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