author | blanchet |
Thu, 18 Sep 2014 16:47:40 +0200 | |
changeset 58377 | c6f93b8d2d8e |
parent 58353 | c9f374b64d99 |
child 58446 | e89f57d1e46c |
permissions | -rw-r--r-- |
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(* Title: HOL/Tools/BNF/bnf_lfp_basic_sugar.ML |
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Author: Jasmin Blanchette, TU Muenchen |
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Copyright 2014 |
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Registration of basic types as BNF least fixpoints (datatypes). |
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*) |
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structure BNF_LFP_Basic_Sugar : sig end = |
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struct |
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open Ctr_Sugar |
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open BNF_Util |
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open BNF_Def |
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open BNF_Comp |
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open BNF_FP_Rec_Sugar_Util |
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open BNF_FP_Util |
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open BNF_FP_Def_Sugar |
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fun trivial_absT_info_of fpT = |
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{absT = fpT, |
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repT = fpT, |
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abs = Const (@{const_name id_bnf}, fpT --> fpT), |
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rep = Const (@{const_name id_bnf}, fpT --> fpT), |
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abs_inject = @{thm type_definition.Abs_inject[OF type_definition_id_bnf_UNIV UNIV_I UNIV_I]}, |
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abs_inverse = @{thm type_definition.Abs_inverse[OF type_definition_id_bnf_UNIV UNIV_I]}, |
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type_definition = @{thm type_definition_id_bnf_UNIV}}; |
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fun the_frozen_ctr_sugar_of ctxt fpT_name = |
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the (ctr_sugar_of ctxt fpT_name) |
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|> morph_ctr_sugar (Morphism.typ_morphism "BNF" Logic.unvarifyT_global |
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$> Morphism.term_morphism "BNF" (Term.map_types Logic.unvarifyT_global)); |
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fun trivial_fp_result_of fp_bnf fpT C xtor_map xtor_sets xtor_rel ctor_rec_o_map xtor_rel_induct = |
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{Ts = [fpT], |
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bnfs = [fp_bnf], |
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ctors = [Const (@{const_name xtor}, fpT --> fpT)], |
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dtors = [Const (@{const_name xtor}, fpT --> fpT)], |
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xtor_co_recs = [Const (@{const_name ctor_rec}, (fpT --> C) --> (fpT --> C))], |
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xtor_co_induct = @{thm xtor_induct}, |
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dtor_ctors = @{thms xtor_xtor}, |
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ctor_dtors = @{thms xtor_xtor}, |
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ctor_injects = @{thms xtor_inject}, |
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dtor_injects = @{thms xtor_inject}, |
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xtor_map_thms = [xtor_map], |
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xtor_set_thmss = [xtor_sets], |
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xtor_rel_thms = [xtor_rel], |
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xtor_co_rec_thms = [map_id0_of_bnf fp_bnf RS @{thm ctor_rec}], |
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xtor_co_rec_o_map_thms = [ctor_rec_o_map], |
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rel_xtor_co_induct_thm = xtor_rel_induct, |
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dtor_set_induct_thms = []}; |
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fun fp_sugar_of_sum ctxt = |
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let |
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val fpT as Type (fpT_name, As) = @{typ "'a + 'b"}; |
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val fpBT = @{typ "'c + 'd"}; |
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val C = @{typ 'e}; |
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val X = @{typ 'sum}; |
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val ctr_Tss = map single As; |
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val fp_bnf = the (bnf_of ctxt fpT_name); |
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val xtor_map = @{thm xtor_map[of "map_sum f1 f2" for f1 f2]}; |
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val xtor_sets = @{thms xtor_set[of setl] xtor_set[of setr]}; |
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val xtor_rel = @{thm xtor_rel[of "rel_sum R1 R2" for R1 R2]}; |
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val ctor_rec_o_map = @{thm ctor_rec_o_map[of _ "map_sum g1 g2" for g1 g2]}; |
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val xtor_rel_induct = @{thm xtor_rel_induct[of "rel_sum R1 R2" for R1 R2]}; |
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in |
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{T = fpT, |
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BT = fpBT, |
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X = X, |
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fp = Least_FP, |
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fp_res_index = 0, |
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fp_res = |
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trivial_fp_result_of fp_bnf fpT C xtor_map xtor_sets xtor_rel ctor_rec_o_map xtor_rel_induct, |
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pre_bnf = ID_bnf (*wrong*), |
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absT_info = trivial_absT_info_of fpT, |
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fp_nesting_bnfs = [], |
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live_nesting_bnfs = [], |
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ctrXs_Tss = ctr_Tss, |
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ctr_defs = @{thms Inl_def_alt Inr_def_alt}, |
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ctr_sugar = the_frozen_ctr_sugar_of ctxt fpT_name, |
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co_rec = Const (@{const_name case_sum}, map (fn Ts => (Ts ---> C)) ctr_Tss ---> fpT --> C), |
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co_rec_def = @{thm ctor_rec_def_alt[of "case_sum f1 f2" for f1 f2]}, |
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maps = @{thms map_sum.simps}, |
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common_co_inducts = @{thms sum.induct}, |
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co_inducts = @{thms sum.induct}, |
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co_rec_thms = @{thms sum.case}, |
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co_rec_discs = [], |
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co_rec_selss = [], |
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rel_injects = @{thms rel_sum_simps(1,4)}, |
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rel_distincts = @{thms rel_sum_simps(2,3)[THEN eq_False[THEN iffD1]]}} |
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end; |
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fun fp_sugar_of_prod ctxt = |
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let |
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val fpT as Type (fpT_name, As) = @{typ "'a * 'b"}; |
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val fpBT = @{typ "'c * 'd"}; |
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val C = @{typ 'e}; |
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val X = @{typ 'prod}; |
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val ctr_Ts = As; |
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val fp_bnf = the (bnf_of ctxt fpT_name); |
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val xtor_map = @{thm xtor_map[of "map_prod f1 f2" for f1 f2]}; |
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val xtor_sets = @{thms xtor_set[of fsts] xtor_set[of snds]}; |
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val xtor_rel = @{thm xtor_rel[of "rel_prod R1 R2" for R1 R2]}; |
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val ctor_rec_o_map = @{thm ctor_rec_o_map[of _ "map_prod g1 g2" for g1 g2]}; |
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val xtor_rel_induct = @{thm xtor_rel_induct[of "rel_prod R1 R2" for R1 R2]}; |
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in |
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{T = fpT, |
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BT = fpBT, |
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X = X, |
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fp = Least_FP, |
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fp_res_index = 0, |
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fp_res = |
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trivial_fp_result_of fp_bnf fpT C xtor_map xtor_sets xtor_rel ctor_rec_o_map xtor_rel_induct, |
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115 |
pre_bnf = ID_bnf (*wrong*), |
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116 |
absT_info = trivial_absT_info_of fpT, |
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117 |
fp_nesting_bnfs = [], |
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118 |
live_nesting_bnfs = [], |
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119 |
ctrXs_Tss = [ctr_Ts], |
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120 |
ctr_defs = @{thms Pair_def_alt}, |
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121 |
ctr_sugar = the_frozen_ctr_sugar_of ctxt fpT_name, |
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122 |
co_rec = Const (@{const_name case_prod}, (ctr_Ts ---> C) --> fpT --> C), |
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123 |
co_rec_def = @{thm ctor_rec_def_alt[of "case_prod f" for f]}, |
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124 |
maps = @{thms map_prod_simp}, |
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125 |
common_co_inducts = @{thms prod.induct}, |
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126 |
co_inducts = @{thms prod.induct}, |
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127 |
co_rec_thms = @{thms prod.case}, |
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128 |
co_rec_discs = [], |
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129 |
co_rec_selss = [], |
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130 |
rel_injects = @{thms rel_prod_apply}, |
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131 |
rel_distincts = []} |
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132 |
end; |
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133 |
|
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134 |
val _ = Theory.setup (map_local_theory (fn lthy => |
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135 |
fold (BNF_FP_Def_Sugar.register_fp_sugars (K true) o single o (fn f => f lthy)) |
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136 |
[fp_sugar_of_sum, fp_sugar_of_prod] lthy)); |
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137 |
|
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138 |
end; |