Subst/subst.thy

Initial revision

(*  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.Cons(<x,y <| bl>,g))"

  sdom_def
  "sdom(al) == alist_rec(al, {},  \
\                        %x y xs g.if(Var(x)=y, g Int Compl({x}), g Un {x}))"
  srange_def   
  "srange(al) == Union({y. EX x:sdom(al).y=vars_of(Var(x) <| al)})"

end