src/HOL/Tools/Ctr_Sugar/ctr_sugar.ML
author blanchet
Mon Apr 28 00:54:31 2014 +0200 (2014-04-28)
changeset 56767 9b311dbd0f55
parent 56657 558afd429255
child 56858 0c3d0bc98abe
permissions -rw-r--r--
restored naming trick
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(*  Title:      HOL/Tools/Ctr_Sugar/ctr_sugar.ML
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    Author:     Jasmin Blanchette, TU Muenchen
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    Copyright   2012, 2013
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Wrapping existing freely generated type's constructors.
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*)
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signature CTR_SUGAR =
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sig
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  type ctr_sugar =
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    {ctrs: term list,
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     casex: term,
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     discs: term list,
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     selss: term list list,
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     exhaust: thm,
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     nchotomy: thm,
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     injects: thm list,
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     distincts: thm list,
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     case_thms: thm list,
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     case_cong: thm,
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     weak_case_cong: thm,
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     split: thm,
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     split_asm: thm,
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     disc_thmss: thm list list,
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     discIs: thm list,
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     sel_thmss: thm list list,
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     disc_excludesss: thm list list list,
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     disc_exhausts: thm list,
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     sel_exhausts: thm list,
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     collapses: thm list,
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     expands: thm list,
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     sel_splits: thm list,
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     sel_split_asms: thm list,
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     case_eq_ifs: thm list};
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  val morph_ctr_sugar: morphism -> ctr_sugar -> ctr_sugar
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  val transfer_ctr_sugar: Proof.context -> ctr_sugar -> ctr_sugar
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  val ctr_sugar_of: Proof.context -> string -> ctr_sugar option
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  val ctr_sugars_of: Proof.context -> ctr_sugar list
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  val ctr_sugar_of_case: Proof.context -> string -> ctr_sugar option
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  val ctr_sugar_interpretation: (ctr_sugar -> theory -> theory) -> theory -> theory
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  val register_ctr_sugar: string -> ctr_sugar -> local_theory -> local_theory
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  val default_register_ctr_sugar_global: string -> ctr_sugar -> theory -> theory
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  val mk_half_pairss: 'a list * 'a list -> ('a * 'a) list list
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  val join_halves: int -> 'a list list -> 'a list list -> 'a list * 'a list list list
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  val mk_ctr: typ list -> term -> term
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  val mk_case: typ list -> typ -> term -> term
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  val mk_disc_or_sel: typ list -> term -> term
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  val name_of_ctr: term -> string
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  val name_of_disc: term -> string
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  val dest_ctr: Proof.context -> string -> term -> term * term list
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  val dest_case: Proof.context -> string -> typ list -> term ->
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    (ctr_sugar * term list * term list) option
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  type ('c, 'a, 'v) ctr_spec = ((binding * 'c) * 'a list) * (binding * 'v) list
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  val disc_of_ctr_spec: ('c, 'a, 'v) ctr_spec -> binding
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  val ctr_of_ctr_spec: ('c, 'a, 'v) ctr_spec -> 'c
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  val args_of_ctr_spec: ('c, 'a, 'v) ctr_spec -> 'a list
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  val sel_defaults_of_ctr_spec: ('c, 'a, 'v) ctr_spec -> (binding * 'v) list
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  val free_constructors: ({prems: thm list, context: Proof.context} -> tactic) list list ->
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    ((bool * bool) * binding) * (term, binding, term) ctr_spec list -> local_theory ->
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    ctr_sugar * local_theory
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  val parse_bound_term: (binding * string) parser
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  val parse_ctr_options: (bool * bool) parser
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  val parse_ctr_spec: 'c parser -> 'a parser -> ('c, 'a, string) ctr_spec parser
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end;
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structure Ctr_Sugar : CTR_SUGAR =
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struct
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open Ctr_Sugar_Util
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open Ctr_Sugar_Tactics
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open Ctr_Sugar_Code
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type ctr_sugar =
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  {ctrs: term list,
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   casex: term,
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   discs: term list,
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   selss: term list list,
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   exhaust: thm,
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   nchotomy: thm,
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   injects: thm list,
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   distincts: thm list,
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   case_thms: thm list,
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   case_cong: thm,
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   weak_case_cong: thm,
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   split: thm,
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   split_asm: thm,
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   disc_thmss: thm list list,
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   discIs: thm list,
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   sel_thmss: thm list list,
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   disc_excludesss: thm list list list,
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   disc_exhausts: thm list,
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   sel_exhausts: thm list,
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   collapses: thm list,
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   expands: thm list,
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   sel_splits: thm list,
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   sel_split_asms: thm list,
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   case_eq_ifs: thm list};
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fun morph_ctr_sugar phi {ctrs, casex, discs, selss, exhaust, nchotomy, injects, distincts,
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    case_thms, case_cong, weak_case_cong, split, split_asm, disc_thmss, discIs, sel_thmss,
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    disc_excludesss, disc_exhausts, sel_exhausts, collapses, expands, sel_splits, sel_split_asms,
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    case_eq_ifs} =
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  {ctrs = map (Morphism.term phi) ctrs,
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   casex = Morphism.term phi casex,
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   discs = map (Morphism.term phi) discs,
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   selss = map (map (Morphism.term phi)) selss,
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   exhaust = Morphism.thm phi exhaust,
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   nchotomy = Morphism.thm phi nchotomy,
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   injects = map (Morphism.thm phi) injects,
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   distincts = map (Morphism.thm phi) distincts,
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   case_thms = map (Morphism.thm phi) case_thms,
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   case_cong = Morphism.thm phi case_cong,
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   weak_case_cong = Morphism.thm phi weak_case_cong,
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   split = Morphism.thm phi split,
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   split_asm = Morphism.thm phi split_asm,
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   disc_thmss = map (map (Morphism.thm phi)) disc_thmss,
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   discIs = map (Morphism.thm phi) discIs,
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   sel_thmss = map (map (Morphism.thm phi)) sel_thmss,
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   disc_excludesss = map (map (map (Morphism.thm phi))) disc_excludesss,
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   disc_exhausts = map (Morphism.thm phi) disc_exhausts,
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   sel_exhausts = map (Morphism.thm phi) sel_exhausts,
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   collapses = map (Morphism.thm phi) collapses,
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   expands = map (Morphism.thm phi) expands,
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   sel_splits = map (Morphism.thm phi) sel_splits,
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   sel_split_asms = map (Morphism.thm phi) sel_split_asms,
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   case_eq_ifs = map (Morphism.thm phi) case_eq_ifs};
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val transfer_ctr_sugar =
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  morph_ctr_sugar o Morphism.transfer_morphism o Proof_Context.theory_of;
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structure Data = Generic_Data
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(
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  type T = ctr_sugar Symtab.table;
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  val empty = Symtab.empty;
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  val extend = I;
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  fun merge data : T = Symtab.merge (K true) data;
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);
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fun ctr_sugar_of ctxt =
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  Symtab.lookup (Data.get (Context.Proof ctxt))
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  #> Option.map (transfer_ctr_sugar ctxt);
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fun ctr_sugars_of ctxt =
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  Symtab.fold (cons o transfer_ctr_sugar ctxt o snd) (Data.get (Context.Proof ctxt)) [];
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fun ctr_sugar_of_case ctxt s =
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  find_first (fn {casex = Const (s', _), ...} => s' = s | _ => false) (ctr_sugars_of ctxt);
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structure Ctr_Sugar_Interpretation = Interpretation
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(
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  type T = ctr_sugar;
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  val eq: T * T -> bool = op = o pairself #ctrs;
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);
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fun with_repaired_path f (ctr_sugar as {ctrs = ctr1 :: _, ...} : ctr_sugar) thy =
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  thy
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  |> Sign.root_path
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  |> Sign.add_path (Long_Name.qualifier (fst (dest_Type (body_type (fastype_of ctr1)))))
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  |> (fn thy => f (morph_ctr_sugar (Morphism.transfer_morphism thy) ctr_sugar) thy)
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  |> Sign.restore_naming thy;
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fun ctr_sugar_interpretation f = Ctr_Sugar_Interpretation.interpretation (with_repaired_path f);
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fun register_ctr_sugar key ctr_sugar =
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  Local_Theory.declaration {syntax = false, pervasive = true}
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    (fn phi => Data.map (Symtab.update (key, morph_ctr_sugar phi ctr_sugar)))
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  #> Local_Theory.background_theory (Ctr_Sugar_Interpretation.data ctr_sugar);
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fun default_register_ctr_sugar_global key ctr_sugar thy =
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  let val tab = Data.get (Context.Theory thy) in
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    if Symtab.defined tab key then
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      thy
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    else
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      thy
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      |> Context.theory_map (Data.put (Symtab.update_new (key, ctr_sugar) tab))
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      |> Ctr_Sugar_Interpretation.data ctr_sugar
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  end;
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val isN = "is_";
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val unN = "un_";
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fun mk_unN 1 1 suf = unN ^ suf
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  | mk_unN _ l suf = unN ^ suf ^ string_of_int l;
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val caseN = "case";
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val case_congN = "case_cong";
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val case_eq_ifN = "case_eq_if";
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val collapseN = "collapse";
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val disc_excludeN = "disc_exclude";
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val disc_exhaustN = "disc_exhaust";
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val discN = "disc";
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val discIN = "discI";
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val distinctN = "distinct";
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val exhaustN = "exhaust";
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val expandN = "expand";
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val injectN = "inject";
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val nchotomyN = "nchotomy";
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val selN = "sel";
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val sel_exhaustN = "sel_exhaust";
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val sel_splitN = "sel_split";
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val sel_split_asmN = "sel_split_asm";
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val splitN = "split";
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val splitsN = "splits";
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val split_asmN = "split_asm";
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val weak_case_cong_thmsN = "weak_case_cong";
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val cong_attrs = @{attributes [cong]};
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val dest_attrs = @{attributes [dest]};
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val safe_elim_attrs = @{attributes [elim!]};
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val iff_attrs = @{attributes [iff]};
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val inductsimp_attrs = @{attributes [induct_simp]};
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val nitpicksimp_attrs = @{attributes [nitpick_simp]};
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val simp_attrs = @{attributes [simp]};
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val code_nitpicksimp_attrs = Code.add_default_eqn_attrib :: nitpicksimp_attrs;
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val code_nitpicksimp_simp_attrs = code_nitpicksimp_attrs @ simp_attrs;
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fun unflat_lookup eq xs ys = map (fn xs' => permute_like_unique eq xs xs' ys);
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fun mk_half_pairss' _ ([], []) = []
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  | mk_half_pairss' indent (x :: xs, _ :: ys) =
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    indent @ fold_rev (cons o single o pair x) ys (mk_half_pairss' ([] :: indent) (xs, ys));
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fun mk_half_pairss p = mk_half_pairss' [[]] p;
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fun join_halves n half_xss other_half_xss =
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  (splice (flat half_xss) (flat other_half_xss),
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   map2 (map2 append) (Library.chop_groups n half_xss)
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     (transpose (Library.chop_groups n other_half_xss)));
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fun mk_undefined T = Const (@{const_name undefined}, T);
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fun mk_ctr Ts t =
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  let val Type (_, Ts0) = body_type (fastype_of t) in
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    subst_nonatomic_types (Ts0 ~~ Ts) t
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  end;
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fun mk_case Ts T t =
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  let val (Type (_, Ts0), body) = strip_type (fastype_of t) |>> List.last in
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    subst_nonatomic_types ((body, T) :: (Ts0 ~~ Ts)) t
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  end;
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fun mk_disc_or_sel Ts t =
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  subst_nonatomic_types (snd (Term.dest_Type (domain_type (fastype_of t))) ~~ Ts) t;
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fun name_of_const what t =
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  (case head_of t of
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    Const (s, _) => s
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  | Free (s, _) => s
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  | _ => error ("Cannot extract name of " ^ what));
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val name_of_ctr = name_of_const "constructor";
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val notN = "not_";
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val eqN = "eq_";
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val neqN = "neq_";
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fun name_of_disc t =
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  (case head_of t of
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    Abs (_, _, @{const Not} $ (t' $ Bound 0)) =>
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    Long_Name.map_base_name (prefix notN) (name_of_disc t')
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  | Abs (_, _, Const (@{const_name HOL.eq}, _) $ Bound 0 $ t') =>
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    Long_Name.map_base_name (prefix eqN) (name_of_disc t')
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  | Abs (_, _, @{const Not} $ (Const (@{const_name HOL.eq}, _) $ Bound 0 $ t')) =>
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    Long_Name.map_base_name (prefix neqN) (name_of_disc t')
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  | t' => name_of_const "destructor" t');
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val base_name_of_ctr = Long_Name.base_name o name_of_ctr;
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fun dest_ctr ctxt s t =
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  let val (f, args) = Term.strip_comb t in
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    (case ctr_sugar_of ctxt s of
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      SOME {ctrs, ...} =>
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      (case find_first (can (fo_match ctxt f)) ctrs of
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        SOME f' => (f', args)
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      | NONE => raise Fail "dest_ctr")
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    | NONE => raise Fail "dest_ctr")
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  end;
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fun dest_case ctxt s Ts t =
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  (case Term.strip_comb t of
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    (Const (c, _), args as _ :: _) =>
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    (case ctr_sugar_of ctxt s of
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      SOME (ctr_sugar as {casex = Const (case_name, _), discs = discs0, selss = selss0, ...}) =>
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      if case_name = c then
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        let val n = length discs0 in
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          if n < length args then
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            let
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              val (branches, obj :: leftovers) = chop n args;
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              val discs = map (mk_disc_or_sel Ts) discs0;
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              val selss = map (map (mk_disc_or_sel Ts)) selss0;
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              val conds = map (rapp obj) discs;
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              val branch_argss = map (fn sels => map (rapp obj) sels @ leftovers) selss;
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              val branches' = map2 (curry Term.betapplys) branches branch_argss;
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            in
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              SOME (ctr_sugar, conds, branches')
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            end
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          else
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            NONE
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        end
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      else
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        NONE
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    | _ => NONE)
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  | _ => NONE);
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fun eta_expand_arg xs f_xs = fold_rev Term.lambda xs f_xs;
blanchet@49437
   311
blanchet@55469
   312
type ('c, 'a, 'v) ctr_spec = ((binding * 'c) * 'a list) * (binding * 'v) list;
blanchet@55469
   313
blanchet@55469
   314
fun disc_of_ctr_spec (((disc, _), _), _) = disc;
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   315
fun ctr_of_ctr_spec (((_, ctr), _), _) = ctr;
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   316
fun args_of_ctr_spec ((_, args), _) = args;
blanchet@55469
   317
fun sel_defaults_of_ctr_spec (_, ds) = ds;
blanchet@55469
   318
blanchet@55469
   319
fun prepare_free_constructors prep_term (((no_discs_sels, no_code), raw_case_binding), ctr_specs)
blanchet@55469
   320
    no_defs_lthy =
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   321
  let
blanchet@49019
   322
    (* TODO: sanity checks on arguments *)
blanchet@49025
   323
blanchet@55469
   324
    val raw_ctrs = map ctr_of_ctr_spec ctr_specs;
blanchet@55469
   325
    val raw_disc_bindings = map disc_of_ctr_spec ctr_specs;
blanchet@55469
   326
    val raw_sel_bindingss = map args_of_ctr_spec ctr_specs;
blanchet@55469
   327
    val raw_sel_defaultss = map sel_defaults_of_ctr_spec ctr_specs;
blanchet@55469
   328
blanchet@49280
   329
    val n = length raw_ctrs;
blanchet@49054
   330
    val ks = 1 upto n;
blanchet@49054
   331
blanchet@49121
   332
    val _ = if n > 0 then () else error "No constructors specified";
blanchet@49121
   333
blanchet@49280
   334
    val ctrs0 = map (prep_term no_defs_lthy) raw_ctrs;
blanchet@55470
   335
    val sel_defaultss = map (map (apsnd (prep_term no_defs_lthy))) raw_sel_defaultss;
blanchet@49280
   336
blanchet@53908
   337
    val Type (fcT_name, As0) = body_type (fastype_of (hd ctrs0));
blanchet@53908
   338
    val fc_b_name = Long_Name.base_name fcT_name;
blanchet@53908
   339
    val fc_b = Binding.name fc_b_name;
blanchet@49055
   340
blanchet@55410
   341
    fun qualify mandatory = Binding.qualify mandatory fc_b_name;
blanchet@49633
   342
blanchet@54386
   343
    fun dest_TFree_or_TVar (TFree sS) = sS
blanchet@53268
   344
      | dest_TFree_or_TVar (TVar ((s, _), S)) = (s, S)
blanchet@53268
   345
      | dest_TFree_or_TVar _ = error "Invalid type argument";
blanchet@52965
   346
blanchet@53268
   347
    val (unsorted_As, B) =
blanchet@49055
   348
      no_defs_lthy
blanchet@53268
   349
      |> variant_tfrees (map (fst o dest_TFree_or_TVar) As0)
blanchet@49055
   350
      ||> the_single o fst o mk_TFrees 1;
blanchet@49055
   351
blanchet@53268
   352
    val As = map2 (resort_tfree o snd o dest_TFree_or_TVar) As0 unsorted_As;
blanchet@53268
   353
blanchet@53908
   354
    val fcT = Type (fcT_name, As);
blanchet@49055
   355
    val ctrs = map (mk_ctr As) ctrs0;
blanchet@49055
   356
    val ctr_Tss = map (binder_types o fastype_of) ctrs;
blanchet@49055
   357
blanchet@49055
   358
    val ms = map length ctr_Tss;
blanchet@49055
   359
blanchet@55470
   360
    fun can_definitely_rely_on_disc k = not (Binding.is_empty (nth raw_disc_bindings (k - 1)));
blanchet@51790
   361
    fun can_rely_on_disc k =
blanchet@51790
   362
      can_definitely_rely_on_disc k orelse (k = 1 andalso not (can_definitely_rely_on_disc 2));
blanchet@53925
   363
    fun should_omit_disc_binding k = n = 1 orelse (n = 2 andalso can_rely_on_disc (3 - k));
blanchet@51790
   364
blanchet@51790
   365
    fun is_disc_binding_valid b =
blanchet@51790
   366
      not (Binding.is_empty b orelse Binding.eq_name (b, equal_binding));
blanchet@51787
   367
blanchet@52322
   368
    val standard_disc_binding = Binding.name o prefix isN o base_name_of_ctr;
blanchet@49120
   369
blanchet@49336
   370
    val disc_bindings =
blanchet@55470
   371
      raw_disc_bindings
blanchet@49120
   372
      |> map4 (fn k => fn m => fn ctr => fn disc =>
blanchet@51790
   373
        qualify false
blanchet@51787
   374
          (if Binding.is_empty disc then
blanchet@51790
   375
             if should_omit_disc_binding k then disc else standard_disc_binding ctr
blanchet@51790
   376
           else if Binding.eq_name (disc, equal_binding) then
blanchet@51790
   377
             if m = 0 then disc
blanchet@51790
   378
             else error "Cannot use \"=\" syntax for discriminating nonnullary constructor"
blanchet@51790
   379
           else if Binding.eq_name (disc, standard_binding) then
blanchet@51790
   380
             standard_disc_binding ctr
blanchet@49302
   381
           else
blanchet@51790
   382
             disc)) ks ms ctrs0;
blanchet@49056
   383
blanchet@51787
   384
    fun standard_sel_binding m l = Binding.name o mk_unN m l o base_name_of_ctr;
blanchet@49120
   385
blanchet@49336
   386
    val sel_bindingss =
blanchet@55470
   387
      map3 (fn ctr => fn m => map2 (fn l => fn sel =>
blanchet@49633
   388
        qualify false
blanchet@51790
   389
          (if Binding.is_empty sel orelse Binding.eq_name (sel, standard_binding) then
blanchet@51787
   390
            standard_sel_binding m l ctr
blanchet@49302
   391
          else
blanchet@55470
   392
            sel)) (1 upto m) o pad_list Binding.empty m) ctrs0 ms raw_sel_bindingss;
blanchet@49020
   393
blanchet@49201
   394
    val case_Ts = map (fn Ts => Ts ---> B) ctr_Tss;
blanchet@49043
   395
blanchet@55409
   396
    val (((((((([exh_y], (xss, xss')), yss), fs), gs), [u', v']), [w]), (p, p')), names_lthy) =
blanchet@55409
   397
      no_defs_lthy
blanchet@55409
   398
      |> mk_Frees "y" [fcT] (* for compatibility with "datatype_realizer.ML" *)
blanchet@55409
   399
      ||>> mk_Freess' "x" ctr_Tss
blanchet@49025
   400
      ||>> mk_Freess "y" ctr_Tss
blanchet@49201
   401
      ||>> mk_Frees "f" case_Ts
blanchet@49201
   402
      ||>> mk_Frees "g" case_Ts
blanchet@53908
   403
      ||>> (apfst (map (rpair fcT)) oo Variable.variant_fixes) [fc_b_name, fc_b_name ^ "'"]
blanchet@52968
   404
      ||>> mk_Frees "z" [B]
blanchet@49043
   405
      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "P") HOLogic.boolT;
blanchet@49043
   406
blanchet@49498
   407
    val u = Free u';
blanchet@49498
   408
    val v = Free v';
blanchet@49463
   409
    val q = Free (fst p', mk_pred1T B);
blanchet@49020
   410
blanchet@49025
   411
    val xctrs = map2 (curry Term.list_comb) ctrs xss;
blanchet@49025
   412
    val yctrs = map2 (curry Term.list_comb) ctrs yss;
blanchet@49032
   413
blanchet@49043
   414
    val xfs = map2 (curry Term.list_comb) fs xss;
blanchet@49043
   415
    val xgs = map2 (curry Term.list_comb) gs xss;
blanchet@49043
   416
blanchet@52968
   417
    (* TODO: Eta-expension is for compatibility with the old datatype package (but it also provides
blanchet@52968
   418
       nicer names). Consider removing. *)
blanchet@52968
   419
    val eta_fs = map2 eta_expand_arg xss xfs;
blanchet@52968
   420
    val eta_gs = map2 eta_expand_arg xss xgs;
blanchet@52968
   421
blanchet@52968
   422
    val case_binding =
blanchet@52968
   423
      qualify false
blanchet@52968
   424
        (if Binding.is_empty raw_case_binding orelse
blanchet@52968
   425
            Binding.eq_name (raw_case_binding, standard_binding) then
blanchet@54493
   426
           Binding.prefix_name (caseN ^ "_") fc_b
blanchet@52968
   427
         else
blanchet@52968
   428
           raw_case_binding);
blanchet@52968
   429
blanchet@52968
   430
    fun mk_case_disj xctr xf xs =
blanchet@52968
   431
      list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (u, xctr), HOLogic.mk_eq (w, xf)));
blanchet@52968
   432
blanchet@53925
   433
    val case_rhs = fold_rev (fold_rev Term.lambda) [fs, [u]]
blanchet@53925
   434
      (Const (@{const_name The}, (B --> HOLogic.boolT) --> B) $
blanchet@53925
   435
         Term.lambda w (Library.foldr1 HOLogic.mk_disj (map3 mk_case_disj xctrs xfs xss)));
blanchet@52968
   436
blanchet@52968
   437
    val ((raw_case, (_, raw_case_def)), (lthy', lthy)) = no_defs_lthy
blanchet@54155
   438
      |> Local_Theory.define ((case_binding, NoSyn),
blanchet@54155
   439
        ((Binding.conceal (Thm.def_binding case_binding), []), case_rhs))
blanchet@52968
   440
      ||> `Local_Theory.restore;
blanchet@52968
   441
blanchet@52968
   442
    val phi = Proof_Context.export_morphism lthy lthy';
blanchet@52968
   443
blanchet@52968
   444
    val case_def = Morphism.thm phi raw_case_def;
blanchet@52968
   445
blanchet@52968
   446
    val case0 = Morphism.term phi raw_case;
blanchet@52968
   447
    val casex = mk_case As B case0;
blanchet@52968
   448
blanchet@51759
   449
    val fcase = Term.list_comb (casex, fs);
blanchet@51759
   450
blanchet@51759
   451
    val ufcase = fcase $ u;
blanchet@51759
   452
    val vfcase = fcase $ v;
blanchet@51759
   453
blanchet@51759
   454
    val eta_fcase = Term.list_comb (casex, eta_fs);
blanchet@51759
   455
    val eta_gcase = Term.list_comb (casex, eta_gs);
blanchet@49020
   456
blanchet@51759
   457
    val eta_ufcase = eta_fcase $ u;
blanchet@51759
   458
    val eta_vgcase = eta_gcase $ v;
blanchet@49486
   459
blanchet@49591
   460
    fun mk_uu_eq () = HOLogic.mk_eq (u, u);
blanchet@49486
   461
blanchet@49591
   462
    val uv_eq = mk_Trueprop_eq (u, v);
blanchet@49486
   463
blanchet@49486
   464
    val exist_xs_u_eq_ctrs =
blanchet@49486
   465
      map2 (fn xctr => fn xs => list_exists_free xs (HOLogic.mk_eq (u, xctr))) xctrs xss;
blanchet@49022
   466
blanchet@51743
   467
    val unique_disc_no_def = TrueI; (*arbitrary marker*)
blanchet@51743
   468
    val alternate_disc_no_def = FalseE; (*arbitrary marker*)
blanchet@51743
   469
blanchet@49486
   470
    fun alternate_disc_lhs get_udisc k =
blanchet@49116
   471
      HOLogic.mk_not
blanchet@51790
   472
        (let val b = nth disc_bindings (k - 1) in
blanchet@51790
   473
           if is_disc_binding_valid b then get_udisc b (k - 1) else nth exist_xs_u_eq_ctrs (k - 1)
blanchet@51790
   474
         end);
blanchet@49116
   475
blanchet@53917
   476
    val (all_sels_distinct, discs, selss, disc_defs, sel_defs, sel_defss, lthy') =
blanchet@52969
   477
      if no_discs_sels then
blanchet@55407
   478
        (true, [], [], [], [], [], lthy')
blanchet@49278
   479
      else
blanchet@49278
   480
        let
blanchet@53908
   481
          fun disc_free b = Free (Binding.name_of b, mk_pred1T fcT);
blanchet@49025
   482
blanchet@54634
   483
          fun disc_spec b exist_xs_u_eq_ctr = mk_Trueprop_eq (disc_free b $ u, exist_xs_u_eq_ctr);
blanchet@54634
   484
blanchet@49500
   485
          fun alternate_disc k =
blanchet@49500
   486
            Term.lambda u (alternate_disc_lhs (K o rapp u o disc_free) (3 - k));
blanchet@49278
   487
blanchet@49280
   488
          fun mk_sel_case_args b proto_sels T =
blanchet@49280
   489
            map2 (fn Ts => fn k =>
blanchet@49280
   490
              (case AList.lookup (op =) proto_sels k of
blanchet@49280
   491
                NONE =>
blanchet@49364
   492
                (case AList.lookup Binding.eq_name (rev (nth sel_defaultss (k - 1))) b of
blanchet@49364
   493
                  NONE => fold_rev (Term.lambda o curry Free Name.uu) Ts (mk_undefined T)
blanchet@52968
   494
                | SOME t => t |> Type.constraint (Ts ---> T) |> Syntax.check_term lthy)
blanchet@49280
   495
              | SOME (xs, x) => fold_rev Term.lambda xs x)) ctr_Tss ks;
blanchet@49258
   496
blanchet@54634
   497
          fun sel_spec b proto_sels =
blanchet@49278
   498
            let
blanchet@49278
   499
              val _ =
blanchet@49278
   500
                (case duplicates (op =) (map fst proto_sels) of
blanchet@49278
   501
                   k :: _ => error ("Duplicate selector name " ^ quote (Binding.name_of b) ^
blanchet@49278
   502
                     " for constructor " ^
blanchet@52968
   503
                     quote (Syntax.string_of_term lthy (nth ctrs (k - 1))))
blanchet@49278
   504
                 | [] => ())
blanchet@49278
   505
              val T =
blanchet@49278
   506
                (case distinct (op =) (map (fastype_of o snd o snd) proto_sels) of
blanchet@49278
   507
                  [T] => T
blanchet@49278
   508
                | T :: T' :: _ => error ("Inconsistent range type for selector " ^
blanchet@52968
   509
                    quote (Binding.name_of b) ^ ": " ^ quote (Syntax.string_of_typ lthy T) ^ " vs. "
blanchet@52968
   510
                    ^ quote (Syntax.string_of_typ lthy T')));
blanchet@49278
   511
            in
blanchet@54634
   512
              mk_Trueprop_eq (Free (Binding.name_of b, fcT --> T) $ u,
blanchet@54634
   513
                Term.list_comb (mk_case As T case0, mk_sel_case_args b proto_sels T) $ u)
blanchet@49278
   514
            end;
blanchet@49116
   515
blanchet@49336
   516
          val sel_bindings = flat sel_bindingss;
blanchet@49336
   517
          val uniq_sel_bindings = distinct Binding.eq_name sel_bindings;
blanchet@49336
   518
          val all_sels_distinct = (length uniq_sel_bindings = length sel_bindings);
blanchet@49285
   519
blanchet@49336
   520
          val sel_binding_index =
blanchet@49336
   521
            if all_sels_distinct then 1 upto length sel_bindings
blanchet@49336
   522
            else map (fn b => find_index (curry Binding.eq_name b) uniq_sel_bindings) sel_bindings;
blanchet@49285
   523
blanchet@49285
   524
          val proto_sels = flat (map3 (fn k => fn xs => map (fn x => (k, (xs, x)))) ks xss xss);
blanchet@49300
   525
          val sel_infos =
blanchet@49336
   526
            AList.group (op =) (sel_binding_index ~~ proto_sels)
blanchet@49285
   527
            |> sort (int_ord o pairself fst)
blanchet@49336
   528
            |> map snd |> curry (op ~~) uniq_sel_bindings;
blanchet@49336
   529
          val sel_bindings = map fst sel_infos;
blanchet@49258
   530
blanchet@49336
   531
          fun unflat_selss xs = unflat_lookup Binding.eq_name sel_bindings xs sel_bindingss;
blanchet@49258
   532
blanchet@49278
   533
          val (((raw_discs, raw_disc_defs), (raw_sels, raw_sel_defs)), (lthy', lthy)) =
blanchet@52968
   534
            lthy
blanchet@51809
   535
            |> apfst split_list o fold_map3 (fn k => fn exist_xs_u_eq_ctr => fn b =>
blanchet@54634
   536
                if Binding.is_empty b then
blanchet@54634
   537
                  if n = 1 then pair (Term.lambda u (mk_uu_eq ()), unique_disc_no_def)
blanchet@54634
   538
                  else pair (alternate_disc k, alternate_disc_no_def)
blanchet@54634
   539
                else if Binding.eq_name (b, equal_binding) then
blanchet@54634
   540
                  pair (Term.lambda u exist_xs_u_eq_ctr, refl)
blanchet@54634
   541
                else
blanchet@54634
   542
                  Specification.definition (SOME (b, NONE, NoSyn),
blanchet@54634
   543
                    ((Thm.def_binding b, []), disc_spec b exist_xs_u_eq_ctr)) #>> apsnd snd)
blanchet@54634
   544
              ks exist_xs_u_eq_ctrs disc_bindings
blanchet@49278
   545
            ||>> apfst split_list o fold_map (fn (b, proto_sels) =>
blanchet@54634
   546
              Specification.definition (SOME (b, NONE, NoSyn),
blanchet@54634
   547
                ((Thm.def_binding b, []), sel_spec b proto_sels)) #>> apsnd snd) sel_infos
blanchet@49278
   548
            ||> `Local_Theory.restore;
blanchet@49022
   549
blanchet@49278
   550
          val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49025
   551
blanchet@49278
   552
          val disc_defs = map (Morphism.thm phi) raw_disc_defs;
blanchet@49281
   553
          val sel_defs = map (Morphism.thm phi) raw_sel_defs;
blanchet@49281
   554
          val sel_defss = unflat_selss sel_defs;
blanchet@49278
   555
blanchet@49278
   556
          val discs0 = map (Morphism.term phi) raw_discs;
blanchet@49278
   557
          val selss0 = unflat_selss (map (Morphism.term phi) raw_sels);
blanchet@49028
   558
blanchet@49278
   559
          val discs = map (mk_disc_or_sel As) discs0;
blanchet@49278
   560
          val selss = map (map (mk_disc_or_sel As)) selss0;
blanchet@49278
   561
        in
blanchet@53917
   562
          (all_sels_distinct, discs, selss, disc_defs, sel_defs, sel_defss, lthy')
blanchet@49278
   563
        end;
blanchet@49025
   564
blanchet@49032
   565
    fun mk_imp_p Qs = Logic.list_implies (Qs, HOLogic.mk_Trueprop p);
blanchet@49029
   566
blanchet@49458
   567
    val exhaust_goal =
blanchet@55409
   568
      let fun mk_prem xctr xs = fold_rev Logic.all xs (mk_imp_p [mk_Trueprop_eq (exh_y, xctr)]) in
blanchet@55409
   569
        fold_rev Logic.all [p, exh_y] (mk_imp_p (map2 mk_prem xctrs xss))
blanchet@49020
   570
      end;
blanchet@49019
   571
blanchet@49484
   572
    val inject_goalss =
blanchet@49017
   573
      let
blanchet@49034
   574
        fun mk_goal _ _ [] [] = []
blanchet@49025
   575
          | mk_goal xctr yctr xs ys =
blanchet@49121
   576
            [fold_rev Logic.all (xs @ ys) (mk_Trueprop_eq (HOLogic.mk_eq (xctr, yctr),
blanchet@49121
   577
              Library.foldr1 HOLogic.mk_conj (map2 (curry HOLogic.mk_eq) xs ys)))];
blanchet@49017
   578
      in
blanchet@49034
   579
        map4 mk_goal xctrs yctrs xss yss
blanchet@49017
   580
      end;
blanchet@49017
   581
blanchet@49484
   582
    val half_distinct_goalss =
blanchet@49121
   583
      let
blanchet@49203
   584
        fun mk_goal ((xs, xc), (xs', xc')) =
blanchet@49121
   585
          fold_rev Logic.all (xs @ xs')
blanchet@49203
   586
            (HOLogic.mk_Trueprop (HOLogic.mk_not (HOLogic.mk_eq (xc, xc'))));
blanchet@49121
   587
      in
blanchet@49585
   588
        map (map mk_goal) (mk_half_pairss (`I (xss ~~ xctrs)))
blanchet@49121
   589
      end;
blanchet@49019
   590
blanchet@52968
   591
    val goalss = [exhaust_goal] :: inject_goalss @ half_distinct_goalss;
blanchet@49019
   592
blanchet@49019
   593
    fun after_qed thmss lthy =
blanchet@49019
   594
      let
blanchet@55409
   595
        val ([exhaust_thm0], (inject_thmss, half_distinct_thmss)) = (hd thmss, chop n (tl thmss));
blanchet@55409
   596
        (* for "datatype_realizer.ML": *)
blanchet@55409
   597
        val exhaust_thm =
blanchet@55409
   598
          Thm.name_derivation (fcT_name ^ Long_Name.separator ^ exhaustN) exhaust_thm0;
blanchet@49019
   599
blanchet@49438
   600
        val inject_thms = flat inject_thmss;
blanchet@49438
   601
blanchet@53210
   602
        val rho_As = map (pairself (certifyT lthy)) (map Logic.varifyT_global As ~~ As);
blanchet@49486
   603
blanchet@49486
   604
        fun inst_thm t thm =
blanchet@49486
   605
          Drule.instantiate' [] [SOME (certify lthy t)]
blanchet@53210
   606
            (Thm.instantiate (rho_As, []) (Drule.zero_var_indexes thm));
blanchet@49486
   607
blanchet@49486
   608
        val uexhaust_thm = inst_thm u exhaust_thm;
blanchet@49032
   609
blanchet@49300
   610
        val exhaust_cases = map base_name_of_ctr ctrs;
blanchet@49300
   611
blanchet@49048
   612
        val other_half_distinct_thmss = map (map (fn thm => thm RS not_sym)) half_distinct_thmss;
blanchet@49048
   613
blanchet@49486
   614
        val (distinct_thms, (distinct_thmsss', distinct_thmsss)) =
blanchet@49585
   615
          join_halves n half_distinct_thmss other_half_distinct_thmss ||> `transpose;
blanchet@49019
   616
blanchet@49020
   617
        val nchotomy_thm =
blanchet@49020
   618
          let
blanchet@49020
   619
            val goal =
blanchet@49486
   620
              HOLogic.mk_Trueprop (HOLogic.mk_all (fst u', snd u',
blanchet@49486
   621
                Library.foldr1 HOLogic.mk_disj exist_xs_u_eq_ctrs));
blanchet@49020
   622
          in
wenzelm@51551
   623
            Goal.prove_sorry lthy [] [] goal (fn _ => mk_nchotomy_tac n exhaust_thm)
traytel@49667
   624
            |> Thm.close_derivation
blanchet@49020
   625
          end;
blanchet@49020
   626
blanchet@52968
   627
        val case_thms =
blanchet@52968
   628
          let
blanchet@52968
   629
            val goals =
blanchet@52968
   630
              map3 (fn xctr => fn xf => fn xs =>
blanchet@52968
   631
                fold_rev Logic.all (fs @ xs) (mk_Trueprop_eq (fcase $ xctr, xf))) xctrs xfs xss;
blanchet@52968
   632
          in
blanchet@52968
   633
            map4 (fn k => fn goal => fn injects => fn distinctss =>
blanchet@52968
   634
                Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@52968
   635
                  mk_case_tac ctxt n k case_def injects distinctss)
blanchet@52968
   636
                |> Thm.close_derivation)
blanchet@52968
   637
              ks goals inject_thmss distinct_thmsss
blanchet@52968
   638
          end;
blanchet@52968
   639
blanchet@53917
   640
        val (case_cong_thm, weak_case_cong_thm) =
blanchet@53917
   641
          let
blanchet@53917
   642
            fun mk_prem xctr xs xf xg =
blanchet@53917
   643
              fold_rev Logic.all xs (Logic.mk_implies (mk_Trueprop_eq (v, xctr),
blanchet@53917
   644
                mk_Trueprop_eq (xf, xg)));
blanchet@53917
   645
blanchet@53917
   646
            val goal =
blanchet@53917
   647
              Logic.list_implies (uv_eq :: map4 mk_prem xctrs xss xfs xgs,
blanchet@53917
   648
                 mk_Trueprop_eq (eta_ufcase, eta_vgcase));
blanchet@53917
   649
            val weak_goal = Logic.mk_implies (uv_eq, mk_Trueprop_eq (ufcase, vfcase));
blanchet@53917
   650
          in
blanchet@53917
   651
            (Goal.prove_sorry lthy [] [] goal (fn _ => mk_case_cong_tac lthy uexhaust_thm case_thms),
blanchet@53917
   652
             Goal.prove_sorry lthy [] [] weak_goal (K (etac arg_cong 1)))
blanchet@55409
   653
            |> pairself (singleton (Proof_Context.export names_lthy lthy) #>
blanchet@55409
   654
              Thm.close_derivation)
blanchet@53917
   655
          end;
blanchet@53917
   656
blanchet@53917
   657
        val split_lhs = q $ ufcase;
blanchet@53917
   658
blanchet@53917
   659
        fun mk_split_conjunct xctr xs f_xs =
blanchet@53917
   660
          list_all_free xs (HOLogic.mk_imp (HOLogic.mk_eq (u, xctr), q $ f_xs));
blanchet@53917
   661
        fun mk_split_disjunct xctr xs f_xs =
blanchet@53917
   662
          list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (u, xctr),
blanchet@53917
   663
            HOLogic.mk_not (q $ f_xs)));
blanchet@53917
   664
blanchet@53917
   665
        fun mk_split_goal xctrs xss xfs =
blanchet@53917
   666
          mk_Trueprop_eq (split_lhs, Library.foldr1 HOLogic.mk_conj
blanchet@53917
   667
            (map3 mk_split_conjunct xctrs xss xfs));
blanchet@53917
   668
        fun mk_split_asm_goal xctrs xss xfs =
blanchet@53917
   669
          mk_Trueprop_eq (split_lhs, HOLogic.mk_not (Library.foldr1 HOLogic.mk_disj
blanchet@53917
   670
            (map3 mk_split_disjunct xctrs xss xfs)));
blanchet@53917
   671
blanchet@53917
   672
        fun prove_split selss goal =
blanchet@53917
   673
          Goal.prove_sorry lthy [] [] goal (fn _ =>
blanchet@53917
   674
            mk_split_tac lthy uexhaust_thm case_thms selss inject_thmss distinct_thmsss)
blanchet@55409
   675
          |> singleton (Proof_Context.export names_lthy lthy)
blanchet@55409
   676
          |> Thm.close_derivation;
blanchet@53917
   677
blanchet@53917
   678
        fun prove_split_asm asm_goal split_thm =
blanchet@53917
   679
          Goal.prove_sorry lthy [] [] asm_goal (fn {context = ctxt, ...} =>
blanchet@53917
   680
            mk_split_asm_tac ctxt split_thm)
blanchet@55409
   681
          |> singleton (Proof_Context.export names_lthy lthy)
blanchet@55409
   682
          |> Thm.close_derivation;
blanchet@53917
   683
blanchet@53917
   684
        val (split_thm, split_asm_thm) =
blanchet@53917
   685
          let
blanchet@53917
   686
            val goal = mk_split_goal xctrs xss xfs;
blanchet@53917
   687
            val asm_goal = mk_split_asm_goal xctrs xss xfs;
blanchet@53917
   688
blanchet@53917
   689
            val thm = prove_split (replicate n []) goal;
blanchet@53917
   690
            val asm_thm = prove_split_asm asm_goal thm;
blanchet@53917
   691
          in
blanchet@53917
   692
            (thm, asm_thm)
blanchet@53917
   693
          end;
blanchet@53917
   694
blanchet@55464
   695
        val (all_sel_thms, sel_thmss, disc_thmss, nontriv_disc_thmss, discI_thms,
blanchet@55464
   696
             nontriv_discI_thms, disc_exclude_thms, disc_exclude_thmsss, disc_exhaust_thms,
blanchet@55464
   697
             sel_exhaust_thms, all_collapse_thms, safe_collapse_thms, expand_thms, sel_split_thms,
blanchet@55464
   698
             sel_split_asm_thms, case_eq_if_thms) =
blanchet@52969
   699
          if no_discs_sels then
blanchet@54900
   700
            ([], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [])
blanchet@49116
   701
          else
blanchet@49116
   702
            let
blanchet@53917
   703
              val udiscs = map (rapp u) discs;
blanchet@53917
   704
              val uselss = map (map (rapp u)) selss;
blanchet@53917
   705
              val usel_ctrs = map2 (curry Term.list_comb) ctrs uselss;
blanchet@53917
   706
              val usel_fs = map2 (curry Term.list_comb) fs uselss;
blanchet@53917
   707
blanchet@53917
   708
              val vdiscs = map (rapp v) discs;
blanchet@53917
   709
              val vselss = map (map (rapp v)) selss;
blanchet@53917
   710
blanchet@49364
   711
              fun make_sel_thm xs' case_thm sel_def =
blanchet@49364
   712
                zero_var_indexes (Drule.gen_all (Drule.rename_bvars' (map (SOME o fst) xs')
blanchet@54634
   713
                    (Drule.forall_intr_vars (case_thm RS (sel_def RS trans)))));
blanchet@49281
   714
blanchet@53704
   715
              val sel_thmss = map3 (map oo make_sel_thm) xss' case_thms sel_defss;
blanchet@53704
   716
blanchet@49281
   717
              fun has_undefined_rhs thm =
blanchet@49281
   718
                (case snd (HOLogic.dest_eq (HOLogic.dest_Trueprop (prop_of thm))) of
blanchet@49281
   719
                  Const (@{const_name undefined}, _) => true
blanchet@49281
   720
                | _ => false);
blanchet@49281
   721
blanchet@49281
   722
              val all_sel_thms =
blanchet@49285
   723
                (if all_sels_distinct andalso forall null sel_defaultss then
blanchet@49285
   724
                   flat sel_thmss
blanchet@49285
   725
                 else
blanchet@49364
   726
                   map_product (fn s => fn (xs', c) => make_sel_thm xs' c s) sel_defs
blanchet@49364
   727
                     (xss' ~~ case_thms))
blanchet@49285
   728
                |> filter_out has_undefined_rhs;
blanchet@49278
   729
blanchet@49278
   730
              fun mk_unique_disc_def () =
blanchet@49278
   731
                let
blanchet@49278
   732
                  val m = the_single ms;
blanchet@49591
   733
                  val goal = mk_Trueprop_eq (mk_uu_eq (), the_single exist_xs_u_eq_ctrs);
blanchet@49278
   734
                in
wenzelm@51551
   735
                  Goal.prove_sorry lthy [] [] goal (fn _ => mk_unique_disc_def_tac m uexhaust_thm)
blanchet@55409
   736
                  |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49692
   737
                  |> Thm.close_derivation
blanchet@49278
   738
                end;
blanchet@49278
   739
blanchet@49278
   740
              fun mk_alternate_disc_def k =
blanchet@49278
   741
                let
blanchet@49278
   742
                  val goal =
blanchet@49486
   743
                    mk_Trueprop_eq (alternate_disc_lhs (K (nth udiscs)) (3 - k),
blanchet@49486
   744
                      nth exist_xs_u_eq_ctrs (k - 1));
blanchet@49278
   745
                in
wenzelm@51551
   746
                  Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@54634
   747
                    mk_alternate_disc_def_tac ctxt k (nth disc_defs (2 - k))
blanchet@49486
   748
                      (nth distinct_thms (2 - k)) uexhaust_thm)
blanchet@55409
   749
                  |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49692
   750
                  |> Thm.close_derivation
blanchet@49278
   751
                end;
blanchet@49028
   752
blanchet@49278
   753
              val has_alternate_disc_def =
blanchet@49278
   754
                exists (fn def => Thm.eq_thm_prop (def, alternate_disc_no_def)) disc_defs;
blanchet@49278
   755
blanchet@49278
   756
              val disc_defs' =
blanchet@49278
   757
                map2 (fn k => fn def =>
blanchet@49278
   758
                  if Thm.eq_thm_prop (def, unique_disc_no_def) then mk_unique_disc_def ()
blanchet@49278
   759
                  else if Thm.eq_thm_prop (def, alternate_disc_no_def) then mk_alternate_disc_def k
blanchet@54634
   760
                  else def) ks disc_defs;
blanchet@49278
   761
blanchet@49278
   762
              val discD_thms = map (fn def => def RS iffD1) disc_defs';
blanchet@49278
   763
              val discI_thms =
blanchet@49278
   764
                map2 (fn m => fn def => funpow m (fn thm => exI RS thm) (def RS iffD2)) ms
blanchet@49278
   765
                  disc_defs';
blanchet@49278
   766
              val not_discI_thms =
blanchet@49278
   767
                map2 (fn m => fn def => funpow m (fn thm => allI RS thm)
blanchet@49504
   768
                    (unfold_thms lthy @{thms not_ex} (def RS @{thm ssubst[of _ _ Not]})))
blanchet@49278
   769
                  ms disc_defs';
blanchet@49278
   770
blanchet@49278
   771
              val (disc_thmss', disc_thmss) =
blanchet@49278
   772
                let
blanchet@49278
   773
                  fun mk_thm discI _ [] = refl RS discI
blanchet@49278
   774
                    | mk_thm _ not_discI [distinct] = distinct RS not_discI;
blanchet@49278
   775
                  fun mk_thms discI not_discI distinctss = map (mk_thm discI not_discI) distinctss;
blanchet@49278
   776
                in
blanchet@49278
   777
                  map3 mk_thms discI_thms not_discI_thms distinct_thmsss' |> `transpose
blanchet@49278
   778
                end;
blanchet@49278
   779
blanchet@55464
   780
              val nontriv_disc_thmss =
blanchet@55464
   781
                map2 (fn b => if is_disc_binding_valid b then I else K []) disc_bindings disc_thmss;
blanchet@53704
   782
blanchet@53704
   783
              fun is_discI_boring b =
blanchet@53704
   784
                (n = 1 andalso Binding.is_empty b) orelse Binding.eq_name (b, equal_binding);
blanchet@53704
   785
blanchet@53704
   786
              val nontriv_discI_thms =
blanchet@53704
   787
                flat (map2 (fn b => if is_discI_boring b then K [] else single) disc_bindings
blanchet@53704
   788
                  discI_thms);
blanchet@49028
   789
blanchet@49486
   790
              val (disc_exclude_thms, (disc_exclude_thmsss', disc_exclude_thmsss)) =
blanchet@49486
   791
                let
blanchet@49486
   792
                  fun mk_goal [] = []
blanchet@49486
   793
                    | mk_goal [((_, udisc), (_, udisc'))] =
blanchet@49486
   794
                      [Logic.all u (Logic.mk_implies (HOLogic.mk_Trueprop udisc,
blanchet@49486
   795
                         HOLogic.mk_Trueprop (HOLogic.mk_not udisc')))];
blanchet@49486
   796
traytel@49667
   797
                  fun prove tac goal =
wenzelm@51551
   798
                    Goal.prove_sorry lthy [] [] goal (K tac)
traytel@49667
   799
                    |> Thm.close_derivation;
blanchet@49486
   800
blanchet@49585
   801
                  val half_pairss = mk_half_pairss (`I (ms ~~ discD_thms ~~ udiscs));
blanchet@49486
   802
blanchet@49486
   803
                  val half_goalss = map mk_goal half_pairss;
blanchet@49486
   804
                  val half_thmss =
blanchet@49486
   805
                    map3 (fn [] => K (K []) | [goal] => fn [(((m, discD), _), _)] =>
wenzelm@51798
   806
                        fn disc_thm => [prove (mk_half_disc_exclude_tac lthy m discD disc_thm) goal])
blanchet@49486
   807
                      half_goalss half_pairss (flat disc_thmss');
blanchet@49278
   808
blanchet@49486
   809
                  val other_half_goalss = map (mk_goal o map swap) half_pairss;
blanchet@49486
   810
                  val other_half_thmss =
blanchet@49486
   811
                    map2 (map2 (prove o mk_other_half_disc_exclude_tac)) half_thmss
blanchet@49486
   812
                      other_half_goalss;
blanchet@49486
   813
                in
blanchet@49585
   814
                  join_halves n half_thmss other_half_thmss ||> `transpose
blanchet@49486
   815
                  |>> has_alternate_disc_def ? K []
blanchet@49486
   816
                end;
blanchet@49278
   817
blanchet@49486
   818
              val disc_exhaust_thm =
blanchet@49486
   819
                let
blanchet@49486
   820
                  fun mk_prem udisc = mk_imp_p [HOLogic.mk_Trueprop udisc];
blanchet@49486
   821
                  val goal = fold_rev Logic.all [p, u] (mk_imp_p (map mk_prem udiscs));
blanchet@49486
   822
                in
wenzelm@51551
   823
                  Goal.prove_sorry lthy [] [] goal (fn _ =>
blanchet@49486
   824
                    mk_disc_exhaust_tac n exhaust_thm discI_thms)
traytel@49667
   825
                  |> Thm.close_derivation
blanchet@49486
   826
                end;
blanchet@49028
   827
blanchet@53740
   828
              val (safe_collapse_thms, all_collapse_thms) =
blanchet@49486
   829
                let
blanchet@54008
   830
                  fun mk_goal m udisc usel_ctr =
blanchet@49486
   831
                    let
blanchet@49486
   832
                      val prem = HOLogic.mk_Trueprop udisc;
blanchet@53916
   833
                      val concl = mk_Trueprop_eq ((usel_ctr, u) |> m = 0 ? swap);
blanchet@49486
   834
                    in
blanchet@53740
   835
                      (prem aconv concl, Logic.all u (Logic.mk_implies (prem, concl)))
blanchet@49486
   836
                    end;
blanchet@54008
   837
                  val (trivs, goals) = map3 mk_goal ms udiscs usel_ctrs |> split_list;
blanchet@53740
   838
                  val thms =
blanchet@53740
   839
                    map5 (fn m => fn discD => fn sel_thms => fn triv => fn goal =>
blanchet@53740
   840
                        Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@53740
   841
                          mk_collapse_tac ctxt m discD sel_thms ORELSE HEADGOAL atac)
blanchet@53740
   842
                        |> Thm.close_derivation
blanchet@53740
   843
                        |> not triv ? perhaps (try (fn thm => refl RS thm)))
blanchet@53740
   844
                      ms discD_thms sel_thmss trivs goals;
blanchet@49486
   845
                in
blanchet@53740
   846
                  (map_filter (fn (true, _) => NONE | (false, thm) => SOME thm) (trivs ~~ thms),
blanchet@53740
   847
                   thms)
blanchet@49486
   848
                end;
blanchet@49025
   849
blanchet@53916
   850
              val swapped_all_collapse_thms =
blanchet@53916
   851
                map2 (fn m => fn thm => if m = 0 then thm else thm RS sym) ms all_collapse_thms;
blanchet@53916
   852
blanchet@53916
   853
              val sel_exhaust_thm =
blanchet@53916
   854
                let
blanchet@53916
   855
                  fun mk_prem usel_ctr = mk_imp_p [mk_Trueprop_eq (u, usel_ctr)];
blanchet@53916
   856
                  val goal = fold_rev Logic.all [p, u] (mk_imp_p (map mk_prem usel_ctrs));
blanchet@53916
   857
                in
blanchet@53916
   858
                  Goal.prove_sorry lthy [] [] goal (fn _ =>
blanchet@53916
   859
                    mk_sel_exhaust_tac n disc_exhaust_thm swapped_all_collapse_thms)
blanchet@53916
   860
                  |> Thm.close_derivation
blanchet@53916
   861
                end;
blanchet@53916
   862
blanchet@53919
   863
              val expand_thm =
blanchet@49486
   864
                let
blanchet@49486
   865
                  fun mk_prems k udisc usels vdisc vsels =
blanchet@49486
   866
                    (if k = n then [] else [mk_Trueprop_eq (udisc, vdisc)]) @
blanchet@49486
   867
                    (if null usels then
blanchet@49486
   868
                       []
blanchet@49486
   869
                     else
blanchet@49486
   870
                       [Logic.list_implies
blanchet@49486
   871
                          (if n = 1 then [] else map HOLogic.mk_Trueprop [udisc, vdisc],
blanchet@49486
   872
                             HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
blanchet@49486
   873
                               (map2 (curry HOLogic.mk_eq) usels vsels)))]);
blanchet@49486
   874
blanchet@49591
   875
                  val goal =
blanchet@49591
   876
                    Library.foldr Logic.list_implies
blanchet@49591
   877
                      (map5 mk_prems ks udiscs uselss vdiscs vselss, uv_eq);
blanchet@49486
   878
                  val uncollapse_thms =
blanchet@53740
   879
                    map2 (fn thm => fn [] => thm | _ => thm RS sym) all_collapse_thms uselss;
blanchet@49486
   880
                in
blanchet@53919
   881
                  Goal.prove_sorry lthy [] [] goal (fn _ =>
blanchet@53919
   882
                    mk_expand_tac lthy n ms (inst_thm u disc_exhaust_thm)
blanchet@53919
   883
                      (inst_thm v disc_exhaust_thm) uncollapse_thms disc_exclude_thmsss
blanchet@53919
   884
                      disc_exclude_thmsss')
blanchet@55409
   885
                  |> singleton (Proof_Context.export names_lthy lthy)
blanchet@53919
   886
                  |> Thm.close_derivation
blanchet@49486
   887
                end;
blanchet@49278
   888
blanchet@53917
   889
              val (sel_split_thm, sel_split_asm_thm) =
blanchet@53917
   890
                let
blanchet@53917
   891
                  val zss = map (K []) xss;
blanchet@53917
   892
                  val goal = mk_split_goal usel_ctrs zss usel_fs;
blanchet@53917
   893
                  val asm_goal = mk_split_asm_goal usel_ctrs zss usel_fs;
blanchet@53917
   894
blanchet@53917
   895
                  val thm = prove_split sel_thmss goal;
blanchet@53917
   896
                  val asm_thm = prove_split_asm asm_goal thm;
blanchet@53917
   897
                in
blanchet@53917
   898
                  (thm, asm_thm)
blanchet@53917
   899
                end;
blanchet@53917
   900
blanchet@54491
   901
              val case_eq_if_thm =
blanchet@49486
   902
                let
blanchet@53917
   903
                  val goal = mk_Trueprop_eq (ufcase, mk_IfN B udiscs usel_fs);
blanchet@49486
   904
                in
blanchet@53919
   905
                  Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@54491
   906
                    mk_case_eq_if_tac ctxt n uexhaust_thm case_thms disc_thmss' sel_thmss)
blanchet@55409
   907
                  |> singleton (Proof_Context.export names_lthy lthy)
blanchet@53919
   908
                  |> Thm.close_derivation
blanchet@49486
   909
                end;
blanchet@49116
   910
            in
blanchet@55464
   911
              (all_sel_thms, sel_thmss, disc_thmss, nontriv_disc_thmss, discI_thms,
blanchet@54900
   912
               nontriv_discI_thms, disc_exclude_thms, disc_exclude_thmsss, [disc_exhaust_thm],
blanchet@54900
   913
               [sel_exhaust_thm], all_collapse_thms, safe_collapse_thms, [expand_thm],
blanchet@54900
   914
               [sel_split_thm], [sel_split_asm_thm], [case_eq_if_thm])
blanchet@49116
   915
            end;
blanchet@49025
   916
blanchet@49437
   917
        val exhaust_case_names_attr = Attrib.internal (K (Rule_Cases.case_names exhaust_cases));
blanchet@53908
   918
        val cases_type_attr = Attrib.internal (K (Induct.cases_type fcT_name));
blanchet@49300
   919
blanchet@55464
   920
        val nontriv_disc_eq_thmss =
blanchet@55464
   921
          map (map (fn th => th RS @{thm eq_False[THEN iffD2]}
blanchet@55464
   922
            handle THM _ => th RS @{thm eq_True[THEN iffD2]})) nontriv_disc_thmss;
blanchet@55464
   923
blanchet@54151
   924
        val anonymous_notes =
blanchet@54151
   925
          [(map (fn th => th RS notE) distinct_thms, safe_elim_attrs),
blanchet@55464
   926
           (flat nontriv_disc_eq_thmss, code_nitpicksimp_attrs)]
blanchet@54151
   927
          |> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
blanchet@54151
   928
blanchet@49052
   929
        val notes =
blanchet@54145
   930
          [(caseN, case_thms, code_nitpicksimp_simp_attrs),
blanchet@49594
   931
           (case_congN, [case_cong_thm], []),
blanchet@54491
   932
           (case_eq_ifN, case_eq_if_thms, []),
blanchet@53740
   933
           (collapseN, safe_collapse_thms, simp_attrs),
blanchet@55464
   934
           (discN, flat nontriv_disc_thmss, simp_attrs),
blanchet@53700
   935
           (discIN, nontriv_discI_thms, []),
blanchet@53836
   936
           (disc_excludeN, disc_exclude_thms, dest_attrs),
blanchet@49300
   937
           (disc_exhaustN, disc_exhaust_thms, [exhaust_case_names_attr]),
blanchet@54145
   938
           (distinctN, distinct_thms, simp_attrs @ inductsimp_attrs),
blanchet@49300
   939
           (exhaustN, [exhaust_thm], [exhaust_case_names_attr, cases_type_attr]),
blanchet@49486
   940
           (expandN, expand_thms, []),
blanchet@54145
   941
           (injectN, inject_thms, iff_attrs @ inductsimp_attrs),
blanchet@49300
   942
           (nchotomyN, [nchotomy_thm], []),
blanchet@54145
   943
           (selN, all_sel_thms, code_nitpicksimp_simp_attrs),
blanchet@53916
   944
           (sel_exhaustN, sel_exhaust_thms, [exhaust_case_names_attr]),
blanchet@53917
   945
           (sel_splitN, sel_split_thms, []),
blanchet@53917
   946
           (sel_split_asmN, sel_split_asm_thms, []),
blanchet@49300
   947
           (splitN, [split_thm], []),
blanchet@49300
   948
           (split_asmN, [split_asm_thm], []),
blanchet@49633
   949
           (splitsN, [split_thm, split_asm_thm], []),
blanchet@49300
   950
           (weak_case_cong_thmsN, [weak_case_cong_thm], cong_attrs)]
blanchet@49300
   951
          |> filter_out (null o #2)
blanchet@49300
   952
          |> map (fn (thmN, thms, attrs) =>
blanchet@49633
   953
            ((qualify true (Binding.name thmN), attrs), [(thms, [])]));
blanchet@49300
   954
blanchet@53867
   955
        val ctr_sugar =
blanchet@53867
   956
          {ctrs = ctrs, casex = casex, discs = discs, selss = selss, exhaust = exhaust_thm,
blanchet@53867
   957
           nchotomy = nchotomy_thm, injects = inject_thms, distincts = distinct_thms,
blanchet@53867
   958
           case_thms = case_thms, case_cong = case_cong_thm, weak_case_cong = weak_case_cong_thm,
blanchet@53867
   959
           split = split_thm, split_asm = split_asm_thm, disc_thmss = disc_thmss,
blanchet@54900
   960
           discIs = discI_thms, sel_thmss = sel_thmss, disc_excludesss = disc_exclude_thmsss,
blanchet@54900
   961
           disc_exhausts = disc_exhaust_thms, sel_exhausts = sel_exhaust_thms,
blanchet@54900
   962
           collapses = all_collapse_thms, expands = expand_thms, sel_splits = sel_split_thms,
blanchet@54900
   963
           sel_split_asms = sel_split_asm_thms, case_eq_ifs = case_eq_if_thms};
blanchet@49019
   964
      in
blanchet@53867
   965
        (ctr_sugar,
blanchet@51819
   966
         lthy
blanchet@55464
   967
         |> Spec_Rules.add Spec_Rules.Equational ([casex], case_thms)
blanchet@55471
   968
         |> fold (Spec_Rules.add Spec_Rules.Equational)
blanchet@55535
   969
           (AList.group (eq_list (op aconv)) (map (`(single o lhs_head_of)) all_sel_thms))
blanchet@55471
   970
         |> fold (Spec_Rules.add Spec_Rules.Equational)
blanchet@55471
   971
           (filter_out (null o snd) (map single discs ~~ nontriv_disc_eq_thmss))
blanchet@55410
   972
         |> Local_Theory.declaration {syntax = false, pervasive = true}
blanchet@54615
   973
              (fn phi => Case_Translation.register
blanchet@54615
   974
                 (Morphism.term phi casex) (map (Morphism.term phi) ctrs))
traytel@54691
   975
         |> Local_Theory.background_theory (fold (fold Code.del_eqn) [disc_defs, sel_defs])
traytel@54691
   976
         |> not no_code ?
traytel@54691
   977
            Local_Theory.declaration {syntax = false, pervasive = false}
traytel@54691
   978
              (fn phi => Context.mapping
traytel@54691
   979
                (add_ctr_code fcT_name (map (Morphism.typ phi) As)
traytel@54691
   980
                  (map (dest_Const o Morphism.term phi) ctrs) (Morphism.fact phi inject_thms)
traytel@54691
   981
                  (Morphism.fact phi distinct_thms) (Morphism.fact phi case_thms))
traytel@54691
   982
                I)
blanchet@54635
   983
         |> Local_Theory.notes (anonymous_notes @ notes) |> snd
blanchet@54635
   984
         |> register_ctr_sugar fcT_name ctr_sugar)
blanchet@49019
   985
      end;
blanchet@49017
   986
  in
blanchet@49121
   987
    (goalss, after_qed, lthy')
blanchet@49017
   988
  end;
blanchet@49017
   989
blanchet@55468
   990
fun free_constructors tacss = (fn (goalss, after_qed, lthy) =>
wenzelm@51551
   991
  map2 (map2 (Thm.close_derivation oo Goal.prove_sorry lthy [] [])) goalss tacss
blanchet@55468
   992
  |> (fn thms => after_qed thms lthy)) oo prepare_free_constructors (K I);
blanchet@49280
   993
blanchet@55468
   994
val free_constructors_cmd = (fn (goalss, after_qed, lthy) =>
blanchet@49297
   995
  Proof.theorem NONE (snd oo after_qed) (map (map (rpair [])) goalss) lthy) oo
blanchet@55468
   996
  prepare_free_constructors Syntax.read_term;
blanchet@49297
   997
blanchet@55469
   998
val parse_bound_term = parse_binding --| @{keyword ":"} -- Parse.term;
blanchet@49280
   999
blanchet@55469
  1000
val parse_ctr_options =
blanchet@54626
  1001
  Scan.optional (@{keyword "("} |-- Parse.list1
blanchet@55410
  1002
        (Parse.reserved "no_discs_sels" >> K 0 || Parse.reserved "no_code" >> K 1) --|
blanchet@55410
  1003
      @{keyword ")"}
blanchet@55410
  1004
      >> (fn js => (member (op =) js 0, member (op =) js 1)))
blanchet@55410
  1005
    (false, false);
blanchet@49278
  1006
blanchet@55469
  1007
val parse_defaults =
blanchet@55469
  1008
  @{keyword "("} |-- Parse.reserved "defaults" |-- Scan.repeat parse_bound_term --| @{keyword ")"};
blanchet@55469
  1009
blanchet@55469
  1010
fun parse_ctr_spec parse_ctr parse_arg =
blanchet@55469
  1011
  parse_opt_binding_colon -- parse_ctr -- Scan.repeat parse_arg --
blanchet@55469
  1012
  Scan.optional parse_defaults [];
blanchet@55469
  1013
blanchet@55469
  1014
val parse_ctr_specs = Parse.enum1 "|" (parse_ctr_spec Parse.term parse_binding);
blanchet@55469
  1015
blanchet@49017
  1016
val _ =
blanchet@55468
  1017
  Outer_Syntax.local_theory_to_proof @{command_spec "free_constructors"}
blanchet@55468
  1018
    "register an existing freely generated type's constructors"
blanchet@55469
  1019
    (parse_ctr_options -- parse_binding --| @{keyword "for"} -- parse_ctr_specs
blanchet@55468
  1020
     >> free_constructors_cmd);
blanchet@49017
  1021
kuncar@56522
  1022
val _ = Context.>> (Context.map_theory Ctr_Sugar_Interpretation.init);
kuncar@56522
  1023
blanchet@49017
  1024
end;