--- a/src/HOL/Tools/type_mapper.ML Sun Dec 05 14:02:16 2010 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,217 +0,0 @@
-(* Title: HOL/Tools/type_mapper.ML
- Author: Florian Haftmann, TU Muenchen
-
-Functorial mappers on types.
-*)
-
-signature TYPE_MAPPER =
-sig
- val find_atomic: theory -> typ -> (typ * (bool * bool)) list
- val construct_mapper: theory -> (string * bool -> term)
- -> bool -> typ -> typ -> term
- val type_mapper: string option -> term -> theory -> Proof.state
- type entry
- val entries: theory -> entry Symtab.table
-end;
-
-structure Type_Mapper : TYPE_MAPPER =
-struct
-
-val compositionalityN = "compositionality";
-val identityN = "identity";
-
-(** functorial mappers and their properties **)
-
-(* bookkeeping *)
-
-type entry = { mapper: string, variances: (sort * (bool * bool)) list,
- compositionality: thm, identity: thm };
-
-structure Data = Theory_Data(
- type T = entry Symtab.table
- val empty = Symtab.empty
- fun merge (xy : T * T) = Symtab.merge (K true) xy
- 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_compositionality_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 (Long_Name.base_name tyco) 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 (map Free (args21 @ args32) @ [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 (Long_Name.base_name tyco, 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;
-
-
-(* analyzing and registering mappers *)
-
-fun consume eq x [] = (false, [])
- | consume eq x (ys as z :: zs) = if eq (x, z) then (true, zs) else (false, ys);
-
-fun split_mapper_typ "fun" T =
- let
- val (Ts', T') = strip_type T;
- val (Ts'', T'') = split_last Ts';
- val (Ts''', T''') = split_last Ts'';
- in (Ts''', T''', T'' --> T') end
- | split_mapper_typ tyco T =
- let
- val (Ts', T') = strip_type T;
- val (Ts'', T'') = split_last Ts';
- in (Ts'', T'', T') end;
-
-fun analyze_variances thy tyco T =
- let
- fun bad_typ () = error ("Bad mapper type: " ^ Syntax.string_of_typ_global thy T);
- val (Ts, T1, T2) = split_mapper_typ tyco T
- handle List.Empty => bad_typ ();
- val _ = pairself
- ((fn tyco' => if tyco' = tyco then () else bad_typ ()) o fst o dest_Type) (T1, T2)
- val (vs1, vs2) = pairself (map dest_TFree o snd o dest_Type) (T1, T2)
- handle TYPE _ => bad_typ ();
- val _ = if has_duplicates (eq_fst (op =)) (vs1 @ vs2)
- then bad_typ () else ();
- fun check_variance_pair (var1 as (v1, sort1), var2 as (v2, sort2)) =
- let
- val coT = TFree var1 --> TFree var2;
- val contraT = TFree var2 --> TFree var1;
- val sort = Sign.inter_sort thy (sort1, sort2);
- in
- consume (op =) coT
- ##>> consume (op =) contraT
- #>> pair sort
- end;
- val (variances, left_variances) = fold_map check_variance_pair (vs1 ~~ vs2) Ts;
- val _ = if null left_variances then () else bad_typ ();
- in variances end;
-
-fun gen_type_mapper prep_term some_prfx raw_t thy =
- let
- val (mapper, T) = case prep_term thy raw_t
- of Const cT => cT
- | t => error ("No constant: " ^ Syntax.string_of_term_global thy t);
- val prfx = the_default (Long_Name.base_name mapper) some_prfx;
- val _ = Type.no_tvars T;
- fun add_tycos (Type (tyco, Ts)) = insert (op =) tyco #> fold add_tycos Ts
- | add_tycos _ = I;
- val tycos = add_tycos T [];
- val tyco = if tycos = ["fun"] then "fun"
- else case remove (op =) "fun" tycos
- of [tyco] => tyco
- | _ => error ("Bad number of type constructors: " ^ Syntax.string_of_typ_global thy T);
- val variances = analyze_variances thy tyco T;
- val compositionality_prop = uncurry (fold_rev Logic.all)
- (make_compositionality_prop variances (tyco, mapper));
- val identity_prop = uncurry Logic.all
- (make_identity_prop variances (tyco, mapper));
- val qualify = Binding.qualify true prfx o Binding.name;
- fun after_qed [single_compositionality, single_identity] lthy =
- lthy
- |> Local_Theory.note ((qualify compositionalityN, []), single_compositionality)
- ||>> Local_Theory.note ((qualify identityN, []), single_identity)
- |-> (fn ((_, [compositionality]), (_, [identity])) =>
- (Local_Theory.background_theory o Data.map)
- (Symtab.update (tyco, { mapper = mapper, variances = variances,
- compositionality = compositionality, identity = identity })));
- in
- thy
- |> Named_Target.theory_init
- |> Proof.theorem NONE after_qed (map (fn t => [(t, [])]) [compositionality_prop, identity_prop])
- end
-
-val type_mapper = gen_type_mapper Sign.cert_term;
-val type_mapper_cmd = gen_type_mapper Syntax.read_term_global;
-
-val _ =
- Outer_Syntax.command "type_mapper" "register functorial mapper for type with its properties" Keyword.thy_goal
- (Scan.option (Parse.name --| Parse.$$$ ":") -- Parse.term
- >> (fn (prfx, t) => Toplevel.print o (Toplevel.theory_to_proof (type_mapper_cmd prfx t))));
-
-end;