src/HOL/Tools/hologic.ML
author haftmann
Sun Jun 21 08:38:57 2009 +0200 (2009-06-21)
changeset 31736 926ebca5a145
parent 31463 c5681ed50eab
child 32264 0be31453f698
permissions -rw-r--r--
more appropriate mk_typerep
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(*  Title:      HOL/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_eq: 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 prodT_factors: typ -> typ list
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  val mk_tuple: typ -> term list -> term
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  val dest_tuple: term -> term list
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  val ap_split: typ -> typ -> term -> term
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  val prod_factors: term -> int list list
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  val dest_tuple': int list list -> term -> term list
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  val prodT_factors': int list list -> typ -> typ list
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  val ap_split': int list list -> typ -> typ -> term -> term
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  val mk_tuple': int list list -> typ -> term list -> term
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  val mk_tupleT: int list list -> typ list -> typ
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  val strip_split: 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 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 = TypeInfer.anyT typeS;
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(* bool and set *)
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val boolN = "bool";
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val boolT = Type (boolN, []);
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val true_const =  Const ("True", boolT);
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val false_const = Const ("False", boolT);
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fun mk_setT T = T --> boolT;
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fun dest_setT (Type ("fun", [T, Type ("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 ("Set.empty", 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 ("Set.UNIV", mk_setT T);
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fun dest_set (Const ("Set.empty", _)) = []
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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 ("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 ("op :", dest_setT setT --> setT --> boolT) $ x $ A
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  end;
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fun dest_mem (Const ("op :", _) $ 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 ("Trueprop", boolT --> propT);
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fun mk_Trueprop P = Trueprop $ P;
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fun dest_Trueprop (Const ("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 (ObjectLogic.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 (ObjectLogic.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 "op &"}
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and disj = @{term "op |"}
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and imp = @{term "op -->"}
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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 ("op &", _) $ t $ t') = t :: dest_conj t'
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  | dest_conj t = [t];
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fun dest_disj (Const ("op |", _) $ 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 ("op |", _) $ 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("op -->",_) $ A $ B) = (A, B)
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  | dest_imp  t = raise TERM ("dest_imp", [t]);
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fun dest_not (Const ("Not", _) $ t) = t
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  | dest_not t = raise TERM ("dest_not", [t]);
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fun eq_const T = Const ("op =", [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 ("op =", _) $ 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 ("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 ("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_eq = "HOL.eq";
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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 ("*", [T1, T2]);
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fun dest_prodT (Type ("*", [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 ("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 ("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 ("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 ("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 ("split", (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 ("split", T --> mk_prodT (A, B) --> C) $ t
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  | _ => raise TERM ("mk_split: bad body type", [t]));
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(*Maps the type T1 * ... * Tn to [T1, ..., Tn], however nested*)
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fun prodT_factors (Type ("*", [T1, T2])) = prodT_factors T1 @ prodT_factors T2
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  | prodT_factors T = [T];
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(*Makes a nested tuple from a list, following the product type structure*)
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fun mk_tuple (Type ("*", [T1, T2])) tms =
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        mk_prod (mk_tuple T1 tms,
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   329
                 mk_tuple T2 (Library.drop (length (prodT_factors T1), tms)))
berghofe@5096
   330
  | mk_tuple T (t::_) = t;
wenzelm@4571
   331
berghofe@23745
   332
fun dest_tuple (Const ("Pair", _) $ t $ u) = dest_tuple t @ dest_tuple u
berghofe@23745
   333
  | dest_tuple t = [t];
berghofe@23745
   334
berghofe@23745
   335
(*In ap_split S T u, term u expects separate arguments for the factors of S,
berghofe@23745
   336
  with result type T.  The call creates a new term expecting one argument
berghofe@23745
   337
  of type S.*)
berghofe@23745
   338
fun ap_split T T3 u =
berghofe@23745
   339
  let
berghofe@23745
   340
    fun ap (T :: Ts) =
berghofe@23745
   341
          (case T of
berghofe@23745
   342
             Type ("*", [T1, T2]) =>
berghofe@23745
   343
               split_const (T1, T2, Ts ---> T3) $ ap (T1 :: T2 :: Ts)
berghofe@23745
   344
           | _ => Abs ("x", T, ap Ts))
berghofe@23745
   345
      | ap [] =
berghofe@23745
   346
          let val k = length (prodT_factors T)
berghofe@23745
   347
          in list_comb (incr_boundvars k u, map Bound (k - 1 downto 0)) end
berghofe@23745
   348
  in ap [T] end;
berghofe@23745
   349
berghofe@23745
   350
wenzelm@25172
   351
(* operations on tuples with specific arities *)
wenzelm@25172
   352
(*
wenzelm@25172
   353
  an "arity" of a tuple is a list of lists of integers
wenzelm@25172
   354
  ("factors"), denoting paths to subterms that are pairs
wenzelm@25172
   355
*)
berghofe@23745
   356
berghofe@23745
   357
fun prod_err s = raise TERM (s ^ ": inconsistent use of products", []);
berghofe@23745
   358
berghofe@23745
   359
fun prod_factors t =
berghofe@23745
   360
  let
berghofe@23745
   361
    fun factors p (Const ("Pair", _) $ t $ u) =
berghofe@23745
   362
          p :: factors (1::p) t @ factors (2::p) u
berghofe@23745
   363
      | factors p _ = []
berghofe@23745
   364
  in factors [] t end;
berghofe@23745
   365
berghofe@23745
   366
fun dest_tuple' ps =
berghofe@23745
   367
  let
berghofe@23745
   368
    fun dest p t = if p mem ps then (case t of
berghofe@23745
   369
        Const ("Pair", _) $ t $ u =>
berghofe@23745
   370
          dest (1::p) t @ dest (2::p) u
berghofe@23745
   371
      | _ => prod_err "dest_tuple'") else [t]
berghofe@23745
   372
  in dest [] end;
berghofe@23745
   373
berghofe@23745
   374
fun prodT_factors' ps =
berghofe@23745
   375
  let
berghofe@23745
   376
    fun factors p T = if p mem ps then (case T of
berghofe@23745
   377
        Type ("*", [T1, T2]) =>
berghofe@23745
   378
          factors (1::p) T1 @ factors (2::p) T2
berghofe@23745
   379
      | _ => prod_err "prodT_factors'") else [T]
berghofe@23745
   380
  in factors [] end;
berghofe@23745
   381
berghofe@23745
   382
(*In ap_split' ps S T u, term u expects separate arguments for the factors of S,
berghofe@23745
   383
  with result type T.  The call creates a new term expecting one argument
berghofe@23745
   384
  of type S.*)
berghofe@23745
   385
fun ap_split' ps T T3 u =
berghofe@23745
   386
  let
berghofe@23745
   387
    fun ap ((p, T) :: pTs) =
berghofe@23745
   388
          if p mem ps then (case T of
berghofe@23745
   389
              Type ("*", [T1, T2]) =>
berghofe@23745
   390
                split_const (T1, T2, map snd pTs ---> T3) $
berghofe@23745
   391
                  ap ((1::p, T1) :: (2::p, T2) :: pTs)
berghofe@23745
   392
            | _ => prod_err "ap_split'")
berghofe@23745
   393
          else Abs ("x", T, ap pTs)
berghofe@23745
   394
      | ap [] =
berghofe@23745
   395
          let val k = length ps
berghofe@23745
   396
          in list_comb (incr_boundvars (k + 1) u, map Bound (k downto 0)) end
berghofe@23745
   397
  in ap [([], T)] end;
berghofe@23745
   398
berghofe@23745
   399
fun mk_tuple' ps =
berghofe@23745
   400
  let
berghofe@23745
   401
    fun mk p T ts =
berghofe@23745
   402
      if p mem ps then (case T of
berghofe@23745
   403
          Type ("*", [T1, T2]) =>
berghofe@23745
   404
            let
berghofe@23745
   405
              val (t, ts') = mk (1::p) T1 ts;
berghofe@23745
   406
              val (u, ts'') = mk (2::p) T2 ts'
berghofe@23745
   407
            in (pair_const T1 T2 $ t $ u, ts'') end
berghofe@23745
   408
        | _ => prod_err "mk_tuple'")
berghofe@23745
   409
      else (hd ts, tl ts)
berghofe@23745
   410
  in fst oo mk [] end;
berghofe@23745
   411
berghofe@23745
   412
fun mk_tupleT ps =
berghofe@23745
   413
  let
berghofe@23745
   414
    fun mk p Ts =
berghofe@23745
   415
      if p mem ps then
berghofe@23745
   416
        let
berghofe@23745
   417
          val (T, Ts') = mk (1::p) Ts;
berghofe@23745
   418
          val (U, Ts'') = mk (2::p) Ts'
berghofe@23745
   419
        in (mk_prodT (T, U), Ts'') end
berghofe@23745
   420
      else (hd Ts, tl Ts)
berghofe@23745
   421
  in fst o mk [] end;
berghofe@23745
   422
berghofe@23745
   423
fun strip_split t =
berghofe@23745
   424
  let
berghofe@23745
   425
    fun strip [] qs Ts t = (t, Ts, qs)
berghofe@23745
   426
      | strip (p :: ps) qs Ts (Const ("split", _) $ t) =
berghofe@23745
   427
          strip ((1 :: p) :: (2 :: p) :: ps) (p :: qs) Ts t
berghofe@23745
   428
      | strip (p :: ps) qs Ts (Abs (s, T, t)) = strip ps qs (T :: Ts) t
berghofe@23745
   429
      | strip (p :: ps) qs Ts t = strip ps qs
berghofe@23745
   430
          (hd (binder_types (fastype_of1 (Ts, t))) :: Ts)
berghofe@23745
   431
          (incr_boundvars 1 t $ Bound 0)
berghofe@23745
   432
  in strip [[]] [] [] t end;
berghofe@23745
   433
wenzelm@5207
   434
wenzelm@5207
   435
(* nat *)
wenzelm@5207
   436
wenzelm@5207
   437
val natT = Type ("nat", []);
wenzelm@5207
   438
haftmann@22994
   439
val zero = Const ("HOL.zero_class.zero", natT);
wenzelm@5207
   440
haftmann@22994
   441
fun is_zero (Const ("HOL.zero_class.zero", _)) = true
wenzelm@5207
   442
  | is_zero _ = false;
wenzelm@5207
   443
wenzelm@5207
   444
fun mk_Suc t = Const ("Suc", natT --> natT) $ t;
wenzelm@5207
   445
wenzelm@5207
   446
fun dest_Suc (Const ("Suc", _) $ t) = t
wenzelm@5207
   447
  | dest_Suc t = raise TERM ("dest_Suc", [t]);
wenzelm@5207
   448
haftmann@21621
   449
val Suc_zero = mk_Suc zero;
haftmann@21621
   450
wenzelm@24630
   451
fun mk_nat n =
haftmann@22994
   452
  let
haftmann@22994
   453
    fun mk 0 = zero
wenzelm@23297
   454
      | mk n = mk_Suc (mk (n - 1));
wenzelm@23576
   455
  in if n < 0 then raise TERM ("mk_nat: negative number", []) else mk n end;
wenzelm@5207
   456
wenzelm@24630
   457
fun dest_nat (Const ("HOL.zero_class.zero", _)) = 0
wenzelm@23297
   458
  | dest_nat (Const ("Suc", _) $ t) = dest_nat t + 1
wenzelm@5207
   459
  | dest_nat t = raise TERM ("dest_nat", [t]);
wenzelm@5207
   460
haftmann@22994
   461
val class_size = "Nat.size";
haftmann@22994
   462
haftmann@22994
   463
fun size_const T = Const ("Nat.size_class.size", T --> natT);
haftmann@22994
   464
wenzelm@5207
   465
haftmann@31205
   466
(* code numeral *)
haftmann@26036
   467
haftmann@31205
   468
val code_numeralT = Type ("Code_Numeral.code_numeral", []);
haftmann@26036
   469
haftmann@26036
   470
wenzelm@21778
   471
(* binary numerals and int -- non-unique representation due to leading zeros/ones! *)
wenzelm@21778
   472
haftmann@25919
   473
val intT = Type ("Int.int", []);
wenzelm@21778
   474
haftmann@25919
   475
val pls_const = Const ("Int.Pls", intT)
haftmann@25919
   476
and min_const = Const ("Int.Min", intT)
huffman@26086
   477
and bit0_const = Const ("Int.Bit0", intT --> intT)
huffman@26086
   478
and bit1_const = Const ("Int.Bit1", intT --> intT);
huffman@26086
   479
huffman@26086
   480
fun mk_bit 0 = bit0_const
huffman@26086
   481
  | mk_bit 1 = bit1_const
huffman@26086
   482
  | mk_bit _ = raise TERM ("mk_bit", []);
huffman@26086
   483
huffman@26086
   484
fun dest_bit (Const ("Int.Bit0", _)) = 0
huffman@26086
   485
  | dest_bit (Const ("Int.Bit1", _)) = 1
huffman@26086
   486
  | dest_bit t = raise TERM ("dest_bit", [t]);
paulson@8768
   487
wenzelm@21829
   488
fun mk_numeral 0 = pls_const
wenzelm@21829
   489
  | mk_numeral ~1 = min_const
wenzelm@21829
   490
  | mk_numeral i =
wenzelm@24630
   491
      let val (q, r) = Integer.div_mod i 2;
huffman@26086
   492
      in mk_bit r $ mk_numeral q end;
berghofe@13755
   493
haftmann@25919
   494
fun dest_numeral (Const ("Int.Pls", _)) = 0
haftmann@25919
   495
  | dest_numeral (Const ("Int.Min", _)) = ~1
huffman@26086
   496
  | dest_numeral (Const ("Int.Bit0", _) $ bs) = 2 * dest_numeral bs
huffman@26086
   497
  | dest_numeral (Const ("Int.Bit1", _) $ bs) = 2 * dest_numeral bs + 1
wenzelm@21829
   498
  | dest_numeral t = raise TERM ("dest_numeral", [t]);
berghofe@13755
   499
haftmann@25919
   500
fun number_of_const T = Const ("Int.number_class.number_of", intT --> T);
haftmann@21820
   501
haftmann@25919
   502
fun add_numerals (Const ("Int.number_class.number_of", Type (_, [_, T])) $ t) = cons (t, T)
wenzelm@23269
   503
  | add_numerals (t $ u) = add_numerals t #> add_numerals u
wenzelm@23269
   504
  | add_numerals (Abs (_, _, t)) = add_numerals t
wenzelm@23269
   505
  | add_numerals _ = I;
haftmann@22391
   506
haftmann@22994
   507
fun mk_number T 0 = Const ("HOL.zero_class.zero", T)
haftmann@22994
   508
  | mk_number T 1 = Const ("HOL.one_class.one", T)
haftmann@21820
   509
  | mk_number T i = number_of_const T $ mk_numeral i;
haftmann@21820
   510
haftmann@22994
   511
fun dest_number (Const ("HOL.zero_class.zero", T)) = (T, 0)
haftmann@22994
   512
  | dest_number (Const ("HOL.one_class.one", T)) = (T, 1)
haftmann@25919
   513
  | dest_number (Const ("Int.number_class.number_of", Type ("fun", [_, T])) $ t) =
haftmann@22994
   514
      (T, dest_numeral t)
haftmann@21820
   515
  | dest_number t = raise TERM ("dest_number", [t]);
berghofe@13755
   516
wenzelm@21829
   517
berghofe@13755
   518
(* real *)
berghofe@13755
   519
wenzelm@16971
   520
val realT = Type ("RealDef.real", []);
berghofe@13755
   521
berghofe@13755
   522
wenzelm@21755
   523
(* list *)
haftmann@21455
   524
wenzelm@21755
   525
fun listT T = Type ("List.list", [T]);
haftmann@21455
   526
berghofe@25887
   527
fun nil_const T = Const ("List.list.Nil", listT T);
berghofe@25887
   528
berghofe@25887
   529
fun cons_const T =
berghofe@25887
   530
  let val lT = listT T
berghofe@25887
   531
  in Const ("List.list.Cons", T --> lT --> lT) end;
berghofe@25887
   532
wenzelm@21755
   533
fun mk_list T ts =
haftmann@21455
   534
  let
wenzelm@21755
   535
    val lT = listT T;
wenzelm@21755
   536
    val Nil = Const ("List.list.Nil", lT);
wenzelm@21755
   537
    fun Cons t u = Const ("List.list.Cons", T --> lT --> lT) $ t $ u;
wenzelm@21755
   538
  in fold_rev Cons ts Nil end;
wenzelm@21755
   539
wenzelm@21755
   540
fun dest_list (Const ("List.list.Nil", _)) = []
wenzelm@21755
   541
  | dest_list (Const ("List.list.Cons", _) $ t $ u) = t :: dest_list u
wenzelm@21755
   542
  | dest_list t = raise TERM ("dest_list", [t]);
haftmann@21455
   543
haftmann@21455
   544
haftmann@31048
   545
(* nibble *)
haftmann@31048
   546
haftmann@31048
   547
val nibbleT = Type ("String.nibble", []);
haftmann@31048
   548
haftmann@31048
   549
fun mk_nibble n =
haftmann@31048
   550
  let val s =
haftmann@31048
   551
    if 0 <= n andalso n <= 9 then chr (n + ord "0")
haftmann@31048
   552
    else if 10 <= n andalso n <= 15 then chr (n + ord "A" - 10)
haftmann@31048
   553
    else raise TERM ("mk_nibble", [])
haftmann@31048
   554
  in Const ("String.nibble.Nibble" ^ s, nibbleT) end;
haftmann@31048
   555
haftmann@31048
   556
fun dest_nibble t =
haftmann@31048
   557
  let fun err () = raise TERM ("dest_nibble", [t]) in
haftmann@31048
   558
    (case try (unprefix "String.nibble.Nibble" o fst o Term.dest_Const) t of
haftmann@31048
   559
      NONE => err ()
haftmann@31048
   560
    | SOME c =>
haftmann@31048
   561
        if size c <> 1 then err ()
haftmann@31048
   562
        else if "0" <= c andalso c <= "9" then ord c - ord "0"
haftmann@31048
   563
        else if "A" <= c andalso c <= "F" then ord c - ord "A" + 10
haftmann@31048
   564
        else err ())
haftmann@31048
   565
  end;
haftmann@31048
   566
haftmann@31048
   567
haftmann@31048
   568
(* char *)
haftmann@31048
   569
haftmann@31048
   570
val charT = Type ("String.char", []);
haftmann@31048
   571
haftmann@31048
   572
fun mk_char n =
haftmann@31048
   573
  if 0 <= n andalso n <= 255 then
haftmann@31048
   574
    Const ("String.char.Char", nibbleT --> nibbleT --> charT) $
haftmann@31048
   575
      mk_nibble (n div 16) $ mk_nibble (n mod 16)
haftmann@31048
   576
  else raise TERM ("mk_char", []);
haftmann@31048
   577
haftmann@31048
   578
fun dest_char (Const ("String.char.Char", _) $ t $ u) =
haftmann@31048
   579
      dest_nibble t * 16 + dest_nibble u
haftmann@31048
   580
  | dest_char t = raise TERM ("dest_char", [t]);
haftmann@31048
   581
haftmann@31048
   582
haftmann@21455
   583
(* string *)
haftmann@21455
   584
haftmann@31048
   585
val stringT = Type ("String.string", []);
haftmann@21455
   586
wenzelm@21755
   587
val mk_string = mk_list charT o map (mk_char o ord) o explode;
wenzelm@21755
   588
val dest_string = implode o map (chr o dest_char) o dest_list;
haftmann@21455
   589
haftmann@31048
   590
haftmann@31205
   591
(* literal *)
haftmann@31048
   592
haftmann@31205
   593
val literalT = Type ("String.literal", []);
haftmann@31048
   594
haftmann@31205
   595
fun mk_literal s = Const ("String.literal.STR", stringT --> literalT)
haftmann@31048
   596
      $ mk_string s;
haftmann@31205
   597
fun dest_literal (Const ("String.literal.STR", _) $ t) =
haftmann@31048
   598
      dest_string t
haftmann@31205
   599
  | dest_literal t = raise TERM ("dest_literal", [t]);
haftmann@31048
   600
haftmann@31135
   601
haftmann@31135
   602
(* typerep and term *)
haftmann@31135
   603
haftmann@31135
   604
val typerepT = Type ("Typerep.typerep", []);
haftmann@31135
   605
haftmann@31736
   606
fun mk_typerep (Type (tyco, Ts)) = Const ("Typerep.typerep.Typerep",
haftmann@31736
   607
      literalT --> listT typerepT --> typerepT) $ mk_literal tyco
haftmann@31736
   608
        $ mk_list typerepT (map mk_typerep Ts)
haftmann@31736
   609
  | mk_typerep (T as TFree _) = Const ("Typerep.typerep_class.typerep",
haftmann@31736
   610
      Term.itselfT T --> typerepT) $ Logic.mk_type T;
haftmann@31135
   611
haftmann@31135
   612
val termT = Type ("Code_Eval.term", []);
haftmann@31135
   613
haftmann@31135
   614
fun mk_term_of T t = Const ("Code_Eval.term_of_class.term_of", T --> termT) $ t;
haftmann@31135
   615
haftmann@31135
   616
fun reflect_term (Const (c, T)) =
haftmann@31205
   617
      Const ("Code_Eval.Const", literalT --> typerepT --> termT)
haftmann@31205
   618
        $ mk_literal c $ mk_typerep T
haftmann@31135
   619
  | reflect_term (t1 $ t2) =
haftmann@31135
   620
      Const ("Code_Eval.App", termT --> termT --> termT)
haftmann@31135
   621
        $ reflect_term t1 $ reflect_term t2
haftmann@31183
   622
  | reflect_term (Abs (v, _, t)) = Abs (v, termT, reflect_term t)
haftmann@31183
   623
  | reflect_term t = t;
haftmann@31183
   624
haftmann@31463
   625
fun mk_valtermify_app c vs T =
haftmann@31463
   626
  let
haftmann@31463
   627
    fun termifyT T = mk_prodT (T, unitT --> termT);
haftmann@31463
   628
    fun valapp T T' = Const ("Code_Eval.valapp",
haftmann@31463
   629
      termifyT (T --> T') --> termifyT T --> termifyT T');
haftmann@31463
   630
    fun mk_fTs [] _ = []
haftmann@31463
   631
      | mk_fTs (_ :: Ts) T = (Ts ---> T) :: mk_fTs Ts T;
haftmann@31463
   632
    val Ts = map snd vs;
haftmann@31463
   633
    val t = Const (c, Ts ---> T);
haftmann@31463
   634
    val tt = mk_prod (t, Abs ("u", unitT, reflect_term t));
haftmann@31463
   635
    fun app (t, (fT, (v, T))) = valapp T fT $ t $ Free (v, termifyT T);
haftmann@31463
   636
  in Library.foldl app (tt, mk_fTs Ts T ~~ vs) end;
haftmann@31463
   637
haftmann@31183
   638
haftmann@31183
   639
(* open state monads *)
haftmann@31183
   640
haftmann@31183
   641
fun mk_return T U x = pair_const T U $ x;
haftmann@31183
   642
haftmann@31183
   643
fun mk_ST clauses t U (someT, V) =
haftmann@31183
   644
  let
haftmann@31183
   645
    val R = case someT of SOME T => mk_prodT (T, V) | NONE => V
haftmann@31183
   646
    fun mk_clause ((t, U), SOME (v, T)) (t', U') =
haftmann@31183
   647
          (Const ("Product_Type.scomp", (U --> mk_prodT (T, U')) --> (T --> U' --> R) --> U --> R)
haftmann@31183
   648
            $ t $ lambda (Free (v, T)) t', U)
haftmann@31183
   649
      | mk_clause ((t, U), NONE) (t', U') =
haftmann@31183
   650
          (Const ("Product_Type.fcomp", (U --> U') --> (U' --> R) --> U --> R)
haftmann@31183
   651
            $ t $ t', U)
haftmann@31183
   652
  in fold_rev mk_clause clauses (t, U) |> fst end;
haftmann@31135
   653
haftmann@31463
   654
val code_numeralT = Type ("Code_Numeral.code_numeral", []);
haftmann@31463
   655
val random_seedT = mk_prodT (code_numeralT, code_numeralT);
haftmann@31463
   656
haftmann@31463
   657
fun mk_random T t = Const ("Quickcheck.random_class.random", code_numeralT
haftmann@31463
   658
  --> random_seedT --> mk_prodT (mk_prodT (T, unitT --> termT), random_seedT)) $ t;
haftmann@31463
   659
clasohm@923
   660
end;