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32 lines
943 B
Plaintext
32 lines
943 B
Plaintext
module Pascal
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use int.Int
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use ref.Ref
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use array.Array
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(* HINT: https://en.wikipedia.org/wiki/Pascal%27s_triangle *)
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(* You should understand the Pascal's triangle first to find good invariants *)
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let rec function comb (n k: int) : int
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requires { 0 <= k <= n }
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variant { n }
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ensures { result >= 1 }
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= if k = 0 || k = n then 1 else comb (n-1) k + comb (n-1) (k-1)
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(* Insert appropriate invariants so that Why3 can verify this function. *)
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let chooses (n : int) : array int
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requires { n > 0 }
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ensures { forall i: int.
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0 <= i < length result -> result[i] = comb n i }
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=
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let ref row = Array.make 1 1 in
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for r = 1 to n do
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invariant { length row = r }
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invariant { true (*TODO*) }
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let new_row = Array.make (r+1) 1 in
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for c = 1 to r-1 do
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invariant { true (*TODO*) }
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new_row[c] <- row[c-1] + row[c]
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done;
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row <- new_row
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done;
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row
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end |