src/Pure/morphism.ML

 end
 
 signature MORPHISM =
 sig
   include BASIC_MORPHISM
+  type 'a funs = ('a -> 'a) list
   val binding: morphism -> binding -> binding
   val typ: morphism -> typ -> typ
   val term: morphism -> term -> term
   val fact: morphism -> thm list -> thm list
   val thm: morphism -> thm -> thm
   val cterm: morphism -> cterm -> cterm
   val morphism:
-   {binding: binding -> binding,
-    typ: typ -> typ,
-    term: term -> term,
-    fact: thm list -> thm list} -> morphism
+   {binding: binding funs,
+    typ: typ funs,
+    term: term funs,
+    fact: thm list funs} -> morphism
   val binding_morphism: (binding -> binding) -> morphism
   val typ_morphism: (typ -> typ) -> morphism
   val term_morphism: (term -> term) -> morphism
   val fact_morphism: (thm list -> thm list) -> morphism
   val thm_morphism: (thm -> thm) -> morphism

 end;
 
 structure Morphism: MORPHISM =
 struct
 
+type 'a funs = ('a -> 'a) list;
+fun apply fs = fold_rev (fn f => fn x => f x) fs;
+
 datatype morphism = Morphism of
- {binding: binding -> binding,
-  typ: typ -> typ,
-  term: term -> term,
-  fact: thm list -> thm list};
+ {binding: binding funs,
+  typ: typ funs,
+  term: term funs,
+  fact: thm list funs};
 
 type declaration = morphism -> Context.generic -> Context.generic;
 
-fun binding (Morphism {binding, ...}) = binding;
-fun typ (Morphism {typ, ...}) = typ;
-fun term (Morphism {term, ...}) = term;
-fun fact (Morphism {fact, ...}) = fact;
+fun binding (Morphism {binding, ...}) = apply binding;
+fun typ (Morphism {typ, ...}) = apply typ;
+fun term (Morphism {term, ...}) = apply term;
+fun fact (Morphism {fact, ...}) = apply fact;
 val thm = singleton o fact;
 val cterm = Drule.cterm_rule o thm;
 
 val morphism = Morphism;
 
-fun binding_morphism binding = morphism {binding = binding, typ = I, term = I, fact = I};
-fun typ_morphism typ = morphism {binding = I, typ = typ, term = I, fact = I};
-fun term_morphism term = morphism {binding = I, typ = I, term = term, fact = I};
-fun fact_morphism fact = morphism {binding = I, typ = I, term = I, fact = fact};
-fun thm_morphism thm = morphism {binding = I, typ = I, term = I, fact = map thm};
+fun binding_morphism binding = morphism {binding = [binding], typ = [], term = [], fact = []};
+fun typ_morphism typ = morphism {binding = [], typ = [typ], term = [], fact = []};
+fun term_morphism term = morphism {binding = [], typ = [], term = [term], fact = []};
+fun fact_morphism fact = morphism {binding = [], typ = [], term = [], fact = [fact]};
+fun thm_morphism thm = morphism {binding = [], typ = [], term = [], fact = [map thm]};
 
-val identity = morphism {binding = I, typ = I, term = I, fact = I};
+val identity = morphism {binding = [], typ = [], term = [], fact = []};
 
 fun compose
     (Morphism {binding = binding1, typ = typ1, term = term1, fact = fact1})
     (Morphism {binding = binding2, typ = typ2, term = term2, fact = fact2}) =
-  morphism {binding = binding1 o binding2, typ = typ1 o typ2,
-    term = term1 o term2, fact = fact1 o fact2};
+  morphism {binding = binding1 @ binding2, typ = typ1 @ typ2,
+    term = term1 @ term2, fact = fact1 @ fact2};
 
 fun phi1 $> phi2 = compose phi2 phi1;
 
 fun transform phi f = fn psi => f (phi $> psi);
 fun form f = f identity;