src/HOLCF/Tools/domain/domain_axioms.ML
author wenzelm
Sun Mar 08 17:26:14 2009 +0100 (2009-03-08)
changeset 30364 577edc39b501
parent 30280 eb98b49ef835
child 30483 0c398040969c
permissions -rw-r--r--
moved basic algebra of long names from structure NameSpace to Long_Name;
     1 (*  Title:      HOLCF/Tools/domain/domain_axioms.ML
     2     Author:     David von Oheimb
     3 
     4 Syntax generator for domain command.
     5 *)
     6 
     7 structure Domain_Axioms = struct
     8 
     9 local
    10 
    11 open Domain_Library;
    12 infixr 0 ===>;infixr 0 ==>;infix 0 == ; 
    13 infix 1 ===; infix 1 ~= ; infix 1 <<; infix 1 ~<<;
    14 infix 9 `   ; infix 9 `% ; infix 9 `%%; infixr 9 oo;
    15 
    16 fun calc_axioms comp_dname (eqs : eq list) n (((dname,_),cons) : eq)=
    17 let
    18 
    19 (* ----- axioms and definitions concerning the isomorphism ------------------ *)
    20 
    21   val dc_abs = %%:(dname^"_abs");
    22   val dc_rep = %%:(dname^"_rep");
    23   val x_name'= "x";
    24   val x_name = idx_name eqs x_name' (n+1);
    25   val dnam = Long_Name.base_name dname;
    26 
    27   val abs_iso_ax = ("abs_iso", mk_trp(dc_rep`(dc_abs`%x_name') === %:x_name'));
    28   val rep_iso_ax = ("rep_iso", mk_trp(dc_abs`(dc_rep`%x_name') === %:x_name'));
    29 
    30   val when_def = ("when_def",%%:(dname^"_when") == 
    31      List.foldr (uncurry /\ ) (/\x_name'((when_body cons (fn (x,y) =>
    32 				Bound(1+length cons+x-y)))`(dc_rep`Bound 0))) (when_funs cons));
    33   
    34   val copy_def = let
    35     fun idxs z x arg = if is_rec arg
    36 			 then (cproj (Bound z) eqs (rec_of arg))`Bound(z-x)
    37 			 else Bound(z-x);
    38     fun one_con (con,args) =
    39         List.foldr /\# (list_ccomb (%%:con, mapn (idxs (length args)) 1 args)) args;
    40   in ("copy_def", %%:(dname^"_copy") ==
    41        /\ "f" (list_ccomb (%%:(dname^"_when"), map one_con cons))) end;
    42 
    43 (* -- definitions concerning the constructors, discriminators and selectors - *)
    44 
    45   fun con_def m n (_,args) = let
    46     fun idxs z x arg = (if is_lazy arg then mk_up else I) (Bound(z-x));
    47     fun parms vs = mk_stuple (mapn (idxs(length vs)) 1 vs);
    48     fun inj y 1 _ = y
    49     |   inj y _ 0 = mk_sinl y
    50     |   inj y i j = mk_sinr (inj y (i-1) (j-1));
    51   in List.foldr /\# (dc_abs`(inj (parms args) m n)) args end;
    52   
    53   val con_defs = mapn (fn n => fn (con,args) =>
    54     (extern_name con ^"_def", %%:con == con_def (length cons) n (con,args))) 0 cons;
    55   
    56   val dis_defs = let
    57 	fun ddef (con,_) = (dis_name con ^"_def",%%:(dis_name con) == 
    58 		 list_ccomb(%%:(dname^"_when"),map 
    59 			(fn (con',args) => (List.foldr /\#
    60 			   (if con'=con then TT else FF) args)) cons))
    61 	in map ddef cons end;
    62 
    63   val mat_defs = let
    64 	fun mdef (con,_) = (mat_name con ^"_def",%%:(mat_name con) == 
    65 		 list_ccomb(%%:(dname^"_when"),map 
    66 			(fn (con',args) => (List.foldr /\#
    67 			   (if con'=con
    68                                then mk_return (mk_ctuple (map (bound_arg args) args))
    69                                else mk_fail) args)) cons))
    70 	in map mdef cons end;
    71 
    72   val pat_defs =
    73     let
    74       fun pdef (con,args) =
    75         let
    76           val ps = mapn (fn n => fn _ => %:("pat" ^ string_of_int n)) 1 args;
    77           val xs = map (bound_arg args) args;
    78           val r = Bound (length args);
    79           val rhs = case args of [] => mk_return HOLogic.unit
    80                                 | _ => mk_ctuple_pat ps ` mk_ctuple xs;
    81           fun one_con (con',args') = List.foldr /\# (if con'=con then rhs else mk_fail) args';
    82         in (pat_name con ^"_def", list_comb (%%:(pat_name con), ps) == 
    83                list_ccomb(%%:(dname^"_when"), map one_con cons))
    84         end
    85     in map pdef cons end;
    86 
    87   val sel_defs = let
    88 	fun sdef con n arg = Option.map (fn sel => (sel^"_def",%%:sel == 
    89 		 list_ccomb(%%:(dname^"_when"),map 
    90 			(fn (con',args) => if con'<>con then UU else
    91 			 List.foldr /\# (Bound (length args - n)) args) cons))) (sel_of arg);
    92 	in List.mapPartial I (List.concat(map (fn (con,args) => mapn (sdef con) 1 args) cons)) end;
    93 
    94 
    95 (* ----- axiom and definitions concerning induction ------------------------- *)
    96 
    97   val reach_ax = ("reach", mk_trp(cproj (mk_fix (%%:(comp_dname^"_copy"))) eqs n
    98 					`%x_name === %:x_name));
    99   val take_def = ("take_def",%%:(dname^"_take") == mk_lam("n",cproj
   100 	     (mk_iterate (Bound 0, %%:(comp_dname^"_copy"), UU)) eqs n));
   101   val finite_def = ("finite_def",%%:(dname^"_finite") == mk_lam(x_name,
   102 	mk_ex("n",(%%:(dname^"_take") $ Bound 0)`Bound 1 === Bound 1)));
   103 
   104 in (dnam,
   105     [abs_iso_ax, rep_iso_ax, reach_ax],
   106     [when_def, copy_def] @
   107      con_defs @ dis_defs @ mat_defs @ pat_defs @ sel_defs @
   108     [take_def, finite_def])
   109 end; (* let (calc_axioms) *)
   110 
   111 fun infer_props thy = map (apsnd (FixrecPackage.legacy_infer_prop thy));
   112 
   113 fun add_axioms_i x = snd o PureThy.add_axioms (map (Thm.no_attributes o apfst Binding.name) x);
   114 fun add_axioms_infer axms thy = add_axioms_i (infer_props thy axms) thy;
   115 
   116 fun add_defs_i x = snd o (PureThy.add_defs false) (map (Thm.no_attributes o apfst Binding.name) x);
   117 fun add_defs_infer defs thy = add_defs_i (infer_props thy defs) thy;
   118 
   119 fun add_matchers (((dname,_),cons) : eq) thy =
   120   let
   121     val con_names = map fst cons;
   122     val mat_names = map mat_name con_names;
   123     fun qualify n = Sign.full_name thy (Binding.name n);
   124     val ms = map qualify con_names ~~ map qualify mat_names;
   125   in FixrecPackage.add_matchers ms thy end;
   126 
   127 in (* local *)
   128 
   129 fun add_axioms (comp_dnam, eqs : eq list) thy' = let
   130   val comp_dname = Sign.full_bname thy' comp_dnam;
   131   val dnames = map (fst o fst) eqs;
   132   val x_name = idx_name dnames "x"; 
   133   fun copy_app dname = %%:(dname^"_copy")`Bound 0;
   134   val copy_def = ("copy_def" , %%:(comp_dname^"_copy") ==
   135 				    /\ "f"(mk_ctuple (map copy_app dnames)));
   136   val bisim_def = ("bisim_def",%%:(comp_dname^"_bisim")==mk_lam("R",
   137     let
   138       fun one_con (con,args) = let
   139 	val nonrec_args = filter_out is_rec args;
   140 	val    rec_args = List.filter     is_rec args;
   141 	val    recs_cnt = length rec_args;
   142 	val allargs     = nonrec_args @ rec_args
   143 				      @ map (upd_vname (fn s=> s^"'")) rec_args;
   144 	val allvns      = map vname allargs;
   145 	fun vname_arg s arg = if is_rec arg then vname arg^s else vname arg;
   146 	val vns1        = map (vname_arg "" ) args;
   147 	val vns2        = map (vname_arg "'") args;
   148 	val allargs_cnt = length nonrec_args + 2*recs_cnt;
   149 	val rec_idxs    = (recs_cnt-1) downto 0;
   150 	val nonlazy_idxs = map snd (filter_out (fn (arg,_) => is_lazy arg)
   151 					 (allargs~~((allargs_cnt-1) downto 0)));
   152 	fun rel_app i ra = proj (Bound(allargs_cnt+2)) eqs (rec_of ra) $ 
   153 			   Bound (2*recs_cnt-i) $ Bound (recs_cnt-i);
   154 	val capps = List.foldr mk_conj (mk_conj(
   155 	   Bound(allargs_cnt+1)===list_ccomb(%%:con,map (bound_arg allvns) vns1),
   156 	   Bound(allargs_cnt+0)===list_ccomb(%%:con,map (bound_arg allvns) vns2)))
   157            (mapn rel_app 1 rec_args);
   158         in List.foldr mk_ex (Library.foldr mk_conj 
   159 			      (map (defined o Bound) nonlazy_idxs,capps)) allvns end;
   160       fun one_comp n (_,cons) =mk_all(x_name(n+1),mk_all(x_name(n+1)^"'",mk_imp(
   161 	 		proj (Bound 2) eqs n $ Bound 1 $ Bound 0,
   162          		foldr1 mk_disj (mk_conj(Bound 1 === UU,Bound 0 === UU)
   163 					::map one_con cons))));
   164     in foldr1 mk_conj (mapn one_comp 0 eqs)end ));
   165   fun add_one (thy,(dnam,axs,dfs)) = thy
   166 	|> Sign.add_path dnam
   167 	|> add_defs_infer dfs
   168 	|> add_axioms_infer axs
   169 	|> Sign.parent_path;
   170   val thy = Library.foldl add_one (thy', mapn (calc_axioms comp_dname eqs) 0 eqs);
   171 in thy |> Sign.add_path comp_dnam  
   172        |> add_defs_infer (bisim_def::(if length eqs>1 then [copy_def] else []))
   173        |> Sign.parent_path
   174        |> fold add_matchers eqs
   175 end; (* let (add_axioms) *)
   176 
   177 end; (* local *)
   178 end; (* struct *)