src/HOLCF/domain/axioms.ML
author wenzelm
Thu Jul 14 19:28:24 2005 +0200 (2005-07-14)
changeset 16842 5979c46853d1
parent 16778 2162c0de4673
child 17811 10ebcd7032c1
permissions -rw-r--r--
tuned;
     1 (*  Title:      HOLCF/domain/axioms.ML
     2     ID:         $Id$
     3     Author:     David von Oheimb
     4 
     5 Syntax generator for domain section.
     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 infer_types thy' = map (inferT_axm (sign_of thy'));
    18 
    19 fun calc_axioms comp_dname (eqs : eq list) n (((dname,_),cons) : eq)=
    20 let
    21 
    22 (* ----- axioms and definitions concerning the isomorphism ------------------ *)
    23 
    24   val dc_abs = %%:(dname^"_abs");
    25   val dc_rep = %%:(dname^"_rep");
    26   val x_name'= "x";
    27   val x_name = idx_name eqs x_name' (n+1);
    28   val dnam = Sign.base_name dname;
    29 
    30  val abs_iso_ax = ("abs_iso" ,mk_trp(dc_rep`(dc_abs`%x_name')=== %:x_name'));
    31  val rep_iso_ax = ("rep_iso" ,mk_trp(dc_abs`(dc_rep`%x_name')=== %:x_name'));
    32 
    33   val when_def = ("when_def",%%:(dname^"_when") == 
    34      foldr (uncurry /\ ) (/\x_name'((when_body cons (fn (x,y) =>
    35 				Bound(1+length cons+x-y)))`(dc_rep`Bound 0))) (when_funs cons));
    36 
    37   fun con_def outer recu m n (_,args) = let
    38      fun idxs z x arg = (if is_lazy arg then fn t => %%:upN`t else I)
    39 			(if recu andalso is_rec arg then (cproj (Bound z) eqs
    40 				  (rec_of arg))`Bound(z-x) else Bound(z-x));
    41      fun parms [] = %%:ONE_N
    42      |   parms vs = foldr'(fn(x,t)=> %%:spairN`x`t)(mapn (idxs(length vs))1 vs);
    43      fun inj y 1 _ = y
    44      |   inj y _ 0 = %%:sinlN`y
    45      |   inj y i j = %%:sinrN`(inj y (i-1) (j-1));
    46   in foldr /\# (outer (inj (parms args) m n)) args end;
    47 
    48   val copy_def = ("copy_def", %%:(dname^"_copy") == /\"f" (dc_abs oo 
    49 	Library.foldl (op `) (%%:(dname^"_when") , 
    50 	              mapn (con_def I true (length cons)) 0 cons)));
    51 
    52 (* -- definitions concerning the constructors, discriminators and selectors - *)
    53 
    54   val con_defs = mapn (fn n => fn (con,args) => (extern_name con ^"_def",  
    55   %%:con == con_def (fn t => dc_abs`t) false (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 		 mk_cRep_CFun(%%:(dname^"_when"),map 
    60 			(fn (con',args) => (foldr /\#
    61 			   (if con'=con then %%:TT_N else %%:FF_N) 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 		 mk_cRep_CFun(%%:(dname^"_when"),map 
    67 			(fn (con',args) => (foldr /\#
    68 			   (if con'=con
    69                                then %%:returnN`(mk_ctuple (map (bound_arg args) args))
    70                                else %%:failN) args)) cons))
    71 	in map mdef cons end;
    72 
    73   val sel_defs = let
    74 	fun sdef con n arg = Option.map (fn sel => (sel^"_def",%%:sel == 
    75 		 mk_cRep_CFun(%%:(dname^"_when"),map 
    76 			(fn (con',args) => if con'<>con then UU else
    77 			 foldr /\# (Bound (length args - n)) args) cons))) (sel_of arg);
    78 	in List.mapPartial I (List.concat(map (fn (con,args) => mapn (sdef con) 1 args) cons)) end;
    79 
    80 
    81 (* ----- axiom and definitions concerning induction ------------------------- *)
    82 
    83   val reach_ax = ("reach", mk_trp(cproj (%%:fixN`%%(comp_dname^"_copy")) eqs n
    84 					`%x_name === %:x_name));
    85   val take_def = ("take_def",%%:(dname^"_take") == mk_lam("n",cproj' 
    86 	     (%%:iterateN $ Bound 0 $ %%:(comp_dname^"_copy") $ UU) eqs n));
    87   val finite_def = ("finite_def",%%:(dname^"_finite") == mk_lam(x_name,
    88 	mk_ex("n",(%%:(dname^"_take") $ Bound 0)`Bound 1 === Bound 1)));
    89 
    90 in (dnam,
    91     [abs_iso_ax, rep_iso_ax, reach_ax],
    92     [when_def, copy_def] @
    93      con_defs @ dis_defs @ mat_defs @ sel_defs @
    94     [take_def, finite_def])
    95 end; (* let *)
    96 
    97 fun add_axioms_i x = #1 o PureThy.add_axioms_i (map Thm.no_attributes x);
    98 fun add_axioms_infer axms thy = add_axioms_i (infer_types thy axms) thy;
    99 
   100 in (* local *)
   101 
   102 fun add_axioms (comp_dnam, eqs : eq list) thy' = let
   103   val comp_dname = Sign.full_name (sign_of thy') comp_dnam;
   104   val dnames = map (fst o fst) eqs;
   105   val x_name = idx_name dnames "x"; 
   106   fun copy_app dname = %%:(dname^"_copy")`Bound 0;
   107   val copy_def = ("copy_def" , %%:(comp_dname^"_copy") ==
   108 				    /\"f"(foldr' cpair (map copy_app dnames)));
   109   val bisim_def = ("bisim_def",%%:(comp_dname^"_bisim")==mk_lam("R",
   110     let
   111       fun one_con (con,args) = let
   112 	val nonrec_args = filter_out is_rec args;
   113 	val    rec_args = List.filter     is_rec args;
   114 	val    recs_cnt = length rec_args;
   115 	val allargs     = nonrec_args @ rec_args
   116 				      @ map (upd_vname (fn s=> s^"'")) rec_args;
   117 	val allvns      = map vname allargs;
   118 	fun vname_arg s arg = if is_rec arg then vname arg^s else vname arg;
   119 	val vns1        = map (vname_arg "" ) args;
   120 	val vns2        = map (vname_arg "'") args;
   121 	val allargs_cnt = length nonrec_args + 2*recs_cnt;
   122 	val rec_idxs    = (recs_cnt-1) downto 0;
   123 	val nonlazy_idxs = map snd (filter_out (fn (arg,_) => is_lazy arg)
   124 					 (allargs~~((allargs_cnt-1) downto 0)));
   125 	fun rel_app i ra = proj (Bound(allargs_cnt+2)) eqs (rec_of ra) $ 
   126 			   Bound (2*recs_cnt-i) $ Bound (recs_cnt-i);
   127 	val capps = foldr mk_conj (mk_conj(
   128 	   Bound(allargs_cnt+1)===mk_cRep_CFun(%%:con,map (bound_arg allvns) vns1),
   129 	   Bound(allargs_cnt+0)===mk_cRep_CFun(%%:con,map (bound_arg allvns) vns2)))
   130            (mapn rel_app 1 rec_args);
   131         in foldr mk_ex (Library.foldr mk_conj 
   132 			      (map (defined o Bound) nonlazy_idxs,capps)) allvns end;
   133       fun one_comp n (_,cons) =mk_all(x_name(n+1),mk_all(x_name(n+1)^"'",mk_imp(
   134 	 		proj (Bound 2) eqs n $ Bound 1 $ Bound 0,
   135          		foldr' mk_disj (mk_conj(Bound 1 === UU,Bound 0 === UU)
   136 					::map one_con cons))));
   137     in foldr' mk_conj (mapn one_comp 0 eqs)end ));
   138   fun add_one (thy,(dnam,axs,dfs)) = thy
   139 	|> Theory.add_path dnam
   140 	|> add_axioms_infer dfs(*add_defs_i*)
   141 	|> add_axioms_infer axs
   142 	|> Theory.parent_path;
   143   val thy = Library.foldl add_one (thy', mapn (calc_axioms comp_dname eqs) 0 eqs);
   144 in thy |> Theory.add_path comp_dnam  
   145        |> add_axioms_infer (bisim_def::(if length eqs>1 then [copy_def] else []))
   146        |> Theory.parent_path
   147 end;
   148 
   149 end; (* local *)
   150 end; (* struct *)