haftmann@33967
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(* Title: HOL/Tools/Datatype/datatype.ML
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wenzelm@11539
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Author: Stefan Berghofer, TU Muenchen
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berghofe@5177
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haftmann@33967
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Datatype package: definitional introduction of datatypes
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haftmann@33967
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with proof of characteristic theorems: injectivity / distinctness
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haftmann@33967
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of constructors and induction. Main interface to datatypes
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haftmann@33967
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after full bootstrap of datatype package.
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berghofe@5177
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*)
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berghofe@5177
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haftmann@31723
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signature DATATYPE =
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wenzelm@6360
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sig
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haftmann@33962
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include DATATYPE_DATA
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wenzelm@46780
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val distinct_lemma: thm
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wenzelm@46712
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type spec =
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wenzelm@46712
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(binding * (string * sort) list * mixfix) *
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wenzelm@46712
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(binding * typ list * mixfix) list
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wenzelm@46712
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type spec_cmd =
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wenzelm@46712
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(binding * (string * string option) list * mixfix) *
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wenzelm@46712
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(binding * string list * mixfix) list
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wenzelm@46712
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val read_specs: spec_cmd list -> theory -> spec list * Proof.context
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wenzelm@46712
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val check_specs: spec list -> theory -> spec list * Proof.context
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wenzelm@46712
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val add_datatype: config -> spec list -> theory -> string list * theory
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wenzelm@46735
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val add_datatype_cmd: config -> spec_cmd list -> theory -> string list * theory
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wenzelm@46712
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val spec_cmd: spec_cmd parser
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berghofe@5177
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end;
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berghofe@5177
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haftmann@33967
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structure Datatype : DATATYPE =
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berghofe@5177
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struct
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berghofe@5177
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haftmann@33967
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(** auxiliary **)
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haftmann@33967
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val distinct_lemma = @{lemma "f x \<noteq> f y ==> x \<noteq> y" by iprover};
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haftmann@33967
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val (_ $ (_ $ (_ $ (distinct_f $ _) $ _))) = hd (prems_of distinct_lemma);
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haftmann@33967
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haftmann@33967
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val collect_simp = rewrite_rule [mk_meta_eq mem_Collect_eq];
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haftmann@33967
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wenzelm@41671
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fun exh_thm_of (dt_info : Datatype_Aux.info Symtab.table) tname =
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haftmann@33967
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#exhaust (the (Symtab.lookup dt_info tname));
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haftmann@33967
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haftmann@33967
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val In0_inject = @{thm In0_inject};
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haftmann@33967
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val In1_inject = @{thm In1_inject};
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haftmann@33967
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val Scons_inject = @{thm Scons_inject};
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haftmann@33967
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val Leaf_inject = @{thm Leaf_inject};
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haftmann@33967
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val In0_eq = @{thm In0_eq};
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haftmann@33967
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val In1_eq = @{thm In1_eq};
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haftmann@33967
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val In0_not_In1 = @{thm In0_not_In1};
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haftmann@33967
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val In1_not_In0 = @{thm In1_not_In0};
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haftmann@33967
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val Lim_inject = @{thm Lim_inject};
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haftmann@33967
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val Inl_inject = @{thm Inl_inject};
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haftmann@33967
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val Inr_inject = @{thm Inr_inject};
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haftmann@33967
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val Suml_inject = @{thm Suml_inject};
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haftmann@33967
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val Sumr_inject = @{thm Sumr_inject};
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haftmann@33967
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wenzelm@40975
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val datatype_injI =
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wenzelm@40975
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@{lemma "(!!x. ALL y. f x = f y --> x = y) ==> inj f" by (simp add: inj_on_def)};
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haftmann@33967
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haftmann@33967
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haftmann@33967
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(** proof of characteristic theorems **)
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wenzelm@41671
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fun representation_proofs (config : Datatype_Aux.config) (dt_info : Datatype_Aux.info Symtab.table)
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wenzelm@46695
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descr types_syntax constr_syntax case_names_induct thy =
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haftmann@33967
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let
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haftmann@33967
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val descr' = flat descr;
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wenzelm@46572
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val new_type_names = map (Binding.name_of o fst) types_syntax;
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val big_name = space_implode "_" new_type_names;
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val thy1 = Sign.add_path big_name thy;
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haftmann@33967
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val big_rec_name = big_name ^ "_rep_set";
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haftmann@33967
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val rep_set_names' =
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wenzelm@46614
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if length descr' = 1 then [big_rec_name]
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else map (prefix (big_rec_name ^ "_") o string_of_int) (1 upto length descr');
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haftmann@33967
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val rep_set_names = map (Sign.full_bname thy1) rep_set_names';
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haftmann@33967
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val tyvars = map (fn (_, (_, Ts, _)) => map Datatype_Aux.dest_DtTFree Ts) (hd descr);
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wenzelm@46695
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val leafTs' = Datatype_Aux.get_nonrec_types descr';
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val branchTs = Datatype_Aux.get_branching_types descr';
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val branchT =
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if null branchTs then HOLogic.unitT
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haftmann@37678
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else Balanced_Tree.make (fn (T, U) => Type (@{type_name Sum_Type.sum}, [T, U])) branchTs;
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wenzelm@41671
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val arities = remove (op =) 0 (Datatype_Aux.get_arities descr');
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haftmann@33967
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val unneeded_vars =
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wenzelm@46695
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subtract (op =) (fold Term.add_tfreesT (leafTs' @ branchTs) []) (hd tyvars);
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val leafTs = leafTs' @ map TFree unneeded_vars;
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val recTs = Datatype_Aux.get_rec_types descr';
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val (newTs, oldTs) = chop (length (hd descr)) recTs;
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val sumT =
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if null leafTs then HOLogic.unitT
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haftmann@37678
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else Balanced_Tree.make (fn (T, U) => Type (@{type_name Sum_Type.sum}, [T, U])) leafTs;
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wenzelm@46749
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val Univ_elT = HOLogic.mk_setT (Type (@{type_name Datatype.node}, [sumT, branchT]));
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haftmann@33967
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val UnivT = HOLogic.mk_setT Univ_elT;
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val UnivT' = Univ_elT --> HOLogic.boolT;
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val Collect = Const (@{const_name Collect}, UnivT' --> UnivT);
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val In0 = Const (@{const_name Datatype.In0}, Univ_elT --> Univ_elT);
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val In1 = Const (@{const_name Datatype.In1}, Univ_elT --> Univ_elT);
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val Leaf = Const (@{const_name Datatype.Leaf}, sumT --> Univ_elT);
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wenzelm@46749
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val Lim = Const (@{const_name Datatype.Lim}, (branchT --> Univ_elT) --> Univ_elT);
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haftmann@33967
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haftmann@33967
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(* make injections needed for embedding types in leaves *)
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fun mk_inj T' x =
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let
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fun mk_inj' T n i =
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if n = 1 then x
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else
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let
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val n2 = n div 2;
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val Type (_, [T1, T2]) = T;
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in
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if i <= n2
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then Const (@{const_name Inl}, T1 --> T) $ mk_inj' T1 n2 i
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else Const (@{const_name Inr}, T2 --> T) $ mk_inj' T2 (n - n2) (i - n2)
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end;
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wenzelm@46571
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in mk_inj' sumT (length leafTs) (1 + find_index (fn T'' => T'' = T') leafTs) end;
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haftmann@33967
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haftmann@33967
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(* make injections for constructors *)
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haftmann@33967
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fun mk_univ_inj ts = Balanced_Tree.access
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{left = fn t => In0 $ t,
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right = fn t => In1 $ t,
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haftmann@33967
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init =
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haftmann@33967
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if ts = [] then Const (@{const_name undefined}, Univ_elT)
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wenzelm@46749
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else foldr1 (HOLogic.mk_binop @{const_name Datatype.Scons}) ts};
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haftmann@33967
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haftmann@33967
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(* function spaces *)
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haftmann@33967
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haftmann@33967
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fun mk_fun_inj T' x =
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let
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haftmann@33967
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fun mk_inj T n i =
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if n = 1 then x
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wenzelm@46571
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else
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let
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wenzelm@46571
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val n2 = n div 2;
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wenzelm@46571
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val Type (_, [T1, T2]) = T;
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wenzelm@46571
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fun mkT U = (U --> Univ_elT) --> T --> Univ_elT;
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wenzelm@46571
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in
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wenzelm@46749
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if i <= n2 then Const (@{const_name Sum_Type.Suml}, mkT T1) $ mk_inj T1 n2 i
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wenzelm@46749
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else Const (@{const_name Sum_Type.Sumr}, mkT T2) $ mk_inj T2 (n - n2) (i - n2)
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wenzelm@46571
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end;
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wenzelm@46571
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in mk_inj branchT (length branchTs) (1 + find_index (fn T'' => T'' = T') branchTs) end;
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haftmann@33967
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haftmann@33967
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fun mk_lim t Ts = fold_rev (fn T => fn t => Lim $ mk_fun_inj T (Abs ("x", T, t))) Ts t;
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haftmann@33967
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haftmann@33967
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(************** generate introduction rules for representing set **********)
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haftmann@33967
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wenzelm@41671
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val _ = Datatype_Aux.message config "Constructing representing sets ...";
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haftmann@33967
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haftmann@33967
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(* make introduction rule for a single constructor *)
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haftmann@33967
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haftmann@33967
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fun make_intr s n (i, (_, cargs)) =
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haftmann@33967
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let
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haftmann@33967
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fun mk_prem dt (j, prems, ts) =
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wenzelm@41671
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(case Datatype_Aux.strip_dtyp dt of
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wenzelm@41671
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(dts, Datatype_Aux.DtRec k) =>
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haftmann@33967
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let
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wenzelm@46695
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val Ts = map (Datatype_Aux.typ_of_dtyp descr') dts;
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haftmann@33967
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val free_t =
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wenzelm@41671
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Datatype_Aux.app_bnds (Datatype_Aux.mk_Free "x" (Ts ---> Univ_elT) j) (length Ts)
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wenzelm@46571
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in
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wenzelm@47089
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(j + 1, Logic.list_all (map (pair "x") Ts,
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haftmann@33967
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HOLogic.mk_Trueprop
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haftmann@33967
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(Free (nth rep_set_names' k, UnivT') $ free_t)) :: prems,
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haftmann@33967
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mk_lim free_t Ts :: ts)
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haftmann@33967
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end
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haftmann@33967
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| _ =>
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wenzelm@46695
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let val T = Datatype_Aux.typ_of_dtyp descr' dt
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wenzelm@46571
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in (j + 1, prems, (Leaf $ mk_inj T (Datatype_Aux.mk_Free "x" T j)) :: ts) end);
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haftmann@33967
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haftmann@33967
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val (_, prems, ts) = fold_rev mk_prem cargs (1, [], []);
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wenzelm@46571
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val concl = HOLogic.mk_Trueprop (Free (s, UnivT') $ mk_univ_inj ts n i);
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wenzelm@46571
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in Logic.list_implies (prems, concl) end;
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haftmann@33967
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haftmann@33967
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val intr_ts = maps (fn ((_, (_, _, constrs)), rep_set_name) =>
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haftmann@33967
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map (make_intr rep_set_name (length constrs))
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wenzelm@46694
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((1 upto length constrs) ~~ constrs)) (descr' ~~ rep_set_names');
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haftmann@33967
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haftmann@33967
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val ({raw_induct = rep_induct, intrs = rep_intrs, ...}, thy2) =
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haftmann@33967
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thy1
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haftmann@33967
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|> Sign.map_naming Name_Space.conceal
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haftmann@33967
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|> Inductive.add_inductive_global
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haftmann@33967
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{quiet_mode = #quiet config, verbose = false, alt_name = Binding.name big_rec_name,
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haftmann@33967
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coind = false, no_elim = true, no_ind = false, skip_mono = true, fork_mono = false}
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haftmann@33967
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(map (fn s => ((Binding.name s, UnivT'), NoSyn)) rep_set_names') []
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haftmann@33967
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(map (fn x => (Attrib.empty_binding, x)) intr_ts) []
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haftmann@33967
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||> Sign.restore_naming thy1
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haftmann@33967
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||> Theory.checkpoint;
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haftmann@33967
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haftmann@33967
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(********************************* typedef ********************************)
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haftmann@33967
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wenzelm@46572
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val (typedefs, thy3) = thy2
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wenzelm@46572
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|> Sign.parent_path
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wenzelm@46572
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|> fold_map
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wenzelm@46572
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(fn (((name, mx), tvs), c) =>
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wenzelm@46695
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Typedef.add_typedef_global false NONE (name, tvs, mx)
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haftmann@33967
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(Collect $ Const (c, UnivT')) NONE
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haftmann@33967
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(rtac exI 1 THEN rtac CollectI 1 THEN
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haftmann@33967
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QUIET_BREADTH_FIRST (has_fewer_prems 1)
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haftmann@33967
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(resolve_tac rep_intrs 1)))
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wenzelm@46749
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(types_syntax ~~ tyvars ~~ take (length newTs) rep_set_names)
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wenzelm@46572
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||> Sign.add_path big_name;
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haftmann@33967
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haftmann@33967
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(*********************** definition of constructors ***********************)
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haftmann@33967
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wenzelm@46749
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val big_rep_name = big_name ^ "_Rep_";
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wenzelm@46572
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val rep_names' = map (fn i => big_rep_name ^ string_of_int i) (1 upto length (flat (tl descr)));
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wenzelm@46572
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val all_rep_names =
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wenzelm@46750
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map (#Rep_name o #1 o #2) typedefs @
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haftmann@33967
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map (Sign.full_bname thy3) rep_names';
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haftmann@33967
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haftmann@33967
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(* isomorphism declarations *)
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haftmann@33967
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haftmann@33967
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val iso_decls = map (fn (T, s) => (Binding.name s, T --> Univ_elT, NoSyn))
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haftmann@33967
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(oldTs ~~ rep_names');
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haftmann@33967
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haftmann@33967
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(* constructor definitions *)
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haftmann@33967
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wenzelm@46762
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fun make_constr_def (typedef: Typedef.info) T n
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wenzelm@46750
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((cname, cargs), (cname', mx)) (thy, defs, eqns, i) =
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haftmann@33967
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let
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haftmann@33967
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fun constr_arg dt (j, l_args, r_args) =
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wenzelm@41671
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let
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wenzelm@46695
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val T = Datatype_Aux.typ_of_dtyp descr' dt;
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wenzelm@41671
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val free_t = Datatype_Aux.mk_Free "x" T j;
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wenzelm@46571
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in
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wenzelm@46571
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(case (Datatype_Aux.strip_dtyp dt, strip_type T) of
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wenzelm@46571
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((_, Datatype_Aux.DtRec m), (Us, U)) =>
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wenzelm@46571
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(j + 1, free_t :: l_args, mk_lim
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wenzelm@46571
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(Const (nth all_rep_names m, U --> Univ_elT) $
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wenzelm@46571
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Datatype_Aux.app_bnds free_t (length Us)) Us :: r_args)
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wenzelm@46750
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| _ => (j + 1, free_t :: l_args, (Leaf $ mk_inj T free_t) :: r_args))
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haftmann@33967
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end;
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haftmann@33967
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haftmann@33967
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val (_, l_args, r_args) = fold_rev constr_arg cargs (1, [], []);
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wenzelm@46695
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val constrT = map (Datatype_Aux.typ_of_dtyp descr') cargs ---> T;
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wenzelm@46750
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val ({Abs_name, Rep_name, ...}, _) = typedef;
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haftmann@33967
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val lhs = list_comb (Const (cname, constrT), l_args);
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haftmann@33967
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val rhs = mk_univ_inj r_args n i;
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wenzelm@46750
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val def = Logic.mk_equals (lhs, Const (Abs_name, Univ_elT --> T) $ rhs);
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wenzelm@47780
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val def_name = Thm.def_name (Long_Name.base_name cname);
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wenzelm@46694
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val eqn =
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wenzelm@46750
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HOLogic.mk_Trueprop (HOLogic.mk_eq (Const (Rep_name, T --> Univ_elT) $ lhs, rhs));
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haftmann@33967
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val ([def_thm], thy') =
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haftmann@33967
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thy
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haftmann@33967
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243 |
|> Sign.add_consts_i [(cname', constrT, mx)]
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wenzelm@39814
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|> (Global_Theory.add_defs false o map Thm.no_attributes) [(Binding.name def_name, def)];
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haftmann@33967
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haftmann@33967
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246 |
in (thy', defs @ [def_thm], eqns @ [eqn], i + 1) end;
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haftmann@33967
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247 |
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haftmann@33967
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248 |
(* constructor definitions for datatype *)
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haftmann@33967
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wenzelm@46750
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fun dt_constr_defs (((((_, (_, _, constrs)), tname), typedef: Typedef.info), T), constr_syntax)
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haftmann@33967
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251 |
(thy, defs, eqns, rep_congs, dist_lemmas) =
|
haftmann@33967
|
252 |
let
|
haftmann@33967
|
253 |
val _ $ (_ $ (cong_f $ _) $ _) = concl_of arg_cong;
|
wenzelm@46750
|
254 |
val rep_const = cterm_of thy (Const (#Rep_name (#1 typedef), T --> Univ_elT));
|
wenzelm@46781
|
255 |
val cong' = cterm_instantiate [(cterm_of thy cong_f, rep_const)] arg_cong;
|
wenzelm@46781
|
256 |
val dist = cterm_instantiate [(cterm_of thy distinct_f, rep_const)] distinct_lemma;
|
wenzelm@46571
|
257 |
val (thy', defs', eqns', _) =
|
wenzelm@46762
|
258 |
fold (make_constr_def typedef T (length constrs))
|
wenzelm@46571
|
259 |
(constrs ~~ constr_syntax) (Sign.add_path tname thy, defs, [], 1);
|
haftmann@33967
|
260 |
in
|
haftmann@33967
|
261 |
(Sign.parent_path thy', defs', eqns @ [eqns'],
|
haftmann@33967
|
262 |
rep_congs @ [cong'], dist_lemmas @ [dist])
|
haftmann@33967
|
263 |
end;
|
haftmann@33967
|
264 |
|
haftmann@33967
|
265 |
val (thy4, constr_defs, constr_rep_eqns, rep_congs, dist_lemmas) =
|
haftmann@33967
|
266 |
fold dt_constr_defs
|
wenzelm@46750
|
267 |
(hd descr ~~ new_type_names ~~ map #2 typedefs ~~ newTs ~~ constr_syntax)
|
haftmann@33967
|
268 |
(thy3 |> Sign.add_consts_i iso_decls |> Sign.parent_path, [], [], [], []);
|
haftmann@33967
|
269 |
|
haftmann@33967
|
270 |
|
haftmann@33967
|
271 |
(*********** isomorphisms for new types (introduced by typedef) ***********)
|
haftmann@33967
|
272 |
|
wenzelm@41671
|
273 |
val _ = Datatype_Aux.message config "Proving isomorphism properties ...";
|
haftmann@33967
|
274 |
|
wenzelm@46750
|
275 |
val newT_iso_axms = typedefs |> map (fn (_, (_, {Abs_inverse, Rep_inverse, Rep, ...})) =>
|
wenzelm@46750
|
276 |
(collect_simp Abs_inverse, Rep_inverse, collect_simp Rep));
|
haftmann@33967
|
277 |
|
wenzelm@46750
|
278 |
val newT_iso_inj_thms = typedefs |> map (fn (_, (_, {Abs_inject, Rep_inject, ...})) =>
|
wenzelm@46750
|
279 |
(collect_simp Abs_inject RS iffD1, Rep_inject RS iffD1));
|
haftmann@33967
|
280 |
|
haftmann@33967
|
281 |
(********* isomorphisms between existing types and "unfolded" types *******)
|
haftmann@33967
|
282 |
|
haftmann@33967
|
283 |
(*---------------------------------------------------------------------*)
|
haftmann@33967
|
284 |
(* isomorphisms are defined using primrec-combinators: *)
|
haftmann@33967
|
285 |
(* generate appropriate functions for instantiating primrec-combinator *)
|
haftmann@33967
|
286 |
(* *)
|
haftmann@33967
|
287 |
(* e.g. dt_Rep_i = list_rec ... (%h t y. In1 (Scons (Leaf h) y)) *)
|
haftmann@33967
|
288 |
(* *)
|
haftmann@33967
|
289 |
(* also generate characteristic equations for isomorphisms *)
|
haftmann@33967
|
290 |
(* *)
|
haftmann@33967
|
291 |
(* e.g. dt_Rep_i (cons h t) = In1 (Scons (dt_Rep_j h) (dt_Rep_i t)) *)
|
haftmann@33967
|
292 |
(*---------------------------------------------------------------------*)
|
haftmann@33967
|
293 |
|
haftmann@33967
|
294 |
fun make_iso_def k ks n (cname, cargs) (fs, eqns, i) =
|
haftmann@33967
|
295 |
let
|
wenzelm@46695
|
296 |
val argTs = map (Datatype_Aux.typ_of_dtyp descr') cargs;
|
haftmann@33967
|
297 |
val T = nth recTs k;
|
wenzelm@46750
|
298 |
val rep_const = Const (nth all_rep_names k, T --> Univ_elT);
|
haftmann@33967
|
299 |
val constr = Const (cname, argTs ---> T);
|
haftmann@33967
|
300 |
|
haftmann@33967
|
301 |
fun process_arg ks' dt (i2, i2', ts, Ts) =
|
haftmann@33967
|
302 |
let
|
wenzelm@46695
|
303 |
val T' = Datatype_Aux.typ_of_dtyp descr' dt;
|
haftmann@33967
|
304 |
val (Us, U) = strip_type T'
|
wenzelm@46571
|
305 |
in
|
wenzelm@46571
|
306 |
(case Datatype_Aux.strip_dtyp dt of
|
wenzelm@46571
|
307 |
(_, Datatype_Aux.DtRec j) =>
|
wenzelm@46571
|
308 |
if member (op =) ks' j then
|
wenzelm@41671
|
309 |
(i2 + 1, i2' + 1, ts @ [mk_lim (Datatype_Aux.app_bnds
|
wenzelm@41671
|
310 |
(Datatype_Aux.mk_Free "y" (Us ---> Univ_elT) i2') (length Us)) Us],
|
haftmann@33967
|
311 |
Ts @ [Us ---> Univ_elT])
|
haftmann@33967
|
312 |
else
|
haftmann@33967
|
313 |
(i2 + 1, i2', ts @ [mk_lim
|
haftmann@33967
|
314 |
(Const (nth all_rep_names j, U --> Univ_elT) $
|
wenzelm@41671
|
315 |
Datatype_Aux.app_bnds (Datatype_Aux.mk_Free "x" T' i2) (length Us)) Us], Ts)
|
wenzelm@41671
|
316 |
| _ => (i2 + 1, i2', ts @ [Leaf $ mk_inj T' (Datatype_Aux.mk_Free "x" T' i2)], Ts))
|
haftmann@33967
|
317 |
end;
|
haftmann@33967
|
318 |
|
haftmann@33967
|
319 |
val (i2, i2', ts, Ts) = fold (process_arg ks) cargs (1, 1, [], []);
|
wenzelm@41671
|
320 |
val xs = map (uncurry (Datatype_Aux.mk_Free "x")) (argTs ~~ (1 upto (i2 - 1)));
|
wenzelm@41671
|
321 |
val ys = map (uncurry (Datatype_Aux.mk_Free "y")) (Ts ~~ (1 upto (i2' - 1)));
|
wenzelm@46749
|
322 |
val f = fold_rev lambda (xs @ ys) (mk_univ_inj ts n i);
|
haftmann@33967
|
323 |
|
haftmann@33967
|
324 |
val (_, _, ts', _) = fold (process_arg []) cargs (1, 1, [], []);
|
haftmann@33967
|
325 |
val eqn = HOLogic.mk_Trueprop (HOLogic.mk_eq
|
haftmann@33967
|
326 |
(rep_const $ list_comb (constr, xs), mk_univ_inj ts' n i))
|
haftmann@33967
|
327 |
|
haftmann@33967
|
328 |
in (fs @ [f], eqns @ [eqn], i + 1) end;
|
haftmann@33967
|
329 |
|
haftmann@33967
|
330 |
(* define isomorphisms for all mutually recursive datatypes in list ds *)
|
haftmann@33967
|
331 |
|
haftmann@33967
|
332 |
fun make_iso_defs ds (thy, char_thms) =
|
haftmann@33967
|
333 |
let
|
haftmann@33967
|
334 |
val ks = map fst ds;
|
haftmann@33967
|
335 |
val (_, (tname, _, _)) = hd ds;
|
haftmann@33967
|
336 |
val {rec_rewrites, rec_names, ...} = the (Symtab.lookup dt_info tname);
|
haftmann@33967
|
337 |
|
wenzelm@46749
|
338 |
fun process_dt (k, (_, _, constrs)) (fs, eqns, isos) =
|
haftmann@33967
|
339 |
let
|
wenzelm@46571
|
340 |
val (fs', eqns', _) = fold (make_iso_def k ks (length constrs)) constrs (fs, eqns, 1);
|
wenzelm@46571
|
341 |
val iso = (nth recTs k, nth all_rep_names k);
|
haftmann@33967
|
342 |
in (fs', eqns', isos @ [iso]) end;
|
wenzelm@46571
|
343 |
|
haftmann@33967
|
344 |
val (fs, eqns, isos) = fold process_dt ds ([], [], []);
|
haftmann@33967
|
345 |
val fTs = map fastype_of fs;
|
wenzelm@46571
|
346 |
val defs =
|
wenzelm@46571
|
347 |
map (fn (rec_name, (T, iso_name)) =>
|
wenzelm@47780
|
348 |
(Binding.name (Thm.def_name (Long_Name.base_name iso_name)),
|
wenzelm@46571
|
349 |
Logic.mk_equals (Const (iso_name, T --> Univ_elT),
|
wenzelm@46571
|
350 |
list_comb (Const (rec_name, fTs @ [T] ---> Univ_elT), fs)))) (rec_names ~~ isos);
|
haftmann@33967
|
351 |
val (def_thms, thy') =
|
wenzelm@39814
|
352 |
apsnd Theory.checkpoint ((Global_Theory.add_defs false o map Thm.no_attributes) defs thy);
|
haftmann@33967
|
353 |
|
haftmann@33967
|
354 |
(* prove characteristic equations *)
|
haftmann@33967
|
355 |
|
wenzelm@46749
|
356 |
val rewrites = def_thms @ map mk_meta_eq rec_rewrites;
|
wenzelm@46571
|
357 |
val char_thms' =
|
wenzelm@46571
|
358 |
map (fn eqn => Skip_Proof.prove_global thy' [] [] eqn
|
wenzelm@46571
|
359 |
(fn _ => EVERY [rewrite_goals_tac rewrites, rtac refl 1])) eqns;
|
haftmann@33967
|
360 |
|
haftmann@33967
|
361 |
in (thy', char_thms' @ char_thms) end;
|
haftmann@33967
|
362 |
|
wenzelm@46571
|
363 |
val (thy5, iso_char_thms) =
|
wenzelm@46571
|
364 |
apfst Theory.checkpoint (fold_rev make_iso_defs (tl descr) (Sign.add_path big_name thy4, []));
|
haftmann@33967
|
365 |
|
haftmann@33967
|
366 |
(* prove isomorphism properties *)
|
haftmann@33967
|
367 |
|
haftmann@33967
|
368 |
fun mk_funs_inv thy thm =
|
haftmann@33967
|
369 |
let
|
haftmann@33967
|
370 |
val prop = Thm.prop_of thm;
|
haftmann@33967
|
371 |
val _ $ (_ $ ((S as Const (_, Type (_, [U, _]))) $ _ )) $
|
haftmann@33967
|
372 |
(_ $ (_ $ (r $ (a $ _)) $ _)) = Type.legacy_freeze prop;
|
wenzelm@46609
|
373 |
val used = Term.add_tfree_names a [];
|
haftmann@33967
|
374 |
|
haftmann@33967
|
375 |
fun mk_thm i =
|
haftmann@33967
|
376 |
let
|
wenzelm@46571
|
377 |
val Ts = map (TFree o rpair HOLogic.typeS) (Name.variant_list used (replicate i "'t"));
|
wenzelm@46571
|
378 |
val f = Free ("f", Ts ---> U);
|
wenzelm@46571
|
379 |
in
|
wenzelm@46571
|
380 |
Skip_Proof.prove_global thy [] []
|
wenzelm@46571
|
381 |
(Logic.mk_implies
|
wenzelm@46571
|
382 |
(HOLogic.mk_Trueprop (HOLogic.list_all
|
wenzelm@46571
|
383 |
(map (pair "x") Ts, S $ Datatype_Aux.app_bnds f i)),
|
wenzelm@47090
|
384 |
HOLogic.mk_Trueprop (HOLogic.mk_eq (fold_rev (Term.abs o pair "x") Ts
|
wenzelm@47090
|
385 |
(r $ (a $ Datatype_Aux.app_bnds f i)), f))))
|
wenzelm@46571
|
386 |
(fn _ => EVERY [REPEAT_DETERM_N i (rtac ext 1),
|
wenzelm@46571
|
387 |
REPEAT (etac allE 1), rtac thm 1, atac 1])
|
haftmann@33967
|
388 |
end
|
haftmann@33967
|
389 |
in map (fn r => r RS subst) (thm :: map mk_thm arities) end;
|
haftmann@33967
|
390 |
|
haftmann@33967
|
391 |
(* prove inj dt_Rep_i and dt_Rep_i x : dt_rep_set_i *)
|
haftmann@33967
|
392 |
|
wenzelm@46571
|
393 |
val fun_congs =
|
wenzelm@46571
|
394 |
map (fn T => make_elim (Drule.instantiate' [SOME (ctyp_of thy5 T)] [] fun_cong)) branchTs;
|
haftmann@33967
|
395 |
|
haftmann@33967
|
396 |
fun prove_iso_thms ds (inj_thms, elem_thms) =
|
haftmann@33967
|
397 |
let
|
haftmann@33967
|
398 |
val (_, (tname, _, _)) = hd ds;
|
wenzelm@46571
|
399 |
val induct = #induct (the (Symtab.lookup dt_info tname));
|
haftmann@33967
|
400 |
|
haftmann@33967
|
401 |
fun mk_ind_concl (i, _) =
|
haftmann@33967
|
402 |
let
|
haftmann@33967
|
403 |
val T = nth recTs i;
|
haftmann@33967
|
404 |
val Rep_t = Const (nth all_rep_names i, T --> Univ_elT);
|
wenzelm@46571
|
405 |
val rep_set_name = nth rep_set_names i;
|
wenzelm@46750
|
406 |
val concl1 =
|
wenzelm@46750
|
407 |
HOLogic.all_const T $ Abs ("y", T, HOLogic.imp $
|
wenzelm@41671
|
408 |
HOLogic.mk_eq (Rep_t $ Datatype_Aux.mk_Free "x" T i, Rep_t $ Bound 0) $
|
wenzelm@46750
|
409 |
HOLogic.mk_eq (Datatype_Aux.mk_Free "x" T i, Bound 0));
|
wenzelm@46750
|
410 |
val concl2 = Const (rep_set_name, UnivT') $ (Rep_t $ Datatype_Aux.mk_Free "x" T i);
|
wenzelm@46750
|
411 |
in (concl1, concl2) end;
|
haftmann@33967
|
412 |
|
wenzelm@46750
|
413 |
val (ind_concl1, ind_concl2) = split_list (map mk_ind_concl ds);
|
haftmann@33967
|
414 |
|
haftmann@33967
|
415 |
val rewrites = map mk_meta_eq iso_char_thms;
|
wenzelm@46571
|
416 |
val inj_thms' = map snd newT_iso_inj_thms @ map (fn r => r RS @{thm injD}) inj_thms;
|
haftmann@33967
|
417 |
|
wenzelm@46571
|
418 |
val inj_thm =
|
wenzelm@46571
|
419 |
Skip_Proof.prove_global thy5 [] []
|
wenzelm@46571
|
420 |
(HOLogic.mk_Trueprop (Datatype_Aux.mk_conj ind_concl1))
|
wenzelm@46571
|
421 |
(fn _ => EVERY
|
wenzelm@46606
|
422 |
[(Datatype_Aux.ind_tac induct [] THEN_ALL_NEW Object_Logic.atomize_prems_tac) 1,
|
wenzelm@46571
|
423 |
REPEAT (EVERY
|
wenzelm@46571
|
424 |
[rtac allI 1, rtac impI 1,
|
wenzelm@46571
|
425 |
Datatype_Aux.exh_tac (exh_thm_of dt_info) 1,
|
wenzelm@46571
|
426 |
REPEAT (EVERY
|
wenzelm@46571
|
427 |
[hyp_subst_tac 1,
|
wenzelm@46571
|
428 |
rewrite_goals_tac rewrites,
|
wenzelm@46571
|
429 |
REPEAT (dresolve_tac [In0_inject, In1_inject] 1),
|
wenzelm@46571
|
430 |
(eresolve_tac [In0_not_In1 RS notE, In1_not_In0 RS notE] 1)
|
wenzelm@46571
|
431 |
ORELSE (EVERY
|
wenzelm@46571
|
432 |
[REPEAT (eresolve_tac (Scons_inject ::
|
wenzelm@46571
|
433 |
map make_elim [Leaf_inject, Inl_inject, Inr_inject]) 1),
|
wenzelm@46571
|
434 |
REPEAT (cong_tac 1), rtac refl 1,
|
wenzelm@46571
|
435 |
REPEAT (atac 1 ORELSE (EVERY
|
wenzelm@46571
|
436 |
[REPEAT (rtac ext 1),
|
wenzelm@46571
|
437 |
REPEAT (eresolve_tac (mp :: allE ::
|
wenzelm@46571
|
438 |
map make_elim (Suml_inject :: Sumr_inject ::
|
wenzelm@46571
|
439 |
Lim_inject :: inj_thms') @ fun_congs) 1),
|
wenzelm@46571
|
440 |
atac 1]))])])])]);
|
haftmann@33967
|
441 |
|
wenzelm@41671
|
442 |
val inj_thms'' = map (fn r => r RS datatype_injI) (Datatype_Aux.split_conj_thm inj_thm);
|
haftmann@33967
|
443 |
|
wenzelm@46571
|
444 |
val elem_thm =
|
wenzelm@46571
|
445 |
Skip_Proof.prove_global thy5 [] []
|
wenzelm@46571
|
446 |
(HOLogic.mk_Trueprop (Datatype_Aux.mk_conj ind_concl2))
|
wenzelm@41671
|
447 |
(fn _ =>
|
wenzelm@46606
|
448 |
EVERY [(Datatype_Aux.ind_tac induct [] THEN_ALL_NEW Object_Logic.atomize_prems_tac) 1,
|
wenzelm@46571
|
449 |
rewrite_goals_tac rewrites,
|
wenzelm@46571
|
450 |
REPEAT ((resolve_tac rep_intrs THEN_ALL_NEW
|
wenzelm@46571
|
451 |
((REPEAT o etac allE) THEN' ares_tac elem_thms)) 1)]);
|
haftmann@33967
|
452 |
|
wenzelm@46749
|
453 |
in (inj_thms'' @ inj_thms, elem_thms @ Datatype_Aux.split_conj_thm elem_thm) end;
|
haftmann@33967
|
454 |
|
haftmann@33967
|
455 |
val (iso_inj_thms_unfolded, iso_elem_thms) =
|
haftmann@33967
|
456 |
fold_rev prove_iso_thms (tl descr) ([], map #3 newT_iso_axms);
|
wenzelm@46571
|
457 |
val iso_inj_thms =
|
wenzelm@46571
|
458 |
map snd newT_iso_inj_thms @ map (fn r => r RS @{thm injD}) iso_inj_thms_unfolded;
|
haftmann@33967
|
459 |
|
haftmann@33967
|
460 |
(* prove dt_rep_set_i x --> x : range dt_Rep_i *)
|
haftmann@33967
|
461 |
|
haftmann@33967
|
462 |
fun mk_iso_t (((set_name, iso_name), i), T) =
|
wenzelm@46571
|
463 |
let val isoT = T --> Univ_elT in
|
wenzelm@46571
|
464 |
HOLogic.imp $
|
wenzelm@46571
|
465 |
(Const (set_name, UnivT') $ Datatype_Aux.mk_Free "x" Univ_elT i) $
|
wenzelm@46611
|
466 |
(if i < length newTs then @{term True}
|
wenzelm@46571
|
467 |
else HOLogic.mk_mem (Datatype_Aux.mk_Free "x" Univ_elT i,
|
wenzelm@46571
|
468 |
Const (@{const_name image}, isoT --> HOLogic.mk_setT T --> UnivT) $
|
wenzelm@46571
|
469 |
Const (iso_name, isoT) $ Const (@{const_abbrev UNIV}, HOLogic.mk_setT T)))
|
haftmann@33967
|
470 |
end;
|
haftmann@33967
|
471 |
|
wenzelm@41671
|
472 |
val iso_t = HOLogic.mk_Trueprop (Datatype_Aux.mk_conj (map mk_iso_t
|
haftmann@33967
|
473 |
(rep_set_names ~~ all_rep_names ~~ (0 upto (length descr' - 1)) ~~ recTs)));
|
haftmann@33967
|
474 |
|
haftmann@33967
|
475 |
(* all the theorems are proved by one single simultaneous induction *)
|
haftmann@33967
|
476 |
|
wenzelm@46571
|
477 |
val range_eqs = map (fn r => mk_meta_eq (r RS @{thm range_ex1_eq})) iso_inj_thms_unfolded;
|
haftmann@33967
|
478 |
|
wenzelm@46571
|
479 |
val iso_thms =
|
wenzelm@46571
|
480 |
if length descr = 1 then []
|
wenzelm@46571
|
481 |
else
|
wenzelm@46571
|
482 |
drop (length newTs) (Datatype_Aux.split_conj_thm
|
wenzelm@46571
|
483 |
(Skip_Proof.prove_global thy5 [] [] iso_t (fn _ => EVERY
|
wenzelm@46606
|
484 |
[(Datatype_Aux.ind_tac rep_induct [] THEN_ALL_NEW Object_Logic.atomize_prems_tac) 1,
|
wenzelm@46571
|
485 |
REPEAT (rtac TrueI 1),
|
wenzelm@46571
|
486 |
rewrite_goals_tac (mk_meta_eq @{thm choice_eq} ::
|
wenzelm@46571
|
487 |
Thm.symmetric (mk_meta_eq @{thm fun_eq_iff}) :: range_eqs),
|
wenzelm@46571
|
488 |
rewrite_goals_tac (map Thm.symmetric range_eqs),
|
wenzelm@46571
|
489 |
REPEAT (EVERY
|
wenzelm@46571
|
490 |
[REPEAT (eresolve_tac ([rangeE, ex1_implies_ex RS exE] @
|
wenzelm@46571
|
491 |
maps (mk_funs_inv thy5 o #1) newT_iso_axms) 1),
|
wenzelm@46571
|
492 |
TRY (hyp_subst_tac 1),
|
wenzelm@46571
|
493 |
rtac (sym RS range_eqI) 1,
|
wenzelm@46571
|
494 |
resolve_tac iso_char_thms 1])])));
|
haftmann@33967
|
495 |
|
haftmann@33967
|
496 |
val Abs_inverse_thms' =
|
haftmann@33967
|
497 |
map #1 newT_iso_axms @
|
haftmann@33967
|
498 |
map2 (fn r_inj => fn r => @{thm f_the_inv_into_f} OF [r_inj, r RS mp])
|
haftmann@33967
|
499 |
iso_inj_thms_unfolded iso_thms;
|
haftmann@33967
|
500 |
|
haftmann@33967
|
501 |
val Abs_inverse_thms = maps (mk_funs_inv thy5) Abs_inverse_thms';
|
haftmann@33967
|
502 |
|
haftmann@33967
|
503 |
(******************* freeness theorems for constructors *******************)
|
haftmann@33967
|
504 |
|
wenzelm@41671
|
505 |
val _ = Datatype_Aux.message config "Proving freeness of constructors ...";
|
haftmann@33967
|
506 |
|
haftmann@33967
|
507 |
(* prove theorem Rep_i (Constr_j ...) = Inj_j ... *)
|
wenzelm@46571
|
508 |
|
haftmann@33967
|
509 |
fun prove_constr_rep_thm eqn =
|
haftmann@33967
|
510 |
let
|
haftmann@33967
|
511 |
val inj_thms = map fst newT_iso_inj_thms;
|
wenzelm@46749
|
512 |
val rewrites = @{thm o_def} :: constr_defs @ map (mk_meta_eq o #2) newT_iso_axms;
|
wenzelm@46571
|
513 |
in
|
wenzelm@46571
|
514 |
Skip_Proof.prove_global thy5 [] [] eqn
|
wenzelm@46571
|
515 |
(fn _ => EVERY
|
wenzelm@46571
|
516 |
[resolve_tac inj_thms 1,
|
wenzelm@46571
|
517 |
rewrite_goals_tac rewrites,
|
wenzelm@46571
|
518 |
rtac refl 3,
|
wenzelm@46571
|
519 |
resolve_tac rep_intrs 2,
|
wenzelm@46571
|
520 |
REPEAT (resolve_tac iso_elem_thms 1)])
|
haftmann@33967
|
521 |
end;
|
haftmann@33967
|
522 |
|
haftmann@33967
|
523 |
(*--------------------------------------------------------------*)
|
haftmann@33967
|
524 |
(* constr_rep_thms and rep_congs are used to prove distinctness *)
|
haftmann@33967
|
525 |
(* of constructors. *)
|
haftmann@33967
|
526 |
(*--------------------------------------------------------------*)
|
haftmann@33967
|
527 |
|
haftmann@33967
|
528 |
val constr_rep_thms = map (map prove_constr_rep_thm) constr_rep_eqns;
|
haftmann@33967
|
529 |
|
wenzelm@46571
|
530 |
val dist_rewrites =
|
wenzelm@46571
|
531 |
map (fn (rep_thms, dist_lemma) =>
|
wenzelm@46749
|
532 |
dist_lemma :: (rep_thms @ [In0_eq, In1_eq, In0_not_In1, In1_not_In0]))
|
wenzelm@46571
|
533 |
(constr_rep_thms ~~ dist_lemmas);
|
haftmann@33967
|
534 |
|
wenzelm@46762
|
535 |
fun prove_distinct_thms dist_rewrites' =
|
haftmann@33967
|
536 |
let
|
haftmann@33967
|
537 |
fun prove [] = []
|
haftmann@33967
|
538 |
| prove (t :: ts) =
|
haftmann@33967
|
539 |
let
|
haftmann@33967
|
540 |
val dist_thm = Skip_Proof.prove_global thy5 [] [] t (fn _ =>
|
haftmann@33967
|
541 |
EVERY [simp_tac (HOL_ss addsimps dist_rewrites') 1])
|
wenzelm@46781
|
542 |
in dist_thm :: Drule.zero_var_indexes (dist_thm RS not_sym) :: prove ts end;
|
wenzelm@46762
|
543 |
in prove end;
|
haftmann@33967
|
544 |
|
wenzelm@46571
|
545 |
val distinct_thms =
|
wenzelm@46695
|
546 |
map2 (prove_distinct_thms) dist_rewrites (Datatype_Prop.make_distincts descr);
|
haftmann@33967
|
547 |
|
haftmann@33967
|
548 |
(* prove injectivity of constructors *)
|
haftmann@33967
|
549 |
|
haftmann@33967
|
550 |
fun prove_constr_inj_thm rep_thms t =
|
wenzelm@46571
|
551 |
let
|
wenzelm@46571
|
552 |
val inj_thms = Scons_inject ::
|
wenzelm@46571
|
553 |
map make_elim
|
wenzelm@46571
|
554 |
(iso_inj_thms @
|
wenzelm@46571
|
555 |
[In0_inject, In1_inject, Leaf_inject, Inl_inject, Inr_inject,
|
wenzelm@46571
|
556 |
Lim_inject, Suml_inject, Sumr_inject])
|
wenzelm@46571
|
557 |
in
|
wenzelm@46571
|
558 |
Skip_Proof.prove_global thy5 [] [] t
|
wenzelm@46571
|
559 |
(fn _ => EVERY
|
wenzelm@46571
|
560 |
[rtac iffI 1,
|
wenzelm@46571
|
561 |
REPEAT (etac conjE 2), hyp_subst_tac 2, rtac refl 2,
|
wenzelm@46571
|
562 |
dresolve_tac rep_congs 1, dtac box_equals 1,
|
wenzelm@46571
|
563 |
REPEAT (resolve_tac rep_thms 1),
|
wenzelm@46571
|
564 |
REPEAT (eresolve_tac inj_thms 1),
|
wenzelm@46571
|
565 |
REPEAT (ares_tac [conjI] 1 ORELSE (EVERY [REPEAT (rtac ext 1),
|
wenzelm@46571
|
566 |
REPEAT (eresolve_tac (make_elim fun_cong :: inj_thms) 1),
|
wenzelm@46571
|
567 |
atac 1]))])
|
haftmann@33967
|
568 |
end;
|
haftmann@33967
|
569 |
|
wenzelm@46571
|
570 |
val constr_inject =
|
wenzelm@46571
|
571 |
map (fn (ts, thms) => map (prove_constr_inj_thm thms) ts)
|
wenzelm@46695
|
572 |
(Datatype_Prop.make_injs descr ~~ constr_rep_thms);
|
haftmann@33967
|
573 |
|
haftmann@33967
|
574 |
val ((constr_inject', distinct_thms'), thy6) =
|
haftmann@33967
|
575 |
thy5
|
haftmann@33967
|
576 |
|> Sign.parent_path
|
wenzelm@41671
|
577 |
|> Datatype_Aux.store_thmss "inject" new_type_names constr_inject
|
wenzelm@41671
|
578 |
||>> Datatype_Aux.store_thmss "distinct" new_type_names distinct_thms;
|
haftmann@33967
|
579 |
|
haftmann@33967
|
580 |
(*************************** induction theorem ****************************)
|
haftmann@33967
|
581 |
|
wenzelm@41671
|
582 |
val _ = Datatype_Aux.message config "Proving induction rule for datatypes ...";
|
haftmann@33967
|
583 |
|
wenzelm@46571
|
584 |
val Rep_inverse_thms =
|
wenzelm@46571
|
585 |
map (fn (_, iso, _) => iso RS subst) newT_iso_axms @
|
wenzelm@46571
|
586 |
map (fn r => r RS @{thm the_inv_f_f} RS subst) iso_inj_thms_unfolded;
|
haftmann@33967
|
587 |
val Rep_inverse_thms' = map (fn r => r RS @{thm the_inv_f_f}) iso_inj_thms_unfolded;
|
haftmann@33967
|
588 |
|
wenzelm@46750
|
589 |
fun mk_indrule_lemma (i, _) T =
|
haftmann@33967
|
590 |
let
|
wenzelm@46750
|
591 |
val Rep_t = Const (nth all_rep_names i, T --> Univ_elT) $ Datatype_Aux.mk_Free "x" T i;
|
wenzelm@46571
|
592 |
val Abs_t =
|
wenzelm@46571
|
593 |
if i < length newTs then
|
wenzelm@46750
|
594 |
Const (#Abs_name (#1 (#2 (nth typedefs i))), Univ_elT --> T)
|
wenzelm@46750
|
595 |
else
|
wenzelm@46750
|
596 |
Const (@{const_name the_inv_into},
|
haftmann@33967
|
597 |
[HOLogic.mk_setT T, T --> Univ_elT, Univ_elT] ---> T) $
|
wenzelm@46571
|
598 |
HOLogic.mk_UNIV T $ Const (nth all_rep_names i, T --> Univ_elT);
|
wenzelm@46750
|
599 |
val prem =
|
wenzelm@46750
|
600 |
HOLogic.imp $
|
haftmann@33967
|
601 |
(Const (nth rep_set_names i, UnivT') $ Rep_t) $
|
wenzelm@46750
|
602 |
(Datatype_Aux.mk_Free "P" (T --> HOLogic.boolT) (i + 1) $ (Abs_t $ Rep_t));
|
wenzelm@46750
|
603 |
val concl =
|
wenzelm@46750
|
604 |
Datatype_Aux.mk_Free "P" (T --> HOLogic.boolT) (i + 1) $ Datatype_Aux.mk_Free "x" T i;
|
wenzelm@46750
|
605 |
in (prem, concl) end;
|
haftmann@33967
|
606 |
|
haftmann@33967
|
607 |
val (indrule_lemma_prems, indrule_lemma_concls) =
|
wenzelm@46750
|
608 |
split_list (map2 mk_indrule_lemma descr' recTs);
|
haftmann@33967
|
609 |
|
haftmann@33967
|
610 |
val cert = cterm_of thy6;
|
haftmann@33967
|
611 |
|
wenzelm@46571
|
612 |
val indrule_lemma =
|
wenzelm@46571
|
613 |
Skip_Proof.prove_global thy6 [] []
|
wenzelm@46571
|
614 |
(Logic.mk_implies
|
wenzelm@46571
|
615 |
(HOLogic.mk_Trueprop (Datatype_Aux.mk_conj indrule_lemma_prems),
|
wenzelm@46571
|
616 |
HOLogic.mk_Trueprop (Datatype_Aux.mk_conj indrule_lemma_concls)))
|
wenzelm@46571
|
617 |
(fn _ =>
|
wenzelm@46571
|
618 |
EVERY
|
haftmann@33967
|
619 |
[REPEAT (etac conjE 1),
|
haftmann@33967
|
620 |
REPEAT (EVERY
|
haftmann@33967
|
621 |
[TRY (rtac conjI 1), resolve_tac Rep_inverse_thms 1,
|
haftmann@33967
|
622 |
etac mp 1, resolve_tac iso_elem_thms 1])]);
|
haftmann@33967
|
623 |
|
haftmann@33967
|
624 |
val Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of indrule_lemma)));
|
wenzelm@46571
|
625 |
val frees =
|
wenzelm@46571
|
626 |
if length Ps = 1 then [Free ("P", snd (dest_Var (hd Ps)))]
|
wenzelm@46571
|
627 |
else map (Free o apfst fst o dest_Var) Ps;
|
haftmann@33967
|
628 |
val indrule_lemma' = cterm_instantiate (map cert Ps ~~ map cert frees) indrule_lemma;
|
haftmann@33967
|
629 |
|
wenzelm@46695
|
630 |
val dt_induct_prop = Datatype_Prop.make_ind descr;
|
wenzelm@46571
|
631 |
val dt_induct =
|
wenzelm@46571
|
632 |
Skip_Proof.prove_global thy6 []
|
wenzelm@46571
|
633 |
(Logic.strip_imp_prems dt_induct_prop)
|
wenzelm@46571
|
634 |
(Logic.strip_imp_concl dt_induct_prop)
|
wenzelm@46571
|
635 |
(fn {prems, ...} =>
|
wenzelm@46571
|
636 |
EVERY
|
wenzelm@46571
|
637 |
[rtac indrule_lemma' 1,
|
wenzelm@46606
|
638 |
(Datatype_Aux.ind_tac rep_induct [] THEN_ALL_NEW Object_Logic.atomize_prems_tac) 1,
|
wenzelm@46571
|
639 |
EVERY (map (fn (prem, r) => (EVERY
|
wenzelm@46571
|
640 |
[REPEAT (eresolve_tac Abs_inverse_thms 1),
|
wenzelm@46571
|
641 |
simp_tac (HOL_basic_ss addsimps (Thm.symmetric r :: Rep_inverse_thms')) 1,
|
wenzelm@46571
|
642 |
DEPTH_SOLVE_1 (ares_tac [prem] 1 ORELSE etac allE 1)]))
|
wenzelm@46749
|
643 |
(prems ~~ (constr_defs @ map mk_meta_eq iso_char_thms)))]);
|
haftmann@33967
|
644 |
|
wenzelm@46774
|
645 |
val ([(_, [dt_induct'])], thy7) =
|
haftmann@33967
|
646 |
thy6
|
wenzelm@46774
|
647 |
|> Global_Theory.note_thmss ""
|
wenzelm@46774
|
648 |
[((Binding.qualify true big_name (Binding.name "induct"), [case_names_induct]),
|
wenzelm@46774
|
649 |
[([dt_induct], [])])]
|
haftmann@33967
|
650 |
||> Theory.checkpoint;
|
haftmann@33967
|
651 |
|
haftmann@33967
|
652 |
in
|
haftmann@33967
|
653 |
((constr_inject', distinct_thms', dt_induct'), thy7)
|
haftmann@33967
|
654 |
end;
|
haftmann@33967
|
655 |
|
haftmann@33967
|
656 |
|
haftmann@33967
|
657 |
|
wenzelm@46572
|
658 |
(** datatype definition **)
|
haftmann@33967
|
659 |
|
wenzelm@46712
|
660 |
(* specifications *)
|
wenzelm@46712
|
661 |
|
wenzelm@46712
|
662 |
type spec = (binding * (string * sort) list * mixfix) * (binding * typ list * mixfix) list;
|
wenzelm@46712
|
663 |
|
wenzelm@46712
|
664 |
type spec_cmd =
|
wenzelm@46712
|
665 |
(binding * (string * string option) list * mixfix) * (binding * string list * mixfix) list;
|
wenzelm@46712
|
666 |
|
wenzelm@46712
|
667 |
local
|
wenzelm@46712
|
668 |
|
wenzelm@46712
|
669 |
fun parse_spec ctxt ((b, args, mx), constrs) =
|
wenzelm@46712
|
670 |
((b, map (apsnd (Typedecl.read_constraint ctxt)) args, mx),
|
wenzelm@46712
|
671 |
constrs |> map (fn (c, Ts, mx') => (c, map (Syntax.parse_typ ctxt) Ts, mx')));
|
wenzelm@46712
|
672 |
|
wenzelm@46712
|
673 |
fun check_specs ctxt (specs: spec list) =
|
wenzelm@46712
|
674 |
let
|
wenzelm@46712
|
675 |
fun prep_spec ((tname, args, mx), constrs) tys =
|
wenzelm@46712
|
676 |
let
|
wenzelm@46712
|
677 |
val (args', tys1) = chop (length args) tys;
|
wenzelm@46712
|
678 |
val (constrs', tys3) = (constrs, tys1) |-> fold_map (fn (cname, cargs, mx') => fn tys2 =>
|
wenzelm@46712
|
679 |
let val (cargs', tys3) = chop (length cargs) tys2;
|
wenzelm@46712
|
680 |
in ((cname, cargs', mx'), tys3) end);
|
wenzelm@46712
|
681 |
in (((tname, map dest_TFree args', mx), constrs'), tys3) end;
|
wenzelm@46712
|
682 |
|
wenzelm@46712
|
683 |
val all_tys =
|
wenzelm@46712
|
684 |
specs |> maps (fn ((_, args, _), cs) => map TFree args @ maps #2 cs)
|
wenzelm@46712
|
685 |
|> Syntax.check_typs ctxt;
|
wenzelm@46712
|
686 |
|
wenzelm@46712
|
687 |
in #1 (fold_map prep_spec specs all_tys) end;
|
wenzelm@46712
|
688 |
|
wenzelm@46712
|
689 |
fun prep_specs parse raw_specs thy =
|
wenzelm@46712
|
690 |
let
|
wenzelm@46712
|
691 |
val ctxt = thy
|
wenzelm@46712
|
692 |
|> Theory.copy
|
wenzelm@46712
|
693 |
|> Sign.add_types_global (map (fn ((b, args, mx), _) => (b, length args, mx)) raw_specs)
|
wenzelm@46712
|
694 |
|> Proof_Context.init_global
|
wenzelm@46712
|
695 |
|> fold (fn ((_, args, _), _) => fold (fn (a, _) =>
|
wenzelm@46712
|
696 |
Variable.declare_typ (TFree (a, dummyS))) args) raw_specs;
|
wenzelm@46712
|
697 |
val specs = check_specs ctxt (map (parse ctxt) raw_specs);
|
wenzelm@46712
|
698 |
in (specs, ctxt) end;
|
wenzelm@46712
|
699 |
|
wenzelm@46712
|
700 |
in
|
wenzelm@46712
|
701 |
|
wenzelm@46712
|
702 |
val read_specs = prep_specs parse_spec;
|
wenzelm@46712
|
703 |
val check_specs = prep_specs (K I);
|
wenzelm@46712
|
704 |
|
wenzelm@46712
|
705 |
end;
|
wenzelm@46712
|
706 |
|
wenzelm@46712
|
707 |
|
wenzelm@46712
|
708 |
(* main commands *)
|
wenzelm@46712
|
709 |
|
wenzelm@46712
|
710 |
fun gen_add_datatype prep_specs config raw_specs thy =
|
haftmann@33967
|
711 |
let
|
haftmann@33967
|
712 |
val _ = Theory.requires thy "Datatype" "datatype definitions";
|
haftmann@33967
|
713 |
|
wenzelm@46712
|
714 |
val (dts, spec_ctxt) = prep_specs raw_specs thy;
|
wenzelm@46712
|
715 |
val ((_, tyvars, _), _) :: _ = dts;
|
wenzelm@46712
|
716 |
val string_of_tyvar = Syntax.string_of_typ spec_ctxt o TFree;
|
haftmann@33967
|
717 |
|
wenzelm@46712
|
718 |
val (new_dts, types_syntax) = dts |> map (fn ((tname, tvs, mx), _) =>
|
wenzelm@46712
|
719 |
let val full_tname = Sign.full_name thy tname in
|
haftmann@33967
|
720 |
(case duplicates (op =) tvs of
|
haftmann@33967
|
721 |
[] =>
|
haftmann@33967
|
722 |
if eq_set (op =) (tyvars, tvs) then ((full_tname, tvs), (tname, mx))
|
wenzelm@46712
|
723 |
else error "Mutually recursive datatypes must have same type parameters"
|
wenzelm@46571
|
724 |
| dups =>
|
wenzelm@46571
|
725 |
error ("Duplicate parameter(s) for datatype " ^ Binding.print tname ^
|
wenzelm@46712
|
726 |
" : " ^ commas (map string_of_tyvar dups)))
|
wenzelm@46712
|
727 |
end) |> split_list;
|
haftmann@33967
|
728 |
val dt_names = map fst new_dts;
|
haftmann@33967
|
729 |
|
haftmann@33967
|
730 |
val _ =
|
wenzelm@46572
|
731 |
(case duplicates (op =) (map fst new_dts) of
|
haftmann@33967
|
732 |
[] => ()
|
wenzelm@46695
|
733 |
| dups => error ("Duplicate datatypes: " ^ commas_quote dups));
|
haftmann@33967
|
734 |
|
wenzelm@46762
|
735 |
fun prep_dt_spec ((tname, tvs, _), constrs) (dts', constr_syntax, i) =
|
haftmann@33967
|
736 |
let
|
wenzelm@46762
|
737 |
fun prep_constr (cname, cargs, mx) (constrs, constr_syntax') =
|
haftmann@33967
|
738 |
let
|
haftmann@33967
|
739 |
val _ =
|
wenzelm@46712
|
740 |
(case subtract (op =) tvs (fold Term.add_tfreesT cargs []) of
|
haftmann@33967
|
741 |
[] => ()
|
wenzelm@46712
|
742 |
| vs => error ("Extra type variables on rhs: " ^ commas (map string_of_tyvar vs)));
|
wenzelm@46712
|
743 |
val c = Sign.full_name_path thy (Binding.name_of tname) cname;
|
wenzelm@35129
|
744 |
in
|
wenzelm@46712
|
745 |
(constrs @ [(c, map (Datatype_Aux.dtyp_of_typ new_dts) cargs)],
|
wenzelm@46762
|
746 |
constr_syntax' @ [(cname, mx)])
|
wenzelm@46571
|
747 |
end handle ERROR msg =>
|
wenzelm@46571
|
748 |
cat_error msg ("The error above occurred in constructor " ^ Binding.print cname ^
|
wenzelm@46571
|
749 |
" of datatype " ^ Binding.print tname);
|
haftmann@33967
|
750 |
|
wenzelm@46712
|
751 |
val (constrs', constr_syntax') = fold prep_constr constrs ([], []);
|
haftmann@33967
|
752 |
in
|
wenzelm@46571
|
753 |
(case duplicates (op =) (map fst constrs') of
|
wenzelm@35129
|
754 |
[] =>
|
wenzelm@46712
|
755 |
(dts' @ [(i, (Sign.full_name thy tname, map Datatype_Aux.DtTFree tvs, constrs'))],
|
wenzelm@46712
|
756 |
constr_syntax @ [constr_syntax'], i + 1)
|
wenzelm@43252
|
757 |
| dups =>
|
wenzelm@46695
|
758 |
error ("Duplicate constructors " ^ commas_quote dups ^
|
wenzelm@46695
|
759 |
" in datatype " ^ Binding.print tname))
|
haftmann@33967
|
760 |
end;
|
haftmann@33967
|
761 |
|
wenzelm@46712
|
762 |
val (dts', constr_syntax, i) = fold prep_dt_spec dts ([], [], 0);
|
wenzelm@46695
|
763 |
|
haftmann@33967
|
764 |
val dt_info = Datatype_Data.get_all thy;
|
wenzelm@46712
|
765 |
val (descr, _) = Datatype_Aux.unfold_datatypes spec_ctxt dts' dt_info dts' i;
|
wenzelm@41671
|
766 |
val _ =
|
wenzelm@41671
|
767 |
Datatype_Aux.check_nonempty descr
|
wenzelm@41671
|
768 |
handle (exn as Datatype_Aux.Datatype_Empty s) =>
|
wenzelm@46695
|
769 |
if #strict config then error ("Nonemptiness check failed for datatype " ^ quote s)
|
wenzelm@41671
|
770 |
else reraise exn;
|
haftmann@33967
|
771 |
|
wenzelm@46572
|
772 |
val _ =
|
wenzelm@46572
|
773 |
Datatype_Aux.message config
|
wenzelm@46712
|
774 |
("Constructing datatype(s) " ^ commas_quote (map (Binding.name_of o #1 o #1) dts));
|
haftmann@33967
|
775 |
in
|
haftmann@33967
|
776 |
thy
|
wenzelm@46695
|
777 |
|> representation_proofs config dt_info descr types_syntax constr_syntax
|
wenzelm@46572
|
778 |
(Datatype_Data.mk_case_names_induct (flat descr))
|
wenzelm@46571
|
779 |
|-> (fn (inject, distinct, induct) =>
|
wenzelm@46763
|
780 |
Rep_Datatype.derive_datatype_props config dt_names descr induct inject distinct)
|
haftmann@33967
|
781 |
end;
|
haftmann@33967
|
782 |
|
wenzelm@46712
|
783 |
val add_datatype = gen_add_datatype check_specs;
|
wenzelm@46735
|
784 |
val add_datatype_cmd = gen_add_datatype read_specs;
|
haftmann@33967
|
785 |
|
haftmann@33967
|
786 |
|
wenzelm@46712
|
787 |
(* outer syntax *)
|
haftmann@33967
|
788 |
|
wenzelm@46712
|
789 |
val spec_cmd =
|
wenzelm@46712
|
790 |
Parse.type_args_constrained -- Parse.binding -- Parse.opt_mixfix --
|
wenzelm@47823
|
791 |
(@{keyword "="} |-- Parse.enum1 "|" (Parse.binding -- Scan.repeat Parse.typ -- Parse.opt_mixfix))
|
wenzelm@46712
|
792 |
>> (fn (((vs, t), mx), cons) => ((t, vs, mx), map Parse.triple1 cons));
|
haftmann@33967
|
793 |
|
haftmann@33967
|
794 |
val _ =
|
wenzelm@36970
|
795 |
Outer_Syntax.command "datatype" "define inductive datatypes" Keyword.thy_decl
|
wenzelm@46735
|
796 |
(Parse.and_list1 spec_cmd
|
wenzelm@46735
|
797 |
>> (Toplevel.theory o (snd oo add_datatype_cmd Datatype_Aux.default_config)));
|
haftmann@33967
|
798 |
|
wenzelm@41671
|
799 |
|
wenzelm@41671
|
800 |
open Datatype_Data;
|
wenzelm@41671
|
801 |
|
haftmann@33967
|
802 |
end;
|