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9015
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(* untyped functional language, with call by value semantics *)
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Func = HOHH +
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types tm
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arities tm :: term
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consts abs :: (tm => tm) => tm
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app :: tm => tm => tm
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cond :: tm => tm => tm => tm
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fix :: (tm => tm) => tm
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true,
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false :: tm
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"and" :: tm => tm => tm (infixr 999)
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"eq" :: tm => tm => tm (infixr 999)
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"0" :: tm ("Z")
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S :: tm => tm
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(*
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"++", "--",
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"**" :: tm => tm => tm (infixr 999)
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*)
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eval :: [tm, tm] => bool
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arities tm :: plus
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arities tm :: minus
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arities tm :: times
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rules eval "
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eval (abs RR) (abs RR)..
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eval (app F X) V :- eval F (abs R) & eval X U & eval (R U) V..
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eval (cond P L1 R1) D1 :- eval P true & eval L1 D1..
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eval (cond P L2 R2) D2 :- eval P false & eval R2 D2..
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eval (fix G) W :- eval (G (fix G)) W..
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eval true true ..
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eval false false..
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eval (P and Q) true :- eval P true & eval Q true ..
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eval (P and Q) false :- eval P false | eval Q false..
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eval (A1 eq B1) true :- eval A1 C1 & eval B1 C1..
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eval (A2 eq B2) false :- True..
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eval Z Z..
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eval (S N) (S M) :- eval N M..
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eval ( Z + M) K :- eval M K..
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eval ((S N) + M) (S K) :- eval (N + M) K..
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eval (N - Z) K :- eval N K..
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eval ((S N) - (S M)) K :- eval (N- M) K..
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eval ( Z * M) Z..
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eval ((S N) * M) K :- eval (N * M) L & eval (L + M) K"
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end
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