src/HOL/hologic.ML
author wenzelm
Fri Mar 28 19:43:54 2008 +0100 (2008-03-28)
changeset 26462 dac4e2bce00d
parent 26086 3c243098b64a
child 26804 e2b1e6868c2f
permissions -rw-r--r--
avoid rebinding of existing facts;
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(*  Title:      HOL/hologic.ML
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    ID:         $Id$
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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 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 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 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 dest_concls: term -> term list
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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 Collect_const: typ -> term
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  val mk_Collect: string * typ * term -> term
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  val class_eq: string
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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_UNIV: typ -> term
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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 indexT: 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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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 = Type ("set", [T]);
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fun dest_setT (Type ("set", [T])) = T
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  | dest_setT T = raise TYPE ("dest_setT: set type expected", [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 imp_concl_of t = imp_concl_of (#2 (dest_imp t)) handle TERM _ => t;
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val dest_concls = map imp_concl_of o dest_conj o dest_Trueprop;
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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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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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val class_eq = "HOL.eq";
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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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fun mk_UNIV T = Const ("UNIV", mk_setT T);
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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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                 mk_tuple T2 (Library.drop (length (prodT_factors T1), tms)))
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  | mk_tuple T (t::_) = t;
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fun dest_tuple (Const ("Pair", _) $ t $ u) = dest_tuple t @ dest_tuple u
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  | dest_tuple t = [t];
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(*In ap_split S T u, term u expects separate arguments for the factors of S,
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  with result type T.  The call creates a new term expecting one argument
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  of type S.*)
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fun ap_split T T3 u =
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  let
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    fun ap (T :: Ts) =
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          (case T of
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             Type ("*", [T1, T2]) =>
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               split_const (T1, T2, Ts ---> T3) $ ap (T1 :: T2 :: Ts)
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           | _ => Abs ("x", T, ap Ts))
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      | ap [] =
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          let val k = length (prodT_factors T)
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          in list_comb (incr_boundvars k u, map Bound (k - 1 downto 0)) end
berghofe@23745
   330
  in ap [T] end;
berghofe@23745
   331
berghofe@23745
   332
wenzelm@25172
   333
(* operations on tuples with specific arities *)
wenzelm@25172
   334
(*
wenzelm@25172
   335
  an "arity" of a tuple is a list of lists of integers
wenzelm@25172
   336
  ("factors"), denoting paths to subterms that are pairs
wenzelm@25172
   337
*)
berghofe@23745
   338
berghofe@23745
   339
fun prod_err s = raise TERM (s ^ ": inconsistent use of products", []);
berghofe@23745
   340
berghofe@23745
   341
fun prod_factors t =
berghofe@23745
   342
  let
berghofe@23745
   343
    fun factors p (Const ("Pair", _) $ t $ u) =
berghofe@23745
   344
          p :: factors (1::p) t @ factors (2::p) u
berghofe@23745
   345
      | factors p _ = []
berghofe@23745
   346
  in factors [] t end;
berghofe@23745
   347
berghofe@23745
   348
fun dest_tuple' ps =
berghofe@23745
   349
  let
berghofe@23745
   350
    fun dest p t = if p mem ps then (case t of
berghofe@23745
   351
        Const ("Pair", _) $ t $ u =>
berghofe@23745
   352
          dest (1::p) t @ dest (2::p) u
berghofe@23745
   353
      | _ => prod_err "dest_tuple'") else [t]
berghofe@23745
   354
  in dest [] end;
berghofe@23745
   355
berghofe@23745
   356
fun prodT_factors' ps =
berghofe@23745
   357
  let
berghofe@23745
   358
    fun factors p T = if p mem ps then (case T of
berghofe@23745
   359
        Type ("*", [T1, T2]) =>
berghofe@23745
   360
          factors (1::p) T1 @ factors (2::p) T2
berghofe@23745
   361
      | _ => prod_err "prodT_factors'") else [T]
berghofe@23745
   362
  in factors [] end;
berghofe@23745
   363
berghofe@23745
   364
(*In ap_split' ps S T u, term u expects separate arguments for the factors of S,
berghofe@23745
   365
  with result type T.  The call creates a new term expecting one argument
berghofe@23745
   366
  of type S.*)
berghofe@23745
   367
fun ap_split' ps T T3 u =
berghofe@23745
   368
  let
berghofe@23745
   369
    fun ap ((p, T) :: pTs) =
berghofe@23745
   370
          if p mem ps then (case T of
berghofe@23745
   371
              Type ("*", [T1, T2]) =>
berghofe@23745
   372
                split_const (T1, T2, map snd pTs ---> T3) $
berghofe@23745
   373
                  ap ((1::p, T1) :: (2::p, T2) :: pTs)
berghofe@23745
   374
            | _ => prod_err "ap_split'")
berghofe@23745
   375
          else Abs ("x", T, ap pTs)
berghofe@23745
   376
      | ap [] =
berghofe@23745
   377
          let val k = length ps
berghofe@23745
   378
          in list_comb (incr_boundvars (k + 1) u, map Bound (k downto 0)) end
berghofe@23745
   379
  in ap [([], T)] end;
berghofe@23745
   380
berghofe@23745
   381
fun mk_tuple' ps =
berghofe@23745
   382
  let
berghofe@23745
   383
    fun mk p T ts =
berghofe@23745
   384
      if p mem ps then (case T of
berghofe@23745
   385
          Type ("*", [T1, T2]) =>
berghofe@23745
   386
            let
berghofe@23745
   387
              val (t, ts') = mk (1::p) T1 ts;
berghofe@23745
   388
              val (u, ts'') = mk (2::p) T2 ts'
berghofe@23745
   389
            in (pair_const T1 T2 $ t $ u, ts'') end
berghofe@23745
   390
        | _ => prod_err "mk_tuple'")
berghofe@23745
   391
      else (hd ts, tl ts)
berghofe@23745
   392
  in fst oo mk [] end;
berghofe@23745
   393
berghofe@23745
   394
fun mk_tupleT ps =
berghofe@23745
   395
  let
berghofe@23745
   396
    fun mk p Ts =
berghofe@23745
   397
      if p mem ps then
berghofe@23745
   398
        let
berghofe@23745
   399
          val (T, Ts') = mk (1::p) Ts;
berghofe@23745
   400
          val (U, Ts'') = mk (2::p) Ts'
berghofe@23745
   401
        in (mk_prodT (T, U), Ts'') end
berghofe@23745
   402
      else (hd Ts, tl Ts)
berghofe@23745
   403
  in fst o mk [] end;
berghofe@23745
   404
berghofe@23745
   405
fun strip_split t =
berghofe@23745
   406
  let
berghofe@23745
   407
    fun strip [] qs Ts t = (t, Ts, qs)
berghofe@23745
   408
      | strip (p :: ps) qs Ts (Const ("split", _) $ t) =
berghofe@23745
   409
          strip ((1 :: p) :: (2 :: p) :: ps) (p :: qs) Ts t
berghofe@23745
   410
      | strip (p :: ps) qs Ts (Abs (s, T, t)) = strip ps qs (T :: Ts) t
berghofe@23745
   411
      | strip (p :: ps) qs Ts t = strip ps qs
berghofe@23745
   412
          (hd (binder_types (fastype_of1 (Ts, t))) :: Ts)
berghofe@23745
   413
          (incr_boundvars 1 t $ Bound 0)
berghofe@23745
   414
  in strip [[]] [] [] t end;
berghofe@23745
   415
wenzelm@5207
   416
wenzelm@5207
   417
(* nat *)
wenzelm@5207
   418
wenzelm@5207
   419
val natT = Type ("nat", []);
wenzelm@5207
   420
haftmann@22994
   421
val zero = Const ("HOL.zero_class.zero", natT);
wenzelm@5207
   422
haftmann@22994
   423
fun is_zero (Const ("HOL.zero_class.zero", _)) = true
wenzelm@5207
   424
  | is_zero _ = false;
wenzelm@5207
   425
wenzelm@5207
   426
fun mk_Suc t = Const ("Suc", natT --> natT) $ t;
wenzelm@5207
   427
wenzelm@5207
   428
fun dest_Suc (Const ("Suc", _) $ t) = t
wenzelm@5207
   429
  | dest_Suc t = raise TERM ("dest_Suc", [t]);
wenzelm@5207
   430
haftmann@21621
   431
val Suc_zero = mk_Suc zero;
haftmann@21621
   432
wenzelm@24630
   433
fun mk_nat n =
haftmann@22994
   434
  let
haftmann@22994
   435
    fun mk 0 = zero
wenzelm@23297
   436
      | mk n = mk_Suc (mk (n - 1));
wenzelm@23576
   437
  in if n < 0 then raise TERM ("mk_nat: negative number", []) else mk n end;
wenzelm@5207
   438
wenzelm@24630
   439
fun dest_nat (Const ("HOL.zero_class.zero", _)) = 0
wenzelm@23297
   440
  | dest_nat (Const ("Suc", _) $ t) = dest_nat t + 1
wenzelm@5207
   441
  | dest_nat t = raise TERM ("dest_nat", [t]);
wenzelm@5207
   442
haftmann@22994
   443
val class_size = "Nat.size";
haftmann@22994
   444
haftmann@22994
   445
fun size_const T = Const ("Nat.size_class.size", T --> natT);
haftmann@22994
   446
wenzelm@5207
   447
haftmann@26036
   448
(* index *)
haftmann@26036
   449
haftmann@26036
   450
val indexT = Type ("Code_Index.index", []);
haftmann@26036
   451
haftmann@26036
   452
wenzelm@21778
   453
(* binary numerals and int -- non-unique representation due to leading zeros/ones! *)
wenzelm@21778
   454
haftmann@25919
   455
val intT = Type ("Int.int", []);
wenzelm@21778
   456
haftmann@25919
   457
val pls_const = Const ("Int.Pls", intT)
haftmann@25919
   458
and min_const = Const ("Int.Min", intT)
huffman@26086
   459
and bit0_const = Const ("Int.Bit0", intT --> intT)
huffman@26086
   460
and bit1_const = Const ("Int.Bit1", intT --> intT);
huffman@26086
   461
huffman@26086
   462
fun mk_bit 0 = bit0_const
huffman@26086
   463
  | mk_bit 1 = bit1_const
huffman@26086
   464
  | mk_bit _ = raise TERM ("mk_bit", []);
huffman@26086
   465
huffman@26086
   466
fun dest_bit (Const ("Int.Bit0", _)) = 0
huffman@26086
   467
  | dest_bit (Const ("Int.Bit1", _)) = 1
huffman@26086
   468
  | dest_bit t = raise TERM ("dest_bit", [t]);
paulson@8768
   469
wenzelm@21829
   470
fun mk_numeral 0 = pls_const
wenzelm@21829
   471
  | mk_numeral ~1 = min_const
wenzelm@21829
   472
  | mk_numeral i =
wenzelm@24630
   473
      let val (q, r) = Integer.div_mod i 2;
huffman@26086
   474
      in mk_bit r $ mk_numeral q end;
berghofe@13755
   475
haftmann@25919
   476
fun dest_numeral (Const ("Int.Pls", _)) = 0
haftmann@25919
   477
  | dest_numeral (Const ("Int.Min", _)) = ~1
huffman@26086
   478
  | dest_numeral (Const ("Int.Bit0", _) $ bs) = 2 * dest_numeral bs
huffman@26086
   479
  | dest_numeral (Const ("Int.Bit1", _) $ bs) = 2 * dest_numeral bs + 1
wenzelm@21829
   480
  | dest_numeral t = raise TERM ("dest_numeral", [t]);
berghofe@13755
   481
haftmann@25919
   482
fun number_of_const T = Const ("Int.number_class.number_of", intT --> T);
haftmann@21820
   483
haftmann@25919
   484
fun add_numerals (Const ("Int.number_class.number_of", Type (_, [_, T])) $ t) = cons (t, T)
wenzelm@23269
   485
  | add_numerals (t $ u) = add_numerals t #> add_numerals u
wenzelm@23269
   486
  | add_numerals (Abs (_, _, t)) = add_numerals t
wenzelm@23269
   487
  | add_numerals _ = I;
haftmann@22391
   488
haftmann@22994
   489
fun mk_number T 0 = Const ("HOL.zero_class.zero", T)
haftmann@22994
   490
  | mk_number T 1 = Const ("HOL.one_class.one", T)
haftmann@21820
   491
  | mk_number T i = number_of_const T $ mk_numeral i;
haftmann@21820
   492
haftmann@22994
   493
fun dest_number (Const ("HOL.zero_class.zero", T)) = (T, 0)
haftmann@22994
   494
  | dest_number (Const ("HOL.one_class.one", T)) = (T, 1)
haftmann@25919
   495
  | dest_number (Const ("Int.number_class.number_of", Type ("fun", [_, T])) $ t) =
haftmann@22994
   496
      (T, dest_numeral t)
haftmann@21820
   497
  | dest_number t = raise TERM ("dest_number", [t]);
berghofe@13755
   498
wenzelm@21829
   499
berghofe@13755
   500
(* real *)
berghofe@13755
   501
wenzelm@16971
   502
val realT = Type ("RealDef.real", []);
berghofe@13755
   503
berghofe@13755
   504
wenzelm@21755
   505
(* nibble *)
wenzelm@21755
   506
wenzelm@21755
   507
val nibbleT = Type ("List.nibble", []);
berghofe@13755
   508
wenzelm@21755
   509
fun mk_nibble n =
wenzelm@21755
   510
  let val s =
wenzelm@21755
   511
    if 0 <= n andalso n <= 9 then chr (n + ord "0")
wenzelm@21755
   512
    else if 10 <= n andalso n <= 15 then chr (n + ord "A" - 10)
wenzelm@21755
   513
    else raise TERM ("mk_nibble", [])
wenzelm@21755
   514
  in Const ("List.nibble.Nibble" ^ s, nibbleT) end;
nipkow@17083
   515
wenzelm@21755
   516
fun dest_nibble t =
wenzelm@21755
   517
  let fun err () = raise TERM ("dest_nibble", [t]) in
wenzelm@21755
   518
    (case try (unprefix "List.nibble.Nibble" o fst o Term.dest_Const) t of
wenzelm@21755
   519
      NONE => err ()
wenzelm@21755
   520
    | SOME c =>
wenzelm@21755
   521
        if size c <> 1 then err ()
wenzelm@21755
   522
        else if "0" <= c andalso c <= "9" then ord c - ord "0"
wenzelm@21755
   523
        else if "A" <= c andalso c <= "F" then ord c - ord "A" + 10
wenzelm@21755
   524
        else err ())
wenzelm@21755
   525
  end;
berghofe@15062
   526
haftmann@21455
   527
haftmann@21455
   528
(* char *)
haftmann@21455
   529
haftmann@21455
   530
val charT = Type ("List.char", []);
haftmann@21455
   531
wenzelm@21755
   532
fun mk_char n =
wenzelm@21755
   533
  if 0 <= n andalso n <= 255 then
wenzelm@21755
   534
    Const ("List.char.Char", nibbleT --> nibbleT --> charT) $
wenzelm@21755
   535
      mk_nibble (n div 16) $ mk_nibble (n mod 16)
wenzelm@21755
   536
  else raise TERM ("mk_char", []);
haftmann@21455
   537
wenzelm@21755
   538
fun dest_char (Const ("List.char.Char", _) $ t $ u) =
wenzelm@21755
   539
      dest_nibble t * 16 + dest_nibble u
wenzelm@21755
   540
  | dest_char t = raise TERM ("dest_char", [t]);
haftmann@21455
   541
wenzelm@21755
   542
wenzelm@21755
   543
(* list *)
haftmann@21455
   544
wenzelm@21755
   545
fun listT T = Type ("List.list", [T]);
haftmann@21455
   546
berghofe@25887
   547
fun nil_const T = Const ("List.list.Nil", listT T);
berghofe@25887
   548
berghofe@25887
   549
fun cons_const T =
berghofe@25887
   550
  let val lT = listT T
berghofe@25887
   551
  in Const ("List.list.Cons", T --> lT --> lT) end;
berghofe@25887
   552
wenzelm@21755
   553
fun mk_list T ts =
haftmann@21455
   554
  let
wenzelm@21755
   555
    val lT = listT T;
wenzelm@21755
   556
    val Nil = Const ("List.list.Nil", lT);
wenzelm@21755
   557
    fun Cons t u = Const ("List.list.Cons", T --> lT --> lT) $ t $ u;
wenzelm@21755
   558
  in fold_rev Cons ts Nil end;
wenzelm@21755
   559
wenzelm@21755
   560
fun dest_list (Const ("List.list.Nil", _)) = []
wenzelm@21755
   561
  | dest_list (Const ("List.list.Cons", _) $ t $ u) = t :: dest_list u
wenzelm@21755
   562
  | dest_list t = raise TERM ("dest_list", [t]);
haftmann@21455
   563
haftmann@21455
   564
haftmann@21455
   565
(* string *)
haftmann@21455
   566
haftmann@21820
   567
val stringT = Type ("List.string", []);
haftmann@21455
   568
wenzelm@21755
   569
val mk_string = mk_list charT o map (mk_char o ord) o explode;
wenzelm@21755
   570
val dest_string = implode o map (chr o dest_char) o dest_list;
haftmann@21455
   571
clasohm@923
   572
end;