src/HOL/Tools/hologic.ML
author wenzelm
Tue Sep 26 20:54:40 2017 +0200 (23 months ago)
changeset 66695 91500c024c7f
parent 62597 b3f2b8c906a6
child 67149 e61557884799
permissions -rw-r--r--
tuned;
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(*  Title:      HOL/Tools/hologic.ML
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    Author:     Lawrence C Paulson and Markus Wenzel
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Abstract syntax operations for HOL.
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*)
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signature HOLOGIC =
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sig
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  val id_const: typ -> term
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  val mk_comp: term * term -> term
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  val boolN: string
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  val boolT: typ
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  val Trueprop: term
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  val mk_Trueprop: term -> term
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  val dest_Trueprop: term -> term
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  val Trueprop_conv: conv -> conv
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  val mk_induct_forall: typ -> term
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  val mk_setT: typ -> typ
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  val dest_setT: typ -> typ
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  val Collect_const: typ -> term
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  val mk_Collect: string * typ * term -> term
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  val mk_mem: term * term -> term
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  val dest_mem: term -> term * term
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  val mk_set: typ -> term list -> term
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  val dest_set: term -> term list
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  val mk_UNIV: typ -> term
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  val conj_intr: Proof.context -> thm -> thm -> thm
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  val conj_elim: Proof.context -> thm -> thm * thm
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  val conj_elims: Proof.context -> thm -> thm list
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  val conj: term
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  val disj: term
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  val imp: term
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  val Not: term
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  val mk_conj: term * term -> term
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  val mk_disj: term * term -> term
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  val mk_imp: term * term -> term
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  val mk_not: term -> term
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  val dest_conj: term -> term list
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  val conjuncts: term -> term list
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  val dest_disj: term -> term list
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  val disjuncts: term -> term list
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  val dest_imp: term -> term * term
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  val dest_not: term -> term
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  val conj_conv: conv -> conv -> conv
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  val eq_const: typ -> term
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  val mk_eq: term * term -> term
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  val dest_eq: term -> term * term
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  val eq_conv: conv -> conv -> conv
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  val all_const: typ -> term
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  val mk_all: string * typ * term -> term
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  val list_all: (string * typ) list * term -> term
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  val exists_const: typ -> term
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  val mk_exists: string * typ * term -> term
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  val choice_const: typ -> term
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  val class_equal: string
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  val mk_binop: string -> term * term -> term
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  val mk_binrel: string -> term * term -> term
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  val dest_bin: string -> typ -> term -> term * term
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  val unitT: typ
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  val is_unitT: typ -> bool
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  val unit: term
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  val is_unit: term -> bool
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  val mk_prodT: typ * typ -> typ
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  val dest_prodT: typ -> typ * typ
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  val pair_const: typ -> typ -> term
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  val mk_prod: term * term -> term
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  val dest_prod: term -> term * term
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  val mk_fst: term -> term
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  val mk_snd: term -> term
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  val case_prod_const: typ * typ * typ -> term
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  val mk_case_prod: term -> term
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  val flatten_tupleT: typ -> typ list
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  val tupled_lambda: term -> term -> term
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  val mk_tupleT: typ list -> typ
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  val strip_tupleT: typ -> typ list
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  val mk_tuple: term list -> term
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  val strip_tuple: term -> term list
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  val mk_ptupleT: int list list -> typ list -> typ
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  val strip_ptupleT: int list list -> typ -> typ list
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  val flat_tupleT_paths: typ -> int list list
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  val mk_ptuple: int list list -> typ -> term list -> term
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  val strip_ptuple: int list list -> term -> term list
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  val flat_tuple_paths: term -> int list list
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  val mk_ptupleabs: int list list -> typ -> typ -> term -> term
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  val strip_ptupleabs: term -> term * typ list * int list list
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  val natT: typ
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  val zero: term
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  val is_zero: term -> bool
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  val mk_Suc: term -> term
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  val dest_Suc: term -> term
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  val Suc_zero: term
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  val mk_nat: int -> term
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  val dest_nat: term -> int
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  val class_size: string
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  val size_const: typ -> term
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  val intT: typ
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  val one_const: term
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  val bit0_const: term
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  val bit1_const: term
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  val mk_bit: int -> term
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  val dest_bit: term -> int
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  val mk_numeral: int -> term
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  val dest_numeral: term -> int
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  val numeral_const: typ -> term
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  val add_numerals: term -> (term * typ) list -> (term * typ) list
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  val mk_number: typ -> int -> term
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  val dest_number: term -> typ * int
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  val code_integerT: typ
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  val code_naturalT: typ
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  val realT: typ
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  val charT: typ
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  val mk_char: int -> term
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  val dest_char: term -> int
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  val listT: typ -> typ
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  val nil_const: typ -> term
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  val cons_const: typ -> term
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  val mk_list: typ -> term list -> term
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  val dest_list: term -> term list
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  val stringT: typ
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  val mk_string: string -> term
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  val dest_string: term -> string
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  val literalT: typ
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  val mk_literal: string -> term
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  val dest_literal: term -> string
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  val mk_typerep: typ -> term
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  val termT: typ
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  val term_of_const: typ -> term
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  val mk_term_of: typ -> term -> term
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  val reflect_term: term -> term
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  val mk_valtermify_app: string -> (string * typ) list -> typ -> term
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  val mk_return: typ -> typ -> term -> term
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  val mk_ST: ((term * typ) * (string * typ) option)  list -> term -> typ -> typ option * typ -> term
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  val mk_random: typ -> term -> term
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end;
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structure HOLogic: HOLOGIC =
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struct
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(* functions *)
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fun id_const T = Const ("Fun.id", T --> T);
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fun mk_comp (f, g) =
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  let
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    val fT = fastype_of f;
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    val gT = fastype_of g;
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    val compT = fT --> gT --> domain_type gT --> range_type fT;
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  in Const ("Fun.comp", compT) $ f $ g end;
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(* bool and set *)
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val boolN = "HOL.bool";
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val boolT = Type (boolN, []);
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fun mk_induct_forall T = Const ("HOL.induct_forall", (T --> boolT) --> boolT);
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fun mk_setT T = Type ("Set.set", [T]);
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fun dest_setT (Type ("Set.set", [T])) = T
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  | dest_setT T = raise TYPE ("dest_setT: set type expected", [T], []);
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fun mk_set T ts =
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  let
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    val sT = mk_setT T;
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    val empty = Const ("Orderings.bot_class.bot", sT);
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    fun insert t u = Const ("Set.insert", T --> sT --> sT) $ t $ u;
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  in fold_rev insert ts empty end;
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fun mk_UNIV T = Const ("Orderings.top_class.top", mk_setT T);
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fun dest_set (Const ("Orderings.bot_class.bot", _)) = []
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  | dest_set (Const ("Set.insert", _) $ t $ u) = t :: dest_set u
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  | dest_set t = raise TERM ("dest_set", [t]);
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fun Collect_const T = Const ("Set.Collect", (T --> boolT) --> mk_setT T);
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fun mk_Collect (a, T, t) = Collect_const T $ absfree (a, T) t;
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fun mk_mem (x, A) =
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  let val setT = fastype_of A in
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    Const ("Set.member", dest_setT setT --> setT --> boolT) $ x $ A
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  end;
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fun dest_mem (Const ("Set.member", _) $ x $ A) = (x, A)
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  | dest_mem t = raise TERM ("dest_mem", [t]);
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(* logic *)
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val Trueprop = Const (@{const_name Trueprop}, boolT --> propT);
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fun mk_Trueprop P = Trueprop $ P;
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fun dest_Trueprop (Const (@{const_name Trueprop}, _) $ P) = P
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  | dest_Trueprop t = raise TERM ("dest_Trueprop", [t]);
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fun Trueprop_conv cv ct =
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  (case Thm.term_of ct of
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    Const (@{const_name Trueprop}, _) $ _ => Conv.arg_conv cv ct
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  | _ => raise CTERM ("Trueprop_conv", [ct]))
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fun conj_intr ctxt thP thQ =
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  let
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    val (P, Q) = apply2 (Object_Logic.dest_judgment ctxt o Thm.cprop_of) (thP, thQ)
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      handle CTERM (msg, _) => raise THM (msg, 0, [thP, thQ]);
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    val inst = Thm.instantiate ([], [((("P", 0), boolT), P), ((("Q", 0), boolT), Q)]);
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  in Drule.implies_elim_list (inst @{thm conjI}) [thP, thQ] end;
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fun conj_elim ctxt thPQ =
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  let
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    val (P, Q) = Thm.dest_binop (Object_Logic.dest_judgment ctxt (Thm.cprop_of thPQ))
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      handle CTERM (msg, _) => raise THM (msg, 0, [thPQ]);
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    val inst = Thm.instantiate ([], [((("P", 0), boolT), P), ((("Q", 0), boolT), Q)]);
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    val thP = Thm.implies_elim (inst @{thm conjunct1}) thPQ;
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    val thQ = Thm.implies_elim (inst @{thm conjunct2}) thPQ;
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  in (thP, thQ) end;
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fun conj_elims ctxt th =
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  let val (th1, th2) = conj_elim ctxt th
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  in conj_elims ctxt th1 @ conj_elims ctxt th2 end handle THM _ => [th];
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val conj = @{term HOL.conj}
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and disj = @{term HOL.disj}
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and imp = @{term implies}
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and Not = @{term Not};
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fun mk_conj (t1, t2) = conj $ t1 $ t2
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and mk_disj (t1, t2) = disj $ t1 $ t2
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and mk_imp (t1, t2) = imp $ t1 $ t2
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and mk_not t = Not $ t;
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fun dest_conj (Const ("HOL.conj", _) $ t $ t') = t :: dest_conj t'
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  | dest_conj t = [t];
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(*Like dest_conj, but flattens conjunctions however nested*)
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fun conjuncts_aux (Const ("HOL.conj", _) $ t $ t') conjs = conjuncts_aux t (conjuncts_aux t' conjs)
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  | conjuncts_aux t conjs = t::conjs;
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fun conjuncts t = conjuncts_aux t [];
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fun dest_disj (Const ("HOL.disj", _) $ t $ t') = t :: dest_disj t'
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  | dest_disj t = [t];
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(*Like dest_disj, but flattens disjunctions however nested*)
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fun disjuncts_aux (Const ("HOL.disj", _) $ t $ t') disjs = disjuncts_aux t (disjuncts_aux t' disjs)
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  | disjuncts_aux t disjs = t::disjs;
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fun disjuncts t = disjuncts_aux t [];
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fun dest_imp (Const ("HOL.implies", _) $ A $ B) = (A, B)
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  | dest_imp  t = raise TERM ("dest_imp", [t]);
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fun dest_not (Const ("HOL.Not", _) $ t) = t
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  | dest_not t = raise TERM ("dest_not", [t]);
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fun conj_conv cv1 cv2 ct =
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  (case Thm.term_of ct of
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    Const (@{const_name HOL.conj}, _) $ _ $ _ =>
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      Conv.combination_conv (Conv.arg_conv cv1) cv2 ct
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  | _ => raise CTERM ("conj_conv", [ct]));
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fun eq_const T = Const (@{const_name HOL.eq}, T --> T --> boolT);
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fun mk_eq (t, u) = eq_const (fastype_of t) $ t $ u;
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fun dest_eq (Const (@{const_name HOL.eq}, _) $ lhs $ rhs) = (lhs, rhs)
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  | dest_eq t = raise TERM ("dest_eq", [t])
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fun eq_conv cv1 cv2 ct =
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  (case Thm.term_of ct of
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    Const (@{const_name HOL.eq}, _) $ _ $ _ => Conv.combination_conv (Conv.arg_conv cv1) cv2 ct
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  | _ => raise CTERM ("eq_conv", [ct]));
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fun all_const T = Const ("HOL.All", (T --> boolT) --> boolT);
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fun mk_all (x, T, P) = all_const T $ absfree (x, T) P;
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fun list_all (xs, t) = fold_rev (fn (x, T) => fn P => all_const T $ Abs (x, T, P)) xs t;
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fun exists_const T = Const ("HOL.Ex", (T --> boolT) --> boolT);
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fun mk_exists (x, T, P) = exists_const T $ absfree (x, T) P;
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fun choice_const T = Const("Hilbert_Choice.Eps", (T --> boolT) --> T);
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val class_equal = "HOL.equal";
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(* binary operations and relations *)
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fun mk_binop c (t, u) =
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  let val T = fastype_of t
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  in Const (c, T --> T --> T) $ t $ u end;
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fun mk_binrel c (t, u) =
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  let val T = fastype_of t
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  in Const (c, T --> T --> boolT) $ t $ u end;
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(*destruct the application of a binary operator. The dummyT case is a crude
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  way of handling polymorphic operators.*)
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fun dest_bin c T (tm as Const (c', Type ("fun", [T', _])) $ t $ u) =
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      if c = c' andalso (T=T' orelse T=dummyT) then (t, u)
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      else raise TERM ("dest_bin " ^ c, [tm])
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  | dest_bin c _ tm = raise TERM ("dest_bin " ^ c, [tm]);
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(* unit *)
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val unitT = Type ("Product_Type.unit", []);
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fun is_unitT (Type ("Product_Type.unit", [])) = true
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  | is_unitT _ = false;
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val unit = Const ("Product_Type.Unity", unitT);
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fun is_unit (Const ("Product_Type.Unity", _)) = true
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  | is_unit _ = false;
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(* prod *)
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fun mk_prodT (T1, T2) = Type ("Product_Type.prod", [T1, T2]);
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fun dest_prodT (Type ("Product_Type.prod", [T1, T2])) = (T1, T2)
wenzelm@4571
   326
  | dest_prodT T = raise TYPE ("dest_prodT", [T], []);
wenzelm@4571
   327
wenzelm@46216
   328
fun pair_const T1 T2 = Const ("Product_Type.Pair", T1 --> T2 --> mk_prodT (T1, T2));
berghofe@14048
   329
wenzelm@4571
   330
fun mk_prod (t1, t2) =
wenzelm@4571
   331
  let val T1 = fastype_of t1 and T2 = fastype_of t2 in
berghofe@14048
   332
    pair_const T1 T2 $ t1 $ t2
wenzelm@4571
   333
  end;
wenzelm@4571
   334
haftmann@37389
   335
fun dest_prod (Const ("Product_Type.Pair", _) $ t1 $ t2) = (t1, t2)
wenzelm@4571
   336
  | dest_prod t = raise TERM ("dest_prod", [t]);
wenzelm@4571
   337
wenzelm@4571
   338
fun mk_fst p =
wenzelm@4571
   339
  let val pT = fastype_of p in
blanchet@55411
   340
    Const ("Product_Type.prod.fst", pT --> fst (dest_prodT pT)) $ p
wenzelm@4571
   341
  end;
wenzelm@4571
   342
wenzelm@4571
   343
fun mk_snd p =
wenzelm@4571
   344
  let val pT = fastype_of p in
blanchet@55411
   345
    Const ("Product_Type.prod.snd", pT --> snd (dest_prodT pT)) $ p
wenzelm@4571
   346
  end;
wenzelm@4571
   347
haftmann@61424
   348
fun case_prod_const (A, B, C) =
haftmann@61424
   349
  Const ("Product_Type.prod.case_prod", (A --> B --> C) --> mk_prodT (A, B) --> C);
wenzelm@18285
   350
haftmann@61424
   351
fun mk_case_prod t =
wenzelm@18285
   352
  (case Term.fastype_of t of
wenzelm@18285
   353
    T as (Type ("fun", [A, Type ("fun", [B, C])])) =>
haftmann@61424
   354
      Const ("Product_Type.prod.case_prod", T --> mk_prodT (A, B) --> C) $ t
haftmann@61424
   355
  | _ => raise TERM ("mk_case_prod: bad body type", [t]));
wenzelm@18285
   356
berghofe@5096
   357
(*Maps the type T1 * ... * Tn to [T1, ..., Tn], however nested*)
haftmann@37676
   358
fun flatten_tupleT (Type ("Product_Type.prod", [T1, T2])) = flatten_tupleT T1 @ flatten_tupleT T2
haftmann@32287
   359
  | flatten_tupleT T = [T];
berghofe@23745
   360
krauss@39756
   361
(*abstraction over nested tuples*)
krauss@39756
   362
fun tupled_lambda (x as Free _) b = lambda x b
krauss@39756
   363
  | tupled_lambda (x as Var _) b = lambda x b
krauss@39756
   364
  | tupled_lambda (Const ("Product_Type.Pair", _) $ u $ v) b =
haftmann@61424
   365
      mk_case_prod (tupled_lambda u (tupled_lambda v b))
krauss@39756
   366
  | tupled_lambda (Const ("Product_Type.Unity", _)) b =
krauss@39756
   367
      Abs ("x", unitT, b)
krauss@39756
   368
  | tupled_lambda t _ = raise TERM ("tupled_lambda: bad tuple", [t]);
krauss@39756
   369
haftmann@32342
   370
haftmann@32342
   371
(* tuples with right-fold structure *)
haftmann@32342
   372
haftmann@32342
   373
fun mk_tupleT [] = unitT
haftmann@32342
   374
  | mk_tupleT Ts = foldr1 mk_prodT Ts;
haftmann@32342
   375
haftmann@32342
   376
fun strip_tupleT (Type ("Product_Type.unit", [])) = []
haftmann@37676
   377
  | strip_tupleT (Type ("Product_Type.prod", [T1, T2])) = T1 :: strip_tupleT T2
haftmann@32342
   378
  | strip_tupleT T = [T];
haftmann@32342
   379
haftmann@32342
   380
fun mk_tuple [] = unit
haftmann@32342
   381
  | mk_tuple ts = foldr1 mk_prod ts;
haftmann@32342
   382
haftmann@32342
   383
fun strip_tuple (Const ("Product_Type.Unity", _)) = []
haftmann@37389
   384
  | strip_tuple (Const ("Product_Type.Pair", _) $ t1 $ t2) = t1 :: strip_tuple t2
haftmann@32342
   385
  | strip_tuple t = [t];
haftmann@32342
   386
haftmann@32342
   387
haftmann@32287
   388
(* tuples with specific arities
berghofe@23745
   389
haftmann@32342
   390
   an "arity" of a tuple is a list of lists of integers,
haftmann@32342
   391
   denoting paths to subterms that are pairs
wenzelm@25172
   392
*)
berghofe@23745
   393
haftmann@32342
   394
fun ptuple_err s = raise TERM (s ^ ": inconsistent use of nested products", []);
berghofe@23745
   395
haftmann@32342
   396
fun mk_ptupleT ps =
berghofe@23745
   397
  let
berghofe@23745
   398
    fun mk p Ts =
haftmann@36692
   399
      if member (op =) ps p then
berghofe@23745
   400
        let
berghofe@23745
   401
          val (T, Ts') = mk (1::p) Ts;
berghofe@23745
   402
          val (U, Ts'') = mk (2::p) Ts'
berghofe@23745
   403
        in (mk_prodT (T, U), Ts'') end
berghofe@23745
   404
      else (hd Ts, tl Ts)
berghofe@23745
   405
  in fst o mk [] end;
berghofe@23745
   406
haftmann@32342
   407
fun strip_ptupleT ps =
haftmann@32287
   408
  let
haftmann@36692
   409
    fun factors p T = if member (op =) ps p then (case T of
haftmann@37676
   410
        Type ("Product_Type.prod", [T1, T2]) =>
haftmann@32287
   411
          factors (1::p) T1 @ factors (2::p) T2
haftmann@32342
   412
      | _ => ptuple_err "strip_ptupleT") else [T]
haftmann@32287
   413
  in factors [] end;
haftmann@32287
   414
haftmann@32287
   415
val flat_tupleT_paths =
haftmann@32287
   416
  let
haftmann@37676
   417
    fun factors p (Type ("Product_Type.prod", [T1, T2])) =
haftmann@32287
   418
          p :: factors (1::p) T1 @ factors (2::p) T2
haftmann@32287
   419
      | factors p _ = []
haftmann@32287
   420
  in factors [] end;
haftmann@32287
   421
haftmann@32342
   422
fun mk_ptuple ps =
haftmann@32287
   423
  let
haftmann@32287
   424
    fun mk p T ts =
haftmann@36692
   425
      if member (op =) ps p then (case T of
haftmann@37676
   426
          Type ("Product_Type.prod", [T1, T2]) =>
haftmann@32287
   427
            let
haftmann@32287
   428
              val (t, ts') = mk (1::p) T1 ts;
haftmann@32287
   429
              val (u, ts'') = mk (2::p) T2 ts'
haftmann@32287
   430
            in (pair_const T1 T2 $ t $ u, ts'') end
haftmann@32342
   431
        | _ => ptuple_err "mk_ptuple")
haftmann@32287
   432
      else (hd ts, tl ts)
haftmann@32287
   433
  in fst oo mk [] end;
haftmann@32287
   434
haftmann@32342
   435
fun strip_ptuple ps =
haftmann@32287
   436
  let
haftmann@36692
   437
    fun dest p t = if member (op =) ps p then (case t of
haftmann@37389
   438
        Const ("Product_Type.Pair", _) $ t $ u =>
haftmann@32287
   439
          dest (1::p) t @ dest (2::p) u
haftmann@32342
   440
      | _ => ptuple_err "strip_ptuple") else [t]
haftmann@32287
   441
  in dest [] end;
haftmann@32287
   442
haftmann@32287
   443
val flat_tuple_paths =
haftmann@32287
   444
  let
haftmann@37389
   445
    fun factors p (Const ("Product_Type.Pair", _) $ t $ u) =
haftmann@32287
   446
          p :: factors (1::p) t @ factors (2::p) u
haftmann@32287
   447
      | factors p _ = []
haftmann@32287
   448
  in factors [] end;
haftmann@32287
   449
haftmann@61424
   450
(*In mk_ptupleabs ps S T u, term u expects separate arguments for the factors of S,
haftmann@32287
   451
  with result type T.  The call creates a new term expecting one argument
haftmann@32287
   452
  of type S.*)
haftmann@61424
   453
fun mk_ptupleabs ps T T3 u =
haftmann@32287
   454
  let
haftmann@32287
   455
    fun ap ((p, T) :: pTs) =
haftmann@36692
   456
          if member (op =) ps p then (case T of
haftmann@37676
   457
              Type ("Product_Type.prod", [T1, T2]) =>
haftmann@61424
   458
                case_prod_const (T1, T2, map snd pTs ---> T3) $
haftmann@32287
   459
                  ap ((1::p, T1) :: (2::p, T2) :: pTs)
haftmann@61424
   460
            | _ => ptuple_err "mk_ptupleabs")
haftmann@32287
   461
          else Abs ("x", T, ap pTs)
haftmann@32287
   462
      | ap [] =
haftmann@32287
   463
          let val k = length ps
haftmann@32287
   464
          in list_comb (incr_boundvars (k + 1) u, map Bound (k downto 0)) end
haftmann@32287
   465
  in ap [([], T)] end;
haftmann@32287
   466
haftmann@61424
   467
val strip_ptupleabs =
berghofe@23745
   468
  let
haftmann@34962
   469
    fun strip [] qs Ts t = (t, rev Ts, qs)
haftmann@61424
   470
      | strip (p :: ps) qs Ts (Const ("Product_Type.prod.case_prod", _) $ t) =
berghofe@23745
   471
          strip ((1 :: p) :: (2 :: p) :: ps) (p :: qs) Ts t
berghofe@23745
   472
      | strip (p :: ps) qs Ts (Abs (s, T, t)) = strip ps qs (T :: Ts) t
berghofe@23745
   473
      | strip (p :: ps) qs Ts t = strip ps qs
berghofe@23745
   474
          (hd (binder_types (fastype_of1 (Ts, t))) :: Ts)
berghofe@23745
   475
          (incr_boundvars 1 t $ Bound 0)
haftmann@32287
   476
  in strip [[]] [] [] end;
berghofe@23745
   477
wenzelm@5207
   478
wenzelm@5207
   479
(* nat *)
wenzelm@5207
   480
haftmann@37387
   481
val natT = Type ("Nat.nat", []);
wenzelm@5207
   482
haftmann@35267
   483
val zero = Const ("Groups.zero_class.zero", natT);
wenzelm@5207
   484
haftmann@35267
   485
fun is_zero (Const ("Groups.zero_class.zero", _)) = true
wenzelm@5207
   486
  | is_zero _ = false;
wenzelm@5207
   487
haftmann@37387
   488
fun mk_Suc t = Const ("Nat.Suc", natT --> natT) $ t;
wenzelm@5207
   489
haftmann@37387
   490
fun dest_Suc (Const ("Nat.Suc", _) $ t) = t
wenzelm@5207
   491
  | dest_Suc t = raise TERM ("dest_Suc", [t]);
wenzelm@5207
   492
haftmann@21621
   493
val Suc_zero = mk_Suc zero;
haftmann@21621
   494
wenzelm@24630
   495
fun mk_nat n =
haftmann@22994
   496
  let
haftmann@22994
   497
    fun mk 0 = zero
wenzelm@23297
   498
      | mk n = mk_Suc (mk (n - 1));
wenzelm@23576
   499
  in if n < 0 then raise TERM ("mk_nat: negative number", []) else mk n end;
wenzelm@5207
   500
haftmann@35267
   501
fun dest_nat (Const ("Groups.zero_class.zero", _)) = 0
haftmann@37387
   502
  | dest_nat (Const ("Nat.Suc", _) $ t) = dest_nat t + 1
wenzelm@5207
   503
  | dest_nat t = raise TERM ("dest_nat", [t]);
wenzelm@5207
   504
haftmann@22994
   505
val class_size = "Nat.size";
haftmann@22994
   506
haftmann@22994
   507
fun size_const T = Const ("Nat.size_class.size", T --> natT);
haftmann@22994
   508
wenzelm@5207
   509
huffman@47108
   510
(* binary numerals and int *)
wenzelm@21778
   511
huffman@47108
   512
val numT = Type ("Num.num", []);
haftmann@25919
   513
val intT = Type ("Int.int", []);
wenzelm@21778
   514
huffman@47108
   515
val one_const = Const ("Num.num.One", numT)
huffman@47108
   516
and bit0_const = Const ("Num.num.Bit0", numT --> numT)
huffman@47108
   517
and bit1_const = Const ("Num.num.Bit1", numT --> numT);
huffman@26086
   518
huffman@26086
   519
fun mk_bit 0 = bit0_const
huffman@26086
   520
  | mk_bit 1 = bit1_const
huffman@26086
   521
  | mk_bit _ = raise TERM ("mk_bit", []);
huffman@26086
   522
huffman@47108
   523
fun dest_bit (Const ("Num.num.Bit0", _)) = 0
huffman@47108
   524
  | dest_bit (Const ("Num.num.Bit1", _)) = 1
huffman@26086
   525
  | dest_bit t = raise TERM ("dest_bit", [t]);
paulson@8768
   526
huffman@47108
   527
fun mk_numeral i =
huffman@47108
   528
  let fun mk 1 = one_const
huffman@47108
   529
        | mk i = let val (q, r) = Integer.div_mod i 2 in mk_bit r $ mk q end
huffman@47108
   530
  in if i > 0 then mk i else raise TERM ("mk_numeral: " ^ string_of_int i, [])
huffman@47108
   531
  end
berghofe@13755
   532
haftmann@62342
   533
fun dest_numeral (Const ("Num.num.One", _)) = 1
haftmann@62342
   534
  | dest_numeral (Const ("Num.num.Bit0", _) $ bs) = 2 * dest_numeral bs
haftmann@62342
   535
  | dest_numeral (Const ("Num.num.Bit1", _) $ bs) = 2 * dest_numeral bs + 1
haftmann@62342
   536
  | dest_numeral t = raise TERM ("dest_num", [t]);
berghofe@13755
   537
huffman@47108
   538
fun numeral_const T = Const ("Num.numeral_class.numeral", numT --> T);
haftmann@21820
   539
huffman@47108
   540
fun add_numerals (Const ("Num.numeral_class.numeral", Type (_, [_, T])) $ t) = cons (t, T)
wenzelm@23269
   541
  | add_numerals (t $ u) = add_numerals t #> add_numerals u
wenzelm@23269
   542
  | add_numerals (Abs (_, _, t)) = add_numerals t
wenzelm@23269
   543
  | add_numerals _ = I;
haftmann@22391
   544
haftmann@35267
   545
fun mk_number T 0 = Const ("Groups.zero_class.zero", T)
haftmann@35267
   546
  | mk_number T 1 = Const ("Groups.one_class.one", T)
huffman@47108
   547
  | mk_number T i =
huffman@47108
   548
    if i > 0 then numeral_const T $ mk_numeral i
haftmann@54489
   549
    else Const ("Groups.uminus_class.uminus", T --> T) $ mk_number T (~ i);
haftmann@21820
   550
haftmann@35267
   551
fun dest_number (Const ("Groups.zero_class.zero", T)) = (T, 0)
haftmann@35267
   552
  | dest_number (Const ("Groups.one_class.one", T)) = (T, 1)
huffman@47108
   553
  | dest_number (Const ("Num.numeral_class.numeral", Type ("fun", [_, T])) $ t) =
haftmann@62342
   554
      (T, dest_numeral t)
haftmann@54489
   555
  | dest_number (Const ("Groups.uminus_class.uminus", Type ("fun", [_, T])) $ t) =
haftmann@54489
   556
      apsnd (op ~) (dest_number t)
haftmann@21820
   557
  | dest_number t = raise TERM ("dest_number", [t]);
berghofe@13755
   558
wenzelm@21829
   559
haftmann@51143
   560
(* code target numerals *)
haftmann@51143
   561
haftmann@51143
   562
val code_integerT = Type ("Code_Numeral.integer", []);
haftmann@51143
   563
haftmann@51143
   564
val code_naturalT = Type ("Code_Numeral.natural", []);
haftmann@51143
   565
haftmann@51143
   566
berghofe@13755
   567
(* real *)
berghofe@13755
   568
hoelzl@51523
   569
val realT = Type ("Real.real", []);
berghofe@13755
   570
berghofe@13755
   571
wenzelm@21755
   572
(* list *)
haftmann@21455
   573
wenzelm@21755
   574
fun listT T = Type ("List.list", [T]);
haftmann@21455
   575
berghofe@25887
   576
fun nil_const T = Const ("List.list.Nil", listT T);
berghofe@25887
   577
berghofe@25887
   578
fun cons_const T =
berghofe@25887
   579
  let val lT = listT T
berghofe@25887
   580
  in Const ("List.list.Cons", T --> lT --> lT) end;
berghofe@25887
   581
wenzelm@21755
   582
fun mk_list T ts =
haftmann@21455
   583
  let
wenzelm@21755
   584
    val lT = listT T;
wenzelm@21755
   585
    val Nil = Const ("List.list.Nil", lT);
wenzelm@21755
   586
    fun Cons t u = Const ("List.list.Cons", T --> lT --> lT) $ t $ u;
wenzelm@21755
   587
  in fold_rev Cons ts Nil end;
wenzelm@21755
   588
wenzelm@21755
   589
fun dest_list (Const ("List.list.Nil", _)) = []
wenzelm@21755
   590
  | dest_list (Const ("List.list.Cons", _) $ t $ u) = t :: dest_list u
wenzelm@21755
   591
  | dest_list t = raise TERM ("dest_list", [t]);
haftmann@21455
   592
haftmann@21455
   593
haftmann@31048
   594
(* char *)
haftmann@31048
   595
haftmann@31048
   596
val charT = Type ("String.char", []);
haftmann@31048
   597
haftmann@62597
   598
val Char_const = Const ("String.Char", numT --> charT);
haftmann@62597
   599
haftmann@62597
   600
fun mk_char 0 = Const ("Groups.zero_class.zero", charT)
haftmann@62597
   601
  | mk_char i =
haftmann@62597
   602
      if 1 <= i andalso i <= 255 then Char_const $ mk_numeral i
haftmann@62597
   603
      else raise TERM ("mk_char", []);
haftmann@31048
   604
haftmann@62597
   605
fun dest_char t =
haftmann@62597
   606
  let
haftmann@62597
   607
    val (T, n) = case t of
haftmann@62597
   608
      Const ("Groups.zero_class.zero", T) => (T, 0)
haftmann@62597
   609
    | (Const ("String.Char", Type ("fun", [_, T])) $ t) => (T, dest_numeral t)
haftmann@62597
   610
    | _ => raise TERM ("dest_char", [t]);
haftmann@62597
   611
  in
haftmann@62597
   612
    if T = charT then n
haftmann@62597
   613
    else raise TERM ("dest_char", [t])
haftmann@62597
   614
  end;
haftmann@31048
   615
haftmann@31048
   616
haftmann@21455
   617
(* string *)
haftmann@21455
   618
krauss@32446
   619
val stringT = listT charT;
haftmann@21455
   620
wenzelm@40627
   621
val mk_string = mk_list charT o map (mk_char o ord) o raw_explode;
wenzelm@21755
   622
val dest_string = implode o map (chr o dest_char) o dest_list;
haftmann@21455
   623
haftmann@31048
   624
haftmann@31205
   625
(* literal *)
haftmann@31048
   626
haftmann@31205
   627
val literalT = Type ("String.literal", []);
haftmann@31048
   628
wenzelm@62513
   629
fun mk_literal s = Const ("String.literal.STR", stringT --> literalT)
haftmann@31048
   630
      $ mk_string s;
wenzelm@62513
   631
fun dest_literal (Const ("String.literal.STR", _) $ t) =
haftmann@31048
   632
      dest_string t
haftmann@31205
   633
  | dest_literal t = raise TERM ("dest_literal", [t]);
haftmann@31048
   634
haftmann@31135
   635
haftmann@31135
   636
(* typerep and term *)
haftmann@31135
   637
haftmann@31135
   638
val typerepT = Type ("Typerep.typerep", []);
haftmann@31135
   639
haftmann@31736
   640
fun mk_typerep (Type (tyco, Ts)) = Const ("Typerep.typerep.Typerep",
haftmann@31736
   641
      literalT --> listT typerepT --> typerepT) $ mk_literal tyco
haftmann@31736
   642
        $ mk_list typerepT (map mk_typerep Ts)
haftmann@31736
   643
  | mk_typerep (T as TFree _) = Const ("Typerep.typerep_class.typerep",
haftmann@31736
   644
      Term.itselfT T --> typerepT) $ Logic.mk_type T;
haftmann@31135
   645
haftmann@32657
   646
val termT = Type ("Code_Evaluation.term", []);
haftmann@31135
   647
haftmann@32657
   648
fun term_of_const T = Const ("Code_Evaluation.term_of_class.term_of", T --> termT);
haftmann@32339
   649
haftmann@32339
   650
fun mk_term_of T t = term_of_const T $ t;
haftmann@31135
   651
haftmann@31135
   652
fun reflect_term (Const (c, T)) =
haftmann@32657
   653
      Const ("Code_Evaluation.Const", literalT --> typerepT --> termT)
haftmann@31205
   654
        $ mk_literal c $ mk_typerep T
haftmann@31135
   655
  | reflect_term (t1 $ t2) =
haftmann@32657
   656
      Const ("Code_Evaluation.App", termT --> termT --> termT)
haftmann@31135
   657
        $ reflect_term t1 $ reflect_term t2
haftmann@31183
   658
  | reflect_term (Abs (v, _, t)) = Abs (v, termT, reflect_term t)
haftmann@31183
   659
  | reflect_term t = t;
haftmann@31183
   660
haftmann@31463
   661
fun mk_valtermify_app c vs T =
haftmann@31463
   662
  let
haftmann@31463
   663
    fun termifyT T = mk_prodT (T, unitT --> termT);
haftmann@32657
   664
    fun valapp T T' = Const ("Code_Evaluation.valapp",
haftmann@31463
   665
      termifyT (T --> T') --> termifyT T --> termifyT T');
haftmann@31463
   666
    fun mk_fTs [] _ = []
haftmann@31463
   667
      | mk_fTs (_ :: Ts) T = (Ts ---> T) :: mk_fTs Ts T;
haftmann@31463
   668
    val Ts = map snd vs;
haftmann@31463
   669
    val t = Const (c, Ts ---> T);
haftmann@31463
   670
    val tt = mk_prod (t, Abs ("u", unitT, reflect_term t));
wenzelm@33245
   671
    fun app (fT, (v, T)) t = valapp T fT $ t $ Free (v, termifyT T);
wenzelm@33245
   672
  in fold app (mk_fTs Ts T ~~ vs) tt end;
haftmann@31463
   673
haftmann@31183
   674
haftmann@31183
   675
(* open state monads *)
haftmann@31183
   676
haftmann@31183
   677
fun mk_return T U x = pair_const T U $ x;
haftmann@31183
   678
haftmann@31183
   679
fun mk_ST clauses t U (someT, V) =
haftmann@31183
   680
  let
haftmann@31183
   681
    val R = case someT of SOME T => mk_prodT (T, V) | NONE => V
haftmann@31183
   682
    fun mk_clause ((t, U), SOME (v, T)) (t', U') =
haftmann@31183
   683
          (Const ("Product_Type.scomp", (U --> mk_prodT (T, U')) --> (T --> U' --> R) --> U --> R)
haftmann@31183
   684
            $ t $ lambda (Free (v, T)) t', U)
haftmann@31183
   685
      | mk_clause ((t, U), NONE) (t', U') =
haftmann@31183
   686
          (Const ("Product_Type.fcomp", (U --> U') --> (U' --> R) --> U --> R)
haftmann@31183
   687
            $ t $ t', U)
haftmann@31183
   688
  in fold_rev mk_clause clauses (t, U) |> fst end;
haftmann@31135
   689
haftmann@38550
   690
haftmann@38550
   691
(* random seeds *)
haftmann@38550
   692
haftmann@51143
   693
val random_seedT = mk_prodT (code_naturalT, code_naturalT);
haftmann@31463
   694
haftmann@51143
   695
fun mk_random T t = Const ("Quickcheck_Random.random_class.random", code_naturalT
haftmann@31463
   696
  --> random_seedT --> mk_prodT (mk_prodT (T, unitT --> termT), random_seedT)) $ t;
haftmann@31463
   697
clasohm@923
   698
end;