src/HOL/BNF/Tools/bnf_fp.ML
author blanchet
Wed Sep 26 10:00:59 2012 +0200 (2012-09-26)
changeset 49581 4e5bd3883429
parent 49545 8bb6e2d7346b
child 49582 557302525778
permissions -rw-r--r--
renamed "dtor_coinduct" etc. to "dtor_map_coinduct"
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(*  Title:      HOL/BNF/Tools/bnf_fp.ML
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    Author:     Dmitriy Traytel, TU Muenchen
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    Copyright   2012
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Shared library for the datatype and codatatype constructions.
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*)
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signature BNF_FP =
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sig
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  val time: Timer.real_timer -> string -> Timer.real_timer
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  val IITN: string
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  val LevN: string
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  val algN: string
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  val behN: string
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  val bisN: string
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  val carTN: string
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  val caseN: string
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  val coN: string
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  val coinductN: string
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  val corecN: string
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  val corecsN: string
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  val ctorN: string
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  val ctor_dtorN: string
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  val ctor_dtor_unfoldsN: string
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  val ctor_dtor_corecsN: string
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  val ctor_exhaustN: string
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  val ctor_induct2N: string
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  val ctor_inductN: string
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  val ctor_injectN: string
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  val ctor_foldN: string
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  val ctor_fold_uniqueN: string
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  val ctor_foldsN: string
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  val ctor_mapN: string
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  val ctor_map_uniqueN: string
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  val ctor_recN: string
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  val ctor_recsN: string
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  val ctor_relN: string
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  val ctor_set_inclN: string
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  val ctor_set_set_inclN: string
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  val ctor_srelN: string
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  val disc_unfold_iffN: string
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  val disc_unfoldsN: string
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  val disc_corec_iffN: string
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  val disc_corecsN: string
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  val dtorN: string
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  val dtor_corecN: string
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  val dtor_corecsN: string
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  val dtor_ctorN: string
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  val dtor_exhaustN: string
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  val dtor_injectN: string
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  val dtor_mapN: string
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  val dtor_map_coinductN: string
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  val dtor_map_strong_coinductN: string
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  val dtor_map_uniqueN: string
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  val dtor_relN: string
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  val dtor_rel_coinductN: string
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  val dtor_rel_strong_coinductN: string
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  val dtor_set_inclN: string
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  val dtor_set_set_inclN: string
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  val dtor_srelN: string
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  val dtor_srel_coinductN: string
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  val dtor_srel_strong_coinductN: string
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  val dtor_unfoldN: string
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  val dtor_unfold_uniqueN: string
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  val dtor_unfoldsN: string
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  val exhaustN: string
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  val foldN: string
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  val foldsN: string
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  val hsetN: string
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  val hset_recN: string
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  val inductN: string
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  val injectN: string
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  val isNodeN: string
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  val lsbisN: string
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  val map_uniqueN: string
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  val min_algN: string
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  val morN: string
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  val nchotomyN: string
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  val recN: string
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  val recsN: string
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  val relsN: string
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  val rvN: string
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  val sel_corecsN: string
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  val sel_relsN: string
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  val sel_unfoldsN: string
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  val set_inclN: string
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  val set_set_inclN: string
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  val simpsN: string
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  val strTN: string
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  val str_initN: string
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  val strongN: string
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  val sum_bdN: string
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  val sum_bdTN: string
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  val unfoldN: string
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  val unfoldsN: string
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  val uniqueN: string
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  val mk_ctor_setsN: int -> string
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  val mk_dtor_set_inductN: int -> string
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  val mk_dtor_setsN: int -> string
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  val mk_exhaustN: string -> string
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  val mk_injectN: string -> string
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  val mk_nchotomyN: string -> string
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  val mk_setsN: int -> string
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  val mk_set_inductN: int -> string
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  val mk_common_name: string list -> string
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  val split_conj_thm: thm -> thm list
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  val split_conj_prems: int -> thm -> thm
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  val retype_free: typ -> term -> term
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  val mk_sumTN: typ list -> typ
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  val mk_sumTN_balanced: typ list -> typ
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  val id_const: typ -> term
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  val id_abs: typ -> term
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  val Inl_const: typ -> typ -> term
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  val Inr_const: typ -> typ -> term
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  val mk_Inl: typ -> term -> term
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  val mk_Inr: typ -> term -> term
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  val mk_InN: typ list -> term -> int -> term
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  val mk_InN_balanced: typ -> int -> term -> int -> term
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  val mk_sum_case: term * term -> term
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  val mk_sum_caseN: term list -> term
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  val mk_sum_caseN_balanced: term list -> term
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  val dest_sumT: typ -> typ * typ
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  val dest_sumTN: int -> typ -> typ list
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  val dest_sumTN_balanced: int -> typ -> typ list
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  val dest_tupleT: int -> typ -> typ list
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  val mk_Field: term -> term
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  val mk_If: term -> term -> term -> term
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  val mk_union: term * term -> term
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  val mk_sumEN: int -> thm
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  val mk_sumEN_balanced: int -> thm
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  val mk_sumEN_tupled_balanced: int list -> thm
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  val mk_sum_casesN: int -> int -> thm
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  val mk_sum_casesN_balanced: int -> int -> thm
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  val fixpoint: ('a * 'a -> bool) -> ('a list -> 'a list) -> 'a list -> 'a list
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  val fp_bnf: (mixfix list -> (string * sort) list option -> binding list ->
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    typ list * typ list list -> BNF_Def.BNF list -> local_theory -> 'a) ->
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    binding list -> mixfix list -> (string * sort) list -> ((string * sort) * typ) list ->
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    local_theory -> BNF_Def.BNF list * 'a
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  val fp_bnf_cmd: (mixfix list -> (string * sort) list option -> binding list ->
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    typ list * typ list list -> BNF_Def.BNF list -> local_theory -> 'a) ->
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    binding list * (string list * string list) -> local_theory -> 'a
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end;
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structure BNF_FP : BNF_FP =
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struct
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open BNF_Comp
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open BNF_Def
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open BNF_Util
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val timing = true;
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fun time timer msg = (if timing
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  then warning (msg ^ ": " ^ ATP_Util.string_from_time (Timer.checkRealTimer timer))
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  else (); Timer.startRealTimer ());
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val preN = "pre_"
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val rawN = "raw_"
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val coN = "co"
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val unN = "un"
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val algN = "alg"
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val IITN = "IITN"
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val foldN = "fold"
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val foldsN = foldN ^ "s"
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val unfoldN = unN ^ foldN
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val unfoldsN = unfoldN ^ "s"
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val uniqueN = "_unique"
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val simpsN = "simps"
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val ctorN = "ctor"
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val dtorN = "dtor"
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val ctor_foldN = ctorN ^ "_" ^ foldN
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val ctor_foldsN = ctor_foldN ^ "s"
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val dtor_unfoldN = dtorN ^ "_" ^ unfoldN
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val dtor_unfoldsN = dtor_unfoldN ^ "s"
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val ctor_fold_uniqueN = ctor_foldN ^ uniqueN
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val dtor_unfold_uniqueN = dtor_unfoldN ^ uniqueN
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val ctor_dtor_unfoldsN = ctorN ^ "_" ^ dtor_unfoldN ^ "s"
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val ctor_mapN = ctorN ^ "_" ^ mapN
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val dtor_mapN = dtorN ^ "_" ^ mapN
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val map_uniqueN = mapN ^ uniqueN
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val ctor_map_uniqueN = ctorN ^ "_" ^ map_uniqueN
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val dtor_map_uniqueN = dtorN ^ "_" ^ map_uniqueN
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val min_algN = "min_alg"
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val morN = "mor"
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val bisN = "bis"
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val lsbisN = "lsbis"
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val sum_bdTN = "sbdT"
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val sum_bdN = "sbd"
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val carTN = "carT"
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val strTN = "strT"
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val isNodeN = "isNode"
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val LevN = "Lev"
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val rvN = "recover"
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val behN = "beh"
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fun mk_setsN i = mk_setN i ^ "s"
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val mk_ctor_setsN = prefix (ctorN ^ "_") o mk_setsN
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val mk_dtor_setsN = prefix (dtorN ^ "_") o mk_setsN
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fun mk_set_inductN i = mk_setN i ^ "_induct"
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val mk_dtor_set_inductN = prefix (dtorN ^ "_") o mk_set_inductN
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val str_initN = "str_init"
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val recN = "rec"
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val recsN = recN ^ "s"
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val corecN = coN ^ recN
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val corecsN = corecN ^ "s"
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val ctor_recN = ctorN ^ "_" ^ recN
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val ctor_recsN = ctor_recN ^ "s"
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val dtor_corecN = dtorN ^ "_" ^ corecN
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val dtor_corecsN = dtor_corecN ^ "s"
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val ctor_dtor_corecsN = ctorN ^ "_" ^ dtor_corecN ^ "s"
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val ctor_dtorN = ctorN ^ "_" ^ dtorN
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val dtor_ctorN = dtorN ^ "_" ^ ctorN
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val nchotomyN = "nchotomy"
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fun mk_nchotomyN s = s ^ "_" ^ nchotomyN
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val injectN = "inject"
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fun mk_injectN s = s ^ "_" ^ injectN
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val exhaustN = "exhaust"
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fun mk_exhaustN s = s ^ "_" ^ exhaustN
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val ctor_injectN = mk_injectN ctorN
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val ctor_exhaustN = mk_exhaustN ctorN
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val dtor_injectN = mk_injectN dtorN
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val dtor_exhaustN = mk_exhaustN dtorN
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val ctor_relN = ctorN ^ "_" ^ relN
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val dtor_relN = dtorN ^ "_" ^ relN
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val ctor_srelN = ctorN ^ "_" ^ srelN
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val dtor_srelN = dtorN ^ "_" ^ srelN
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val inductN = "induct"
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val coinductN = coN ^ inductN
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val ctor_inductN = ctorN ^ "_" ^ inductN
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val ctor_induct2N = ctor_inductN ^ "2"
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val dtor_map_coinductN = dtor_mapN ^ "_" ^ coinductN
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val dtor_rel_coinductN = dtor_relN ^ "_" ^ coinductN
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val dtor_srel_coinductN = dtor_srelN ^ "_" ^ coinductN
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val strongN = "strong_"
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val dtor_map_strong_coinductN = dtor_mapN ^ "_" ^ strongN ^ coinductN
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val dtor_rel_strong_coinductN = dtor_relN ^ "_" ^ strongN ^ coinductN
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val dtor_srel_strong_coinductN = dtor_srelN ^ "_" ^ strongN ^ coinductN
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val hsetN = "Hset"
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val hset_recN = hsetN ^ "_rec"
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val set_inclN = "set_incl"
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val ctor_set_inclN = ctorN ^ "_" ^ set_inclN
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val dtor_set_inclN = dtorN ^ "_" ^ set_inclN
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val set_set_inclN = "set_set_incl"
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val ctor_set_set_inclN = ctorN ^ "_" ^ set_set_inclN
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val dtor_set_set_inclN = dtorN ^ "_" ^ set_set_inclN
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val caseN = "case"
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val discN = "disc"
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val disc_unfoldsN = discN ^ "_" ^ unfoldsN
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val disc_corecsN = discN ^ "_" ^ corecsN
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val iffN = "_iff"
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val disc_unfold_iffN = discN ^ "_" ^ unfoldN ^ iffN
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val disc_corec_iffN = discN ^ "_" ^ corecN ^ iffN
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val relsN = relN ^ "s"
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val selN = "sel"
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val sel_relsN = selN ^ "_" ^ relsN
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val sel_unfoldsN = selN ^ "_" ^ unfoldsN
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val sel_corecsN = selN ^ "_" ^ corecsN
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val mk_common_name = space_implode "_";
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fun retype_free T (Free (s, _)) = Free (s, T);
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fun dest_sumT (Type (@{type_name sum}, [T, T'])) = (T, T');
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fun dest_sumTN 1 T = [T]
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  | dest_sumTN n (Type (@{type_name sum}, [T, T'])) = T :: dest_sumTN (n - 1) T';
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val dest_sumTN_balanced = Balanced_Tree.dest dest_sumT;
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(* TODO: move something like this to "HOLogic"? *)
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fun dest_tupleT 0 @{typ unit} = []
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  | dest_tupleT 1 T = [T]
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  | dest_tupleT n (Type (@{type_name prod}, [T, T'])) = T :: dest_tupleT (n - 1) T';
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val mk_sumTN = Library.foldr1 mk_sumT;
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val mk_sumTN_balanced = Balanced_Tree.make mk_sumT;
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fun id_const T = Const (@{const_name id}, T --> T);
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fun id_abs T = Abs (Name.uu, T, Bound 0);
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fun Inl_const LT RT = Const (@{const_name Inl}, LT --> mk_sumT (LT, RT));
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fun mk_Inl RT t = Inl_const (fastype_of t) RT $ t;
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fun Inr_const LT RT = Const (@{const_name Inr}, RT --> mk_sumT (LT, RT));
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fun mk_Inr LT t = Inr_const LT (fastype_of t) $ t;
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fun mk_InN [_] t 1 = t
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  | mk_InN (_ :: Ts) t 1 = mk_Inl (mk_sumTN Ts) t
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  | mk_InN (LT :: Ts) t m = mk_Inr LT (mk_InN Ts t (m - 1))
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  | mk_InN Ts t _ = raise (TYPE ("mk_InN", Ts, [t]));
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fun mk_InN_balanced sum_T n t k =
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  let
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    fun repair_types T (Const (s as @{const_name Inl}, _) $ t) = repair_inj_types T s fst t
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      | repair_types T (Const (s as @{const_name Inr}, _) $ t) = repair_inj_types T s snd t
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      | repair_types _ t = t
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    and repair_inj_types T s get t =
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      let val T' = get (dest_sumT T) in
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        Const (s, T' --> T) $ repair_types T' t
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      end;
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  in
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    Balanced_Tree.access {left = mk_Inl dummyT, right = mk_Inr dummyT, init = t} n k
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   319
    |> repair_types sum_T
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   320
  end;
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   321
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   322
fun mk_sum_case (f, g) =
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   323
  let
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   324
    val fT = fastype_of f;
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   325
    val gT = fastype_of g;
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   326
  in
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   327
    Const (@{const_name sum_case},
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   328
      fT --> gT --> mk_sumT (domain_type fT, domain_type gT) --> range_type fT) $ f $ g
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   329
  end;
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   330
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   331
val mk_sum_caseN = Library.foldr1 mk_sum_case;
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   332
val mk_sum_caseN_balanced = Balanced_Tree.make mk_sum_case;
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   333
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   334
fun mk_If p t f =
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   335
  let val T = fastype_of t;
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   336
  in Const (@{const_name If}, HOLogic.boolT --> T --> T --> T) $ p $ t $ f end;
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   337
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   338
fun mk_Field r =
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  let val T = fst (dest_relT (fastype_of r));
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   340
  in Const (@{const_name Field}, mk_relT (T, T) --> HOLogic.mk_setT T) $ r end;
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   341
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   342
val mk_union = HOLogic.mk_binop @{const_name sup};
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   343
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   344
(*dangerous; use with monotonic, converging functions only!*)
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   345
fun fixpoint eq f X = if subset eq (f X, X) then X else fixpoint eq f (f X);
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   346
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   347
(* stolen from "~~/src/HOL/Tools/Datatype/datatype_aux.ML" *)
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fun split_conj_thm th =
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  ((th RS conjunct1) :: split_conj_thm (th RS conjunct2)) handle THM _ => [th];
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   350
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   351
fun split_conj_prems limit th =
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  let
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    fun split n i th =
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   354
      if i = n then th else split n (i + 1) (conjI RSN (i, th)) handle THM _ => th;
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   355
  in split limit 1 th end;
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   356
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   357
fun mk_sumEN 1 = @{thm one_pointE}
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   358
  | mk_sumEN 2 = @{thm sumE}
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   359
  | mk_sumEN n =
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   360
    (fold (fn i => fn thm => @{thm obj_sum_step} RSN (i, thm)) (2 upto n - 1) @{thm obj_sumE}) OF
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   361
      replicate n (impI RS allI);
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   362
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   363
fun mk_obj_sumEN_balanced n =
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   364
  Balanced_Tree.make (fn (thm1, thm2) => thm1 RSN (1, thm2 RSN (2, @{thm obj_sumE_f})))
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   365
    (replicate n asm_rl);
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   366
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   367
fun mk_sumEN_balanced' n all_impIs = mk_obj_sumEN_balanced n OF all_impIs RS @{thm obj_one_pointE};
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   368
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   369
fun mk_sumEN_balanced 1 = @{thm one_pointE} (*optimization*)
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   370
  | mk_sumEN_balanced 2 = @{thm sumE} (*optimization*)
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   371
  | mk_sumEN_balanced n = mk_sumEN_balanced' n (replicate n (impI RS allI));
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   372
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   373
fun mk_tupled_allIN 0 = @{thm unit_all_impI}
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   374
  | mk_tupled_allIN 1 = @{thm impI[THEN allI]}
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   375
  | mk_tupled_allIN 2 = @{thm prod_all_impI} (*optimization*)
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   376
  | mk_tupled_allIN n = mk_tupled_allIN (n - 1) RS @{thm prod_all_impI_step};
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   377
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   378
fun mk_sumEN_tupled_balanced ms =
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   379
  let val n = length ms in
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   380
    if forall (curry (op =) 1) ms then mk_sumEN_balanced n
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   381
    else mk_sumEN_balanced' n (map mk_tupled_allIN ms)
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   382
  end;
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   383
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   384
fun mk_sum_casesN 1 1 = refl
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   385
  | mk_sum_casesN _ 1 = @{thm sum.cases(1)}
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   386
  | mk_sum_casesN 2 2 = @{thm sum.cases(2)}
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   387
  | mk_sum_casesN n k = trans OF [@{thm sum_case_step(2)}, mk_sum_casesN (n - 1) (k - 1)];
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   388
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   389
fun mk_sum_step base step thm =
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   390
  if Thm.eq_thm_prop (thm, refl) then base else trans OF [step, thm];
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   391
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   392
fun mk_sum_casesN_balanced 1 1 = refl
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   393
  | mk_sum_casesN_balanced n k =
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   394
    Balanced_Tree.access {left = mk_sum_step @{thm sum.cases(1)} @{thm sum_case_step(1)},
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   395
      right = mk_sum_step @{thm sum.cases(2)} @{thm sum_case_step(2)}, init = refl} n k;
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   396
blanchet@49141
   397
(* FIXME: because of "@ lhss", the output could contain type variables that are not in the input;
blanchet@49141
   398
   also, "fp_sort" should put the "resBs" first and in the order in which they appear *)
traytel@49185
   399
fun fp_sort lhss NONE Ass = Library.sort (Term_Ord.typ_ord o pairself TFree)
traytel@49185
   400
    (subtract (op =) lhss (fold (fold (insert (op =))) Ass [])) @ lhss
traytel@49185
   401
  | fp_sort lhss (SOME resBs) Ass =
traytel@49185
   402
    (subtract (op =) lhss (filter (fn T => exists (fn Ts => member (op =) Ts T) Ass) resBs)) @ lhss;
blanchet@48975
   403
blanchet@49502
   404
fun mk_fp_bnf timer construct resBs bs sort lhss bnfs deadss livess unfold_set lthy =
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   405
  let
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   406
    val name = mk_common_name (map Binding.name_of bs);
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   407
    fun qualify i =
traytel@49425
   408
      let val namei = name ^ nonzero_string_of_int i;
traytel@49425
   409
      in Binding.qualify true namei end;
blanchet@48975
   410
blanchet@49132
   411
    val Ass = map (map dest_TFree) livess;
traytel@49185
   412
    val resDs = (case resBs of NONE => [] | SOME Ts => fold (subtract (op =)) Ass Ts);
traytel@49185
   413
    val Ds = fold (fold Term.add_tfreesT) deadss [];
blanchet@49132
   414
traytel@49156
   415
    val _ = (case Library.inter (op =) Ds lhss of [] => ()
blanchet@49132
   416
      | A :: _ => error ("Nonadmissible type recursion (cannot take fixed point of dead type \
blanchet@49132
   417
        \variable " ^ quote (Syntax.string_of_typ lthy (TFree A)) ^ ")"));
blanchet@48975
   418
blanchet@48975
   419
    val timer = time (timer "Construction of BNFs");
blanchet@48975
   420
blanchet@49502
   421
    val ((kill_poss, _), (bnfs', (unfold_set', lthy'))) =
blanchet@49502
   422
      normalize_bnfs qualify Ass Ds sort bnfs unfold_set lthy;
blanchet@48975
   423
blanchet@49132
   424
    val Dss = map3 (append oo map o nth) livess kill_poss deadss;
blanchet@48975
   425
traytel@49185
   426
    val ((bnfs'', deadss), lthy'') =
blanchet@49502
   427
      fold_map3 (seal_bnf unfold_set') (map (Binding.prefix_name preN) bs) Dss bnfs' lthy'
traytel@49185
   428
      |>> split_list;
blanchet@48975
   429
blanchet@48975
   430
    val timer = time (timer "Normalization & sealing of BNFs");
blanchet@48975
   431
traytel@49185
   432
    val res = construct resBs bs (map TFree resDs, deadss) bnfs'' lthy'';
blanchet@48975
   433
blanchet@48975
   434
    val timer = time (timer "FP construction in total");
blanchet@48975
   435
  in
blanchet@49308
   436
    timer; (bnfs'', res)
blanchet@48975
   437
  end;
blanchet@48975
   438
blanchet@49169
   439
fun fp_bnf construct bs mixfixes resBs eqs lthy =
blanchet@48975
   440
  let
blanchet@48975
   441
    val timer = time (Timer.startRealTimer ());
blanchet@48975
   442
    val (lhss, rhss) = split_list eqs;
traytel@49185
   443
    val sort = fp_sort lhss (SOME resBs);
traytel@49425
   444
    fun qualify b = Binding.qualify true (Binding.name_of (Binding.prefix_name rawN b));
blanchet@49502
   445
    val ((bnfs, (Dss, Ass)), (unfold_set, lthy')) = apfst (apsnd split_list o split_list)
traytel@49425
   446
      (fold_map2 (fn b => bnf_of_typ Smart_Inline (qualify b) sort) bs rhss
blanchet@49502
   447
        (empty_unfolds, lthy));
blanchet@48975
   448
  in
blanchet@49502
   449
    mk_fp_bnf timer (construct mixfixes) (SOME resBs) bs sort lhss bnfs Dss Ass unfold_set lthy'
blanchet@48975
   450
  end;
blanchet@48975
   451
blanchet@48975
   452
fun fp_bnf_cmd construct (bs, (raw_lhss, raw_bnfs)) lthy =
blanchet@48975
   453
  let
blanchet@48975
   454
    val timer = time (Timer.startRealTimer ());
blanchet@48975
   455
    val lhss = map (dest_TFree o Syntax.read_typ lthy) raw_lhss;
traytel@49185
   456
    val sort = fp_sort lhss NONE;
traytel@49425
   457
    fun qualify b = Binding.qualify true (Binding.name_of (Binding.prefix_name rawN b));
blanchet@49502
   458
    val ((bnfs, (Dss, Ass)), (unfold_set, lthy')) = apfst (apsnd split_list o split_list)
blanchet@48975
   459
      (fold_map2 (fn b => fn rawT =>
traytel@49425
   460
        (bnf_of_typ Smart_Inline (qualify b) sort (Syntax.read_typ lthy rawT)))
blanchet@49502
   461
      bs raw_bnfs (empty_unfolds, lthy));
blanchet@48975
   462
  in
blanchet@49502
   463
    snd (mk_fp_bnf timer
blanchet@49502
   464
      (construct (map (K NoSyn) bs)) NONE bs sort lhss bnfs Dss Ass unfold_set lthy')
blanchet@48975
   465
  end;
blanchet@48975
   466
blanchet@48975
   467
end;