(* Title: Subst/unifier.thy
Author: Martin Coen, Cambridge University Computer Laboratory
Copyright 1993 University of Cambridge
Definition of most general idempotent unifier
*)
Unifier = Subst +
consts
Idem :: "('a*('a uterm))list=> bool"
Unifier :: "[('a*('a uterm))list,'a uterm,'a uterm] => bool"
">>" :: "[('a*('a uterm))list,('a*('a uterm))list] => bool" (infixr 52)
MGUnifier :: "[('a*('a uterm))list,'a uterm,'a uterm] => bool"
MGIUnifier :: "[('a*('a uterm))list,'a uterm,'a uterm] => bool"
UWFD :: "['a uterm,'a uterm,'a uterm,'a uterm] => bool"
rules (*Definitions*)
Idem_def "Idem(s) == s <> s =s= s"
Unifier_def "Unifier s t u == t <| s = u <| s"
MoreGeneral_def "r >> s == ? q.s =s= r <> q"
MGUnifier_def "MGUnifier s t u == Unifier s t u & \
\ (! r.Unifier r t u --> s >> r)"
MGIUnifier_def "MGIUnifier s t u == MGUnifier s t u & Idem(s)"
UWFD_def
"UWFD x y x' y' == \
\ (vars_of(x) Un vars_of(y) < vars_of(x') Un vars_of(y')) | \
\ (vars_of(x) Un vars_of(y) = vars_of(x') Un vars_of(y') & x <: x')"
end