TFL/examples/Subst/Subst.thy

+(*  Title:      Substitutions/subst.thy
+    Author:     Martin Coen, Cambridge University Computer Laboratory
+    Copyright   1993  University of Cambridge
+
+Substitutions on uterms
+*)
+
+Subst = Setplus + AList + UTerm +
+
+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"
+
+
+primrec "op <|"   uterm
+  subst_Var      "(Var v <| s) = assoc v (Var v) s"
+  subst_Const  "(Const c <| s) = Const c"
+  subst_Comb  "(Comb M N <| s) = Comb (M <| s) (N <| s)"
+
+
+rules 
+
+  subst_eq_def  "r =s= s == ALL t.t <| r = t <| s"
+
+  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 - {x} else g Un {x})"
+
+  srange_def   
+   "srange(al) == Union({y. EX x:sdom(al). y=vars_of(Var(x) <| al)})"
+
+end