# HG changeset patch
# User haftmann
# Date 1289988558 -3600
# Node ID 968c481aa18ce10a265fd8010dbe3c674e4589e4
# Parent  0592d3a39c085d0c327d5e1cfb0a20cf956f39b8
module for functorial mappers

diff -r 0592d3a39c08 -r 968c481aa18c src/HOL/HOL.thy
--- a/src/HOL/HOL.thy	Wed Nov 17 09:22:23 2010 +0100
+++ b/src/HOL/HOL.thy	Wed Nov 17 11:09:18 2010 +0100
@@ -32,6 +32,7 @@
   "Tools/async_manager.ML"
   "Tools/try.ML"
   ("Tools/cnf_funcs.ML")
+  ("Tools/functorial_mappers.ML")
 begin
 
 setup {* Intuitionistic.method_setup @{binding iprover} *}
@@ -708,6 +709,7 @@
   and [Pure.elim?] = iffD1 iffD2 impE
 
 use "Tools/hologic.ML"
+use "Tools/functorial_mappers.ML"
 
 
 subsubsection {* Atomizing meta-level connectives *}
diff -r 0592d3a39c08 -r 968c481aa18c src/HOL/IsaMakefile
--- a/src/HOL/IsaMakefile	Wed Nov 17 09:22:23 2010 +0100
+++ b/src/HOL/IsaMakefile	Wed Nov 17 11:09:18 2010 +0100
@@ -136,6 +136,7 @@
   $(SRC)/Tools/solve_direct.ML \
   $(SRC)/Tools/value.ML \
   HOL.thy \
+  Tools/functorial_mappers.ML \
   Tools/hologic.ML \
   Tools/recfun_codegen.ML \
   Tools/simpdata.ML
diff -r 0592d3a39c08 -r 968c481aa18c src/HOL/Tools/functorial_mappers.ML
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/functorial_mappers.ML	Wed Nov 17 11:09:18 2010 +0100
@@ -0,0 +1,150 @@
+(*  Title:      HOL/Tools/functorial-mappers.ML
+    Author:     Florian Haftmann, TU Muenchen
+
+Functorial mappers on types.
+*)
+
+signature FUNCTORIAL_MAPPERS =
+sig
+  val find_atomic: theory -> typ -> (typ * (bool * bool)) list
+  val construct_mapper: theory -> (string * bool -> term)
+    -> bool -> typ -> typ -> term
+  val register: string -> string -> (sort * (bool * bool)) list -> thm -> thm
+    -> theory -> theory
+  type entry
+  val entries: theory -> entry Symtab.table
+end;
+
+structure Functorial_Mappers : FUNCTORIAL_MAPPERS =
+struct
+
+(** functorial mappers and their properties **)
+
+(* bookkeeping *)
+
+type entry = { mapper: string, variances: (sort * (bool * bool)) list,
+  concatenate: thm, identity: thm };
+
+structure Data = Theory_Data(
+  type T = entry Symtab.table
+  val empty = Symtab.empty
+  val merge = Symtab.merge (K true)
+  val extend = I
+);
+
+val entries = Data.get;
+
+
+(* type analysis *)
+
+fun find_atomic thy T =
+  let
+    val variances_of = Option.map #variances o Symtab.lookup (Data.get thy);
+    fun add_variance is_contra T =
+      AList.map_default (op =) (T, (false, false))
+        ((if is_contra then apsnd else apfst) (K true));
+    fun analyze' is_contra (_, (co, contra)) T =
+      (if co then analyze is_contra T else I)
+      #> (if contra then analyze (not is_contra) T else I)
+    and analyze is_contra (T as Type (tyco, Ts)) = (case variances_of tyco
+          of NONE => add_variance is_contra T
+           | SOME variances => fold2 (analyze' is_contra) variances Ts)
+      | analyze is_contra T = add_variance is_contra T;
+  in analyze false T [] end;
+
+fun construct_mapper thy atomic =
+  let
+    val lookup = the o Symtab.lookup (Data.get thy);
+    fun constructs is_contra (_, (co, contra)) T T' =
+      (if co then [construct is_contra T T'] else [])
+      @ (if contra then [construct (not is_contra) T T'] else [])
+    and construct is_contra (T as Type (tyco, Ts)) (T' as Type (_, Ts')) =
+          let
+            val { mapper, variances, ... } = lookup tyco;
+            val args = maps (fn (arg_pattern, (T, T')) =>
+              constructs is_contra arg_pattern T T')
+                (variances ~~ (Ts ~~ Ts'));
+            val (U, U') = if is_contra then (T', T) else (T, T');
+          in list_comb (Const (mapper, map fastype_of args ---> U --> U'), args) end
+      | construct is_contra (TFree (v, _)) (TFree _) = atomic (v, is_contra);
+  in construct end;
+
+
+(* mapper properties *)
+
+fun make_concatenate_prop variances (tyco, mapper) =
+  let
+    fun invents n k nctxt =
+      let
+        val names = Name.invents nctxt n k;
+      in (names, fold Name.declare names nctxt) end;
+    val (((vs1, vs2), vs3), _) = Name.context
+      |> invents Name.aT (length variances)
+      ||>> invents Name.aT (length variances)
+      ||>> invents Name.aT (length variances);
+    fun mk_Ts vs = map2 (fn v => fn (sort, _) => TFree (v, sort))
+      vs variances;
+    val (Ts1, Ts2, Ts3) = (mk_Ts vs1, mk_Ts vs2, mk_Ts vs3);
+    fun mk_argT ((T, T'), (_, (co, contra))) =
+      (if co then [(T --> T')] else [])
+      @ (if contra then [(T' --> T)] else []);
+    val contras = maps (fn (_, (co, contra)) =>
+      (if co then [false] else []) @ (if contra then [true] else [])) variances;
+    val Ts21 = maps mk_argT ((Ts2 ~~ Ts1) ~~ variances);
+    val Ts32 = maps mk_argT ((Ts3 ~~ Ts2) ~~ variances);
+    val ((names21, names32), nctxt) = Name.context
+      |> invents "f" (length Ts21)
+      ||>> invents "f" (length Ts32);
+    val T1 = Type (tyco, Ts1);
+    val T2 = Type (tyco, Ts2);
+    val T3 = Type (tyco, Ts3);
+    val x = Free (the_single (Name.invents nctxt "a" 1), T3);
+    val (args21, args32) = (names21 ~~ Ts21, names32 ~~ Ts32);
+    val args31 = map2 (fn is_contra => fn ((f21, T21), (f32, T32)) =>
+      if not is_contra then
+        Abs ("x", domain_type T32, Free (f21, T21) $ (Free (f32, T32) $ Bound 0))
+      else
+        Abs ("x", domain_type T21, Free (f32, T32) $ (Free (f21, T21) $ Bound 0))
+      ) contras (args21 ~~ args32)
+    fun mk_mapper T T' args = list_comb (Const (mapper,
+      map fastype_of args ---> T --> T'), args);
+    val lhs = mk_mapper T2 T1 (map Free args21) $
+      (mk_mapper T3 T2 (map Free args32) $ x);
+    val rhs = mk_mapper T3 T1 args31 $ x;
+  in (x, (HOLogic.mk_Trueprop o HOLogic.mk_eq) (lhs, rhs)) end;
+
+fun make_identity_prop variances (tyco, mapper) =
+  let
+    val vs = Name.invents Name.context Name.aT (length variances);
+    val Ts = map2 (fn v => fn (sort, _) => TFree (v, sort)) vs variances;
+    fun bool_num b = if b then 1 else 0;
+    fun mk_argT (T, (_, (co, contra))) =
+      replicate (bool_num co + bool_num contra) (T --> T)
+    val Ts' = maps mk_argT (Ts ~~ variances)
+    val T = Type (tyco, Ts);
+    val x = Free ("a", T);
+    val lhs = list_comb (Const (mapper, Ts' ---> T --> T),
+      map (fn T => Abs ("x", domain_type T, Bound 0)) Ts') $ x;
+  in (x, (HOLogic.mk_Trueprop o HOLogic.mk_eq) (lhs, x)) end;
+
+
+(* registering primitive mappers *)
+
+fun register tyco mapper variances raw_concatenate raw_identity thy =
+  let
+    val (_, concatenate_prop) = make_concatenate_prop variances (tyco, mapper);
+    val (_, identity_prop) = make_identity_prop variances (tyco, mapper);
+    val concatenate = Goal.prove_global thy
+      (Term.add_free_names concatenate_prop []) [] concatenate_prop
+      (K (ALLGOALS (ProofContext.fact_tac [raw_concatenate])));
+    val identity = Goal.prove_global thy
+      (Term.add_free_names identity_prop []) [] identity_prop
+      (K (ALLGOALS (ProofContext.fact_tac [raw_identity])));
+  in
+    thy
+    |> Data.map (Symtab.update (tyco, { mapper = mapper,
+        variances = variances,
+        concatenate = concatenate, identity = identity }))
+  end;
+
+end;