1 theory Test

     2 imports "Nominal2_Atoms" "Nominal2_Eqvt" "Nominal2_Supp"

     3 begin

     4 

     5 atom_decl name

     6 

     7 

     8 section{* Interface for nominal_datatype *}

     9 

    10 text {*

    11 

    12 Nominal-Datatype-part:

    13 

    14 1st Arg: string list  

    15          ^^^^^^^^^^^

    16          strings of the types to be defined

    17 

    18 2nd Arg: (string list * binding * mixfix * (binding * typ list * mixfix) list) list

    19          ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^   ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

    20                type(s) to be defined             constructors list

    21                (ty args, name, syn)              (name, typs, syn)

    22 

    23 Binder-Function-part:

    24 

    25 3rd Arg: (binding * typ option * mixfix) list 

    26          ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^    

    27             binding function(s)           

    28               to be defined               

    29             (name, type, syn)             

    30 

    31 4th Arg:  term list 

    32           ^^^^^^^^^

    33           the equations of the binding functions

    34           (Trueprop equations)

    35 *}

    36 

    37 text {*****************************************************}

    38 ML {* 

    39 (* nominal datatype parser *)

    40 local

    41   structure P = OuterParse

    42 in

    43 

    44 val _ = OuterKeyword.keyword "bind"

    45 val anno_typ = Scan.option (P.name --| P.$$$ "::") -- P.typ

    46 

    47 (* binding specification *)

    48 (* should use and_list *)

    49 val bind_parser = 

    50   P.enum "," ((P.$$$ "bind" |-- P.term) -- (P.$$$ "in" |-- P.name))

    51 

    52 val constr_parser =

    53   P.binding -- Scan.repeat anno_typ

    54 

    55 (* datatype parser *)

    56 val dt_parser =

    57   ((P.type_args -- P.binding -- P.opt_infix) >> P.triple1) -- 

    58     (P.$$$ "=" |-- P.enum1 "|" ((constr_parser -- bind_parser -- P.opt_mixfix) >> P.triple_swap))

    59 

    60 (* function equation parser *)

    61 val fun_parser = 

    62   Scan.optional (P.$$$ "binder" |-- P.fixes -- SpecParse.where_alt_specs) ([],[])

    63 

    64 (* main parser *)

    65 val main_parser =

    66   (P.and_list1 dt_parser) -- fun_parser

    67 

    68 end

    69 *}

    70 

    71 (* adds "_raw" to the end of constants and types *)

    72 ML {*

    73 fun add_raw s = s ^ "_raw"

    74 fun add_raws ss = map add_raw ss

    75 fun raw_bind bn = Binding.suffix_name "_raw" bn

    76 

    77 fun replace_str ss s = 

    78   case (AList.lookup (op=) ss s) of 

    79      SOME s' => s'

    80    | NONE => s

    81 

    82 fun replace_typ ty_ss (Type (a, Ts)) = Type (replace_str ty_ss a, map (replace_typ ty_ss) Ts)

    83   | replace_typ ty_ss T = T  

    84 

    85 fun raw_dts ty_ss dts =

    86 let

    87   val ty_ss' = ty_ss ~~ (add_raws ty_ss)

    88 

    89   fun raw_dts_aux1 (bind, tys, mx) =

    90     (raw_bind bind, map (replace_typ ty_ss') tys, mx)

    91 

    92   fun raw_dts_aux2 (ty_args, bind, mx, constrs) =

    93     (ty_args, raw_bind bind, mx, map raw_dts_aux1 constrs)

    94 in

    95   map raw_dts_aux2 dts

    96 end

    97 

    98 fun replace_aterm trm_ss (Const (a, T)) = Const (replace_str trm_ss a, T)

    99   | replace_aterm trm_ss (Free (a, T)) = Free (replace_str trm_ss a, T)

   100   | replace_aterm trm_ss trm = trm

   101 

   102 fun replace_term trm_ss ty_ss trm =

   103   trm |> Term.map_aterms (replace_aterm trm_ss) |> map_types (replace_typ ty_ss) 

   104 *}

   105 

   106 ML {*

   107 fun get_constrs dts =

   108   flat (map (fn (_, _, _, constrs) => constrs) dts)

   109 

   110 fun get_typed_constrs dts =

   111   flat (map (fn (_, bn, _, constrs) => 

   112    (map (fn (bn', _, _) => (Binding.name_of bn, Binding.name_of bn')) constrs)) dts)

   113 

   114 fun get_constr_strs dts =

   115   map (fn (bn, _, _) => Binding.name_of bn) (get_constrs dts)

   116 

   117 fun get_bn_fun_strs bn_funs =

   118   map (fn (bn_fun, _, _) => Binding.name_of bn_fun) bn_funs

   119 *}

   120 

   121 ML {*

   122 fun raw_dts_decl dt_names dts lthy =

   123 let

   124   val thy = ProofContext.theory_of lthy

   125   val conf = Datatype.default_config

   126 

   127   val dt_names' = add_raws dt_names

   128   val dt_full_names = map (Sign.full_bname thy) dt_names 

   129   val dts' = raw_dts dt_full_names dts

   130 in

   131   lthy

   132   |> Local_Theory.theory_result (Datatype.add_datatype conf dt_names' dts')

   133 end 

   134 *}

   135 

   136 ML {*

   137 fun raw_bn_fun_decl dt_names dts bn_funs bn_eqs lthy =

   138 let

   139   val thy = ProofContext.theory_of lthy

   140 

   141   val dt_names' = add_raws dt_names

   142   val dt_full_names = map (Sign.full_bname thy) dt_names 

   143   val dt_full_names' = map (Sign.full_bname thy) dt_names' 

   144   

   145   val ctrs_names = map (Sign.full_bname thy) (get_constr_strs dts)

   146   val ctrs_names' = map (fn (x, y) => (Sign.full_bname_path thy (add_raw x) (add_raw y))) 

   147     (get_typed_constrs dts)

   148 

   149   val bn_fun_strs = get_bn_fun_strs bn_funs

   150   val bn_fun_strs' = add_raws bn_fun_strs

   151   

   152   val bn_funs' = map (fn (bn, opt_ty, mx) => 

   153     (raw_bind bn, Option.map (replace_typ (dt_full_names ~~ dt_full_names')) opt_ty, mx)) bn_funs

   154   

   155   val bn_eqs' = map (fn trm => 

   156     (Attrib.empty_binding, 

   157       (replace_term ((ctrs_names ~~ ctrs_names') @ (bn_fun_strs ~~ bn_fun_strs')) (dt_full_names ~~ dt_full_names') trm))) bn_eqs

   158 in

   159   if null bn_eqs 

   160   then (([], []), lthy)

   161   else Primrec.add_primrec bn_funs' bn_eqs' lthy 

   162 end 

   163 *}

   164 

   165 ML {* 

   166 fun nominal_datatype2 dts bn_funs bn_eqs lthy =

   167 let

   168   val dts_names = map (fn (_, s, _, _) => Binding.name_of s) dts

   169 in

   170   lthy

   171   |> raw_dts_decl dts_names dts

   172   ||>> raw_bn_fun_decl dts_names dts bn_funs bn_eqs

   173 end

   174 *}

   175 

   176 ML {*

   177 (* makes a full named type out of a binding with tvars applied to it *)

   178 fun mk_type thy bind tvrs =

   179   Type (Sign.full_name thy bind, map (fn s => TVar ((s, 0), [])) tvrs)

   180 

   181 fun get_constrs2 thy dts =

   182 let

   183   val dts' = map (fn (tvrs, tname, _, constrs) => (mk_type thy tname tvrs, constrs)) dts

   184 in

   185   flat (map (fn (ty, constrs) => map (fn (bn, tys, mx) =>  (bn, tys ---> ty, mx)) constrs) dts')

   186 end

   187 *}

   188 

   189 ML {*

   190 fun nominal_datatype2_cmd (dt_strs, (bn_fun_strs, bn_eq_strs)) lthy =

   191 let

   192   val thy = ProofContext.theory_of lthy

   193 

   194   fun prep_typ ((tvs, tname, mx), _) = (tname, length tvs, mx);

   195 

   196   (* adding the types for parsing datatypes *)

   197   val lthy_tmp = lthy

   198     |> Local_Theory.theory (Sign.add_types (map prep_typ dt_strs))

   199 

   200   fun prep_cnstr lthy (((cname, atys), mx), binders) =

   201     (cname, map (Syntax.read_typ lthy o snd) atys, mx)

   202   

   203   fun prep_dt lthy ((tvs, tname, mx), cnstrs) = 

   204     (tvs, tname, mx, map (prep_cnstr lthy) cnstrs)

   205 

   206   (* parsing the datatypes *)

   207   val dts_prep = map (prep_dt lthy_tmp) dt_strs

   208 

   209   (* adding constructors for parsing functions *)

   210   val lthy_tmp2 = lthy_tmp

   211     |> Local_Theory.theory (Sign.add_consts_i (get_constrs2 thy dts_prep))

   212 

   213   val (bn_fun_aux, bn_eq_aux) = fst (Specification.read_spec bn_fun_strs bn_eq_strs lthy_tmp2)

   214 

   215   fun prep_bn_fun ((bn, T), mx) = (bn, SOME T, mx) 

   216 

   217   fun prep_bn_eq (attr, t) = t

   218 

   219   val bn_fun_prep = map prep_bn_fun bn_fun_aux

   220   val bn_eq_prep = map prep_bn_eq bn_eq_aux 

   221 in

   222   nominal_datatype2 dts_prep bn_fun_prep bn_eq_prep lthy |> snd

   223 end

   224 *}

   225 

   226 (* Command Keyword *)

   227 ML {*

   228 let

   229    val kind = OuterKeyword.thy_decl

   230 in

   231    OuterSyntax.local_theory "nominal_datatype" "test" kind 

   232      (main_parser >> nominal_datatype2_cmd)

   233 end

   234 *}

   235 

   236 text {* example 1 *}

   237 

   238 nominal_datatype lam =

   239   VAR "name"

   240 | APP "lam" "lam"

   241 | LET bp::"bp" t::"lam"   bind "bi bp" in t ("Let _ in _" [100,100] 100)

   242 and bp = 

   243   BP "name" "lam"  ("_ ::= _" [100,100] 100)

   244 binder

   245   bi::"bp \<Rightarrow> name set"

   246 where

   247   "bi (BP x t) = {x}"

   248 

   249 typ lam_raw

   250 term VAR_raw

   251 term Test.BP_raw

   252 thm bi_raw.simps

   253 

   254 print_theorems

   255 

   256 text {* examples 2 *}

   257 nominal_datatype trm =

   258   Var "name"

   259 | App "trm" "trm"

   260 | Lam x::"name" t::"trm"        bind x in t 

   261 | Let p::"pat" "trm" t::"trm"   bind "f p" in t

   262 and pat =

   263   PN

   264 | PS "name"

   265 | PD "name" "name"

   266 binder

   267   f::"pat \<Rightarrow> name set"

   268 where 

   269   "f PN = {}"

   270 | "f (PS x) = {x}"

   271 | "f (PD x y) = {x,y}"

   272 

   273 thm f_raw.simps

   274 

   275 nominal_datatype trm0 =

   276   Var0 "name"

   277 | App0 "trm0" "trm0"

   278 | Lam0 x::"name" t::"trm0"          bind x in t 

   279 | Let0 p::"pat0" "trm0" t::"trm0"   bind "f0 p" in t

   280 and pat0 =

   281   PN0

   282 | PS0 "name"

   283 | PD0 "pat0" "pat0"

   284 binder

   285   f0::"pat0 \<Rightarrow> name set"

   286 where 

   287   "f0 PN0 = {}"

   288 | "f0 (PS0 x) = {x}"

   289 | "f0 (PD0 p1 p2) = (f0 p1) \<union> (f0 p2)"

   290 

   291 thm f0_raw.simps

   292 

   293 text {* example type schemes *}

   294 datatype ty = 

   295   Var "name" 

   296 | Fun "ty" "ty"

   297 

   298 nominal_datatype tyS = 

   299   All xs::"name list" ty::"ty" bind xs in ty

   300 

   301 

   302 

   303 (* example 1 from Terms.thy *)

   304 

   305 nominal_datatype trm1 =

   306   Vr1 "name"

   307 | Ap1 "trm1" "trm1"

   308 | Lm1 x::"name" t::"trm1"      bind x in t 

   309 | Lt1 p::"bp1" "trm1" t::"trm1" bind "bv1 p" in t 

   310 and bp1 =

   311   BUnit1

   312 | BV1 "name"

   313 | BP1 "bp1" "bp1"

   314 binder

   315   bv1

   316 where

   317   "bv1 (BUnit1) = {}"

   318 | "bv1 (BV1 x) = {atom x}"

   319 | "bv1 (BP1 bp1 bp2) = (bv1 bp1) \<union> (bv1 bp2)"

   320 

   321 thm bv1_raw.simps

   322 

   323 (* example 2 from Terms.thy *)

   324 

   325 nominal_datatype trm2 =

   326   Vr2 "name"

   327 | Ap2 "trm2" "trm2"

   328 | Lm2 x::"name" t::"trm2"       bind x in t

   329 | Lt2 r::"rassign" t::"trm2"    bind "bv2 r" in t

   330 and rassign = 

   331   As "name" "trm2"

   332 binder

   333   bv2

   334 where

   335   "bv2 (As x t) = {atom x}"

   336 

   337 (* example 3 from Terms.thy *)

   338 

   339 nominal_datatype trm3 =

   340   Vr3 "name"

   341 | Ap3 "trm3" "trm3"

   342 | Lm3 x::"name" t::"trm3"        bind x in t

   343 | Lt3 r::"rassigns3" t::"trm3"   bind "bv3 r" in t

   344 and rassigns3 =

   345   ANil

   346 | ACons "name" "trm3" "rassigns3"

   347 binder

   348   bv3

   349 where

   350   "bv3 ANil = {}"

   351 | "bv3 (ACons x t as) = {atom x} \<union> (bv3 as)"

   352 

   353 (* example 4 from Terms.thy *)

   354 

   355 nominal_datatype trm4 =

   356   Vr4 "name"

   357 | Ap4 "trm4" "trm4 list"

   358 | Lm4 x::"name" t::"trm4"  bind x in t

   359 

   360 (* example 5 from Terms.thy *)

   361 

   362 nominal_datatype trm5 =

   363   Vr5 "name"

   364 | Ap5 "trm5" "trm5"

   365 | Lt5 l::"lts" t::"trm5"  bind "bv5 l" in t

   366 and lts =

   367   Lnil

   368 | Lcons "name" "trm5" "lts"

   369 binder

   370   bv5

   371 where

   372   "bv5 Lnil = {}"

   373 | "bv5 (Lcons n t ltl) = {atom n} \<union> (bv5 ltl)"

   374 

   375 (* example 6 from Terms.thy *)

   376 

   377 nominal_datatype trm6 =

   378   Vr6 "name"

   379 | Lm6 x::"name" t::"trm6"         bind x in t

   380 | Lt6 left::"trm6" right::"trm6"  bind "bv6 left" in right

   381 binder

   382   bv6

   383 where

   384   "bv6 (Vr6 n) = {}"

   385 | "bv6 (Lm6 n t) = {atom n} \<union> bv6 t"

   386 | "bv6 (Lt6 l r) = bv6 l \<union> bv6 r"

   387 

   388 (* example 7 from Terms.thy *)

   389 

   390 nominal_datatype trm7 =

   391   Vr7 "name"

   392 | Lm7 l::"name" r::"trm7"   bind l in r

   393 | Lt7 l::"trm7" r::"trm7"   bind "bv7 l" in r

   394 binder 

   395   bv7 

   396 where

   397   "bv7 (Vr7 n) = {atom n}"

   398 | "bv7 (Lm7 n t) = bv7 t - {atom n}"

   399 | "bv7 (Lt7 l r) = bv7 l \<union> bv7 r"

   400 

   401 (* example 8 from Terms.thy *)

   402 

   403 nominal_datatype foo8 =

   404   Foo0 "name"

   405 | Foo1 b::"bar8" f::"foo8" bind "bv8 b" in foo

   406 and bar8 =

   407   Bar0 "name"

   408 | Bar1 "name" s::"name" b::"bar8" bind s in b

   409 binder 

   410   bv8

   411 where

   412   "bv8 (Bar0 x) = {}"

   413 | "bv8 (Bar1 v x b) = {atom v}"

   414 

   415 (* example 9 from Terms.thy *)

   416 

   417 nominal_datatype lam9 =

   418   Var9 "name"

   419 | Lam9 n::"name" l::"lam9" bind n in l

   420 and bla9 =

   421   Bla9 f::"lam9" s::"lam9" bind "bv9 f" in s

   422 binder

   423   bv9

   424 where

   425   "bv9 (Var9 x) = {}"

   426 | "bv9 (Lam9 x b) = {atom x}"

   427 

   428 end

   429 

   430 

   431