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- assignment05/pascal.mlw: lowered the difficulty (one more invariant given) - assignment02, 03: minor fixes & divide into sub-problems
30 lines
639 B
Plaintext
30 lines
639 B
Plaintext
(* Euclidean division
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1. Prove correctness of euclideian divison:
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`division a b` returns an integer `q` such that
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`a = bq+r` and `0 <= r < b` for some `r`.
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- You have to strengthen the precondition.
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- You have to strengthen the loop invariant.
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*)
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module Division
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use int.Int
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let division (a b: int) : int
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requires { a >= 0 }
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requires { b > 0 }
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ensures { exists r: int. a = b * result + r /\ 0 <= r < b }
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=
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let ref q = 0 in
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let ref r = a in
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while r >= b do
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invariant { a = b * q + r /\ 0 <= r }
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variant { r }
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q <- q + 1;
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r <- r - b
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done;
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q
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end |