(* Title: Substitutions/subst.thy
Author: Martin Coen, Cambridge University Computer Laboratory
Copyright 1993 University of Cambridge
Substitutions on uterms
*)
Subst = Setplus + AList + UTLemmas +
consts
"=s=" :: "[('a*('a uterm)) list,('a*('a uterm)) list] => bool" (infixr 52)
"<|" :: "['a uterm,('a*('a uterm)) list] => 'a uterm" (infixl 55)
"<>" :: "[('a*('a uterm)) list, ('a*('a uterm)) list] =>
('a*('a uterm)) list" (infixl 56)
sdom :: "('a*('a uterm)) list => 'a set"
srange :: "('a*('a uterm)) list => 'a set"
rules
subst_eq_def "r =s= s == ALL t.t <| r = t <| s"
subst_def
"t <| al == uterm_rec t (%x.assoc x (Var x) al)
(%x.Const(x))
(%u v q r.Comb q r)"
comp_def "al <> bl == alist_rec al bl (%x y xs g.(x,y <| bl)#g)"
sdom_def
"sdom(al) == alist_rec al {}
(%x y xs g.if Var(x)=y then g Int Compl({x}) else g Un {x})"
srange_def
"srange(al) == Union({y. EX x:sdom(al).y=vars_of(Var(x) <| al)})"
end