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