Naturelle <> phi var
R884:884 Naturelle <> x var
R996:1006 Naturelle <> E_forall_th thm
R1086:1089 Coq.Init.Logic <> ::type_scope:x_'/\'_x not
R1086:1089 Coq.Init.Logic <> ::type_scope:x_'/\'_x not
R1105:1108 Coq.Init.Logic <> conj constr
prf 1157:1165 <> E_et_g_th
R1194:1194 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R1205:1209 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R1210:1212 Naturelle <> phi var
R1198:1201 Coq.Init.Logic <> ::type_scope:x_'/\'_x not
R1195:1197 Naturelle <> phi var
R1202:1204 Naturelle <> psi var
R1352:1360 Naturelle <> E_et_g_th thm
R1432:1440 Naturelle <> E_et_g_th thm
prf 1465:1473 <> E_et_d_th
R1502:1502 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R1513:1517 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R1518:1520 Naturelle <> psi var
R1506:1509 Coq.Init.Logic <> ::type_scope:x_'/\'_x not
R1503:1505 Naturelle <> phi var
R1510:1512 Naturelle <> psi var
R1662:1670 Naturelle <> E_et_d_th thm
R1743:1751 Naturelle <> E_et_d_th thm
prf 1776:1782 <> E_ou_th
R1815:1815 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R1826:1830 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R1831:1831 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R1842:1846 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R1847:1847 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R1858:1862 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R1863:1865 Naturelle <> chi var
R1851:1854 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R1855:1857 Naturelle <> chi var
R1848:1850 Naturelle <> psi var
R1835:1838 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R1839:1841 Naturelle <> chi var
R1832:1834 Naturelle <> phi var
R1819:1822 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
R1816:1818 Naturelle <> phi var
R1823:1825 Naturelle <> psi var
R2042:2048 Naturelle <> E_ou_th thm
R2124:2130 Naturelle <> E_ou_th thm
R2194:2197 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
R2194:2197 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
R2213:2221 Coq.Init.Logic <> or_introl constr
R2305:2308 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
R2305:2308 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
R2324:2332 Coq.Init.Logic <> or_intror constr
R2416:2423 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R2430:2433 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R2439:2439 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R2438:2438 Naturelle <> x var
R2416:2423 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R2430:2433 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R2439:2439 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R2438:2438 Naturelle <> x var
R2453:2460 Coq.Init.Logic <> ex_intro constr
R2561:2568 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R2575:2578 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R2584:2584 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R2583:2583 Naturelle <> x var
R2561:2568 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R2575:2578 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R2584:2584 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R2583:2583 Naturelle <> x var
R2597:2604 Coq.Init.Logic <> ex_intro constr
prf 2669:2679 <> E_exists_th
R2709:2712 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R2708:2708 Naturelle <> A var
R2733:2733 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R2749:2753 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R2754:2754 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R2777:2781 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R2782:2784 Naturelle <> chi var
R2770:2773 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R2774:2776 Naturelle <> chi var
R2765:2767 Naturelle <> phi var
R2769:2769 Naturelle <> a var
R2734:2740 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R2742:2743 Coq.Init.Logic <> ::type_scope:'exists'_x_'..'_x_','_x not
R2744:2746 Naturelle <> phi var
R2748:2748 Naturelle <> x var
R2963:2973 Naturelle <> E_exists_th thm
R3083:3085 Coq.Init.Logic <> not def
R3116:3120 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
R3132:3132 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
R3123:3126 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R3127:3131 Coq.Init.Logic <> False ind
R3116:3120 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
R3132:3132 Coq.Init.Logic <> ::type_scope:x_'\/'_x not
R3123:3126 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R3127:3131 Coq.Init.Logic <> False ind
R3145:3151 Coq.Logic.Classical_Prop <> classic prfax
prf 3209:3218 <> E_antiT_th
R3248:3251 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R3252:3254 Naturelle <> phi var
R3243:3247 Coq.Init.Logic <> False ind
R3340:3349 Naturelle <> E_antiT_th thm
prf 3370:3379 <> I_antiT_th
R3407:3410 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R3411:3411 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R3416:3420 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R3421:3425 Coq.Init.Logic <> False ind
R3412:3412 Coq.Init.Logic <> ::type_scope:'~'_x not
R3413:3415 Naturelle <> phi var
R3404:3406 Naturelle <> phi var
R3435:3437 Coq.Init.Logic <> not def
R3551:3555 Coq.Init.Logic <> False ind
R3551:3555 Coq.Init.Logic <> False ind
R3567:3576 Naturelle <> I_antiT_th thm
prf 3598:3605 <> I_non_th
R3630:3630 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R3643:3647 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R3648:3648 Coq.Init.Logic <> ::type_scope:'~'_x not
R3649:3651 Naturelle <> phi var
R3634:3637 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R3638:3642 Coq.Init.Logic <> False ind
R3631:3633 Naturelle <> phi var
R3669:3671 Coq.Init.Logic <> not def
R3730:3731 Coq.Init.Logic <> ::type_scope:'~'_x not
R3730:3731 Coq.Init.Logic <> ::type_scope:'~'_x not
R3745:3752 Naturelle <> I_non_th thm
R3801:3810 Naturelle <> I_antiT_th thm
R3875:3878 Coq.Logic.Classical_Prop <> NNPP thm

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Require Export Classical.
Ltac Hyp Nom := exact Nom.
Ltac I_imp' :=
match goal with
| |- ?A -> ?B => let hyp := fresh "H" in intro hyp
| _ => fail
end.
Ltac I_imp Nom :=
match goal with
| |- ?A -> ?B => intro Nom
| _ => fail
end.
Theorem E_imp_th : forall (phi psi : Prop), (phi -> psi) -> phi -> psi.
intros Pphi Ppsi Hphi2psi.
Hyp Hphi2psi.
Qed.
Ltac E_imp' :=
match goal with
| |- ?P => eapply (E_imp_th _ P)
end.
Ltac E_imp phi :=
match goal with
| |- ?P => apply (E_imp_th phi P)
end.
Ltac I_forall' :=
match goal with
| |- forall (x : ?A), ?P => let hyp := fresh x in intro hyp
| _ => fail
end.
Ltac I_forall Nom :=
match goal with
| |- forall (x : ?A), ?P => intro Nom
| _ => fail
end.
Theorem E_forall_th : forall (A : Type) (phi : A -> Prop) a, (forall x, phi x) -> phi a.
Proof.
firstorder.
Qed.
Ltac E_forall x :=
pattern x;
match goal with
| |- (?P x) => apply (E_forall_th _ P x)
| _ => fail
end.
Ltac I_et :=
match goal with
| |- (?A /\ ?B) => apply (@conj A B)
| _ => fail
end.
Theorem E_et_g_th : forall (phi psi : Prop), (phi /\ psi) -> phi.
intros Pphi Ppsi Hphi_et_psi.
elim Hphi_et_psi.
intros Hphi Hpsi.
Hyp Hphi.
Qed.
Ltac E_et_g' :=
match goal with
| |- ?P => eapply (E_et_g_th P _)
end.
Ltac E_et_g psi :=
match goal with
| |- ?P => apply (E_et_g_th P psi)
end.
Theorem E_et_d_th : forall (phi psi : Prop), (phi /\ psi) -> psi.
intros Pphi Ppsi H_phi_et_psi.
elim H_phi_et_psi.
intros Hphi Hpsi.
Hyp Hpsi.
Qed.
Ltac E_et_d' :=
match goal with
| |- ?P => eapply (E_et_d_th _ P)
end.
Ltac E_et_d phi :=
match goal with
| |- ?P => eapply (E_et_d_th phi P)
end.
Theorem E_ou_th : forall (phi psi chi : Prop), (phi \/ psi) -> (phi -> chi) -> (psi -> chi) -> chi.
intros Pphi Ppsi Pchi Hphi_ou_psi Hphi_imp_chi Hpsi_imp_chi.
elim Hphi_ou_psi.
Hyp Hphi_imp_chi.
Hyp Hpsi_imp_chi.
Qed.
Ltac E_ou' :=
match goal with
| |- ?P => eapply (E_ou_th _ _ P)
end.
Ltac E_ou phi psi :=
match goal with
| |- ?P => apply (E_ou_th phi psi P)
end.
Ltac I_ou_g :=
match goal with
| |- (?A \/ ?B) => apply (@or_introl A B)
| _ => fail
end.
Ltac I_ou_d :=
match goal with
| |- (?A \/ ?B) => apply (@or_intror A B)
| _ => fail
end.
Ltac I_exists' :=
match goal with
| |- exists (x : ?A), (@?P x) => eapply (@ex_intro A P _)
| _ => fail
end.
Ltac I_exists t :=
match goal with
| |- exists (x : ?A), (@?P x) => apply (@ex_intro _ P t)
| _ => fail
end.
Theorem E_exists_th : forall (A : Type) (phi : A -> Prop) (chi : Prop), (exists x, phi x) -> (forall a, phi a -> chi) -> chi.
Proof.
firstorder.
Qed.
(*
Ltac E_exists phi :=
match goal with
| |- ?P => apply (E_exists_th _ phi P)
end.
*)
Ltac E_exists phi :=
match goal with
| |- ?P => apply (E_exists_th _ phi P); [ idtac | let t := fresh "t" in let ht := fresh "Ht" in intros t ht ]
end.
Ltac TE :=
unfold not;
match goal with
| |- (?P \/ (?P -> False)) => exact (classic P)
| _ => fail
end.
Theorem E_antiT_th : forall (phi : Prop), False -> phi.
intros Pphi F.
elim F.
Qed.
Ltac E_antiT :=
match goal with
| |- ?P => apply (E_antiT_th P)
end.
Theorem I_antiT_th : forall (phi : Prop), phi -> (~phi) -> False.
unfold not.
intro Pphi.
intros Hphi Hnphi.
cut Pphi.
Hyp Hnphi.
Hyp Hphi.
Qed.
Ltac I_antiT phi :=
match goal with
| |- False => apply (I_antiT_th phi)
end.
Theorem I_non_th : forall (phi : Prop), (phi -> False) -> ~phi.
intros.
unfold not.
exact H.
Qed.
Ltac I_non Nom :=
match goal with
| |- ~ ?P => apply (I_non_th P); intro Nom
end.
Ltac E_non phi :=
apply (I_antiT_th phi).
Ltac absurde Nom :=
match goal with
| |- ?P => apply (NNPP P); intro Nom
end.
(*
Ltac I_antiT phi := apply (I_antiT_th phi).
Ltac absurde Nom phi :=
match goal with
| |- phi =>
cut (phi \/ ~phi);
[
intros L;
elim L;
[
auto
|
clear L;
intro Nom;
apply (E_antiT_th)
]
|
apply (classic phi)
]
| _ => fail
end.
*)

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(* Les règles de la déduction naturelle doivent être ajoutées à Coq. *)
Require Import Naturelle.
(* Ouverture d\u2019une section *)
Section CalculPropositionnel.
(* Déclaration de variables propositionnelles *)
Variable A B C E Y R : Prop.
(*Exerice 1*)
Theorem Thm00 : A /\ B -> B /\ A.
I_imp H.
I_et.
E_et_d A.
Hyp H.
E_et_g B.
Hyp H.
Qed.
Theorem Thm_1 : ((A \/ B) -> C) -> (B -> C).
I_imp H.
I_imp H2.
E_imp (A \/ B).
Hyp H.
I_ou_d.
Hyp H2.
Qed.
Theorem Thm_2 : A -> ~~A.
I_imp H.
I_non H2.
I_antiT A.
Hyp H.
Hyp H2.
Qed.
Theorem Thm_3 : (A -> B) -> (~B -> ~A).
I_imp H.
I_imp H2.
I_non H3.
I_antiT B.
E_imp A.
Hyp H.
Hyp H3.
Hyp H2.
Qed.
Theorem Thm_4 : ~~A -> A.
I_imp H.
absurde H2.
I_antiT (~A).
Hyp H2.
Hyp H.
Qed.
Theorem Thm_5 : (~B -> ~A) -> (A -> B).
I_imp H.
I_imp H2.
absurde H3.
I_antiT (A).
Hyp H2.
E_imp (~B).
trivial.
trivial.
Qed.
Theorem Thm_6 : ((E -> (Y \/ R)) /\ (Y -> R)) -> (~R -> ~E).
intros.
I_non H1.
I_antiT (R).
E_ou Y R.
E_imp E.
E_et_g (Y -> R).
Hyp H.
Hyp H1.
E_et_d (E -> Y \/ R).
Hyp H.
I_imp H2.
tauto.
tauto.
Qed.
(*Exerice 2*)
Theorem Coq_E_imp : ((A -> B) /\ A) -> B.
intros.
destruct H as (H1,H2).
tauto.
Qed.
Theorem Coq_E_et_g : (A /\ B) -> A.
intros.
destruct H as (H1,H2).
trivial.
Qed.
Theorem Coq_E_ou : ((A \/ B) /\ (A -> C) /\ (B -> C)) -> C.
intros.
destruct H as (H1,H2).
destruct H2 as (H2,H3).
destruct H1 as [H4 | H5].
E_imp A.
Hyp H2.
Hyp H4.
E_imp B.
trivial.
trivial.
Qed.
Theorem Thm_7 : ((E -> (Y \/ R)) /\ (Y -> R)) -> (~R -> ~E).
intros.
destruct H as (H1,H2).
tauto. (* à détailler *)
Qed.
End CalculPropositionnel.

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theory Enigme
predicate a
predicate b
predicate c
predicate da = b /\ (not c)
predicate db = a -> c
predicate dc = (not c) /\ ( a \/ b )
goal Q1: not (da /\ db /\ dc)
(* on demande ensuite un contre exemple *)
goal Q2c: da /\ db -> dc (* vrai *)
goal Q2b: dc /\ da -> db (* faux *)
goal Q2a: db /\ dc -> da (* vrai *)
goal Q3a: (not a) /\ (not b) /\ (not c) -> da (* faux, a ment *)
goal Q3b: (not a) /\ (not b) /\ (not c) -> db (* b dit la vérité *)
goal Q3c: (not a) /\ (not b) /\ (not c) -> dc (* faux, c ment *)
goal Q4a: da /\ db /\ dc -> a (* faux, a innocent *)
goal Q4b: da /\ db /\ dc -> b (* b coupable *)
goal Q4c: da /\ db /\ dc -> c (* faux, c innocent *)
goal Q5: not ( (a -> (not da)) /\ (b -> (not db)) /\ (c -> (not dc)) )
(* on demande ensuite un contre exemple *)
end

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(* Ouverture d’une section *)
Section CalculPredicats.
(* Définition de 2 domaines pour les prédicats *)
Variable A B : Type.
(* Formule du second ordre : Quantification des prédicats phi et psi *)
Theorem Thm_8 : forall (P Q : A -> Prop),
(forall x1 : A, (P x1) /\ (Q x1))
-> (forall x2 : A, (P x2)) /\ (forall x3 : A, (Q x3)).
intros.
split.
intro x2.
destruct (H x2).
exact H0.
intro x3.
destruct (H x3).
exact H1.
Qed.
(* Formule du second ordre : Quantification des prédicats phi et psi *)
Theorem Thm_9 : forall (P : A -> B -> Prop),
(exists x1 : A, forall y1 : B, (P x1 y1))
-> forall y2 : B, exists x2 : A, (P x2 y2).
intros.
destruct H.
exists x.
generalize y2.
exact H.
Qed.
(* Formule du second ordre : Quantification des prédicats phi et psi *)
Theorem Thm_10 : forall (P Q : A -> Prop),
(exists x1 : A, (P x1) -> (Q x1))
-> (forall x2 : A, (P x2)) -> exists x3 : A, (Q x3).
intros.
destruct H.
exists x.
cut (P x).
exact H.
generalize x.
exact H0.
Qed.
End CalculPredicats.

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(* Ouverture d’une section *)
Section CalculPredicats.
(* Définition de 2 domaines pour les prédicats *)
Variable A B : Type.
(* Formule du second ordre : Quantification des prédicats phi et psi *)
Theorem Thm_8 : forall (P Q : A -> Prop),
(forall x1 : A, (P x1) /\ (Q x1))
-> (forall x2 : A, (P x2)) /\ (forall x3 : A, (Q x3)).
intros.
split.
intro x2.
exists.
(* Formule du second ordre : Quantification des prédicats phi et psi
Theorem Thm_9 : forall (P : A -> B -> Prop),
(exists x1 : A, forall y1 : B, (P x1 y1))
-> forall y2 : B, exists x2 : A, (P x2 y2).
intros.*)
(* Formule du second ordre : Quantification des prédicats phi et psi
Theorem Thm_10 : forall (P Q : A -> Prop),
(exists x1 : A, (P x1) -> (Q x1))
-> (forall x2 : A, (P x2)) -> exists x3 : A, (Q x3).
intros.
exists x2.*)
End CalculPredicats.

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theory Enigme
predicate a
predicate b
predicate c
predicate da = b /\ (not c)
predicate db = a -> c
predicate dc = (not c) /\ ( a \/ b )
goal Q1: not (da /\ db /\ dc)
(* on demande ensuite un contre exemple *)
goal Q2c: da /\ db -> dc (* vrai *)
goal Q2b: dc /\ da -> db (* faux *)
goal Q2a: db /\ dc -> da (* vrai *)
goal Q3a: (not a) /\ (not b) /\ (not c) -> da (* faux, a ment *)
goal Q3b: (not a) /\ (not b) /\ (not c) -> db (* b dit la vérité *)
goal Q3c: (not a) /\ (not b) /\ (not c) -> dc (* faux, c ment *)
goal Q4a: da /\ db /\ dc -> a (* faux, a innocent *)
goal Q4b: da /\ db /\ dc -> b (* b coupable *)
goal Q4c: da /\ db /\ dc -> c (* faux, c innocent *)
goal Q5: not ( (a -> (not da)) /\ (b -> (not db)) /\ (c -> (not dc)) )
(* on demande ensuite un contre exemple *)
end

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%%% this is a prelude for CVC3
uni : TYPE;
ty : TYPE;
sort: (ty, uni) -> BOOLEAN;
witness: (ty) -> uni;
% witness_sort
ASSERT (FORALL (a : ty): (sort(a, witness(a))));
int: ty;
real: ty;
bool: ty;
match_bool: (ty, BITVECTOR(1), uni, uni) -> uni;
% match_bool_sort
ASSERT
(FORALL (a : ty):
(FORALL (x : BITVECTOR(1), x1 : uni, x2 : uni): (sort(a, match_bool(a, x,
x1, x2)))));
% match_bool_True
ASSERT
(FORALL (a : ty):
(FORALL (z : uni, z1 : uni):
((sort(a, z)) => (match_bool(a, 0bin1, z, z1) = z))));
% match_bool_False
ASSERT
(FORALL (a : ty):
(FORALL (z : uni, z1 : uni):
((sort(a, z1)) => (match_bool(a, 0bin0, z, z1) = z1))));
index_bool: (BITVECTOR(1)) -> INT;
% index_bool_True
ASSERT (index_bool(0bin1) = 0);
% index_bool_False
ASSERT (index_bool(0bin0) = 1);
% bool_inversion
ASSERT (FORALL (u : BITVECTOR(1)): ((u = 0bin1) OR (u = 0bin0)));
tuple0 : TYPE;
tuple01: ty;
Tuple0: tuple0;
% tuple0_inversion
ASSERT (FORALL (u : tuple0): (u = Tuple0));
a: BOOLEAN;
b: BOOLEAN;
c: BOOLEAN;
da: BOOLEAN;
% da_def
ASSERT (da <=> (b AND (NOT c)));
db: BOOLEAN;
% db_def
ASSERT (db <=> (a => c));
dc: BOOLEAN;
% dc_def
ASSERT (dc <=> ((NOT c) AND (a OR b)));
QUERY
% Thm01
% File "enigme.mlw", line 13, characters 7-12
(da AND (db AND dc));

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;;; generated by SMT-LIB2 driver
;;; SMT-LIB2 driver: bit-vectors, common part
(declare-datatypes () ((tuple0 (Tuple0))))
(declare-fun a () Bool)
(declare-fun b () Bool)
(declare-fun c () Bool)
(declare-fun da () Bool)
;; da_def
(assert (= da (and b (not c))))
(declare-fun db () Bool)
;; db_def
(assert (= db (=> a c)))
(declare-fun dc () Bool)
;; dc_def
(assert (= dc (and (not c) (or a b))))
(assert
;; Thm01
;; File "enigme.mlw", line 13, characters 7-12
(not (and da (and db dc))))
(check-sat)

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;;; generated by SMT-LIB2 driver
;;; SMT-LIB2 driver: bit-vectors, common part
(declare-datatypes () ((tuple0 (Tuple0))))
(declare-fun a () Bool)
(declare-fun b () Bool)
(declare-fun c () Bool)
(declare-fun da () Bool)
;; da_def
(assert (= da (and b (not c))))
(declare-fun db () Bool)
;; db_def
(assert (= db (=> a c)))
(declare-fun dc () Bool)
;; dc_def
(assert (= dc (and (not c) (or a b))))
(declare-fun compat () Bool)
;; compat_def
(assert (= compat (and da (and db dc))))
(assert
;; Q1
;; File "enigme/../enigme.mlw", line 15, characters 7-9
(not (not compat)))
(check-sat)

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(* This file is generated by Why3's Coq driver *)
(* Beware! Only edit allowed sections below *)
Require Import BuiltIn.
Require BuiltIn.
Parameter a: Prop.
Parameter b: Prop.
Parameter c: Prop.
(* Why3 assumption *)
Definition da : Prop := b /\ ~ c.
(* Why3 assumption *)
Definition db : Prop := a -> c.
(* Why3 assumption *)
Definition dc : Prop := ~ c /\ (a \/ b).
(* Why3 goal *)
Theorem Thm01 : da /\ (db /\ dc).
Proof.
Qed.

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<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
"http://why3.lri.fr/why3session.dtd">
<why3session shape_version="5">
<prover id="0" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="1" name="Z3" version="4.4.1" alternative="counterexamples" timelimit="5" steplimit="0" memlimit="1000"/>
<file>
<path name=".."/>
<path name="enigme.mlw"/>
<theory name="Enigme">
<goal name="Q1">
<proof prover="1"><result status="unknown" time="0.00"/></proof>
</goal>
<goal name="Q2c" proved="true">
<proof prover="0"><result status="valid" time="0.00"/></proof>
</goal>
<goal name="Q2b">
<proof prover="0"><result status="unknown" time="0.00"/></proof>
</goal>
<goal name="Q2a" proved="true">
<proof prover="0"><result status="valid" time="0.00"/></proof>
</goal>
<goal name="Q3a">
<proof prover="0"><result status="unknown" time="0.00"/></proof>
</goal>
<goal name="Q3b" proved="true">
<proof prover="0"><result status="valid" time="0.00"/></proof>
</goal>
<goal name="Q3c">
<proof prover="0"><result status="unknown" time="0.00"/></proof>
</goal>
<goal name="Q4a">
<proof prover="0"><result status="unknown" time="0.00"/></proof>
</goal>
<goal name="Q4b" proved="true">
<proof prover="0"><result status="valid" time="0.00"/></proof>
</goal>
<goal name="Q4c">
<proof prover="0"><result status="unknown" time="0.00"/></proof>
</goal>
<goal name="Q5">
<proof prover="1"><result status="unknown" time="0.00"/></proof>
</goal>
</theory>
</file>
</why3session>

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(* Ouverture d’une section *)
Section CalculPredicats.
(* Définition de 2 domaines pour les prédicats *)
Variable A B : Type.
(* Formule du second ordre : Quantification des prédicats phi et psi *)
Theorem Thm_8 : forall (P Q : A -> Prop),
(forall x1 : A, (P x1) /\ (Q x1))
-> (forall x2 : A, (P x2)) /\ (forall x3 : A, (Q x3)).
intros.
split.
intro x2.
destruct (H x2).
exact H0.
intro x3.
destruct (H x3).
exact H1.
Qed.
(* Formule du second ordre : Quantification des prédicats phi et psi *)
Theorem Thm_9 : forall (P : A -> B -> Prop),
(exists x1 : A, forall y1 : B, (P x1 y1))
-> forall y2 : B, exists x2 : A, (P x2 y2).
intros.
destruct H.
exists x.
generalize y2.
exact H.
Qed.
(* Formule du second ordre : Quantification des prédicats phi et psi *)
Theorem Thm_10 : forall (P Q : A -> Prop),
(exists x1 : A, (P x1) -> (Q x1))
-> (forall x2 : A, (P x2)) -> exists x3 : A, (Q x3).
intros.
destruct H.
exists x.
cut (P x).
exact H.
generalize x.
exact H0.
Qed.
End CalculPredicats.

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(* Ouverture d’une section *)
Section CalculPredicats.
(* Définition de 2 domaines pour les prédicats *)
Variable A B : Type.
(* Formule du second ordre : Quantification des prédicats phi et psi *)
Theorem Thm_8 : forall (P Q : A -> Prop),
(forall x1 : A, (P x1) /\ (Q x1))
-> (forall x2 : A, (P x2)) /\ (forall x3 : A, (Q x3)).
intros.
split.
intro x2.
exists.
(* Formule du second ordre : Quantification des prédicats phi et psi
Theorem Thm_9 : forall (P : A -> B -> Prop),
(exists x1 : A, forall y1 : B, (P x1 y1))
-> forall y2 : B, exists x2 : A, (P x2 y2).
intros.*)
(* Formule du second ordre : Quantification des prédicats phi et psi
Theorem Thm_10 : forall (P Q : A -> Prop),
(exists x1 : A, (P x1) -> (Q x1))
-> (forall x2 : A, (P x2)) -> exists x3 : A, (Q x3).
intros.
exists x2.*)
End CalculPredicats.

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theory Enigme
predicate a
predicate b
predicate c
predicate da = b /\ (not c)
predicate db = a -> c
predicate dc = (not c) /\ ( a \/ b )
goal Q1: not (da /\ db /\ dc)
(* on demande ensuite un contre exemple *)
goal Q2c: da /\ db -> dc (* vrai *)
goal Q2b: dc /\ da -> db (* faux *)
goal Q2a: db /\ dc -> da (* vrai *)
goal Q3a: (not a) /\ (not b) /\ (not c) -> da (* faux, a ment *)
goal Q3b: (not a) /\ (not b) /\ (not c) -> db (* b dit la vérité *)
goal Q3c: (not a) /\ (not b) /\ (not c) -> dc (* faux, c ment *)
goal Q4a: da /\ db /\ dc -> a (* faux, a innocent *)
goal Q4b: da /\ db /\ dc -> b (* b coupable *)
goal Q4c: da /\ db /\ dc -> c (* faux, c innocent *)
goal Q5: not ( (a -> (not da)) /\ (b -> (not db)) /\ (c -> (not dc)) )
(* on demande ensuite un contre exemple *)
end

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%%% this is a prelude for CVC3
uni : TYPE;
ty : TYPE;
sort: (ty, uni) -> BOOLEAN;
witness: (ty) -> uni;
% witness_sort
ASSERT (FORALL (a : ty): (sort(a, witness(a))));
int: ty;
real: ty;
bool: ty;
match_bool: (ty, BITVECTOR(1), uni, uni) -> uni;
% match_bool_sort
ASSERT
(FORALL (a : ty):
(FORALL (x : BITVECTOR(1), x1 : uni, x2 : uni): (sort(a, match_bool(a, x,
x1, x2)))));
% match_bool_True
ASSERT
(FORALL (a : ty):
(FORALL (z : uni, z1 : uni):
((sort(a, z)) => (match_bool(a, 0bin1, z, z1) = z))));
% match_bool_False
ASSERT
(FORALL (a : ty):
(FORALL (z : uni, z1 : uni):
((sort(a, z1)) => (match_bool(a, 0bin0, z, z1) = z1))));
index_bool: (BITVECTOR(1)) -> INT;
% index_bool_True
ASSERT (index_bool(0bin1) = 0);
% index_bool_False
ASSERT (index_bool(0bin0) = 1);
% bool_inversion
ASSERT (FORALL (u : BITVECTOR(1)): ((u = 0bin1) OR (u = 0bin0)));
tuple0 : TYPE;
tuple01: ty;
Tuple0: tuple0;
% tuple0_inversion
ASSERT (FORALL (u : tuple0): (u = Tuple0));
a: BOOLEAN;
b: BOOLEAN;
c: BOOLEAN;
da: BOOLEAN;
% da_def
ASSERT (da <=> (b AND (NOT c)));
db: BOOLEAN;
% db_def
ASSERT (db <=> (a => c));
dc: BOOLEAN;
% dc_def
ASSERT (dc <=> ((NOT c) AND (a OR b)));
QUERY
% Thm01
% File "enigme.mlw", line 13, characters 7-12
(da AND (db AND dc));

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TP2/enigme/enigme-Predicats-Thm01_1.smt2 Executable file
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;;; generated by SMT-LIB2 driver
;;; SMT-LIB2 driver: bit-vectors, common part
(declare-datatypes () ((tuple0 (Tuple0))))
(declare-fun a () Bool)
(declare-fun b () Bool)
(declare-fun c () Bool)
(declare-fun da () Bool)
;; da_def
(assert (= da (and b (not c))))
(declare-fun db () Bool)
;; db_def
(assert (= db (=> a c)))
(declare-fun dc () Bool)
;; dc_def
(assert (= dc (and (not c) (or a b))))
(assert
;; Thm01
;; File "enigme.mlw", line 13, characters 7-12
(not (and da (and db dc))))
(check-sat)

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;;; generated by SMT-LIB2 driver
;;; SMT-LIB2 driver: bit-vectors, common part
(declare-datatypes () ((tuple0 (Tuple0))))
(declare-fun a () Bool)
(declare-fun b () Bool)
(declare-fun c () Bool)
(declare-fun da () Bool)
;; da_def
(assert (= da (and b (not c))))
(declare-fun db () Bool)
;; db_def
(assert (= db (=> a c)))
(declare-fun dc () Bool)
;; dc_def
(assert (= dc (and (not c) (or a b))))
(declare-fun compat () Bool)
;; compat_def
(assert (= compat (and da (and db dc))))
(assert
;; Q1
;; File "enigme/../enigme.mlw", line 15, characters 7-9
(not (not compat)))
(check-sat)

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(* This file is generated by Why3's Coq driver *)
(* Beware! Only edit allowed sections below *)
Require Import BuiltIn.
Require BuiltIn.
Parameter a: Prop.
Parameter b: Prop.
Parameter c: Prop.
(* Why3 assumption *)
Definition da : Prop := b /\ ~ c.
(* Why3 assumption *)
Definition db : Prop := a -> c.
(* Why3 assumption *)
Definition dc : Prop := ~ c /\ (a \/ b).
(* Why3 goal *)
Theorem Thm01 : da /\ (db /\ dc).
Proof.
Qed.

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<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
"http://why3.lri.fr/why3session.dtd">
<why3session shape_version="5">
<prover id="0" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="1" name="Z3" version="4.4.1" alternative="counterexamples" timelimit="5" steplimit="0" memlimit="1000"/>
<file>
<path name=".."/>
<path name="enigme.mlw"/>
<theory name="Enigme">
<goal name="Q1">
<proof prover="1"><result status="unknown" time="0.00"/></proof>
</goal>
<goal name="Q2c" proved="true">
<proof prover="0"><result status="valid" time="0.00"/></proof>
</goal>
<goal name="Q2b">
<proof prover="0"><result status="unknown" time="0.00"/></proof>
</goal>
<goal name="Q2a" proved="true">
<proof prover="0"><result status="valid" time="0.00"/></proof>
</goal>
<goal name="Q3a">
<proof prover="0"><result status="unknown" time="0.00"/></proof>
</goal>
<goal name="Q3b" proved="true">
<proof prover="0"><result status="valid" time="0.00"/></proof>
</goal>
<goal name="Q3c">
<proof prover="0"><result status="unknown" time="0.00"/></proof>
</goal>
<goal name="Q4a">
<proof prover="0"><result status="unknown" time="0.00"/></proof>
</goal>
<goal name="Q4b" proved="true">
<proof prover="0"><result status="valid" time="0.00"/></proof>
</goal>
<goal name="Q4c">
<proof prover="0"><result status="unknown" time="0.00"/></proof>
</goal>
<goal name="Q5">
<proof prover="1"><result status="unknown" time="0.00"/></proof>
</goal>
</theory>
</file>
</why3session>

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theory Induction
(* Définition du type inductif liste *)
type liste 'a = Nil | Cons 'a (liste 'a)
(* Concaténation de deux listes *)
function append (l1 l2 : liste 'a) : liste 'a =
match l1 with
| Nil -> l2
| Cons t q -> Cons t (append q l2)
end
lemma append_Nil_left : forall l : liste 'a. append Nil l = l
lemma append_Cons_left : forall e : 'a. forall l1 l2 : liste 'a.
append (Cons e l1) l2 = Cons e (append l1 l2)
lemma append_Nil_right: forall l : liste 'a. append l Nil = l
lemma append_associative : forall l1 [@induction] l2 l3 : liste 'a.
append l1 (append l2 l3) = append (append l1 l2) l3
end

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Require Import Extraction.
(* Ouverture d’une section *)
Section Induction.
(* Déclaration d’un domaine pour les éléments des listes *)
Variable A : Set.
Inductive liste : Set :=
Nil : liste
| Cons : A -> liste -> liste.
(* Déclaration du nom de la fonction *)
Variable append_spec : liste -> liste -> liste.
(* Spécification du comportement pour Nil *)
Axiom append_Nil : forall (l : liste), append_spec Nil l = l.
(* Spécification du comportement pour Cons *)
Axiom append_Cons : forall (t : A), forall (q l : liste),
append_spec (Cons t q) l = Cons t (append_spec q l).
Theorem append_Nil_right : forall (l : liste), (append_spec l Nil) = l.
intros.
induction l.
(*cas de base*)
apply append_Nil.
(*cas general*)
rewrite append_Cons.
rewrite IHl.
reflexivity.
Qed.
Theorem append_associative : forall (l1 l2 l3 : liste),
(append_spec l1 (append_spec l2 l3)) = (append_spec (append_spec l1 l2) l3).
intros.
induction l1.
(*cas de base*)
rewrite append_Nil.
rewrite append_Nil.
reflexivity.
(*cas general*)
rewrite append_Cons.
rewrite IHl1.
rewrite append_Cons.
rewrite append_Cons.
reflexivity.
Qed.
(* Implantation de la fonction append *)
Fixpoint append_impl (l1 l2 : liste) {struct l1} : liste :=
match l1 with
Nil => l2
| (Cons t1 q1) => (Cons t1 (append_impl q1 l2))
end.
Theorem append_correctness : forall (l1 l2 : liste),
(append_spec l1 l2) = (append_impl l1 l2).
intros.
induction l1.
(*cas de base*)
rewrite append_Nil.
simpl append_impl.
reflexivity.
(*cas general*)
rewrite append_Cons.
simpl append_impl.
rewrite IHl1.
reflexivity.
Qed.
(* Implantation de la fonction rev (reverse d'une liste) *)
Fixpoint rev_impl (l : liste) : liste :=
match l with
Nil => Nil
| (Cons t1 q1) => (append_impl (rev_impl q1)( Cons t1 Nil))
end.
Lemma rev_append : forall (l1 l2 : liste),
(rev_impl (append_impl l1 l2)) = (append_impl (rev_impl l2) (rev_impl l1)).
intros.
induction l1.
(*cas de base *)
simpl append_impl.
rewrite <- append_correctness.
rewrite append_Nil_right.
reflexivity.
(*cas general*)
simpl rev_impl.
rewrite IHl1.
rewrite <- append_correctness.
rewrite <- append_correctness.
rewrite <- append_correctness.
rewrite <- append_correctness.
rewrite append_associative.
reflexivity.
Qed.
Theorem rev_rev : forall (l : liste), (rev_impl (rev_impl l)) = l.
intros.
induction l.
(*Cas de base*)
simpl rev_impl.
reflexivity.
(*cas general*)
simpl rev_impl.
rewrite rev_append.
rewrite IHl.
simpl rev_impl.
rewrite <- append_correctness.
rewrite append_Cons.
rewrite append_Nil.
reflexivity.
Qed.
End Induction.
Extraction Language Ocaml.
Extraction "/tmp/induction" append_impl rev_impl.
Extraction Language Haskell.
Extraction "/tmp/induction" append_impl rev_impl.
Extraction Language Scheme.
Extraction "/tmp/induction" append_impl rev_impl.

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2020-10-13
Modélisation TP4
http://moodle-n7.inp-toulouse.fr/pluginfile.php/90409/mod_resource/content/4/equipes-TD5TD6.txt
Membres de groupe G-5:
EL HADFI Younes
HAMMAMI Linda
HAUTEVILLE Leane
FAINSIN Laurent

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TP5/induction-etu.mlw Executable file
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theory Induction
(* Définition du type inductif liste *)
type liste 'a = Nil | Cons 'a (liste 'a)
(* Concaténation de deux listes *)
function append (l1 l2 : liste 'a) : liste 'a =
match l1 with
| Nil -> l2
| Cons t q -> Cons t (append q l2)
end
lemma append_Nil_left : forall l : liste 'a. append Nil l = l
lemma append_Cons_left : forall e : 'a. forall l1 l2 : liste 'a.
append (Cons e l1) l2 = Cons e (append l1 l2)
lemma append_Nil_right: forall l : liste 'a. append l Nil = l
lemma append_associative : forall l1 [@induction] l2 l3 : liste 'a.
append l1 (append l2 l3) = append (append l1 l2) l3
end

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Require Import Extraction.
(* Ouverture d’une section *)
Section Induction.
(* Déclaration d’un domaine pour les éléments des listes *)
Variable A : Set.
Inductive liste : Set :=
Nil : liste
| Cons : A -> liste -> liste.
(* Déclaration du nom de la fonction *)
Variable append_spec : liste -> liste -> liste.
(* Spécification du comportement pour Nil *)
Axiom append_Nil : forall (l : liste), append_spec Nil l = l.
(* Spécification du comportement pour Cons *)
Axiom append_Cons : forall (t : A), forall (q l : liste),
append_spec (Cons t q) l = Cons t (append_spec q l).
Theorem append_Nil_right : forall (l : liste), (append_spec l Nil) = l.
intros.
induction l.
(* cas de base *)
apply append_Nil.
(* cas général *)
rewrite append_Cons.
rewrite IHl.
reflexivity.
Qed.
Theorem append_associative : forall (l1 l2 l3 : liste),
(append_spec l1 (append_spec l2 l3)) = (append_spec (append_spec l1 l2) l3).
intros.
induction l1.
(* cas de base *)
rewrite append_Nil.
rewrite append_Nil.
reflexivity.
(* cas général *)
rewrite append_Cons.
rewrite append_Cons.
rewrite append_Cons.
rewrite IHl1.
reflexivity.
Qed.
(* Implantation de la fonction append *)
Fixpoint append_impl (l1 l2 : liste) {struct l1} : liste :=
match l1 with
Nil => l2
| (Cons t1 q1) => (Cons t1 (append_impl q1 l2))
end.
Theorem append_correctness : forall (l1 l2 : liste),
(append_spec l1 l2) = (append_impl l1 l2).
intros.
induction l1.
(* cas de base *)
rewrite append_Nil.
simpl append_impl.
reflexivity.
(* cas général *)
rewrite append_Cons.
simpl append_impl.
rewrite IHl1.
reflexivity.
Qed.
(* Implantation de la fonction rev (reverse d'une liste) *)
Fixpoint rev_impl (l : liste) : liste :=
match l with
Nil => l
| (Cons x y) => ( append_impl (rev_impl y) (Cons x Nil) )
end.
Lemma rev_append : forall (l1 l2 : liste),
(rev_impl (append_impl l1 l2)) = (append_impl (rev_impl l2) (rev_impl l1)).
intros.
induction l1.
(* cas de base *)
simpl rev_impl.
rewrite <- append_correctness.
rewrite append_Nil_right.
reflexivity.
(* cas général *)
simpl rev_impl.
rewrite IHl1.
rewrite <- append_correctness.
rewrite <- append_correctness.
rewrite <- append_correctness.
rewrite <- append_correctness.
rewrite append_associative.
reflexivity.
Qed.
Theorem rev_rev : forall (l : liste), (rev_impl (rev_impl l)) = l.
intros.
induction l.
(* cas de base *)
simpl rev_impl.
reflexivity.
(* cas général *)
simpl rev_impl.
rewrite rev_append.
rewrite IHl.
simpl rev_impl.
rewrite <- append_correctness.
rewrite append_Cons.
rewrite append_Nil.
reflexivity.
Qed.
End Induction.
Extraction Language Ocaml.
Extraction "/tmp/induction" append_impl rev_impl.
Extraction Language Haskell.
Extraction "/tmp/induction" append_impl rev_impl.
Extraction Language Scheme.
Extraction "/tmp/induction" append_impl rev_impl.

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TP5/induction-etu.wlm Executable file
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theory Induction
(* Définition du type inductif liste *)
type liste 'a = Nil | Cons 'a (liste 'a)
(* Concaténation de deux listes *)
function append (l1 l2 : liste 'a) : liste 'a =
match l1 with
| Nil -> l2
| Cons t q -> Cons t (append q l2)
end
lemma append_Nil_left : forall l : liste 'a. append Nil l = l
lemma append_Cons_left : forall e : 'a. forall l1 l2 : liste 'a.
append (Cons e l1) l2 = Cons e (append l1 l2)
lemma append_Nil_right: forall l : liste 'a. append l Nil = l
lemma append_associative : forall l1 [@induction] l2 l3 : liste 'a.
append l1 (append l2 l3) = append (append l1 l2) l3
end

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TP5/induction-etu/why3session.xml Executable file
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<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
"http://why3.lri.fr/why3session.dtd">
<why3session shape_version="5">
<prover id="0" name="Z3" version="4.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
<file proved="true">
<path name=".."/>
<path name="induction-etu.mlw"/>
<theory name="Induction" proved="true">
<goal name="append_Nil_left" proved="true">
<proof prover="0"><result status="valid" time="0.01"/></proof>
</goal>
<goal name="append_Cons_left" proved="true">
<proof prover="0"><result status="valid" time="0.01"/></proof>
</goal>
<goal name="append_Nil_right" proved="true">
<transf name="induction_ty_lex" proved="true" >
<goal name="append_Nil_right.0" proved="true">
<proof prover="0"><result status="valid" time="0.00"/></proof>
</goal>
</transf>
</goal>
<goal name="append_associative" proved="true">
<transf name="induction_ty_lex" proved="true" >
<goal name="append_associative.0" proved="true">
<proof prover="0"><result status="valid" time="0.01"/></proof>
</goal>
</transf>
</goal>
</theory>
</file>
</why3session>

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(* Spécification de la fonction factorielle *)
theory Factorielle
use int.Int
function factorielle( n : int ) : int
axiom factorielle_zero : (factorielle zero) = one
axiom factorielle_succ : forall n : int. (n > 0) -> (factorielle n) = (n * (factorielle (n - 1)))
end
(* Implémentation de la fonction factorielle par un algorithme ascendant *)
module FactorielleAscendant
use int.Int
use ref.Refint
use Factorielle
let factorielle_ascendant (n: int) : int
requires { 0 <= n }
ensures { result = (factorielle n) }
=
let i = ref 0 in
let r = ref 1 in
while (!i < n) do
invariant { !r = (factorielle !i) && ( 0 <= !i <= n ) }
variant { n - !i }
i := (!i) + 1;
r := (!i) * (!r)
done;
!r
end

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TP6/ascendant/ascendant_FactorielleAscendant_VC_factorielle_ascendant_1.v Executable file
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(* This file is generated by Why3's Coq driver *)
(* Beware! Only edit allowed sections below *)
Require Import BuiltIn.
Require BuiltIn.
Require int.Int.
(* Why3 assumption *)
Inductive ref (a:Type) :=
| mk_ref : a -> ref a.
Axiom ref_WhyType : forall (a:Type) {a_WT:WhyType a}, WhyType (ref a).
Existing Instance ref_WhyType.
Arguments mk_ref {a}.
(* Why3 assumption *)
Definition contents {a:Type} {a_WT:WhyType a} (v:ref a) : a :=
match v with
| mk_ref x => x
end.
Parameter factorielle: Z -> Z.
Axiom factorielle_zero : ((factorielle 0%Z) = 1%Z).
Axiom factorielle_succ :
forall (n:Z), (0%Z < n)%Z ->
((factorielle n) = (n * (factorielle (n - 1%Z)%Z))%Z).
Parameter n: Z.
Axiom H : (0%Z <= n)%Z.
(* Why3 goal *)
Theorem VC_factorielle_ascendant :
(1%Z = (factorielle 0%Z)) /\ ((0%Z <= 0%Z)%Z /\ (0%Z <= n)%Z).
split.
rewrite factorielle_zero.
reflexivity.
split.
omega.
apply H.
Qed.

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(* This file is generated by Why3's Coq driver *)
(* Beware! Only edit allowed sections below *)
Require Import BuiltIn.
Require BuiltIn.
Require int.Int.
(* Why3 assumption *)
Inductive ref (a:Type) :=
| mk_ref : a -> ref a.
Axiom ref_WhyType : forall (a:Type) {a_WT:WhyType a}, WhyType (ref a).
Existing Instance ref_WhyType.
Arguments mk_ref {a}.
(* Why3 assumption *)
Definition contents {a:Type} {a_WT:WhyType a} (v:ref a) : a :=
match v with
| mk_ref x => x
end.
Parameter factorielle: Z -> Z.
Axiom factorielle_zero : ((factorielle 0%Z) = 1%Z).
Axiom factorielle_succ :
forall (n:Z), (0%Z < n)%Z ->
((factorielle n) = (n * (factorielle (n - 1%Z)%Z))%Z).
Parameter n: Z.
Axiom H : (0%Z <= n)%Z.
Parameter r: Z.
Parameter i: Z.
Axiom H1 : (r = (factorielle i)).
Axiom H2 : (0%Z <= i)%Z.
Axiom H3 : (i <= n)%Z.
Axiom H4 : (i < n)%Z.
Parameter i1: Z.
Axiom H5 : (i1 = (i + 1%Z)%Z).
Parameter r1: Z.
Axiom H6 : (r1 = (i1 * r)%Z).
(* Why3 goal *)
Theorem VC_factorielle_ascendant :
(0%Z <= (n - i)%Z)%Z /\ ((n - i1)%Z < (n - i)%Z)%Z.
split.
generalize H.
intros.
generalize H3.
intros.
omega.
generalize H.
intros.
generalize H5.
intros.
omega.
Qed.

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(* This file is generated by Why3's Coq driver *)
(* Beware! Only edit allowed sections below *)
Require Import BuiltIn.
Require BuiltIn.
Require int.Int.
(* Why3 assumption *)
Inductive ref (a:Type) :=
| mk_ref : a -> ref a.
Axiom ref_WhyType : forall (a:Type) {a_WT:WhyType a}, WhyType (ref a).
Existing Instance ref_WhyType.
Arguments mk_ref {a}.
(* Why3 assumption *)
Definition contents {a:Type} {a_WT:WhyType a} (v:ref a) : a :=
match v with
| mk_ref x => x
end.
Parameter factorielle: Z -> Z.
Axiom factorielle_zero : ((factorielle 0%Z) = 1%Z).
Axiom factorielle_succ :
forall (n:Z), (0%Z < n)%Z ->
((factorielle n) = (n * (factorielle (n - 1%Z)%Z))%Z).
Parameter n: Z.
Axiom H : (0%Z <= n)%Z.
Parameter r: Z.
Parameter i: Z.
Axiom H1 : (r = (factorielle i)).
Axiom H2 : (0%Z <= i)%Z.
Axiom H3 : (i <= n)%Z.
Axiom H4 : (i < n)%Z.
Parameter i1: Z.
Axiom H5 : (i1 = (i + 1%Z)%Z).
Parameter r1: Z.
Axiom H6 : (r1 = (i1 * r)%Z).
Axiom H7 : ((i+1-1) = i)%Z.
(* Why3 goal *)
Theorem VC_factorielle_ascendant :
(r1 = (factorielle i1)) /\ ((0%Z <= i1)%Z /\ (i1 <= n)%Z).
split.
generalize H1.
intros.
rewrite H6.
rewrite -> factorielle_succ.
rewrite H5.
rewrite H0.
rewrite H7.
reflexivity.
generalize H2.
intros.
rewrite H5.
Qed.

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TP6/ascendant/ascendant_FactorielleAscendant_VC_factorielle_ascendant_4.v Executable file
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(* This file is generated by Why3's Coq driver *)
(* Beware! Only edit allowed sections below *)
Require Import BuiltIn.
Require BuiltIn.
Require int.Int.
(* Why3 assumption *)
Inductive ref (a:Type) :=
| mk_ref : a -> ref a.
Axiom ref_WhyType : forall (a:Type) {a_WT:WhyType a}, WhyType (ref a).
Existing Instance ref_WhyType.
Arguments mk_ref {a}.
(* Why3 assumption *)
Definition contents {a:Type} {a_WT:WhyType a} (v:ref a) : a :=
match v with
| mk_ref x => x
end.
Parameter factorielle: Z -> Z.
Axiom factorielle_zero : ((factorielle 0%Z) = 1%Z).
Axiom factorielle_succ :
forall (n:Z), (0%Z < n)%Z ->
((factorielle n) = (n * (factorielle (n - 1%Z)%Z))%Z).
Parameter n: Z.
Axiom H : (0%Z <= n)%Z.
Parameter r: Z.
Parameter i: Z.
Axiom H1 : (r = (factorielle i)).
Axiom H2 : (0%Z <= i)%Z.
Axiom H3 : (i <= n)%Z.
Axiom H4 : ~ (i < n)%Z.
(* H3 et H4 implique H43 *)
Axiom H34 : ( i = n )%Z.
(* Why3 goal *)
Theorem VC_factorielle_ascendant : (r = (factorielle n)).
rewrite H1.
rewrite H34.
reflexivity.
Qed.

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<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
"http://why3.lri.fr/why3session.dtd">
<why3session shape_version="5">
<prover id="0" name="Coq" version="8.9.1" timelimit="0" steplimit="0" memlimit="0"/>
<prover id="1" name="Alt-Ergo" version="2.0.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="2" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="3" name="Z3" version="4.4.1" alternative="noBV" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="4" name="Z3" version="4.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="5" name="CVC4" version="1.5" timelimit="5" steplimit="0" memlimit="1000"/>
<file proved="true">
<path name=".."/>
<path name="ascendant.mlw"/>
<theory name="FactorielleAscendant" proved="true">
<goal name="VC factorielle_ascendant" expl="VC for factorielle_ascendant" proved="true">
<transf name="split_vc" proved="true" >
<goal name="VC factorielle_ascendant.0" expl="loop invariant init" proved="true">
<proof prover="0" edited="ascendant_FactorielleAscendant_VC_factorielle_ascendant_1.v"><result status="valid" time="0.35"/></proof>
<proof prover="1"><result status="valid" time="0.00" steps="3"/></proof>
<proof prover="2"><result status="valid" time="0.00"/></proof>
<proof prover="3"><result status="valid" time="0.01"/></proof>
<proof prover="4"><result status="valid" time="0.00"/></proof>
<proof prover="5"><result status="valid" time="0.00"/></proof>
</goal>
<goal name="VC factorielle_ascendant.1" expl="loop variant decrease" proved="true">
<proof prover="0" edited="ascendant_FactorielleAscendant_VC_factorielle_ascendant_2.v"><result status="unknown" time="0.33"/></proof>
<proof prover="1"><result status="valid" time="0.00" steps="9"/></proof>
</goal>
<goal name="VC factorielle_ascendant.2" expl="loop invariant preservation" proved="true">
<proof prover="0" edited="ascendant_FactorielleAscendant_VC_factorielle_ascendant_3.v"><result status="unknown" time="0.30"/></proof>
<proof prover="1"><result status="valid" time="0.00" steps="10"/></proof>
<proof prover="2"><result status="valid" time="0.00"/></proof>
<proof prover="3"><result status="valid" time="0.05"/></proof>
<proof prover="4"><result status="valid" time="0.05"/></proof>
<proof prover="5"><result status="valid" time="0.00"/></proof>
</goal>
<goal name="VC factorielle_ascendant.3" expl="postcondition" proved="true">
<proof prover="0" edited="ascendant_FactorielleAscendant_VC_factorielle_ascendant_4.v"><result status="unknown" time="0.31"/></proof>
<proof prover="1"><result status="valid" time="0.00" steps="7"/></proof>
</goal>
</transf>
</goal>
</theory>
</file>
</why3session>

37
TP6/descendant.mlw Executable file
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@ -0,0 +1,37 @@
(* Spécification de la fonction factorielle *)
theory Factorielle
use int.Int
function factorielle( n : int ) : int
axiom factorielle_zero : (factorielle zero) = one
axiom factorielle_succ : forall n : int. (n > 0) -> (factorielle n) = (n * (factorielle (n - 1)))
end
(* Implémentation de la fonction factorielle par un algorithme descendant *)
module FactorielleDescendant
use int.Int
use Factorielle
use ref.Refint
let factorielle_descendant (n: int) : int
requires { 0 <= n }
ensures { result = (factorielle n) }
=
let i = ref n in
let r = ref 1 in
while (0 < !i) do
invariant { !r * factorielle !i = factorielle n && 0 <= !i }
variant { !i }
r := !i * !r;
i := !i - 1
done;
!r
end

47
TP6/descendant/why3session.xml Executable file
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@ -0,0 +1,47 @@
<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
"http://why3.lri.fr/why3session.dtd">
<why3session shape_version="5">
<prover id="0" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="1" name="Z3" version="4.4.1" alternative="noBV" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="2" name="Alt-Ergo" version="2.0.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="3" name="Z3" version="4.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="4" name="CVC4" version="1.5" timelimit="5" steplimit="0" memlimit="1000"/>
<file proved="true">
<path name=".."/>
<path name="descendant.mlw"/>
<theory name="FactorielleDescendant" proved="true">
<goal name="VC factorielle_descendant" expl="VC for factorielle_descendant" proved="true">
<transf name="split_vc" proved="true" >
<goal name="VC factorielle_descendant.0" expl="loop invariant init" proved="true">
<proof prover="0"><result status="valid" time="0.00"/></proof>
<proof prover="1"><result status="valid" time="0.00"/></proof>
<proof prover="2"><result status="valid" time="0.00" steps="3"/></proof>
<proof prover="3"><result status="valid" time="0.01"/></proof>
<proof prover="4"><result status="valid" time="0.00"/></proof>
</goal>
<goal name="VC factorielle_descendant.1" expl="loop variant decrease" proved="true">
<proof prover="0"><result status="valid" time="0.00"/></proof>
<proof prover="1"><result status="valid" time="0.01"/></proof>
<proof prover="2"><result status="valid" time="0.00" steps="8"/></proof>
<proof prover="3"><result status="valid" time="0.01"/></proof>
<proof prover="4"><result status="valid" time="0.01"/></proof>
</goal>
<goal name="VC factorielle_descendant.2" expl="loop invariant preservation" proved="true">
<proof prover="0"><result status="valid" time="0.01"/></proof>
<proof prover="1"><result status="timeout" time="5.00"/></proof>
<proof prover="2"><result status="valid" time="0.01" steps="10"/></proof>
<proof prover="3"><result status="timeout" time="5.00"/></proof>
<proof prover="4"><result status="failure" time="0.00"/></proof>
</goal>
<goal name="VC factorielle_descendant.3" expl="postcondition" proved="true">
<proof prover="0"><result status="valid" time="0.00"/></proof>
<proof prover="2"><result status="valid" time="0.00" steps="6"/></proof>
<proof prover="3"><result status="valid" time="0.00"/></proof>
<proof prover="4"><result status="failure" time="0.00"/></proof>
</goal>
</transf>
</goal>
</theory>
</file>
</why3session>

23
TP6/division.mlw Executable file
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@ -0,0 +1,23 @@
(* Division entière par l'algorithme d'Euclide *)
module Division
use int.Int
use ref.Refint
let division (a b: int) (* renvoie une paire d'entiers (quotient,reste) *)
requires { 0 <= a && 0 < b }
ensures { let (q,r) = result in q * b + r = a && 0 <= r < b }
=
let q = ref 0 in
let r = ref a in
while !r >= b do
invariant { a = !q * b + !r && 0 <= !q && 0 <= !r }
variant { !r - b }
q := (!q) + 1;
r := (!r) - b
done;
(!q,!r)
end

28
TP6/division/why3session.xml Executable file
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@ -0,0 +1,28 @@
<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
"http://why3.lri.fr/why3session.dtd">
<why3session shape_version="5">
<prover id="0" name="Alt-Ergo" version="2.0.0" timelimit="5" steplimit="0" memlimit="1000"/>
<file proved="true">
<path name=".."/>
<path name="division.mlw"/>
<theory name="Division" proved="true">
<goal name="VC division" expl="VC for division" proved="true">
<transf name="split_vc" proved="true" >
<goal name="VC division.0" expl="loop invariant init" proved="true">
<proof prover="0"><result status="valid" time="0.00" steps="3"/></proof>
</goal>
<goal name="VC division.1" expl="loop variant decrease" proved="true">
<proof prover="0"><result status="valid" time="0.00" steps="9"/></proof>
</goal>
<goal name="VC division.2" expl="loop invariant preservation" proved="true">
<proof prover="0"><result status="valid" time="0.00" steps="9"/></proof>
</goal>
<goal name="VC division.3" expl="postcondition" proved="true">
<proof prover="0"><result status="valid" time="0.00" steps="7"/></proof>
</goal>
</transf>
</goal>
</theory>
</file>
</why3session>

38
TP6/pgcd.mlw Executable file
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@ -0,0 +1,38 @@
(* PGCD : Algorithme Euclide *)
theory PGCD
use int.Int
function pgcd(a b : int) : int
axiom A1 : forall a: int. (a>0) -> ( pgcd a a ) = a
axiom A2 : forall a,b: int. (a>0 && b>0) -> ( pgcd a b ) = ( pgcd b a )
axiom A3 : forall a,b: int. (a>b>0) -> ( pgcd a b ) = (pgcd (a-b) b )
end
module PGCDEuclide
use import int.Int
use import ref.Refint
use import PGCD
let pgcd_euclide (a b: int) : int
requires { 0 < a && 0 < b }
ensures { result = (pgcd a b)}
=
let ap = ref a in
let bp = ref b in
while (!ap <> !bp) do
invariant { (pgcd a b ) = ( pgcd !ap !bp ) && !ap > 0 && !bp > 0 }
variant { !ap + !bp }
if (!ap <= !bp) then
bp := !bp - !ap
else
ap := !ap - !bp
done;
!ap
end

58
TP6/pgcd/why3session.xml Executable file
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@ -0,0 +1,58 @@
<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
"http://why3.lri.fr/why3session.dtd">
<why3session shape_version="5">
<prover id="0" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="1" name="Z3" version="4.4.1" alternative="noBV" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="2" name="Alt-Ergo" version="2.0.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="3" name="Z3" version="4.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="4" name="CVC4" version="1.5" timelimit="5" steplimit="0" memlimit="1000"/>
<file proved="true">
<path name=".."/>
<path name="pgcd.mlw"/>
<theory name="PGCDEuclide" proved="true">
<goal name="VC pgcd_euclide" expl="VC for pgcd_euclide" proved="true">
<transf name="split_vc" proved="true" >
<goal name="VC pgcd_euclide.0" expl="loop invariant init" proved="true">
<proof prover="2"><result status="valid" time="0.00" steps="3"/></proof>
</goal>
<goal name="VC pgcd_euclide.1" expl="loop variant decrease" proved="true">
<proof prover="0"><result status="valid" time="0.01"/></proof>
<proof prover="1"><result status="valid" time="0.00"/></proof>
<proof prover="2"><result status="valid" time="0.00" steps="9"/></proof>
<proof prover="3"><result status="valid" time="0.00"/></proof>
<proof prover="4"><result status="valid" time="0.00"/></proof>
</goal>
<goal name="VC pgcd_euclide.2" expl="loop invariant preservation" proved="true">
<proof prover="0"><result status="valid" time="0.01"/></proof>
<proof prover="1"><result status="valid" time="0.02"/></proof>
<proof prover="2"><result status="valid" time="0.01" steps="21"/></proof>
<proof prover="3"><result status="valid" time="0.01"/></proof>
<proof prover="4"><result status="valid" time="0.01"/></proof>
</goal>
<goal name="VC pgcd_euclide.3" expl="loop variant decrease" proved="true">
<proof prover="0"><result status="valid" time="0.00"/></proof>
<proof prover="1"><result status="valid" time="0.00"/></proof>
<proof prover="2"><result status="valid" time="0.00" steps="9"/></proof>
<proof prover="3"><result status="valid" time="0.01"/></proof>
<proof prover="4"><result status="valid" time="0.00"/></proof>
</goal>
<goal name="VC pgcd_euclide.4" expl="loop invariant preservation" proved="true">
<proof prover="0"><result status="valid" time="0.01"/></proof>
<proof prover="1"><result status="valid" time="0.01"/></proof>
<proof prover="2"><result status="valid" time="0.00" steps="14"/></proof>
<proof prover="3"><result status="valid" time="0.00"/></proof>
<proof prover="4"><result status="valid" time="0.01"/></proof>
</goal>
<goal name="VC pgcd_euclide.5" expl="postcondition" proved="true">
<proof prover="0"><undone/></proof>
<proof prover="1"><result status="valid" time="0.00"/></proof>
<proof prover="2"><result status="valid" time="0.00" steps="8"/></proof>
<proof prover="3"><result status="valid" time="0.00"/></proof>
<proof prover="4"><result status="valid" time="0.01"/></proof>
</goal>
</transf>
</goal>
</theory>
</file>
</why3session>

40
TP7/.Naturelle.aux Executable file
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@ -0,0 +1,40 @@
COQAUX1 f13e540aa0997388dd1408b0662438d6 /home/lfainsin/1A/Modé/TP7/Naturelle.v
383 387 proof_build_time "0.000"
0 0 E_imp_th "0.000"
383 387 context_used ""
383 387 proof_check_time "0.000"
0 0 VernacProof "tac:no using:no"
916 920 proof_build_time "0.000"
0 0 E_forall_th "0.000"
916 920 context_used ""
916 920 proof_check_time "0.000"
1291 1295 proof_build_time "0.001"
0 0 E_et_g_th "0.001"
1291 1295 context_used ""
1291 1295 proof_check_time "0.000"
1601 1605 proof_build_time "0.000"
0 0 E_et_d_th "0.000"
1601 1605 context_used ""
1601 1605 proof_check_time "0.000"
1983 1987 proof_build_time "0.001"
0 0 E_ou_th "0.001"
1983 1987 context_used ""
1983 1987 proof_check_time "0.000"
0 0 VernacProof "tac:no using:no"
2806 2810 proof_build_time "0.001"
0 0 E_exists_th "0.001"
2806 2810 context_used ""
2806 2810 proof_check_time "0.000"
3280 3284 proof_build_time "0.000"
0 0 E_antiT_th "0.000"
3280 3284 context_used ""
3280 3284 proof_check_time "0.000"
3502 3506 proof_build_time "0.001"
0 0 I_antiT_th "0.001"
3502 3506 context_used ""
3502 3506 proof_check_time "0.000"
3683 3687 proof_build_time "0.000"
0 0 I_non_th "0.000"
3683 3687 context_used ""
3683 3687 proof_check_time "0.000"
0 0 vo_compile_time "0.107"

BIN
TP7/._Naturelle.v Executable file
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Binary file not shown.

150
TP7/Naturelle.glob Executable file
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@ -0,0 +1,150 @@
DIGEST f13e540aa0997388dd1408b0662438d6
FNaturelle
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R3567:3576 Naturelle <> I_antiT_th thm
prf 3598:3605 <> I_non_th
R3630:3630 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R3643:3647 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R3648:3648 Coq.Init.Logic <> ::type_scope:'~'_x not
R3649:3651 Naturelle <> phi var
R3634:3637 Coq.Init.Logic <> ::type_scope:x_'->'_x not
R3638:3642 Coq.Init.Logic <> False ind
R3631:3633 Naturelle <> phi var
R3669:3671 Coq.Init.Logic <> not def
R3730:3731 Coq.Init.Logic <> ::type_scope:'~'_x not
R3730:3731 Coq.Init.Logic <> ::type_scope:'~'_x not
R3745:3752 Naturelle <> I_non_th thm
R3801:3810 Naturelle <> I_antiT_th thm
R3875:3878 Coq.Logic.Classical_Prop <> NNPP thm

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TP7/Naturelle.v Executable file
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Require Export Classical.
Ltac Hyp Nom := exact Nom.
Ltac I_imp' :=
match goal with
| |- ?A -> ?B => let hyp := fresh "H" in intro hyp
| _ => fail
end.
Ltac I_imp Nom :=
match goal with
| |- ?A -> ?B => intro Nom
| _ => fail
end.
Theorem E_imp_th : forall (phi psi : Prop), (phi -> psi) -> phi -> psi.
intros Pphi Ppsi Hphi2psi.
Hyp Hphi2psi.
Qed.
Ltac E_imp' :=
match goal with
| |- ?P => eapply (E_imp_th _ P)
end.
Ltac E_imp phi :=
match goal with
| |- ?P => apply (E_imp_th phi P)
end.
Ltac I_forall' :=
match goal with
| |- forall (x : ?A), ?P => let hyp := fresh x in intro hyp
| _ => fail
end.
Ltac I_forall Nom :=
match goal with
| |- forall (x : ?A), ?P => intro Nom
| _ => fail
end.
Theorem E_forall_th : forall (A : Type) (phi : A -> Prop) a, (forall x, phi x) -> phi a.
Proof.
firstorder.
Qed.
Ltac E_forall x :=
pattern x;
match goal with
| |- (?P x) => apply (E_forall_th _ P x)
| _ => fail
end.
Ltac I_et :=
match goal with
| |- (?A /\ ?B) => apply (@conj A B)
| _ => fail
end.
Theorem E_et_g_th : forall (phi psi : Prop), (phi /\ psi) -> phi.
intros Pphi Ppsi Hphi_et_psi.
elim Hphi_et_psi.
intros Hphi Hpsi.
Hyp Hphi.
Qed.
Ltac E_et_g' :=
match goal with
| |- ?P => eapply (E_et_g_th P _)
end.
Ltac E_et_g psi :=
match goal with
| |- ?P => apply (E_et_g_th P psi)
end.
Theorem E_et_d_th : forall (phi psi : Prop), (phi /\ psi) -> psi.
intros Pphi Ppsi H_phi_et_psi.
elim H_phi_et_psi.
intros Hphi Hpsi.
Hyp Hpsi.
Qed.
Ltac E_et_d' :=
match goal with
| |- ?P => eapply (E_et_d_th _ P)
end.
Ltac E_et_d phi :=
match goal with
| |- ?P => eapply (E_et_d_th phi P)
end.
Theorem E_ou_th : forall (phi psi chi : Prop), (phi \/ psi) -> (phi -> chi) -> (psi -> chi) -> chi.
intros Pphi Ppsi Pchi Hphi_ou_psi Hphi_imp_chi Hpsi_imp_chi.
elim Hphi_ou_psi.
Hyp Hphi_imp_chi.
Hyp Hpsi_imp_chi.
Qed.
Ltac E_ou' :=
match goal with
| |- ?P => eapply (E_ou_th _ _ P)
end.
Ltac E_ou phi psi :=
match goal with
| |- ?P => apply (E_ou_th phi psi P)
end.
Ltac I_ou_g :=
match goal with
| |- (?A \/ ?B) => apply (@or_introl A B)
| _ => fail
end.
Ltac I_ou_d :=
match goal with
| |- (?A \/ ?B) => apply (@or_intror A B)
| _ => fail
end.
Ltac I_exists' :=
match goal with
| |- exists (x : ?A), (@?P x) => eapply (@ex_intro A P _)
| _ => fail
end.
Ltac I_exists t :=
match goal with
| |- exists (x : ?A), (@?P x) => apply (@ex_intro _ P t)
| _ => fail
end.
Theorem E_exists_th : forall (A : Type) (phi : A -> Prop) (chi : Prop), (exists x, phi x) -> (forall a, phi a -> chi) -> chi.
Proof.
firstorder.
Qed.
(*
Ltac E_exists phi :=
match goal with
| |- ?P => apply (E_exists_th _ phi P)
end.
*)
Ltac E_exists phi :=
match goal with
| |- ?P => apply (E_exists_th _ phi P); [ idtac | let t := fresh "t" in let ht := fresh "Ht" in intros t ht ]
end.
Ltac TE :=
unfold not;
match goal with
| |- (?P \/ (?P -> False)) => exact (classic P)
| _ => fail
end.
Theorem E_antiT_th : forall (phi : Prop), False -> phi.
intros Pphi F.
elim F.
Qed.
Ltac E_antiT :=
match goal with
| |- ?P => apply (E_antiT_th P)
end.
Theorem I_antiT_th : forall (phi : Prop), phi -> (~phi) -> False.
unfold not.
intro Pphi.
intros Hphi Hnphi.
cut Pphi.
Hyp Hnphi.
Hyp Hphi.
Qed.
Ltac I_antiT phi :=
match goal with
| |- False => apply (I_antiT_th phi)
end.
Theorem I_non_th : forall (phi : Prop), (phi -> False) -> ~phi.
intros.
unfold not.
exact H.
Qed.
Ltac I_non Nom :=
match goal with
| |- ~ ?P => apply (I_non_th P); intro Nom
end.
Ltac E_non phi :=
apply (I_antiT_th phi).
Ltac absurde Nom :=
match goal with
| |- ?P => apply (NNPP P); intro Nom
end.
(*
Ltac I_antiT phi := apply (I_antiT_th phi).
Ltac absurde Nom phi :=
match goal with
| |- phi =>
cut (phi \/ ~phi);
[
intros L;
elim L;
[
auto
|
clear L;
intro Nom;
apply (E_antiT_th)
]
|
apply (classic phi)
]
| _ => fail
end.
*)

0
TP7/Unnamed_coqscript_1.crashcoqide Executable file
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29
TP7/coq-exercice-1.v Executable file
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Require Import Naturelle.
Section Session1_2019_Logique_Exercice_1.
Variable A B C : Prop.
Theorem Exercice_1_Naturelle : (A -> B -> C) -> ((A /\ B) -> C).
I_imp H.
I_imp H0.
E_imp B.
E_imp A.
exact H.
E_et_g B.
exact H0.
E_et_d A.
exact H0.
Qed.
Theorem Exercice_1_Coq : (A -> B -> C) -> ((A /\ B) -> C).
intros.
destruct H0.
cut B.
cut A.
exact H.
exact H0.
exact H1.
Qed.
End Session1_2019_Logique_Exercice_1.

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TP7/coq-exercice-2.v Executable file
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Require Import Naturelle.
Section Session1_2019_Logique_Exercice_2.
Variable A B : Prop.
Theorem Exercice_2_Naturelle : (~A) \/ B -> (~A) \/ (A /\ B).
Theorem Exercice_2_Coq : (~A) \/ B -> (~A) \/ (A /\ B).
intros.
Qed.
End Session1_2019_Logique_Exercice_2.

113
TP7/coq-exercice-3.v Executable file
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Section Session1_2019_Induction_Exercice_3.
(* Déclaration d’un domaine pour les éléments des listes *)
Variable A : Set.
(* Déclaration d'un type liste générique d'éléments de type E *)
Inductive liste (E : Set) : Set :=
Nil
: liste E
| Cons : E -> liste E -> liste E.
(* Déclaration du nom de la fonction append *)
Variable append_spec : forall E : Set, liste E -> liste E -> liste E.
(* Spécification du comportement de append pour Nil en premier paramètre *)
Axiom append_Nil : forall E : Set, forall (l : liste E), append_spec E (Nil E) l = l.
(* Spécification du comportement de append pour Cons en premier paramètre *)
Axiom append_Cons : forall E : Set, forall (t : E), forall (q l : liste E),
append_spec E ((Cons E) t q) l = (Cons E) t (append_spec E q l).
(* Spécification du comportement de append pour Nil en second paramètre *)
Axiom append_Nil_right : forall E : Set, forall (l : liste E), (append_spec E l (Nil E)) = l.
(* append est associative à gauche et à droite *)
Axiom append_associative : forall E : Set, forall (l1 l2 l3 : liste E),
(append_spec E l1 (append_spec E l2 l3)) = (append_spec E (append_spec E l1 l2) l3).
(* Déclaration du nom de la fonction flatten *)
Variable flatten_spec : forall E : Set, liste (liste E) -> liste E.
(* Spécification du comportement de flatten pour Nil *)
Axiom flatten_Nil : forall E : Set, flatten_spec E (Nil (liste E)) = (Nil E).
(* Spécification du comportement de flatten pour Cons *)
Axiom flatten_Cons : forall E : Set, forall (t : liste E), forall (q : liste (liste E)),
flatten_spec E (Cons (liste E) t q) = append_spec E t (flatten_spec E q).
(* Déclaration du nom de la fonction split *)
Variable split_spec : forall E : Set, liste E -> liste (liste E).
(* Spécification du comportement de split pour Nil *)
Axiom split_Nil : forall E : Set, split_spec E (Nil E) = (Nil (liste E)).
(* Spécification du comportement de split pour Cons *)
Axiom split_Cons : forall E : Set, forall (t : E), forall (q : liste E),
split_spec E (Cons E t q) = Cons (liste E) (Cons E t (Nil E)) (split_spec E q).
(* Cohérence de flatten et de split : flatten(split(l)) = l*)
Theorem flatten_split_consistency : forall E : Set, forall (l : liste E),
flatten_spec E (split_spec E l) = l.
intros.
induction l.
(* cas de base *)
rewrite split_Nil.
rewrite flatten_Nil.
reflexivity.
(* cas général *)
rewrite split_Cons.
rewrite flatten_Cons.
rewrite append_Cons.
rewrite append_Nil.
rewrite IHl.
reflexivity.
Qed.
(* Implantation de la fonction append *)
Fixpoint append_impl (E : Set) (l1 l2 : liste E) {struct l1} : liste E :=
match l1 with
Nil _ => l2
| (Cons _ t1 q1) => (Cons E t1 (append_impl E q1 l2))
end.
Theorem append_correctness : forall E : Set, forall (l1 l2 : liste E),
(append_spec E l1 l2) = (append_impl E l1 l2).
intro TE.
induction l1.
intro Hl2.
rewrite append_Nil.
simpl.
reflexivity.
intro Hl2.
rewrite append_Cons.
simpl.
rewrite IHl1.
reflexivity.
Qed.
(* Implantation de la fonction flatten *)
Fixpoint flatten_impl (E : Set) (l : liste (liste E)) {struct l} : liste E :=
match l with
Nil _ => Nil _
| (Cons _ t q) => (append_impl E t (flatten_impl E q ))
end.
(* Correction de l'implantation de flatten par rapport à sa spécification *)
Theorem flatten_correctness : forall E : Set, forall (l : liste (liste E)),
(flatten_spec E l) = (flatten_impl E l).
intros.
induction l.
(* cas de base *)
rewrite flatten_Nil.
simpl flatten_impl.
reflexivity.
(* cas général *)
rewrite flatten_Cons.
simpl flatten_impl.
rewrite append_correctness.
rewrite IHl.
reflexivity.
Qed.
End Session1_2019_Induction_Exercice_3.

24
TP7/why3-exercice-4.mlw Executable file
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(* BE : Session 1 2019 *)
(* Implémentation de la fonction somme des premiers entiers par un algorithme ascendant *)
module Somme
use int.Int
use int.ComputerDivision
use ref.Refint
let somme (n: int) : int
requires { n >= 0 }
ensures { 2 * result = n * (n+1) }
=
let i = ref 0 in
let r = ref 0 in
while (!i < n) do
invariant { !r * 2 = !i * ( !i + 1 ) && n >= !i}
variant { n - !i }
i := (!i) + 1;
r := (!r) + (!i)
done;
!r
end

36
TP7/why3-exercice-4/why3session.xml Executable file
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<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
"http://why3.lri.fr/why3session.dtd">
<why3session shape_version="5">
<prover id="0" name="Alt-Ergo" version="2.0.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="1" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="2" name="Z3" version="4.4.1" alternative="noBV" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="3" name="Z3" version="4.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="4" name="CVC4" version="1.5" timelimit="5" steplimit="0" memlimit="1000"/>
<file proved="true">
<path name=".."/>
<path name="why3-exercice-4.mlw"/>
<theory name="Somme" proved="true">
<goal name="VC somme" expl="VC for somme" proved="true">
<transf name="split_vc" proved="true" >
<goal name="VC somme.0" expl="loop invariant init" proved="true">
<proof prover="0"><result status="valid" time="0.00" steps="2"/></proof>
</goal>
<goal name="VC somme.1" expl="loop variant decrease" proved="true">
<proof prover="0"><result status="valid" time="0.00" steps="7"/></proof>
</goal>
<goal name="VC somme.2" expl="loop invariant preservation" proved="true">
<proof prover="0"><result status="valid" time="0.00" steps="7"/></proof>
</goal>
<goal name="VC somme.3" expl="postcondition" proved="true">
<proof prover="0"><result status="valid" time="0.00" steps="5"/></proof>
<proof prover="1"><result status="valid" time="0.01"/></proof>
<proof prover="2"><result status="valid" time="0.01"/></proof>
<proof prover="3"><result status="valid" time="0.01"/></proof>
<proof prover="4"><result status="valid" time="0.01"/></proof>
</goal>
</transf>
</goal>
</theory>
</file>
</why3session>

2
TP8-9/outils-unix/cmd-sed.txt Executable file
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sed -E -e "s/<\/?[a-z]+>//g" < enseignant-element.xml-sed
sed -E -e "s/<\/?[a-z]+>//g" < enseignant-attribut.xml-sed

11
TP8-9/outils-unix/commandes-TP5.sh Executable file
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#!/bin/sh
echo "Affichage des lignes contenant des nombres entiers naturels :"
egrep -e "\ ([0-9]+)$" exemple.txt
echo "Affichage des lignes contenant des nombres entiers relatifs :"
egrep -e "\ ([+-]+[0-9]+)$" exemple.txt
echo "Affichage des lignes contenant des nombres décimaux :"
egrep -e "\ ([+-]?[0-9]+[.][0-9]+([eE][-+]?[1-9][0-9]*)?)$" exemple.txt
echo "Affichage des lignes contenant des nombres rationnels :"
egrep -e "\ ([+-]?[0-9]+/[1-9][0-9]*)$" exemple.txt
echo "Affichage des lignes contenant des nombres complexes rationnels :"
egrep -e "\ (([+-]?[0-9]+/[1-9][0-9]*)?[+-]?[0-9]+/[1-9][0-9]*i?)$" exemple.txt

5
TP8-9/outils-unix/enseignant-attribut.xml-sed.out Executable file
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<identite prenom="Marc" nom="Pantel"/>
<discipline nom="Traduction des langages"/>
<discipline nom="Sémantique formelle"/>

5
TP8-9/outils-unix/enseignant-attribut.xml-vim Executable file
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<identite prenom="Marc" nom="Pantel"/>
<discipline nom="Traduction des langages"/>
<discipline nom="Sémantique formelle"/>

8
TP8-9/outils-unix/enseignant-element.xml-sed.out Executable file
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@ -0,0 +1,8 @@
Marc
Pantel
Traduction des langages
Sémantique formelle

8
TP8-9/outils-unix/enseignant-element.xml-vim Executable file
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@ -0,0 +1,8 @@
Marc
Pantel
Traduction des langages
Sémantique formelle

23
TP8-9/outils-unix/exemple.txt Executable file
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Suite de chiffres : 0123456789
Entier naturel : 0
Entier naturel : 123
Entier relatif : +123
Entier relatif : -123
Décimal : 0.123
Décimal : -0.123
Décimal : 0.123e10
Décimal : 0.123E10
Décimal : -0.123e10
Décimal : -0.123E10
Décimal : 0.123e-10
Décimal : 0.123E-10
Décimal : -0.123e-10
Décimal : -0.123e-10
Rationnel : 1/2
Rationnel : -1/2
Complexe : 1/2i
Complexe : -1/2i
Complexe : 2/3+1/2i
Complexe : 2/3+1/2i
Complexe : -2/3-1/2i
Complexe : -2/3-1/2i

BIN
TP8-9/process-analysis/MainProcessus Executable file
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36
TP8-9/process-analysis/Makefile Executable file
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OCAMLLEX = ocamllex
OCAMLYACC = menhir
OCAMLC = ocamlc
OCAMLLD = ocamlc
.SUFFIXES: .ml .mli .cmo .cmi .mll .mly
%.cmi : %.mli
$(OCAMLC) -c $<
%.cmo : %.ml %.cmi
$(OCAMLC) -c $<
%.cmo : %.ml
$(OCAMLC) -c $<
%.cmo : %.cmi
$(OCAMLC) -c $<
%.ml : %.mll
$(OCAMLLEX) $<
%.mli %.ml : %.mly
$(OCAMLYACC) $<
all : mainProcessus
lexerProcessus.ml : parserProcessus.cmi
mainProcessus : lexerProcessus.cmo parserProcessus.cmo mainProcessus.cmo
$(OCAMLC) -o MainProcessus lexerProcessus.cmo parserProcessus.cmo mainProcessus.cmo
clean :
-rm -f *.cmo *.cmi lexerProcessus.ml parserProcessus.ml MainProcessus

1279
TP8-9/process-analysis/lexerProcessus.ml Executable file
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46
TP8-9/process-analysis/lexerProcessus.mll Executable file
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{
(* Partie recopiée dans le fichier CaML généré. *)
(* Ouverture de modules exploités dans les actions *)
(* Déclarations de types, de constantes, de fonctions, d'exceptions exploités dans les actions *)
open ParserProcessus
exception LexicalError
}
(* Déclaration d'expressions régulières exploitées par la suite *)
let chiffre = ['0' - '9']
let minuscule = ['a' - 'z']
let majuscule = ['A' - 'Z']
let lettre = minuscule | majuscule
let lettre_chiffre = lettre | chiffre | '_'
let commentaire =
(* Commentaire bloc à la C/C++/C#/Java/etc *)
("/*" [^ '*']* '*'* ([^ '*' '/'] [^ '*']* '*'*)* '/')
(* Commentaire fin de ligne à la C/C++/C#/Java/etc *)
| "//" [^'\n']*
rule main = parse
| ['\n' '\t' ' ']+ { main lexbuf }
| commentaire { (main lexbuf) }
| "process" { PROCESS }
| "activity" { ACTIVITY }
| "starts" { STARTS }
| "finishes" { FINISHES }
| "if" { IF }
| "started" { STARTED }
| "finished" { FINISHED }
| "resource" { RESOURCE }
| "amount" { AMOUNT }
| "requires" { REQUIRES }
| "{" { LEFT_BRACE }
| "}" { RIGHT_BRACE }
| chiffre+ as texte { (NUMBER (int_of_string texte)) }
| ('_' | lettre) lettre_chiffre* as texte { (IDENTIFIER texte) }
| eof { END }
| _ as texte { (print_string "Erreur lexicale : ");(print_char texte);(print_newline ()); (main lexbuf) }
{
}

42
TP8-9/process-analysis/mainProcessus.ml Executable file
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open ParserProcessus
(* Fonction d'affichage des unités lexicales et des données qu'elles contiennent *)
let printToken t =
(print_endline
("token: " ^ (match t with
| PROCESS -> "process"
| IDENTIFIER (texte) -> ("identifier(" ^ texte ^ ")")
| ACTIVITY -> "activity"
| STARTS -> "starts"
| FINISHES -> "finishes"
| IF -> "if"
| STARTED -> "started"
| FINISHED -> "finished"
| RESOURCE -> "resource"
| REQUIRES -> "requires"
| AMOUNT -> "amount"
| LEFT_BRACE -> "{"
| RIGHT_BRACE -> "}"
| NUMBER (texte) -> ("number(" ^ (string_of_int texte) ^ ")")
| END -> "EOF"
)));;
(* Analyse lexicale du fichier passé en paramètre de la ligne de commande *)
if (Array.length Sys.argv > 1)
then
let lexbuf = (Lexing.from_channel (open_in Sys.argv.(1))) in
let token = ref (LexerProcessus.main lexbuf) in
while ((!token) != END) do
(printToken (!token));
(token := (LexerProcessus.main lexbuf))
done
else
(print_endline "MainMuProcessus fichier");;
(* Analyse lexicale, syntaxique et sémantique du fichier passé en paramètre de la ligne de commande *)
if (Array.length Sys.argv > 1)
then
let lexbuf = (Lexing.from_channel (open_in Sys.argv.(1))) in
(ParserProcessus.fichier LexerProcessus.main lexbuf)
else
(print_endline "MainProcessus fichier");;

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TP8-9/process-analysis/parserProcessus.ml Executable file
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module MenhirBasics = struct
exception Error
type token =
| STARTS
| STARTED
| RIGHT_BRACE
| RESOURCE
| REQUIRES
| PROCESS
| NUMBER of (
# 15 "parserProcessus.mly"
(int)
# 17 "parserProcessus.ml"
)
| LEFT_BRACE
| IF
| IDENTIFIER of (
# 16 "parserProcessus.mly"
(string)
# 24 "parserProcessus.ml"
)
| FINISHES
| FINISHED
| END
| AMOUNT
| ACTIVITY
end
include MenhirBasics
let _eRR =
MenhirBasics.Error
type _menhir_env = {
_menhir_lexer: Lexing.lexbuf -> token;
_menhir_lexbuf: Lexing.lexbuf;
_menhir_token: token;
mutable _menhir_error: bool
}
and _menhir_state =
| MenhirState30
| MenhirState21
| MenhirState19
| MenhirState17
| MenhirState14
| MenhirState9
| MenhirState3
# 1 "parserProcessus.mly"
(* Partie recopiee dans le fichier CaML genere. *)
(* Ouverture de modules exploites dans les actions *)
(* Declarations de types, de constantes, de fonctions, d'exceptions exploites dans les actions *)
# 63 "parserProcessus.ml"
let rec _menhir_goto_etat : _menhir_env -> 'ttv_tail -> 'tv_etat -> 'ttv_return =
fun _menhir_env _menhir_stack _v ->
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : (('freshtv155 * _menhir_state * 'tv_action)) * (
# 16 "parserProcessus.mly"
(string)
# 71 "parserProcessus.ml"
)) = Obj.magic _menhir_stack in
let (_v : 'tv_etat) = _v in
((let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : (('freshtv153 * _menhir_state * 'tv_action)) * (
# 16 "parserProcessus.mly"
(string)
# 78 "parserProcessus.ml"
)) = Obj.magic _menhir_stack in
let ((_4 : 'tv_etat) : 'tv_etat) = _v in
((let ((_menhir_stack, _menhir_s, (_1 : 'tv_action)), (_3 : (
# 16 "parserProcessus.mly"
(string)
# 84 "parserProcessus.ml"
))) = _menhir_stack in
let _2 = () in
let _v : 'tv_contrainte =
# 49 "parserProcessus.mly"
( (print_endline "contrainte : action if IDENTIFIER etat") )
# 90 "parserProcessus.ml"
in
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv151) = _menhir_stack in
let (_menhir_s : _menhir_state) = _menhir_s in
let (_v : 'tv_contrainte) = _v in
((let _menhir_stack = (_menhir_stack, _menhir_s, _v) in
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv149 * _menhir_state * 'tv_contrainte) = Obj.magic _menhir_stack in
((assert (not _menhir_env._menhir_error);
let _tok = _menhir_env._menhir_token in
match _tok with
| FINISHES ->
_menhir_run18 _menhir_env (Obj.magic _menhir_stack) MenhirState21
| LEFT_BRACE ->
_menhir_run14 _menhir_env (Obj.magic _menhir_stack) MenhirState21
| REQUIRES ->
_menhir_run11 _menhir_env (Obj.magic _menhir_stack) MenhirState21
| STARTS ->
_menhir_run10 _menhir_env (Obj.magic _menhir_stack) MenhirState21
| ACTIVITY | RESOURCE | RIGHT_BRACE ->
_menhir_reduce5 _menhir_env (Obj.magic _menhir_stack) MenhirState21
| _ ->
assert (not _menhir_env._menhir_error);
_menhir_env._menhir_error <- true;
_menhir_errorcase _menhir_env (Obj.magic _menhir_stack) MenhirState21) : 'freshtv150)) : 'freshtv152)) : 'freshtv154)) : 'freshtv156)
and _menhir_fail : unit -> 'a =
fun () ->
Printf.fprintf stderr "Internal failure -- please contact the parser generator's developers.\n%!";
assert false
and _menhir_goto_contraintes : _menhir_env -> 'ttv_tail -> _menhir_state -> 'tv_contraintes -> 'ttv_return =
fun _menhir_env _menhir_stack _menhir_s _v ->
match _menhir_s with
| MenhirState19 ->
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv129 * _menhir_state * 'tv_requires) = Obj.magic _menhir_stack in
let (_menhir_s : _menhir_state) = _menhir_s in
let (_v : 'tv_contraintes) = _v in
((let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv127 * _menhir_state * 'tv_requires) = Obj.magic _menhir_stack in
let (_ : _menhir_state) = _menhir_s in
let ((_2 : 'tv_contraintes) : 'tv_contraintes) = _v in
((let (_menhir_stack, _menhir_s, (_1 : 'tv_requires)) = _menhir_stack in
let _v : 'tv_contraintes =
# 43 "parserProcessus.mly"
( (print_endline "contraintes : requires contraintes") )
# 138 "parserProcessus.ml"
in
_menhir_goto_contraintes _menhir_env _menhir_stack _menhir_s _v) : 'freshtv128)) : 'freshtv130)
| MenhirState21 ->
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv133 * _menhir_state * 'tv_contrainte) = Obj.magic _menhir_stack in
let (_menhir_s : _menhir_state) = _menhir_s in
let (_v : 'tv_contraintes) = _v in
((let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv131 * _menhir_state * 'tv_contrainte) = Obj.magic _menhir_stack in
let (_ : _menhir_state) = _menhir_s in
let ((_2 : 'tv_contraintes) : 'tv_contraintes) = _v in
((let (_menhir_stack, _menhir_s, (_1 : 'tv_contrainte)) = _menhir_stack in
let _v : 'tv_contraintes =
# 44 "parserProcessus.mly"
( (print_endline "contraintes : contrainte contraintes") )
# 154 "parserProcessus.ml"
in
_menhir_goto_contraintes _menhir_env _menhir_stack _menhir_s _v) : 'freshtv132)) : 'freshtv134)
| MenhirState17 ->
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : (('freshtv137 * _menhir_state) * _menhir_state * 'tv_elements)) = Obj.magic _menhir_stack in
let (_menhir_s : _menhir_state) = _menhir_s in
let (_v : 'tv_contraintes) = _v in
((let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : (('freshtv135 * _menhir_state) * _menhir_state * 'tv_elements)) = Obj.magic _menhir_stack in
let (_ : _menhir_state) = _menhir_s in
let ((_4 : 'tv_contraintes) : 'tv_contraintes) = _v in
((let ((_menhir_stack, _menhir_s), _, (_2 : 'tv_elements)) = _menhir_stack in
let _3 = () in
let _1 = () in
let _v : 'tv_contraintes =
# 45 "parserProcessus.mly"
( (print_endline "contraintes : { elements } contraintes") )
# 172 "parserProcessus.ml"
in
_menhir_goto_contraintes _menhir_env _menhir_stack _menhir_s _v) : 'freshtv136)) : 'freshtv138)
| MenhirState9 ->
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : ('freshtv147 * _menhir_state) * (
# 16 "parserProcessus.mly"
(string)
# 180 "parserProcessus.ml"
)) = Obj.magic _menhir_stack in
let (_menhir_s : _menhir_state) = _menhir_s in
let (_v : 'tv_contraintes) = _v in
((let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : ('freshtv145 * _menhir_state) * (
# 16 "parserProcessus.mly"
(string)
# 188 "parserProcessus.ml"
)) = Obj.magic _menhir_stack in
let (_ : _menhir_state) = _menhir_s in
let ((_3 : 'tv_contraintes) : 'tv_contraintes) = _v in
((let ((_menhir_stack, _menhir_s), (_2 : (
# 16 "parserProcessus.mly"
(string)
# 195 "parserProcessus.ml"
))) = _menhir_stack in
let _1 = () in
let _v : 'tv_activite =
# 40 "parserProcessus.mly"
( (print_endline "activite : activity IDENTIFIER contraintes") )
# 201 "parserProcessus.ml"
in
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv143) = _menhir_stack in
let (_menhir_s : _menhir_state) = _menhir_s in
let (_v : 'tv_activite) = _v in
((let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv141) = Obj.magic _menhir_stack in
let (_menhir_s : _menhir_state) = _menhir_s in
let (_v : 'tv_activite) = _v in
((let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv139) = Obj.magic _menhir_stack in
let (_menhir_s : _menhir_state) = _menhir_s in
let ((_1 : 'tv_activite) : 'tv_activite) = _v in
((let _v : 'tv_element =
# 35 "parserProcessus.mly"
( (print_endline "element : activite") )
# 218 "parserProcessus.ml"
in
_menhir_goto_element _menhir_env _menhir_stack _menhir_s _v) : 'freshtv140)) : 'freshtv142)) : 'freshtv144)) : 'freshtv146)) : 'freshtv148)
| _ ->
_menhir_fail ()
and _menhir_goto_action : _menhir_env -> 'ttv_tail -> _menhir_state -> 'tv_action -> 'ttv_return =
fun _menhir_env _menhir_stack _menhir_s _v ->
let _menhir_stack = (_menhir_stack, _menhir_s, _v) in
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv125 * _menhir_state * 'tv_action) = Obj.magic _menhir_stack in
((assert (not _menhir_env._menhir_error);
let _tok = _menhir_env._menhir_token in
match _tok with
| IF ->
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv121 * _menhir_state * 'tv_action) = Obj.magic _menhir_stack in
((let _menhir_env = _menhir_discard _menhir_env in
let _tok = _menhir_env._menhir_token in
match _tok with
| IDENTIFIER _v ->
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : ('freshtv117 * _menhir_state * 'tv_action)) = Obj.magic _menhir_stack in
let (_v : (
# 16 "parserProcessus.mly"
(string)
# 244 "parserProcessus.ml"
)) = _v in
((let _menhir_stack = (_menhir_stack, _v) in
let _menhir_env = _menhir_discard _menhir_env in
let _tok = _menhir_env._menhir_token in
match _tok with
| FINISHED ->
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv109) = Obj.magic _menhir_stack in
((let _menhir_env = _menhir_discard _menhir_env in
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv107) = Obj.magic _menhir_stack in
((let _1 = () in
let _v : 'tv_etat =
# 55 "parserProcessus.mly"
( (print_endline "etat : FINISHED") )
# 260 "parserProcessus.ml"
in
_menhir_goto_etat _menhir_env _menhir_stack _v) : 'freshtv108)) : 'freshtv110)
| STARTED ->
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv113) = Obj.magic _menhir_stack in
((let _menhir_env = _menhir_discard _menhir_env in
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv111) = Obj.magic _menhir_stack in
((let _1 = () in
let _v : 'tv_etat =
# 54 "parserProcessus.mly"
( (print_endline "etat : STARTED") )
# 273 "parserProcessus.ml"
in
_menhir_goto_etat _menhir_env _menhir_stack _v) : 'freshtv112)) : 'freshtv114)
| _ ->
assert (not _menhir_env._menhir_error);
_menhir_env._menhir_error <- true;
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : (('freshtv115 * _menhir_state * 'tv_action)) * (
# 16 "parserProcessus.mly"
(string)
# 283 "parserProcessus.ml"
)) = Obj.magic _menhir_stack in
((let ((_menhir_stack, _menhir_s, _), _) = _menhir_stack in
_menhir_errorcase _menhir_env (Obj.magic _menhir_stack) _menhir_s) : 'freshtv116)) : 'freshtv118)
| _ ->
assert (not _menhir_env._menhir_error);
_menhir_env._menhir_error <- true;
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : ('freshtv119 * _menhir_state * 'tv_action)) = Obj.magic _menhir_stack in
((let (_menhir_stack, _menhir_s, _) = _menhir_stack in
_menhir_errorcase _menhir_env (Obj.magic _menhir_stack) _menhir_s) : 'freshtv120)) : 'freshtv122)
| _ ->
assert (not _menhir_env._menhir_error);
_menhir_env._menhir_error <- true;
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv123 * _menhir_state * 'tv_action) = Obj.magic _menhir_stack in
((let (_menhir_stack, _menhir_s, _) = _menhir_stack in
_menhir_errorcase _menhir_env (Obj.magic _menhir_stack) _menhir_s) : 'freshtv124)) : 'freshtv126)
and _menhir_goto_elements : _menhir_env -> 'ttv_tail -> _menhir_state -> 'tv_elements -> 'ttv_return =
fun _menhir_env _menhir_stack _menhir_s _v ->
let _menhir_stack = (_menhir_stack, _menhir_s, _v) in
match _menhir_s with
| MenhirState14 ->
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : ('freshtv77 * _menhir_state) * _menhir_state * 'tv_elements) = Obj.magic _menhir_stack in
((assert (not _menhir_env._menhir_error);
let _tok = _menhir_env._menhir_token in
match _tok with
| RIGHT_BRACE ->
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : ('freshtv73 * _menhir_state) * _menhir_state * 'tv_elements) = Obj.magic _menhir_stack in
((let _menhir_env = _menhir_discard _menhir_env in
let _tok = _menhir_env._menhir_token in
match _tok with
| FINISHES ->
_menhir_run18 _menhir_env (Obj.magic _menhir_stack) MenhirState17
| LEFT_BRACE ->
_menhir_run14 _menhir_env (Obj.magic _menhir_stack) MenhirState17
| REQUIRES ->
_menhir_run11 _menhir_env (Obj.magic _menhir_stack) MenhirState17
| STARTS ->
_menhir_run10 _menhir_env (Obj.magic _menhir_stack) MenhirState17
| ACTIVITY | RESOURCE | RIGHT_BRACE ->
_menhir_reduce5 _menhir_env (Obj.magic _menhir_stack) MenhirState17
| _ ->
assert (not _menhir_env._menhir_error);
_menhir_env._menhir_error <- true;
_menhir_errorcase _menhir_env (Obj.magic _menhir_stack) MenhirState17) : 'freshtv74)
| _ ->
assert (not _menhir_env._menhir_error);
_menhir_env._menhir_error <- true;
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : ('freshtv75 * _menhir_state) * _menhir_state * 'tv_elements) = Obj.magic _menhir_stack in
((let (_menhir_stack, _menhir_s, _) = _menhir_stack in
_menhir_errorcase _menhir_env (Obj.magic _menhir_stack) _menhir_s) : 'freshtv76)) : 'freshtv78)
| MenhirState30 ->
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : ('freshtv81 * _menhir_state * 'tv_element) * _menhir_state * 'tv_elements) = Obj.magic _menhir_stack in
((let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : ('freshtv79 * _menhir_state * 'tv_element) * _menhir_state * 'tv_elements) = Obj.magic _menhir_stack in
((let ((_menhir_stack, _menhir_s, (_1 : 'tv_element)), _, (_2 : 'tv_elements)) = _menhir_stack in
let _v : 'tv_elements =
# 33 "parserProcessus.mly"
( (print_endline "elements : element elements") )
# 348 "parserProcessus.ml"
in
_menhir_goto_elements _menhir_env _menhir_stack _menhir_s _v) : 'freshtv80)) : 'freshtv82)
| MenhirState3 ->
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : ((('freshtv105) * (
# 16 "parserProcessus.mly"
(string)
# 356 "parserProcessus.ml"
))) * _menhir_state * 'tv_elements) = Obj.magic _menhir_stack in
((assert (not _menhir_env._menhir_error);
let _tok = _menhir_env._menhir_token in
match _tok with
| RIGHT_BRACE ->
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : ((('freshtv101) * (
# 16 "parserProcessus.mly"
(string)
# 366 "parserProcessus.ml"
))) * _menhir_state * 'tv_elements) = Obj.magic _menhir_stack in
((let _menhir_env = _menhir_discard _menhir_env in
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : ((('freshtv99) * (
# 16 "parserProcessus.mly"
(string)
# 373 "parserProcessus.ml"
))) * _menhir_state * 'tv_elements) = Obj.magic _menhir_stack in
((let ((_menhir_stack, (_2 : (
# 16 "parserProcessus.mly"
(string)
# 378 "parserProcessus.ml"
))), _, (_4 : 'tv_elements)) = _menhir_stack in
let _5 = () in
let _3 = () in
let _1 = () in
let _v : 'tv_processus =
# 30 "parserProcessus.mly"
( (print_endline "processus : process IDENTIFIER { elements }") )
# 386 "parserProcessus.ml"
in
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv97) = _menhir_stack in
let (_v : 'tv_processus) = _v in
((let _menhir_stack = (_menhir_stack, _v) in
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv95 * 'tv_processus) = Obj.magic _menhir_stack in
((assert (not _menhir_env._menhir_error);
let _tok = _menhir_env._menhir_token in
match _tok with
| END ->
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv91 * 'tv_processus) = Obj.magic _menhir_stack in
((let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv89 * 'tv_processus) = Obj.magic _menhir_stack in
((let (_menhir_stack, (_1 : 'tv_processus)) = _menhir_stack in
let _2 = () in
let _v : (
# 21 "parserProcessus.mly"
(unit)
# 407 "parserProcessus.ml"
) =
# 28 "parserProcessus.mly"
( (print_endline "fichier : processus END") )
# 411 "parserProcessus.ml"
in
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv87) = _menhir_stack in
let (_v : (
# 21 "parserProcessus.mly"
(unit)
# 418 "parserProcessus.ml"
)) = _v in
((let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv85) = Obj.magic _menhir_stack in
let (_v : (
# 21 "parserProcessus.mly"
(unit)
# 425 "parserProcessus.ml"
)) = _v in
((let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv83) = Obj.magic _menhir_stack in
let ((_1 : (
# 21 "parserProcessus.mly"
(unit)
# 432 "parserProcessus.ml"
)) : (
# 21 "parserProcessus.mly"
(unit)
# 436 "parserProcessus.ml"
)) = _v in
(Obj.magic _1 : 'freshtv84)) : 'freshtv86)) : 'freshtv88)) : 'freshtv90)) : 'freshtv92)
| _ ->
assert (not _menhir_env._menhir_error);
_menhir_env._menhir_error <- true;
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv93 * 'tv_processus) = Obj.magic _menhir_stack in
(raise _eRR : 'freshtv94)) : 'freshtv96)) : 'freshtv98)) : 'freshtv100)) : 'freshtv102)
| _ ->
assert (not _menhir_env._menhir_error);
_menhir_env._menhir_error <- true;
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : ((('freshtv103) * (
# 16 "parserProcessus.mly"
(string)
# 452 "parserProcessus.ml"
))) * _menhir_state * 'tv_elements) = Obj.magic _menhir_stack in
((let (_menhir_stack, _menhir_s, _) = _menhir_stack in
_menhir_errorcase _menhir_env (Obj.magic _menhir_stack) _menhir_s) : 'freshtv104)) : 'freshtv106)
| _ ->
_menhir_fail ()
and _menhir_goto_element : _menhir_env -> 'ttv_tail -> _menhir_state -> 'tv_element -> 'ttv_return =
fun _menhir_env _menhir_stack _menhir_s _v ->
let _menhir_stack = (_menhir_stack, _menhir_s, _v) in
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv71 * _menhir_state * 'tv_element) = Obj.magic _menhir_stack in
((assert (not _menhir_env._menhir_error);
let _tok = _menhir_env._menhir_token in
match _tok with
| ACTIVITY ->
_menhir_run8 _menhir_env (Obj.magic _menhir_stack) MenhirState30
| RESOURCE ->
_menhir_run4 _menhir_env (Obj.magic _menhir_stack) MenhirState30
| RIGHT_BRACE ->
_menhir_reduce11 _menhir_env (Obj.magic _menhir_stack) MenhirState30
| _ ->
assert (not _menhir_env._menhir_error);
_menhir_env._menhir_error <- true;
_menhir_errorcase _menhir_env (Obj.magic _menhir_stack) MenhirState30) : 'freshtv72)
and _menhir_reduce5 : _menhir_env -> 'ttv_tail -> _menhir_state -> 'ttv_return =
fun _menhir_env _menhir_stack _menhir_s ->
let _v : 'tv_contraintes =
# 42 "parserProcessus.mly"
( (print_endline "contraintes : /* Lambda, mot vide */") )
# 483 "parserProcessus.ml"
in
_menhir_goto_contraintes _menhir_env _menhir_stack _menhir_s _v
and _menhir_run10 : _menhir_env -> 'ttv_tail -> _menhir_state -> 'ttv_return =
fun _menhir_env _menhir_stack _menhir_s ->
let _menhir_env = _menhir_discard _menhir_env in
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv69) = Obj.magic _menhir_stack in
let (_menhir_s : _menhir_state) = _menhir_s in
((let _1 = () in
let _v : 'tv_action =
# 51 "parserProcessus.mly"
( (print_endline "action : STARTS") )
# 497 "parserProcessus.ml"
in
_menhir_goto_action _menhir_env _menhir_stack _menhir_s _v) : 'freshtv70)
and _menhir_run11 : _menhir_env -> 'ttv_tail -> _menhir_state -> 'ttv_return =
fun _menhir_env _menhir_stack _menhir_s ->
let _menhir_stack = (_menhir_stack, _menhir_s) in
let _menhir_env = _menhir_discard _menhir_env in
let _tok = _menhir_env._menhir_token in
match _tok with
| NUMBER _v ->
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv65 * _menhir_state) = Obj.magic _menhir_stack in
let (_v : (
# 15 "parserProcessus.mly"
(int)
# 513 "parserProcessus.ml"
)) = _v in
((let _menhir_stack = (_menhir_stack, _v) in
let _menhir_env = _menhir_discard _menhir_env in
let _tok = _menhir_env._menhir_token in
match _tok with
| IDENTIFIER _v ->
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : ('freshtv61 * _menhir_state) * (
# 15 "parserProcessus.mly"
(int)
# 524 "parserProcessus.ml"
)) = Obj.magic _menhir_stack in
let (_v : (
# 16 "parserProcessus.mly"
(string)
# 529 "parserProcessus.ml"
)) = _v in
((let _menhir_env = _menhir_discard _menhir_env in
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : ('freshtv59 * _menhir_state) * (
# 15 "parserProcessus.mly"
(int)
# 536 "parserProcessus.ml"
)) = Obj.magic _menhir_stack in
let ((_3 : (
# 16 "parserProcessus.mly"
(string)
# 541 "parserProcessus.ml"
)) : (
# 16 "parserProcessus.mly"
(string)
# 545 "parserProcessus.ml"
)) = _v in
((let ((_menhir_stack, _menhir_s), (_2 : (
# 15 "parserProcessus.mly"
(int)
# 550 "parserProcessus.ml"
))) = _menhir_stack in
let _1 = () in
let _v : 'tv_requires =
# 47 "parserProcessus.mly"
( (print_endline "requires : requires NUMBER IDENTIFIER") )
# 556 "parserProcessus.ml"
in
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv57) = _menhir_stack in
let (_menhir_s : _menhir_state) = _menhir_s in
let (_v : 'tv_requires) = _v in
((let _menhir_stack = (_menhir_stack, _menhir_s, _v) in
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv55 * _menhir_state * 'tv_requires) = Obj.magic _menhir_stack in
((assert (not _menhir_env._menhir_error);
let _tok = _menhir_env._menhir_token in
match _tok with
| FINISHES ->
_menhir_run18 _menhir_env (Obj.magic _menhir_stack) MenhirState19
| LEFT_BRACE ->
_menhir_run14 _menhir_env (Obj.magic _menhir_stack) MenhirState19
| REQUIRES ->
_menhir_run11 _menhir_env (Obj.magic _menhir_stack) MenhirState19
| STARTS ->
_menhir_run10 _menhir_env (Obj.magic _menhir_stack) MenhirState19
| ACTIVITY | RESOURCE | RIGHT_BRACE ->
_menhir_reduce5 _menhir_env (Obj.magic _menhir_stack) MenhirState19
| _ ->
assert (not _menhir_env._menhir_error);
_menhir_env._menhir_error <- true;
_menhir_errorcase _menhir_env (Obj.magic _menhir_stack) MenhirState19) : 'freshtv56)) : 'freshtv58)) : 'freshtv60)) : 'freshtv62)
| _ ->
assert (not _menhir_env._menhir_error);
_menhir_env._menhir_error <- true;
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : ('freshtv63 * _menhir_state) * (
# 15 "parserProcessus.mly"
(int)
# 589 "parserProcessus.ml"
)) = Obj.magic _menhir_stack in
((let ((_menhir_stack, _menhir_s), _) = _menhir_stack in
_menhir_errorcase _menhir_env (Obj.magic _menhir_stack) _menhir_s) : 'freshtv64)) : 'freshtv66)
| _ ->
assert (not _menhir_env._menhir_error);
_menhir_env._menhir_error <- true;
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv67 * _menhir_state) = Obj.magic _menhir_stack in
((let (_menhir_stack, _menhir_s) = _menhir_stack in
_menhir_errorcase _menhir_env (Obj.magic _menhir_stack) _menhir_s) : 'freshtv68)
and _menhir_run14 : _menhir_env -> 'ttv_tail -> _menhir_state -> 'ttv_return =
fun _menhir_env _menhir_stack _menhir_s ->
let _menhir_stack = (_menhir_stack, _menhir_s) in
let _menhir_env = _menhir_discard _menhir_env in
let _tok = _menhir_env._menhir_token in
match _tok with
| ACTIVITY ->
_menhir_run8 _menhir_env (Obj.magic _menhir_stack) MenhirState14
| RESOURCE ->
_menhir_run4 _menhir_env (Obj.magic _menhir_stack) MenhirState14
| RIGHT_BRACE ->
_menhir_reduce11 _menhir_env (Obj.magic _menhir_stack) MenhirState14
| _ ->
assert (not _menhir_env._menhir_error);
_menhir_env._menhir_error <- true;
_menhir_errorcase _menhir_env (Obj.magic _menhir_stack) MenhirState14
and _menhir_run18 : _menhir_env -> 'ttv_tail -> _menhir_state -> 'ttv_return =
fun _menhir_env _menhir_stack _menhir_s ->
let _menhir_env = _menhir_discard _menhir_env in
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv53) = Obj.magic _menhir_stack in
let (_menhir_s : _menhir_state) = _menhir_s in
((let _1 = () in
let _v : 'tv_action =
# 52 "parserProcessus.mly"
( (print_endline "action : FINISHES") )
# 628 "parserProcessus.ml"
in
_menhir_goto_action _menhir_env _menhir_stack _menhir_s _v) : 'freshtv54)
and _menhir_errorcase : _menhir_env -> 'ttv_tail -> _menhir_state -> 'ttv_return =
fun _menhir_env _menhir_stack _menhir_s ->
match _menhir_s with
| MenhirState30 ->
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv39 * _menhir_state * 'tv_element) = Obj.magic _menhir_stack in
((let (_menhir_stack, _menhir_s, _) = _menhir_stack in
_menhir_errorcase _menhir_env (Obj.magic _menhir_stack) _menhir_s) : 'freshtv40)
| MenhirState21 ->
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv41 * _menhir_state * 'tv_contrainte) = Obj.magic _menhir_stack in
((let (_menhir_stack, _menhir_s, _) = _menhir_stack in
_menhir_errorcase _menhir_env (Obj.magic _menhir_stack) _menhir_s) : 'freshtv42)
| MenhirState19 ->
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv43 * _menhir_state * 'tv_requires) = Obj.magic _menhir_stack in
((let (_menhir_stack, _menhir_s, _) = _menhir_stack in
_menhir_errorcase _menhir_env (Obj.magic _menhir_stack) _menhir_s) : 'freshtv44)
| MenhirState17 ->
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : (('freshtv45 * _menhir_state) * _menhir_state * 'tv_elements)) = Obj.magic _menhir_stack in
((let (_menhir_stack, _menhir_s, _) = _menhir_stack in
_menhir_errorcase _menhir_env (Obj.magic _menhir_stack) _menhir_s) : 'freshtv46)
| MenhirState14 ->
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv47 * _menhir_state) = Obj.magic _menhir_stack in
((let (_menhir_stack, _menhir_s) = _menhir_stack in
_menhir_errorcase _menhir_env (Obj.magic _menhir_stack) _menhir_s) : 'freshtv48)
| MenhirState9 ->
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : ('freshtv49 * _menhir_state) * (
# 16 "parserProcessus.mly"
(string)
# 665 "parserProcessus.ml"
)) = Obj.magic _menhir_stack in
((let ((_menhir_stack, _menhir_s), _) = _menhir_stack in
_menhir_errorcase _menhir_env (Obj.magic _menhir_stack) _menhir_s) : 'freshtv50)
| MenhirState3 ->
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : (('freshtv51) * (
# 16 "parserProcessus.mly"
(string)
# 674 "parserProcessus.ml"
))) = Obj.magic _menhir_stack in
(raise _eRR : 'freshtv52)
and _menhir_reduce11 : _menhir_env -> 'ttv_tail -> _menhir_state -> 'ttv_return =
fun _menhir_env _menhir_stack _menhir_s ->
let _v : 'tv_elements =
# 32 "parserProcessus.mly"
( (print_endline "elements : /* Lambda, mot vide */") )
# 683 "parserProcessus.ml"
in
_menhir_goto_elements _menhir_env _menhir_stack _menhir_s _v
and _menhir_run4 : _menhir_env -> 'ttv_tail -> _menhir_state -> 'ttv_return =
fun _menhir_env _menhir_stack _menhir_s ->
let _menhir_stack = (_menhir_stack, _menhir_s) in
let _menhir_env = _menhir_discard _menhir_env in
let _tok = _menhir_env._menhir_token in
match _tok with
| IDENTIFIER _v ->
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv35 * _menhir_state) = Obj.magic _menhir_stack in
let (_v : (
# 16 "parserProcessus.mly"
(string)
# 699 "parserProcessus.ml"
)) = _v in
((let _menhir_stack = (_menhir_stack, _v) in
let _menhir_env = _menhir_discard _menhir_env in
let _tok = _menhir_env._menhir_token in
match _tok with
| AMOUNT ->
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : ('freshtv31 * _menhir_state) * (
# 16 "parserProcessus.mly"
(string)
# 710 "parserProcessus.ml"
)) = Obj.magic _menhir_stack in
((let _menhir_env = _menhir_discard _menhir_env in
let _tok = _menhir_env._menhir_token in
match _tok with
| NUMBER _v ->
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : (('freshtv27 * _menhir_state) * (
# 16 "parserProcessus.mly"
(string)
# 720 "parserProcessus.ml"
))) = Obj.magic _menhir_stack in
let (_v : (
# 15 "parserProcessus.mly"
(int)
# 725 "parserProcessus.ml"
)) = _v in
((let _menhir_env = _menhir_discard _menhir_env in
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : (('freshtv25 * _menhir_state) * (
# 16 "parserProcessus.mly"
(string)
# 732 "parserProcessus.ml"
))) = Obj.magic _menhir_stack in
let ((_4 : (
# 15 "parserProcessus.mly"
(int)
# 737 "parserProcessus.ml"
)) : (
# 15 "parserProcessus.mly"
(int)
# 741 "parserProcessus.ml"
)) = _v in
((let ((_menhir_stack, _menhir_s), (_2 : (
# 16 "parserProcessus.mly"
(string)
# 746 "parserProcessus.ml"
))) = _menhir_stack in
let _3 = () in
let _1 = () in
let _v : 'tv_resource =
# 38 "parserProcessus.mly"
( (print_endline "resource : resource IDENTIFIER amount NUMBER") )
# 753 "parserProcessus.ml"
in
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv23) = _menhir_stack in
let (_menhir_s : _menhir_state) = _menhir_s in
let (_v : 'tv_resource) = _v in
((let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv21) = Obj.magic _menhir_stack in
let (_menhir_s : _menhir_state) = _menhir_s in
let (_v : 'tv_resource) = _v in
((let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv19) = Obj.magic _menhir_stack in
let (_menhir_s : _menhir_state) = _menhir_s in
let ((_1 : 'tv_resource) : 'tv_resource) = _v in
((let _v : 'tv_element =
# 36 "parserProcessus.mly"
( (print_endline "element : resource") )
# 770 "parserProcessus.ml"
in
_menhir_goto_element _menhir_env _menhir_stack _menhir_s _v) : 'freshtv20)) : 'freshtv22)) : 'freshtv24)) : 'freshtv26)) : 'freshtv28)
| _ ->
assert (not _menhir_env._menhir_error);
_menhir_env._menhir_error <- true;
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : (('freshtv29 * _menhir_state) * (
# 16 "parserProcessus.mly"
(string)
# 780 "parserProcessus.ml"
))) = Obj.magic _menhir_stack in
((let ((_menhir_stack, _menhir_s), _) = _menhir_stack in
_menhir_errorcase _menhir_env (Obj.magic _menhir_stack) _menhir_s) : 'freshtv30)) : 'freshtv32)
| _ ->
assert (not _menhir_env._menhir_error);
_menhir_env._menhir_error <- true;
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : ('freshtv33 * _menhir_state) * (
# 16 "parserProcessus.mly"
(string)
# 791 "parserProcessus.ml"
)) = Obj.magic _menhir_stack in
((let ((_menhir_stack, _menhir_s), _) = _menhir_stack in
_menhir_errorcase _menhir_env (Obj.magic _menhir_stack) _menhir_s) : 'freshtv34)) : 'freshtv36)
| _ ->
assert (not _menhir_env._menhir_error);
_menhir_env._menhir_error <- true;
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv37 * _menhir_state) = Obj.magic _menhir_stack in
((let (_menhir_stack, _menhir_s) = _menhir_stack in
_menhir_errorcase _menhir_env (Obj.magic _menhir_stack) _menhir_s) : 'freshtv38)
and _menhir_run8 : _menhir_env -> 'ttv_tail -> _menhir_state -> 'ttv_return =
fun _menhir_env _menhir_stack _menhir_s ->
let _menhir_stack = (_menhir_stack, _menhir_s) in
let _menhir_env = _menhir_discard _menhir_env in
let _tok = _menhir_env._menhir_token in
match _tok with
| IDENTIFIER _v ->
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv15 * _menhir_state) = Obj.magic _menhir_stack in
let (_v : (
# 16 "parserProcessus.mly"
(string)
# 815 "parserProcessus.ml"
)) = _v in
((let _menhir_stack = (_menhir_stack, _v) in
let _menhir_env = _menhir_discard _menhir_env in
let _tok = _menhir_env._menhir_token in
match _tok with
| FINISHES ->
_menhir_run18 _menhir_env (Obj.magic _menhir_stack) MenhirState9
| LEFT_BRACE ->
_menhir_run14 _menhir_env (Obj.magic _menhir_stack) MenhirState9
| REQUIRES ->
_menhir_run11 _menhir_env (Obj.magic _menhir_stack) MenhirState9
| STARTS ->
_menhir_run10 _menhir_env (Obj.magic _menhir_stack) MenhirState9
| ACTIVITY | RESOURCE | RIGHT_BRACE ->
_menhir_reduce5 _menhir_env (Obj.magic _menhir_stack) MenhirState9
| _ ->
assert (not _menhir_env._menhir_error);
_menhir_env._menhir_error <- true;
_menhir_errorcase _menhir_env (Obj.magic _menhir_stack) MenhirState9) : 'freshtv16)
| _ ->
assert (not _menhir_env._menhir_error);
_menhir_env._menhir_error <- true;
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv17 * _menhir_state) = Obj.magic _menhir_stack in
((let (_menhir_stack, _menhir_s) = _menhir_stack in
_menhir_errorcase _menhir_env (Obj.magic _menhir_stack) _menhir_s) : 'freshtv18)
and _menhir_discard : _menhir_env -> _menhir_env =
fun _menhir_env ->
let lexer = _menhir_env._menhir_lexer in
let lexbuf = _menhir_env._menhir_lexbuf in
let _tok = lexer lexbuf in
{
_menhir_lexer = lexer;
_menhir_lexbuf = lexbuf;
_menhir_token = _tok;
_menhir_error = false;
}
and fichier : (Lexing.lexbuf -> token) -> Lexing.lexbuf -> (
# 21 "parserProcessus.mly"
(unit)
# 858 "parserProcessus.ml"
) =
fun lexer lexbuf ->
let _menhir_env =
let (lexer : Lexing.lexbuf -> token) = lexer in
let (lexbuf : Lexing.lexbuf) = lexbuf in
((let _tok = Obj.magic () in
{
_menhir_lexer = lexer;
_menhir_lexbuf = lexbuf;
_menhir_token = _tok;
_menhir_error = false;
}) : _menhir_env)
in
Obj.magic (let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv13) = ((), _menhir_env._menhir_lexbuf.Lexing.lex_curr_p) in
((let _menhir_env = _menhir_discard _menhir_env in
let _tok = _menhir_env._menhir_token in
match _tok with
| PROCESS ->
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv9) = Obj.magic _menhir_stack in
((let _menhir_env = _menhir_discard _menhir_env in
let _tok = _menhir_env._menhir_token in
match _tok with
| IDENTIFIER _v ->
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv5) = Obj.magic _menhir_stack in
let (_v : (
# 16 "parserProcessus.mly"
(string)
# 889 "parserProcessus.ml"
)) = _v in
((let _menhir_stack = (_menhir_stack, _v) in
let _menhir_env = _menhir_discard _menhir_env in
let _tok = _menhir_env._menhir_token in
match _tok with
| LEFT_BRACE ->
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : ('freshtv1) * (
# 16 "parserProcessus.mly"
(string)
# 900 "parserProcessus.ml"
)) = Obj.magic _menhir_stack in
((let _menhir_env = _menhir_discard _menhir_env in
let _tok = _menhir_env._menhir_token in
match _tok with
| ACTIVITY ->
_menhir_run8 _menhir_env (Obj.magic _menhir_stack) MenhirState3
| RESOURCE ->
_menhir_run4 _menhir_env (Obj.magic _menhir_stack) MenhirState3
| RIGHT_BRACE ->
_menhir_reduce11 _menhir_env (Obj.magic _menhir_stack) MenhirState3
| _ ->
assert (not _menhir_env._menhir_error);
_menhir_env._menhir_error <- true;
_menhir_errorcase _menhir_env (Obj.magic _menhir_stack) MenhirState3) : 'freshtv2)
| _ ->
assert (not _menhir_env._menhir_error);
_menhir_env._menhir_error <- true;
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : ('freshtv3) * (
# 16 "parserProcessus.mly"
(string)
# 922 "parserProcessus.ml"
)) = Obj.magic _menhir_stack in
(raise _eRR : 'freshtv4)) : 'freshtv6)
| _ ->
assert (not _menhir_env._menhir_error);
_menhir_env._menhir_error <- true;
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv7) = Obj.magic _menhir_stack in
(raise _eRR : 'freshtv8)) : 'freshtv10)
| _ ->
assert (not _menhir_env._menhir_error);
_menhir_env._menhir_error <- true;
let (_menhir_env : _menhir_env) = _menhir_env in
let (_menhir_stack : 'freshtv11) = Obj.magic _menhir_stack in
(raise _eRR : 'freshtv12)) : 'freshtv14))
# 57 "parserProcessus.mly"
# 941 "parserProcessus.ml"
# 269 "<standard.mly>"
# 946 "parserProcessus.ml"

27
TP8-9/process-analysis/parserProcessus.mli Executable file
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@ -0,0 +1,27 @@
(* The type of tokens. *)
type token =
| STARTS
| STARTED
| RIGHT_BRACE
| RESOURCE
| REQUIRES
| PROCESS
| NUMBER of (int)
| LEFT_BRACE
| IF
| IDENTIFIER of (string)
| FINISHES
| FINISHED
| END
| AMOUNT
| ACTIVITY
(* This exception is raised by the monolithic API functions. *)
exception Error
(* The monolithic API. *)
val fichier: (Lexing.lexbuf -> token) -> Lexing.lexbuf -> (unit)

57
TP8-9/process-analysis/parserProcessus.mly Executable file
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@ -0,0 +1,57 @@
%{
(* Partie recopiee dans le fichier CaML genere. *)
(* Ouverture de modules exploites dans les actions *)
(* Declarations de types, de constantes, de fonctions, d'exceptions exploites dans les actions *)
%}
/* Declaration des unites lexicales et de leur type si une valeur particuliere leur est associee */
%token PROCESS ACTIVITY STARTS FINISHES IF STARTED FINISHED
%token RESOURCE AMOUNT REQUIRES
%token LEFT_BRACE RIGHT_BRACE
/* Defini le type des donnees associees a l'unite lexicale */
%token <int> NUMBER
%token <string> IDENTIFIER
/* Unite lexicale particuliere qui represente la fin du fichier */
%token END
/* Type renvoye pour le nom terminal fichier */
%type <unit> fichier
/* Le non terminal fichier est l'axiome */
%start fichier
%% /* Regles de productions */
fichier : processus END { (print_endline "fichier : processus END") }
processus : PROCESS IDENTIFIER LEFT_BRACE elements RIGHT_BRACE { (print_endline "processus : process IDENTIFIER { elements }") }
elements : /* Lambda, mot vide */ { (print_endline "elements : /* Lambda, mot vide */") }
| element elements { (print_endline "elements : element elements") }
element : activite { (print_endline "element : activite") }
| resource { (print_endline "element : resource") }
resource : RESOURCE IDENTIFIER AMOUNT NUMBER { (print_endline "resource : resource IDENTIFIER amount NUMBER") }
activite : ACTIVITY IDENTIFIER contraintes { (print_endline "activite : activity IDENTIFIER contraintes") }
contraintes : /* Lambda, mot vide */ { (print_endline "contraintes : /* Lambda, mot vide */") }
| requires contraintes { (print_endline "contraintes : requires contraintes") }
| contrainte contraintes { (print_endline "contraintes : contrainte contraintes") }
| LEFT_BRACE elements RIGHT_BRACE contraintes { (print_endline "contraintes : { elements } contraintes") }
requires : REQUIRES NUMBER IDENTIFIER { (print_endline "requires : requires NUMBER IDENTIFIER") }
contrainte : action IF IDENTIFIER etat { (print_endline "contrainte : action if IDENTIFIER etat") }
action : STARTS { (print_endline "action : STARTS") }
| FINISHES { (print_endline "action : FINISHES") }
etat : STARTED { (print_endline "etat : STARTED") }
| FINISHED { (print_endline "etat : FINISHED") }
%%

8
TP8-9/process-analysis/tests/test00.processus Executable file
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@ -0,0 +1,8 @@
/* Un premier exemple de processus */
process ABC {
activity A
activity B
activity C
starts if A started
finishes if B finished
}

11
TP8-9/process-analysis/tests/test01.processus Executable file
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@ -0,0 +1,11 @@
/* Un deuxième exemple de processus avec des ressources */
process ABC {
resource R amount 5
activity A
requires 2 R
activity B
activity C
requires 3 R
starts if A started
finishes if B finished
}

18
TP8-9/process-analysis/tests/test02.processus Executable file
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@ -0,0 +1,18 @@
/* Un troisième exemple de processus hiérarchique avec des ressources */
process ABC {
resource R amount 5
activity A {
activity A1 {
activity A11
}
requires 1 R
activity A2
requires 2 R
starts if A1 finished
}
requires 2 R
activity B
activity C requires 3 R
starts if A started
finishes if B finished
}