Subst/subst.thy

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Subst/subst.thy	Thu Sep 16 12:21:07 1993 +0200
@@ -0,0 +1,37 @@
+(*  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