diff -r 4b0563bc4b03 -r 7d8949da7d99 Nominal/Test.thy --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/Nominal/Test.thy Thu Feb 25 07:48:33 2010 +0100 @@ -0,0 +1,431 @@ +theory Test +imports "Nominal2_Atoms" "Nominal2_Eqvt" "Nominal2_Supp" +begin + +atom_decl name + + +section{* Interface for nominal_datatype *} + +text {* + +Nominal-Datatype-part: + +1st Arg: string list + ^^^^^^^^^^^ + strings of the types to be defined + +2nd Arg: (string list * binding * mixfix * (binding * typ list * mixfix) list) list + ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + type(s) to be defined constructors list + (ty args, name, syn) (name, typs, syn) + +Binder-Function-part: + +3rd Arg: (binding * typ option * mixfix) list + ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + binding function(s) + to be defined + (name, type, syn) + +4th Arg: term list + ^^^^^^^^^ + the equations of the binding functions + (Trueprop equations) +*} + +text {*****************************************************} +ML {* +(* nominal datatype parser *) +local + structure P = OuterParse +in + +val _ = OuterKeyword.keyword "bind" +val anno_typ = Scan.option (P.name --| P.$$$ "::") -- P.typ + +(* binding specification *) +(* should use and_list *) +val bind_parser = + P.enum "," ((P.$$$ "bind" |-- P.term) -- (P.$$$ "in" |-- P.name)) + +val constr_parser = + P.binding -- Scan.repeat anno_typ + +(* datatype parser *) +val dt_parser = + ((P.type_args -- P.binding -- P.opt_infix) >> P.triple1) -- + (P.$$$ "=" |-- P.enum1 "|" ((constr_parser -- bind_parser -- P.opt_mixfix) >> P.triple_swap)) + +(* function equation parser *) +val fun_parser = + Scan.optional (P.$$$ "binder" |-- P.fixes -- SpecParse.where_alt_specs) ([],[]) + +(* main parser *) +val main_parser = + (P.and_list1 dt_parser) -- fun_parser + +end +*} + +(* adds "_raw" to the end of constants and types *) +ML {* +fun add_raw s = s ^ "_raw" +fun add_raws ss = map add_raw ss +fun raw_bind bn = Binding.suffix_name "_raw" bn + +fun replace_str ss s = + case (AList.lookup (op=) ss s) of + SOME s' => s' + | NONE => s + +fun replace_typ ty_ss (Type (a, Ts)) = Type (replace_str ty_ss a, map (replace_typ ty_ss) Ts) + | replace_typ ty_ss T = T + +fun raw_dts ty_ss dts = +let + val ty_ss' = ty_ss ~~ (add_raws ty_ss) + + fun raw_dts_aux1 (bind, tys, mx) = + (raw_bind bind, map (replace_typ ty_ss') tys, mx) + + fun raw_dts_aux2 (ty_args, bind, mx, constrs) = + (ty_args, raw_bind bind, mx, map raw_dts_aux1 constrs) +in + map raw_dts_aux2 dts +end + +fun replace_aterm trm_ss (Const (a, T)) = Const (replace_str trm_ss a, T) + | replace_aterm trm_ss (Free (a, T)) = Free (replace_str trm_ss a, T) + | replace_aterm trm_ss trm = trm + +fun replace_term trm_ss ty_ss trm = + trm |> Term.map_aterms (replace_aterm trm_ss) |> map_types (replace_typ ty_ss) +*} + +ML {* +fun get_constrs dts = + flat (map (fn (_, _, _, constrs) => constrs) dts) + +fun get_typed_constrs dts = + flat (map (fn (_, bn, _, constrs) => + (map (fn (bn', _, _) => (Binding.name_of bn, Binding.name_of bn')) constrs)) dts) + +fun get_constr_strs dts = + map (fn (bn, _, _) => Binding.name_of bn) (get_constrs dts) + +fun get_bn_fun_strs bn_funs = + map (fn (bn_fun, _, _) => Binding.name_of bn_fun) bn_funs +*} + +ML {* +fun raw_dts_decl dt_names dts lthy = +let + val thy = ProofContext.theory_of lthy + val conf = Datatype.default_config + + val dt_names' = add_raws dt_names + val dt_full_names = map (Sign.full_bname thy) dt_names + val dts' = raw_dts dt_full_names dts +in + lthy + |> Local_Theory.theory_result (Datatype.add_datatype conf dt_names' dts') +end +*} + +ML {* +fun raw_bn_fun_decl dt_names dts bn_funs bn_eqs lthy = +let + val thy = ProofContext.theory_of lthy + + val dt_names' = add_raws dt_names + val dt_full_names = map (Sign.full_bname thy) dt_names + val dt_full_names' = map (Sign.full_bname thy) dt_names' + + val ctrs_names = map (Sign.full_bname thy) (get_constr_strs dts) + val ctrs_names' = map (fn (x, y) => (Sign.full_bname_path thy (add_raw x) (add_raw y))) + (get_typed_constrs dts) + + val bn_fun_strs = get_bn_fun_strs bn_funs + val bn_fun_strs' = add_raws bn_fun_strs + + val bn_funs' = map (fn (bn, opt_ty, mx) => + (raw_bind bn, Option.map (replace_typ (dt_full_names ~~ dt_full_names')) opt_ty, mx)) bn_funs + + val bn_eqs' = map (fn trm => + (Attrib.empty_binding, + (replace_term ((ctrs_names ~~ ctrs_names') @ (bn_fun_strs ~~ bn_fun_strs')) (dt_full_names ~~ dt_full_names') trm))) bn_eqs +in + if null bn_eqs + then (([], []), lthy) + else Primrec.add_primrec bn_funs' bn_eqs' lthy +end +*} + +ML {* +fun nominal_datatype2 dts bn_funs bn_eqs lthy = +let + val dts_names = map (fn (_, s, _, _) => Binding.name_of s) dts +in + lthy + |> raw_dts_decl dts_names dts + ||>> raw_bn_fun_decl dts_names dts bn_funs bn_eqs +end +*} + +ML {* +(* makes a full named type out of a binding with tvars applied to it *) +fun mk_type thy bind tvrs = + Type (Sign.full_name thy bind, map (fn s => TVar ((s, 0), [])) tvrs) + +fun get_constrs2 thy dts = +let + val dts' = map (fn (tvrs, tname, _, constrs) => (mk_type thy tname tvrs, constrs)) dts +in + flat (map (fn (ty, constrs) => map (fn (bn, tys, mx) => (bn, tys ---> ty, mx)) constrs) dts') +end +*} + +ML {* +fun nominal_datatype2_cmd (dt_strs, (bn_fun_strs, bn_eq_strs)) lthy = +let + val thy = ProofContext.theory_of lthy + + fun prep_typ ((tvs, tname, mx), _) = (tname, length tvs, mx); + + (* adding the types for parsing datatypes *) + val lthy_tmp = lthy + |> Local_Theory.theory (Sign.add_types (map prep_typ dt_strs)) + + fun prep_cnstr lthy (((cname, atys), mx), binders) = + (cname, map (Syntax.read_typ lthy o snd) atys, mx) + + fun prep_dt lthy ((tvs, tname, mx), cnstrs) = + (tvs, tname, mx, map (prep_cnstr lthy) cnstrs) + + (* parsing the datatypes *) + val dts_prep = map (prep_dt lthy_tmp) dt_strs + + (* adding constructors for parsing functions *) + val lthy_tmp2 = lthy_tmp + |> Local_Theory.theory (Sign.add_consts_i (get_constrs2 thy dts_prep)) + + val (bn_fun_aux, bn_eq_aux) = fst (Specification.read_spec bn_fun_strs bn_eq_strs lthy_tmp2) + + fun prep_bn_fun ((bn, T), mx) = (bn, SOME T, mx) + + fun prep_bn_eq (attr, t) = t + + val bn_fun_prep = map prep_bn_fun bn_fun_aux + val bn_eq_prep = map prep_bn_eq bn_eq_aux +in + nominal_datatype2 dts_prep bn_fun_prep bn_eq_prep lthy |> snd +end +*} + +(* Command Keyword *) +ML {* +let + val kind = OuterKeyword.thy_decl +in + OuterSyntax.local_theory "nominal_datatype" "test" kind + (main_parser >> nominal_datatype2_cmd) +end +*} + +text {* example 1 *} + +nominal_datatype lam = + VAR "name" +| APP "lam" "lam" +| LET bp::"bp" t::"lam" bind "bi bp" in t ("Let _ in _" [100,100] 100) +and bp = + BP "name" "lam" ("_ ::= _" [100,100] 100) +binder + bi::"bp \ name set" +where + "bi (BP x t) = {x}" + +typ lam_raw +term VAR_raw +term Test.BP_raw +thm bi_raw.simps + +print_theorems + +text {* examples 2 *} +nominal_datatype trm = + Var "name" +| App "trm" "trm" +| Lam x::"name" t::"trm" bind x in t +| Let p::"pat" "trm" t::"trm" bind "f p" in t +and pat = + PN +| PS "name" +| PD "name" "name" +binder + f::"pat \ name set" +where + "f PN = {}" +| "f (PS x) = {x}" +| "f (PD x y) = {x,y}" + +thm f_raw.simps + +nominal_datatype trm0 = + Var0 "name" +| App0 "trm0" "trm0" +| Lam0 x::"name" t::"trm0" bind x in t +| Let0 p::"pat0" "trm0" t::"trm0" bind "f0 p" in t +and pat0 = + PN0 +| PS0 "name" +| PD0 "pat0" "pat0" +binder + f0::"pat0 \ name set" +where + "f0 PN0 = {}" +| "f0 (PS0 x) = {x}" +| "f0 (PD0 p1 p2) = (f0 p1) \ (f0 p2)" + +thm f0_raw.simps + +text {* example type schemes *} +datatype ty = + Var "name" +| Fun "ty" "ty" + +nominal_datatype tyS = + All xs::"name list" ty::"ty" bind xs in ty + + + +(* example 1 from Terms.thy *) + +nominal_datatype trm1 = + Vr1 "name" +| Ap1 "trm1" "trm1" +| Lm1 x::"name" t::"trm1" bind x in t +| Lt1 p::"bp1" "trm1" t::"trm1" bind "bv1 p" in t +and bp1 = + BUnit1 +| BV1 "name" +| BP1 "bp1" "bp1" +binder + bv1 +where + "bv1 (BUnit1) = {}" +| "bv1 (BV1 x) = {atom x}" +| "bv1 (BP1 bp1 bp2) = (bv1 bp1) \ (bv1 bp2)" + +thm bv1_raw.simps + +(* example 2 from Terms.thy *) + +nominal_datatype trm2 = + Vr2 "name" +| Ap2 "trm2" "trm2" +| Lm2 x::"name" t::"trm2" bind x in t +| Lt2 r::"rassign" t::"trm2" bind "bv2 r" in t +and rassign = + As "name" "trm2" +binder + bv2 +where + "bv2 (As x t) = {atom x}" + +(* example 3 from Terms.thy *) + +nominal_datatype trm3 = + Vr3 "name" +| Ap3 "trm3" "trm3" +| Lm3 x::"name" t::"trm3" bind x in t +| Lt3 r::"rassigns3" t::"trm3" bind "bv3 r" in t +and rassigns3 = + ANil +| ACons "name" "trm3" "rassigns3" +binder + bv3 +where + "bv3 ANil = {}" +| "bv3 (ACons x t as) = {atom x} \ (bv3 as)" + +(* example 4 from Terms.thy *) + +nominal_datatype trm4 = + Vr4 "name" +| Ap4 "trm4" "trm4 list" +| Lm4 x::"name" t::"trm4" bind x in t + +(* example 5 from Terms.thy *) + +nominal_datatype trm5 = + Vr5 "name" +| Ap5 "trm5" "trm5" +| Lt5 l::"lts" t::"trm5" bind "bv5 l" in t +and lts = + Lnil +| Lcons "name" "trm5" "lts" +binder + bv5 +where + "bv5 Lnil = {}" +| "bv5 (Lcons n t ltl) = {atom n} \ (bv5 ltl)" + +(* example 6 from Terms.thy *) + +nominal_datatype trm6 = + Vr6 "name" +| Lm6 x::"name" t::"trm6" bind x in t +| Lt6 left::"trm6" right::"trm6" bind "bv6 left" in right +binder + bv6 +where + "bv6 (Vr6 n) = {}" +| "bv6 (Lm6 n t) = {atom n} \ bv6 t" +| "bv6 (Lt6 l r) = bv6 l \ bv6 r" + +(* example 7 from Terms.thy *) + +nominal_datatype trm7 = + Vr7 "name" +| Lm7 l::"name" r::"trm7" bind l in r +| Lt7 l::"trm7" r::"trm7" bind "bv7 l" in r +binder + bv7 +where + "bv7 (Vr7 n) = {atom n}" +| "bv7 (Lm7 n t) = bv7 t - {atom n}" +| "bv7 (Lt7 l r) = bv7 l \ bv7 r" + +(* example 8 from Terms.thy *) + +nominal_datatype foo8 = + Foo0 "name" +| Foo1 b::"bar8" f::"foo8" bind "bv8 b" in foo +and bar8 = + Bar0 "name" +| Bar1 "name" s::"name" b::"bar8" bind s in b +binder + bv8 +where + "bv8 (Bar0 x) = {}" +| "bv8 (Bar1 v x b) = {atom v}" + +(* example 9 from Terms.thy *) + +nominal_datatype lam9 = + Var9 "name" +| Lam9 n::"name" l::"lam9" bind n in l +and bla9 = + Bla9 f::"lam9" s::"lam9" bind "bv9 f" in s +binder + bv9 +where + "bv9 (Var9 x) = {}" +| "bv9 (Lam9 x b) = {atom x}" + +end + + +