src/HOLCF/Tools/domain/domain_axioms.ML
author huffman
Tue Jan 29 18:00:12 2008 +0100 (2008-01-29)
changeset 26012 f6917792f8a4
parent 24712 64ed05609568
child 27691 ce171cbd4b93
permissions -rw-r--r--
new term-building combinators
     1 (*  Title:      HOLCF/Tools/domain/domain_axioms.ML
     2     ID:         $Id$
     3     Author:     David von Oheimb
     4 
     5 Syntax generator for domain command.
     6 *)
     7 
     8 structure Domain_Axioms = struct
     9 
    10 local
    11 
    12 open Domain_Library;
    13 infixr 0 ===>;infixr 0 ==>;infix 0 == ; 
    14 infix 1 ===; infix 1 ~= ; infix 1 <<; infix 1 ~<<;
    15 infix 9 `   ; infix 9 `% ; infix 9 `%%; infixr 9 oo;
    16 
    17 fun calc_axioms comp_dname (eqs : eq list) n (((dname,_),cons) : eq)=
    18 let
    19 
    20 (* ----- axioms and definitions concerning the isomorphism ------------------ *)
    21 
    22   val dc_abs = %%:(dname^"_abs");
    23   val dc_rep = %%:(dname^"_rep");
    24   val x_name'= "x";
    25   val x_name = idx_name eqs x_name' (n+1);
    26   val dnam = Sign.base_name dname;
    27 
    28   val abs_iso_ax = ("abs_iso", mk_trp(dc_rep`(dc_abs`%x_name') === %:x_name'));
    29   val rep_iso_ax = ("rep_iso", mk_trp(dc_abs`(dc_rep`%x_name') === %:x_name'));
    30 
    31   val when_def = ("when_def",%%:(dname^"_when") == 
    32      foldr (uncurry /\ ) (/\x_name'((when_body cons (fn (x,y) =>
    33 				Bound(1+length cons+x-y)))`(dc_rep`Bound 0))) (when_funs cons));
    34   
    35   val copy_def = let
    36     fun idxs z x arg = if is_rec arg
    37 			 then (cproj (Bound z) eqs (rec_of arg))`Bound(z-x)
    38 			 else Bound(z-x);
    39     fun one_con (con,args) =
    40         foldr /\# (list_ccomb (%%:con, mapn (idxs (length args)) 1 args)) args;
    41   in ("copy_def", %%:(dname^"_copy") ==
    42        /\"f" (list_ccomb (%%:(dname^"_when"), map one_con cons))) end;
    43 
    44 (* -- definitions concerning the constructors, discriminators and selectors - *)
    45 
    46   fun con_def m n (_,args) = let
    47     fun idxs z x arg = (if is_lazy arg then mk_up else I) (Bound(z-x));
    48     fun parms vs = mk_stuple (mapn (idxs(length vs)) 1 vs);
    49     fun inj y 1 _ = y
    50     |   inj y _ 0 = mk_sinl y
    51     |   inj y i j = mk_sinr (inj y (i-1) (j-1));
    52   in foldr /\# (dc_abs`(inj (parms args) m n)) args end;
    53   
    54   val con_defs = mapn (fn n => fn (con,args) =>
    55     (extern_name con ^"_def", %%:con == con_def (length cons) n (con,args))) 0 cons;
    56   
    57   val dis_defs = let
    58 	fun ddef (con,_) = (dis_name con ^"_def",%%:(dis_name con) == 
    59 		 list_ccomb(%%:(dname^"_when"),map 
    60 			(fn (con',args) => (foldr /\#
    61 			   (if con'=con then TT else FF) args)) cons))
    62 	in map ddef cons end;
    63 
    64   val mat_defs = let
    65 	fun mdef (con,_) = (mat_name con ^"_def",%%:(mat_name con) == 
    66 		 list_ccomb(%%:(dname^"_when"),map 
    67 			(fn (con',args) => (foldr /\#
    68 			   (if con'=con
    69                                then mk_return (mk_ctuple (map (bound_arg args) args))
    70                                else mk_fail) args)) cons))
    71 	in map mdef cons end;
    72 
    73   val pat_defs =
    74     let
    75       fun pdef (con,args) =
    76         let
    77           val ps = mapn (fn n => fn _ => %:("pat" ^ string_of_int n)) 1 args;
    78           val xs = map (bound_arg args) args;
    79           val r = Bound (length args);
    80           val rhs = case args of [] => mk_return HOLogic.unit
    81                                 | _ => mk_ctuple_pat ps ` mk_ctuple xs;
    82           fun one_con (con',args') = foldr /\# (if con'=con then rhs else mk_fail) args';
    83         in (pat_name con ^"_def", list_comb (%%:(pat_name con), ps) == 
    84                list_ccomb(%%:(dname^"_when"), map one_con cons))
    85         end
    86     in map pdef cons end;
    87 
    88   val sel_defs = let
    89 	fun sdef con n arg = Option.map (fn sel => (sel^"_def",%%:sel == 
    90 		 list_ccomb(%%:(dname^"_when"),map 
    91 			(fn (con',args) => if con'<>con then UU else
    92 			 foldr /\# (Bound (length args - n)) args) cons))) (sel_of arg);
    93 	in List.mapPartial I (List.concat(map (fn (con,args) => mapn (sdef con) 1 args) cons)) end;
    94 
    95 
    96 (* ----- axiom and definitions concerning induction ------------------------- *)
    97 
    98   val reach_ax = ("reach", mk_trp(cproj (mk_fix (%%:(comp_dname^"_copy"))) eqs n
    99 					`%x_name === %:x_name));
   100   val take_def = ("take_def",%%:(dname^"_take") == mk_lam("n",cproj
   101 	     (mk_iterate (Bound 0, %%:(comp_dname^"_copy"), UU)) eqs n));
   102   val finite_def = ("finite_def",%%:(dname^"_finite") == mk_lam(x_name,
   103 	mk_ex("n",(%%:(dname^"_take") $ Bound 0)`Bound 1 === Bound 1)));
   104 
   105 in (dnam,
   106     [abs_iso_ax, rep_iso_ax, reach_ax],
   107     [when_def, copy_def] @
   108      con_defs @ dis_defs @ mat_defs @ pat_defs @ sel_defs @
   109     [take_def, finite_def])
   110 end; (* let *)
   111 
   112 fun infer_props thy = map (apsnd (FixrecPackage.legacy_infer_prop thy));
   113 
   114 fun add_axioms_i x = snd o PureThy.add_axioms_i (map Thm.no_attributes x);
   115 fun add_axioms_infer axms thy = add_axioms_i (infer_props thy axms) thy;
   116 
   117 fun add_defs_i x = snd o (PureThy.add_defs_i false) (map Thm.no_attributes x);
   118 fun add_defs_infer defs thy = add_defs_i (infer_props thy defs) thy;
   119 
   120 in (* local *)
   121 
   122 fun add_axioms (comp_dnam, eqs : eq list) thy' = let
   123   val comp_dname = Sign.full_name thy' comp_dnam;
   124   val dnames = map (fst o fst) eqs;
   125   val x_name = idx_name dnames "x"; 
   126   fun copy_app dname = %%:(dname^"_copy")`Bound 0;
   127   val copy_def = ("copy_def" , %%:(comp_dname^"_copy") ==
   128 				    /\"f"(mk_ctuple (map copy_app dnames)));
   129   val bisim_def = ("bisim_def",%%:(comp_dname^"_bisim")==mk_lam("R",
   130     let
   131       fun one_con (con,args) = let
   132 	val nonrec_args = filter_out is_rec args;
   133 	val    rec_args = List.filter     is_rec args;
   134 	val    recs_cnt = length rec_args;
   135 	val allargs     = nonrec_args @ rec_args
   136 				      @ map (upd_vname (fn s=> s^"'")) rec_args;
   137 	val allvns      = map vname allargs;
   138 	fun vname_arg s arg = if is_rec arg then vname arg^s else vname arg;
   139 	val vns1        = map (vname_arg "" ) args;
   140 	val vns2        = map (vname_arg "'") args;
   141 	val allargs_cnt = length nonrec_args + 2*recs_cnt;
   142 	val rec_idxs    = (recs_cnt-1) downto 0;
   143 	val nonlazy_idxs = map snd (filter_out (fn (arg,_) => is_lazy arg)
   144 					 (allargs~~((allargs_cnt-1) downto 0)));
   145 	fun rel_app i ra = proj (Bound(allargs_cnt+2)) eqs (rec_of ra) $ 
   146 			   Bound (2*recs_cnt-i) $ Bound (recs_cnt-i);
   147 	val capps = foldr mk_conj (mk_conj(
   148 	   Bound(allargs_cnt+1)===list_ccomb(%%:con,map (bound_arg allvns) vns1),
   149 	   Bound(allargs_cnt+0)===list_ccomb(%%:con,map (bound_arg allvns) vns2)))
   150            (mapn rel_app 1 rec_args);
   151         in foldr mk_ex (Library.foldr mk_conj 
   152 			      (map (defined o Bound) nonlazy_idxs,capps)) allvns end;
   153       fun one_comp n (_,cons) =mk_all(x_name(n+1),mk_all(x_name(n+1)^"'",mk_imp(
   154 	 		proj (Bound 2) eqs n $ Bound 1 $ Bound 0,
   155          		foldr1 mk_disj (mk_conj(Bound 1 === UU,Bound 0 === UU)
   156 					::map one_con cons))));
   157     in foldr1 mk_conj (mapn one_comp 0 eqs)end ));
   158   fun add_one (thy,(dnam,axs,dfs)) = thy
   159 	|> Sign.add_path dnam
   160 	|> add_defs_infer dfs
   161 	|> add_axioms_infer axs
   162 	|> Sign.parent_path;
   163   val thy = Library.foldl add_one (thy', mapn (calc_axioms comp_dname eqs) 0 eqs);
   164 in thy |> Sign.add_path comp_dnam  
   165        |> add_defs_infer (bisim_def::(if length eqs>1 then [copy_def] else []))
   166        |> Sign.parent_path
   167 end;
   168 
   169 end; (* local *)
   170 end; (* struct *)