src/HOL/Tools/hologic.ML
author krauss
Tue Sep 28 12:34:41 2010 +0200 (2010-09-28)
changeset 39756 6c8e83d94536
parent 39250 548a3e5521ab
child 40627 becf5d5187cc
permissions -rw-r--r--
consolidated tupled_lambda; moved to structure HOLogic
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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 typeS: sort
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  val typeT: typ
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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 true_const: term
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  val false_const: 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: thm -> thm -> thm
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  val conj_elim: thm -> thm * thm
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  val conj_elims: 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 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 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 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 split_const: typ * typ * typ -> term
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  val mk_split: 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_psplits: int list list -> typ -> typ -> term -> term
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  val strip_psplits: 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 code_numeralT: typ
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  val intT: typ
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  val pls_const: term
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  val min_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 number_of_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 realT: typ
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  val nibbleT: typ
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  val mk_nibble: int -> term
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  val dest_nibble: term -> int
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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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(* HOL syntax *)
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val typeS: sort = ["HOL.type"];
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val typeT = Type_Infer.anyT typeS;
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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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val true_const =  Const ("HOL.True", boolT);
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val false_const = Const ("HOL.False", boolT);
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fun mk_setT T = T --> boolT;
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fun dest_setT (Type ("fun", [T, Type ("HOL.bool", [])])) = 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 ("HOL.Trueprop", boolT --> propT);
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fun mk_Trueprop P = Trueprop $ P;
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fun dest_Trueprop (Const ("HOL.Trueprop", _) $ P) = P
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  | dest_Trueprop t = raise TERM ("dest_Trueprop", [t]);
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fun conj_intr thP thQ =
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  let
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    val (P, Q) = pairself (Object_Logic.dest_judgment 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 ([], [(@{cpat "?P::bool"}, P), (@{cpat "?Q::bool"}, Q)]);
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  in Drule.implies_elim_list (inst @{thm conjI}) [thP, thQ] end;
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fun conj_elim thPQ =
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  let
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    val (P, Q) = Thm.dest_binop (Object_Logic.dest_judgment (Thm.cprop_of thPQ))
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      handle CTERM (msg, _) => raise THM (msg, 0, [thPQ]);
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    val inst = Thm.instantiate ([], [(@{cpat "?P::bool"}, P), (@{cpat "?Q::bool"}, 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 th =
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  let val (th1, th2) = conj_elim th
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  in conj_elims th1 @ conj_elims 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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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 eq_const T = Const ("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 ("HOL.eq", _) $ lhs $ rhs) = (lhs, rhs)
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  | dest_eq t = raise TERM ("dest_eq", [t])
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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 in
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    Const (c, [T, T] ---> T) $ t $ u
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  end;
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fun mk_binrel c (t, u) =
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  let val T = fastype_of t in
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    Const (c, [T, T] ---> boolT) $ t $ u
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  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)
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  | dest_prodT T = raise TYPE ("dest_prodT", [T], []);
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fun pair_const T1 T2 = Const ("Product_Type.Pair", [T1, T2] ---> mk_prodT (T1, T2));
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fun mk_prod (t1, t2) =
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  let val T1 = fastype_of t1 and T2 = fastype_of t2 in
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    pair_const T1 T2 $ t1 $ t2
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  end;
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fun dest_prod (Const ("Product_Type.Pair", _) $ t1 $ t2) = (t1, t2)
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  | dest_prod t = raise TERM ("dest_prod", [t]);
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fun mk_fst p =
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  let val pT = fastype_of p in
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    Const ("Product_Type.fst", pT --> fst (dest_prodT pT)) $ p
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  end;
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fun mk_snd p =
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  let val pT = fastype_of p in
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    Const ("Product_Type.snd", pT --> snd (dest_prodT pT)) $ p
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  end;
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fun split_const (A, B, C) =
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  Const ("Product_Type.prod.prod_case", (A --> B --> C) --> mk_prodT (A, B) --> C);
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fun mk_split t =
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  (case Term.fastype_of t of
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    T as (Type ("fun", [A, Type ("fun", [B, C])])) =>
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      Const ("Product_Type.prod.prod_case", T --> mk_prodT (A, B) --> C) $ t
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  | _ => raise TERM ("mk_split: bad body type", [t]));
wenzelm@18285
   326
berghofe@5096
   327
(*Maps the type T1 * ... * Tn to [T1, ..., Tn], however nested*)
haftmann@37676
   328
fun flatten_tupleT (Type ("Product_Type.prod", [T1, T2])) = flatten_tupleT T1 @ flatten_tupleT T2
haftmann@32287
   329
  | flatten_tupleT T = [T];
berghofe@23745
   330
krauss@39756
   331
(*abstraction over nested tuples*)
krauss@39756
   332
fun tupled_lambda (x as Free _) b = lambda x b
krauss@39756
   333
  | tupled_lambda (x as Var _) b = lambda x b
krauss@39756
   334
  | tupled_lambda (Const ("Product_Type.Pair", _) $ u $ v) b =
krauss@39756
   335
      mk_split (tupled_lambda u (tupled_lambda v b))
krauss@39756
   336
  | tupled_lambda (Const ("Product_Type.Unity", _)) b =
krauss@39756
   337
      Abs ("x", unitT, b)
krauss@39756
   338
  | tupled_lambda t _ = raise TERM ("tupled_lambda: bad tuple", [t]);
krauss@39756
   339
haftmann@32342
   340
haftmann@32342
   341
(* tuples with right-fold structure *)
haftmann@32342
   342
haftmann@32342
   343
fun mk_tupleT [] = unitT
haftmann@32342
   344
  | mk_tupleT Ts = foldr1 mk_prodT Ts;
haftmann@32342
   345
haftmann@32342
   346
fun strip_tupleT (Type ("Product_Type.unit", [])) = []
haftmann@37676
   347
  | strip_tupleT (Type ("Product_Type.prod", [T1, T2])) = T1 :: strip_tupleT T2
haftmann@32342
   348
  | strip_tupleT T = [T];
haftmann@32342
   349
haftmann@32342
   350
fun mk_tuple [] = unit
haftmann@32342
   351
  | mk_tuple ts = foldr1 mk_prod ts;
haftmann@32342
   352
haftmann@32342
   353
fun strip_tuple (Const ("Product_Type.Unity", _)) = []
haftmann@37389
   354
  | strip_tuple (Const ("Product_Type.Pair", _) $ t1 $ t2) = t1 :: strip_tuple t2
haftmann@32342
   355
  | strip_tuple t = [t];
haftmann@32342
   356
haftmann@32342
   357
haftmann@32287
   358
(* tuples with specific arities
berghofe@23745
   359
haftmann@32342
   360
   an "arity" of a tuple is a list of lists of integers,
haftmann@32342
   361
   denoting paths to subterms that are pairs
wenzelm@25172
   362
*)
berghofe@23745
   363
haftmann@32342
   364
fun ptuple_err s = raise TERM (s ^ ": inconsistent use of nested products", []);
berghofe@23745
   365
haftmann@32342
   366
fun mk_ptupleT ps =
berghofe@23745
   367
  let
berghofe@23745
   368
    fun mk p Ts =
haftmann@36692
   369
      if member (op =) ps p then
berghofe@23745
   370
        let
berghofe@23745
   371
          val (T, Ts') = mk (1::p) Ts;
berghofe@23745
   372
          val (U, Ts'') = mk (2::p) Ts'
berghofe@23745
   373
        in (mk_prodT (T, U), Ts'') end
berghofe@23745
   374
      else (hd Ts, tl Ts)
berghofe@23745
   375
  in fst o mk [] end;
berghofe@23745
   376
haftmann@32342
   377
fun strip_ptupleT ps =
haftmann@32287
   378
  let
haftmann@36692
   379
    fun factors p T = if member (op =) ps p then (case T of
haftmann@37676
   380
        Type ("Product_Type.prod", [T1, T2]) =>
haftmann@32287
   381
          factors (1::p) T1 @ factors (2::p) T2
haftmann@32342
   382
      | _ => ptuple_err "strip_ptupleT") else [T]
haftmann@32287
   383
  in factors [] end;
haftmann@32287
   384
haftmann@32287
   385
val flat_tupleT_paths =
haftmann@32287
   386
  let
haftmann@37676
   387
    fun factors p (Type ("Product_Type.prod", [T1, T2])) =
haftmann@32287
   388
          p :: factors (1::p) T1 @ factors (2::p) T2
haftmann@32287
   389
      | factors p _ = []
haftmann@32287
   390
  in factors [] end;
haftmann@32287
   391
haftmann@32342
   392
fun mk_ptuple ps =
haftmann@32287
   393
  let
haftmann@32287
   394
    fun mk p T ts =
haftmann@36692
   395
      if member (op =) ps p then (case T of
haftmann@37676
   396
          Type ("Product_Type.prod", [T1, T2]) =>
haftmann@32287
   397
            let
haftmann@32287
   398
              val (t, ts') = mk (1::p) T1 ts;
haftmann@32287
   399
              val (u, ts'') = mk (2::p) T2 ts'
haftmann@32287
   400
            in (pair_const T1 T2 $ t $ u, ts'') end
haftmann@32342
   401
        | _ => ptuple_err "mk_ptuple")
haftmann@32287
   402
      else (hd ts, tl ts)
haftmann@32287
   403
  in fst oo mk [] end;
haftmann@32287
   404
haftmann@32342
   405
fun strip_ptuple ps =
haftmann@32287
   406
  let
haftmann@36692
   407
    fun dest p t = if member (op =) ps p then (case t of
haftmann@37389
   408
        Const ("Product_Type.Pair", _) $ t $ u =>
haftmann@32287
   409
          dest (1::p) t @ dest (2::p) u
haftmann@32342
   410
      | _ => ptuple_err "strip_ptuple") else [t]
haftmann@32287
   411
  in dest [] end;
haftmann@32287
   412
haftmann@32287
   413
val flat_tuple_paths =
haftmann@32287
   414
  let
haftmann@37389
   415
    fun factors p (Const ("Product_Type.Pair", _) $ t $ u) =
haftmann@32287
   416
          p :: factors (1::p) t @ factors (2::p) u
haftmann@32287
   417
      | factors p _ = []
haftmann@32287
   418
  in factors [] end;
haftmann@32287
   419
haftmann@32342
   420
(*In mk_psplits ps S T u, term u expects separate arguments for the factors of S,
haftmann@32287
   421
  with result type T.  The call creates a new term expecting one argument
haftmann@32287
   422
  of type S.*)
haftmann@32342
   423
fun mk_psplits ps T T3 u =
haftmann@32287
   424
  let
haftmann@32287
   425
    fun ap ((p, T) :: pTs) =
haftmann@36692
   426
          if member (op =) ps p then (case T of
haftmann@37676
   427
              Type ("Product_Type.prod", [T1, T2]) =>
haftmann@32287
   428
                split_const (T1, T2, map snd pTs ---> T3) $
haftmann@32287
   429
                  ap ((1::p, T1) :: (2::p, T2) :: pTs)
haftmann@32342
   430
            | _ => ptuple_err "mk_psplits")
haftmann@32287
   431
          else Abs ("x", T, ap pTs)
haftmann@32287
   432
      | ap [] =
haftmann@32287
   433
          let val k = length ps
haftmann@32287
   434
          in list_comb (incr_boundvars (k + 1) u, map Bound (k downto 0)) end
haftmann@32287
   435
  in ap [([], T)] end;
haftmann@32287
   436
haftmann@32342
   437
val strip_psplits =
berghofe@23745
   438
  let
haftmann@34962
   439
    fun strip [] qs Ts t = (t, rev Ts, qs)
haftmann@37591
   440
      | strip (p :: ps) qs Ts (Const ("Product_Type.prod.prod_case", _) $ t) =
berghofe@23745
   441
          strip ((1 :: p) :: (2 :: p) :: ps) (p :: qs) Ts t
berghofe@23745
   442
      | strip (p :: ps) qs Ts (Abs (s, T, t)) = strip ps qs (T :: Ts) t
berghofe@23745
   443
      | strip (p :: ps) qs Ts t = strip ps qs
berghofe@23745
   444
          (hd (binder_types (fastype_of1 (Ts, t))) :: Ts)
berghofe@23745
   445
          (incr_boundvars 1 t $ Bound 0)
haftmann@32287
   446
  in strip [[]] [] [] end;
berghofe@23745
   447
wenzelm@5207
   448
wenzelm@5207
   449
(* nat *)
wenzelm@5207
   450
haftmann@37387
   451
val natT = Type ("Nat.nat", []);
wenzelm@5207
   452
haftmann@35267
   453
val zero = Const ("Groups.zero_class.zero", natT);
wenzelm@5207
   454
haftmann@35267
   455
fun is_zero (Const ("Groups.zero_class.zero", _)) = true
wenzelm@5207
   456
  | is_zero _ = false;
wenzelm@5207
   457
haftmann@37387
   458
fun mk_Suc t = Const ("Nat.Suc", natT --> natT) $ t;
wenzelm@5207
   459
haftmann@37387
   460
fun dest_Suc (Const ("Nat.Suc", _) $ t) = t
wenzelm@5207
   461
  | dest_Suc t = raise TERM ("dest_Suc", [t]);
wenzelm@5207
   462
haftmann@21621
   463
val Suc_zero = mk_Suc zero;
haftmann@21621
   464
wenzelm@24630
   465
fun mk_nat n =
haftmann@22994
   466
  let
haftmann@22994
   467
    fun mk 0 = zero
wenzelm@23297
   468
      | mk n = mk_Suc (mk (n - 1));
wenzelm@23576
   469
  in if n < 0 then raise TERM ("mk_nat: negative number", []) else mk n end;
wenzelm@5207
   470
haftmann@35267
   471
fun dest_nat (Const ("Groups.zero_class.zero", _)) = 0
haftmann@37387
   472
  | dest_nat (Const ("Nat.Suc", _) $ t) = dest_nat t + 1
wenzelm@5207
   473
  | dest_nat t = raise TERM ("dest_nat", [t]);
wenzelm@5207
   474
haftmann@22994
   475
val class_size = "Nat.size";
haftmann@22994
   476
haftmann@22994
   477
fun size_const T = Const ("Nat.size_class.size", T --> natT);
haftmann@22994
   478
wenzelm@5207
   479
haftmann@31205
   480
(* code numeral *)
haftmann@26036
   481
haftmann@31205
   482
val code_numeralT = Type ("Code_Numeral.code_numeral", []);
haftmann@26036
   483
haftmann@26036
   484
wenzelm@21778
   485
(* binary numerals and int -- non-unique representation due to leading zeros/ones! *)
wenzelm@21778
   486
haftmann@25919
   487
val intT = Type ("Int.int", []);
wenzelm@21778
   488
haftmann@25919
   489
val pls_const = Const ("Int.Pls", intT)
haftmann@25919
   490
and min_const = Const ("Int.Min", intT)
huffman@26086
   491
and bit0_const = Const ("Int.Bit0", intT --> intT)
huffman@26086
   492
and bit1_const = Const ("Int.Bit1", intT --> intT);
huffman@26086
   493
huffman@26086
   494
fun mk_bit 0 = bit0_const
huffman@26086
   495
  | mk_bit 1 = bit1_const
huffman@26086
   496
  | mk_bit _ = raise TERM ("mk_bit", []);
huffman@26086
   497
huffman@26086
   498
fun dest_bit (Const ("Int.Bit0", _)) = 0
huffman@26086
   499
  | dest_bit (Const ("Int.Bit1", _)) = 1
huffman@26086
   500
  | dest_bit t = raise TERM ("dest_bit", [t]);
paulson@8768
   501
wenzelm@21829
   502
fun mk_numeral 0 = pls_const
wenzelm@21829
   503
  | mk_numeral ~1 = min_const
wenzelm@21829
   504
  | mk_numeral i =
wenzelm@24630
   505
      let val (q, r) = Integer.div_mod i 2;
huffman@26086
   506
      in mk_bit r $ mk_numeral q end;
berghofe@13755
   507
haftmann@25919
   508
fun dest_numeral (Const ("Int.Pls", _)) = 0
haftmann@25919
   509
  | dest_numeral (Const ("Int.Min", _)) = ~1
huffman@26086
   510
  | dest_numeral (Const ("Int.Bit0", _) $ bs) = 2 * dest_numeral bs
huffman@26086
   511
  | dest_numeral (Const ("Int.Bit1", _) $ bs) = 2 * dest_numeral bs + 1
wenzelm@21829
   512
  | dest_numeral t = raise TERM ("dest_numeral", [t]);
berghofe@13755
   513
haftmann@25919
   514
fun number_of_const T = Const ("Int.number_class.number_of", intT --> T);
haftmann@21820
   515
haftmann@25919
   516
fun add_numerals (Const ("Int.number_class.number_of", Type (_, [_, T])) $ t) = cons (t, T)
wenzelm@23269
   517
  | add_numerals (t $ u) = add_numerals t #> add_numerals u
wenzelm@23269
   518
  | add_numerals (Abs (_, _, t)) = add_numerals t
wenzelm@23269
   519
  | add_numerals _ = I;
haftmann@22391
   520
haftmann@35267
   521
fun mk_number T 0 = Const ("Groups.zero_class.zero", T)
haftmann@35267
   522
  | mk_number T 1 = Const ("Groups.one_class.one", T)
haftmann@21820
   523
  | mk_number T i = number_of_const T $ mk_numeral i;
haftmann@21820
   524
haftmann@35267
   525
fun dest_number (Const ("Groups.zero_class.zero", T)) = (T, 0)
haftmann@35267
   526
  | dest_number (Const ("Groups.one_class.one", T)) = (T, 1)
haftmann@25919
   527
  | dest_number (Const ("Int.number_class.number_of", Type ("fun", [_, T])) $ t) =
haftmann@22994
   528
      (T, dest_numeral t)
haftmann@21820
   529
  | dest_number t = raise TERM ("dest_number", [t]);
berghofe@13755
   530
wenzelm@21829
   531
berghofe@13755
   532
(* real *)
berghofe@13755
   533
wenzelm@16971
   534
val realT = Type ("RealDef.real", []);
berghofe@13755
   535
berghofe@13755
   536
wenzelm@21755
   537
(* list *)
haftmann@21455
   538
wenzelm@21755
   539
fun listT T = Type ("List.list", [T]);
haftmann@21455
   540
berghofe@25887
   541
fun nil_const T = Const ("List.list.Nil", listT T);
berghofe@25887
   542
berghofe@25887
   543
fun cons_const T =
berghofe@25887
   544
  let val lT = listT T
berghofe@25887
   545
  in Const ("List.list.Cons", T --> lT --> lT) end;
berghofe@25887
   546
wenzelm@21755
   547
fun mk_list T ts =
haftmann@21455
   548
  let
wenzelm@21755
   549
    val lT = listT T;
wenzelm@21755
   550
    val Nil = Const ("List.list.Nil", lT);
wenzelm@21755
   551
    fun Cons t u = Const ("List.list.Cons", T --> lT --> lT) $ t $ u;
wenzelm@21755
   552
  in fold_rev Cons ts Nil end;
wenzelm@21755
   553
wenzelm@21755
   554
fun dest_list (Const ("List.list.Nil", _)) = []
wenzelm@21755
   555
  | dest_list (Const ("List.list.Cons", _) $ t $ u) = t :: dest_list u
wenzelm@21755
   556
  | dest_list t = raise TERM ("dest_list", [t]);
haftmann@21455
   557
haftmann@21455
   558
haftmann@31048
   559
(* nibble *)
haftmann@31048
   560
haftmann@31048
   561
val nibbleT = Type ("String.nibble", []);
haftmann@31048
   562
haftmann@31048
   563
fun mk_nibble n =
haftmann@31048
   564
  let val s =
haftmann@31048
   565
    if 0 <= n andalso n <= 9 then chr (n + ord "0")
haftmann@31048
   566
    else if 10 <= n andalso n <= 15 then chr (n + ord "A" - 10)
haftmann@31048
   567
    else raise TERM ("mk_nibble", [])
haftmann@31048
   568
  in Const ("String.nibble.Nibble" ^ s, nibbleT) end;
haftmann@31048
   569
haftmann@31048
   570
fun dest_nibble t =
haftmann@31048
   571
  let fun err () = raise TERM ("dest_nibble", [t]) in
haftmann@31048
   572
    (case try (unprefix "String.nibble.Nibble" o fst o Term.dest_Const) t of
haftmann@31048
   573
      NONE => err ()
haftmann@31048
   574
    | SOME c =>
haftmann@31048
   575
        if size c <> 1 then err ()
haftmann@31048
   576
        else if "0" <= c andalso c <= "9" then ord c - ord "0"
haftmann@31048
   577
        else if "A" <= c andalso c <= "F" then ord c - ord "A" + 10
haftmann@31048
   578
        else err ())
haftmann@31048
   579
  end;
haftmann@31048
   580
haftmann@31048
   581
haftmann@31048
   582
(* char *)
haftmann@31048
   583
haftmann@31048
   584
val charT = Type ("String.char", []);
haftmann@31048
   585
haftmann@31048
   586
fun mk_char n =
haftmann@31048
   587
  if 0 <= n andalso n <= 255 then
haftmann@31048
   588
    Const ("String.char.Char", nibbleT --> nibbleT --> charT) $
haftmann@31048
   589
      mk_nibble (n div 16) $ mk_nibble (n mod 16)
haftmann@31048
   590
  else raise TERM ("mk_char", []);
haftmann@31048
   591
haftmann@31048
   592
fun dest_char (Const ("String.char.Char", _) $ t $ u) =
haftmann@31048
   593
      dest_nibble t * 16 + dest_nibble u
haftmann@31048
   594
  | dest_char t = raise TERM ("dest_char", [t]);
haftmann@31048
   595
haftmann@31048
   596
haftmann@21455
   597
(* string *)
haftmann@21455
   598
krauss@32446
   599
val stringT = listT charT;
haftmann@21455
   600
wenzelm@21755
   601
val mk_string = mk_list charT o map (mk_char o ord) o explode;
wenzelm@21755
   602
val dest_string = implode o map (chr o dest_char) o dest_list;
haftmann@21455
   603
haftmann@31048
   604
haftmann@31205
   605
(* literal *)
haftmann@31048
   606
haftmann@31205
   607
val literalT = Type ("String.literal", []);
haftmann@31048
   608
bulwahn@39250
   609
fun mk_literal s = Const ("String.STR", stringT --> literalT)
haftmann@31048
   610
      $ mk_string s;
bulwahn@39250
   611
fun dest_literal (Const ("String.STR", _) $ t) =
haftmann@31048
   612
      dest_string t
haftmann@31205
   613
  | dest_literal t = raise TERM ("dest_literal", [t]);
haftmann@31048
   614
haftmann@31135
   615
haftmann@31135
   616
(* typerep and term *)
haftmann@31135
   617
haftmann@31135
   618
val typerepT = Type ("Typerep.typerep", []);
haftmann@31135
   619
haftmann@31736
   620
fun mk_typerep (Type (tyco, Ts)) = Const ("Typerep.typerep.Typerep",
haftmann@31736
   621
      literalT --> listT typerepT --> typerepT) $ mk_literal tyco
haftmann@31736
   622
        $ mk_list typerepT (map mk_typerep Ts)
haftmann@31736
   623
  | mk_typerep (T as TFree _) = Const ("Typerep.typerep_class.typerep",
haftmann@31736
   624
      Term.itselfT T --> typerepT) $ Logic.mk_type T;
haftmann@31135
   625
haftmann@32657
   626
val termT = Type ("Code_Evaluation.term", []);
haftmann@31135
   627
haftmann@32657
   628
fun term_of_const T = Const ("Code_Evaluation.term_of_class.term_of", T --> termT);
haftmann@32339
   629
haftmann@32339
   630
fun mk_term_of T t = term_of_const T $ t;
haftmann@31135
   631
haftmann@31135
   632
fun reflect_term (Const (c, T)) =
haftmann@32657
   633
      Const ("Code_Evaluation.Const", literalT --> typerepT --> termT)
haftmann@31205
   634
        $ mk_literal c $ mk_typerep T
haftmann@31135
   635
  | reflect_term (t1 $ t2) =
haftmann@32657
   636
      Const ("Code_Evaluation.App", termT --> termT --> termT)
haftmann@31135
   637
        $ reflect_term t1 $ reflect_term t2
haftmann@31183
   638
  | reflect_term (Abs (v, _, t)) = Abs (v, termT, reflect_term t)
haftmann@31183
   639
  | reflect_term t = t;
haftmann@31183
   640
haftmann@31463
   641
fun mk_valtermify_app c vs T =
haftmann@31463
   642
  let
haftmann@31463
   643
    fun termifyT T = mk_prodT (T, unitT --> termT);
haftmann@32657
   644
    fun valapp T T' = Const ("Code_Evaluation.valapp",
haftmann@31463
   645
      termifyT (T --> T') --> termifyT T --> termifyT T');
haftmann@31463
   646
    fun mk_fTs [] _ = []
haftmann@31463
   647
      | mk_fTs (_ :: Ts) T = (Ts ---> T) :: mk_fTs Ts T;
haftmann@31463
   648
    val Ts = map snd vs;
haftmann@31463
   649
    val t = Const (c, Ts ---> T);
haftmann@31463
   650
    val tt = mk_prod (t, Abs ("u", unitT, reflect_term t));
wenzelm@33245
   651
    fun app (fT, (v, T)) t = valapp T fT $ t $ Free (v, termifyT T);
wenzelm@33245
   652
  in fold app (mk_fTs Ts T ~~ vs) tt end;
haftmann@31463
   653
haftmann@31183
   654
haftmann@31183
   655
(* open state monads *)
haftmann@31183
   656
haftmann@31183
   657
fun mk_return T U x = pair_const T U $ x;
haftmann@31183
   658
haftmann@31183
   659
fun mk_ST clauses t U (someT, V) =
haftmann@31183
   660
  let
haftmann@31183
   661
    val R = case someT of SOME T => mk_prodT (T, V) | NONE => V
haftmann@31183
   662
    fun mk_clause ((t, U), SOME (v, T)) (t', U') =
haftmann@31183
   663
          (Const ("Product_Type.scomp", (U --> mk_prodT (T, U')) --> (T --> U' --> R) --> U --> R)
haftmann@31183
   664
            $ t $ lambda (Free (v, T)) t', U)
haftmann@31183
   665
      | mk_clause ((t, U), NONE) (t', U') =
haftmann@31183
   666
          (Const ("Product_Type.fcomp", (U --> U') --> (U' --> R) --> U --> R)
haftmann@31183
   667
            $ t $ t', U)
haftmann@31183
   668
  in fold_rev mk_clause clauses (t, U) |> fst end;
haftmann@31135
   669
haftmann@38550
   670
haftmann@38550
   671
(* random seeds *)
haftmann@38550
   672
haftmann@31463
   673
val random_seedT = mk_prodT (code_numeralT, code_numeralT);
haftmann@31463
   674
haftmann@31463
   675
fun mk_random T t = Const ("Quickcheck.random_class.random", code_numeralT
haftmann@31463
   676
  --> random_seedT --> mk_prodT (mk_prodT (T, unitT --> termT), random_seedT)) $ t;
haftmann@31463
   677
clasohm@923
   678
end;