(* Title: Subst/Unify
Author: Konrad Slind, Cambridge University Computer Laboratory
Copyright 1997 University of Cambridge
Unification algorithm
*)
Unify = Unifier + WF_Rel +
datatype 'a subst = Fail | Subst ('a list)
consts
uterm_less :: "(('a uterm * 'a uterm) * ('a uterm * 'a uterm)) set"
unifyRel :: "(('a uterm * 'a uterm) * ('a uterm * 'a uterm)) set"
unify :: "'a uterm * 'a uterm => ('a * 'a uterm) subst"
defs
uterm_less_def "uterm_less == rprod (measure uterm_size)
(measure uterm_size)"
(* Termination relation for the Unify function *)
unifyRel_def "unifyRel == inv_image (finite_psubset ** uterm_less)
(%(x,y). (vars_of x Un vars_of y, (x,y)))"
recdef unify "unifyRel"
"unify(Const m, Const n) = (if (m=n) then Subst[] else Fail)"
"unify(Const m, Comb M N) = Fail"
"unify(Const m, Var v) = Subst[(v,Const m)]"
"unify(Var v, M) = (if (Var v <: M) then Fail else Subst[(v,M)])"
"unify(Comb M N, Const x) = Fail"
"unify(Comb M N, Var v) = (if (Var v <: Comb M N) then Fail
else Subst[(v,Comb M N)])"
"unify(Comb M1 N1, Comb M2 N2) =
(case unify(M1,M2)
of Fail => Fail
| Subst theta => (case unify(N1 <| theta, N2 <| theta)
of Fail => Fail
| Subst sigma => Subst (theta <> sigma)))"
end