src/HOL/Tools/hologic.ML
author haftmann
Wed Mar 11 16:20:07 2009 +0100 (2009-03-11)
changeset 30453 1e7e0d171653
parent 30450 7655e6533209
child 31048 ac146fc38b51
permissions -rw-r--r--
fixed typo
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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 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 = 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 ("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 ("Orderings.bot", _)) = []
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  | dest_set (Const ("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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                 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
berghofe@23745
   332
             Type ("*", [T1, T2]) =>
berghofe@23745
   333
               split_const (T1, T2, Ts ---> T3) $ ap (T1 :: T2 :: Ts)
berghofe@23745
   334
           | _ => Abs ("x", T, ap Ts))
berghofe@23745
   335
      | ap [] =
berghofe@23745
   336
          let val k = length (prodT_factors T)
berghofe@23745
   337
          in list_comb (incr_boundvars k u, map Bound (k - 1 downto 0)) end
berghofe@23745
   338
  in ap [T] end;
berghofe@23745
   339
berghofe@23745
   340
wenzelm@25172
   341
(* operations on tuples with specific arities *)
wenzelm@25172
   342
(*
wenzelm@25172
   343
  an "arity" of a tuple is a list of lists of integers
wenzelm@25172
   344
  ("factors"), denoting paths to subterms that are pairs
wenzelm@25172
   345
*)
berghofe@23745
   346
berghofe@23745
   347
fun prod_err s = raise TERM (s ^ ": inconsistent use of products", []);
berghofe@23745
   348
berghofe@23745
   349
fun prod_factors t =
berghofe@23745
   350
  let
berghofe@23745
   351
    fun factors p (Const ("Pair", _) $ t $ u) =
berghofe@23745
   352
          p :: factors (1::p) t @ factors (2::p) u
berghofe@23745
   353
      | factors p _ = []
berghofe@23745
   354
  in factors [] t end;
berghofe@23745
   355
berghofe@23745
   356
fun dest_tuple' ps =
berghofe@23745
   357
  let
berghofe@23745
   358
    fun dest p t = if p mem ps then (case t of
berghofe@23745
   359
        Const ("Pair", _) $ t $ u =>
berghofe@23745
   360
          dest (1::p) t @ dest (2::p) u
berghofe@23745
   361
      | _ => prod_err "dest_tuple'") else [t]
berghofe@23745
   362
  in dest [] end;
berghofe@23745
   363
berghofe@23745
   364
fun prodT_factors' ps =
berghofe@23745
   365
  let
berghofe@23745
   366
    fun factors p T = if p mem ps then (case T of
berghofe@23745
   367
        Type ("*", [T1, T2]) =>
berghofe@23745
   368
          factors (1::p) T1 @ factors (2::p) T2
berghofe@23745
   369
      | _ => prod_err "prodT_factors'") else [T]
berghofe@23745
   370
  in factors [] end;
berghofe@23745
   371
berghofe@23745
   372
(*In ap_split' ps S T u, term u expects separate arguments for the factors of S,
berghofe@23745
   373
  with result type T.  The call creates a new term expecting one argument
berghofe@23745
   374
  of type S.*)
berghofe@23745
   375
fun ap_split' ps T T3 u =
berghofe@23745
   376
  let
berghofe@23745
   377
    fun ap ((p, T) :: pTs) =
berghofe@23745
   378
          if p mem ps then (case T of
berghofe@23745
   379
              Type ("*", [T1, T2]) =>
berghofe@23745
   380
                split_const (T1, T2, map snd pTs ---> T3) $
berghofe@23745
   381
                  ap ((1::p, T1) :: (2::p, T2) :: pTs)
berghofe@23745
   382
            | _ => prod_err "ap_split'")
berghofe@23745
   383
          else Abs ("x", T, ap pTs)
berghofe@23745
   384
      | ap [] =
berghofe@23745
   385
          let val k = length ps
berghofe@23745
   386
          in list_comb (incr_boundvars (k + 1) u, map Bound (k downto 0)) end
berghofe@23745
   387
  in ap [([], T)] end;
berghofe@23745
   388
berghofe@23745
   389
fun mk_tuple' ps =
berghofe@23745
   390
  let
berghofe@23745
   391
    fun mk p T ts =
berghofe@23745
   392
      if p mem ps then (case T of
berghofe@23745
   393
          Type ("*", [T1, T2]) =>
berghofe@23745
   394
            let
berghofe@23745
   395
              val (t, ts') = mk (1::p) T1 ts;
berghofe@23745
   396
              val (u, ts'') = mk (2::p) T2 ts'
berghofe@23745
   397
            in (pair_const T1 T2 $ t $ u, ts'') end
berghofe@23745
   398
        | _ => prod_err "mk_tuple'")
berghofe@23745
   399
      else (hd ts, tl ts)
berghofe@23745
   400
  in fst oo mk [] end;
berghofe@23745
   401
berghofe@23745
   402
fun mk_tupleT ps =
berghofe@23745
   403
  let
berghofe@23745
   404
    fun mk p Ts =
berghofe@23745
   405
      if p mem ps then
berghofe@23745
   406
        let
berghofe@23745
   407
          val (T, Ts') = mk (1::p) Ts;
berghofe@23745
   408
          val (U, Ts'') = mk (2::p) Ts'
berghofe@23745
   409
        in (mk_prodT (T, U), Ts'') end
berghofe@23745
   410
      else (hd Ts, tl Ts)
berghofe@23745
   411
  in fst o mk [] end;
berghofe@23745
   412
berghofe@23745
   413
fun strip_split t =
berghofe@23745
   414
  let
berghofe@23745
   415
    fun strip [] qs Ts t = (t, Ts, qs)
berghofe@23745
   416
      | strip (p :: ps) qs Ts (Const ("split", _) $ t) =
berghofe@23745
   417
          strip ((1 :: p) :: (2 :: p) :: ps) (p :: qs) Ts t
berghofe@23745
   418
      | strip (p :: ps) qs Ts (Abs (s, T, t)) = strip ps qs (T :: Ts) t
berghofe@23745
   419
      | strip (p :: ps) qs Ts t = strip ps qs
berghofe@23745
   420
          (hd (binder_types (fastype_of1 (Ts, t))) :: Ts)
berghofe@23745
   421
          (incr_boundvars 1 t $ Bound 0)
berghofe@23745
   422
  in strip [[]] [] [] t end;
berghofe@23745
   423
wenzelm@5207
   424
wenzelm@5207
   425
(* nat *)
wenzelm@5207
   426
wenzelm@5207
   427
val natT = Type ("nat", []);
wenzelm@5207
   428
haftmann@22994
   429
val zero = Const ("HOL.zero_class.zero", natT);
wenzelm@5207
   430
haftmann@22994
   431
fun is_zero (Const ("HOL.zero_class.zero", _)) = true
wenzelm@5207
   432
  | is_zero _ = false;
wenzelm@5207
   433
wenzelm@5207
   434
fun mk_Suc t = Const ("Suc", natT --> natT) $ t;
wenzelm@5207
   435
wenzelm@5207
   436
fun dest_Suc (Const ("Suc", _) $ t) = t
wenzelm@5207
   437
  | dest_Suc t = raise TERM ("dest_Suc", [t]);
wenzelm@5207
   438
haftmann@21621
   439
val Suc_zero = mk_Suc zero;
haftmann@21621
   440
wenzelm@24630
   441
fun mk_nat n =
haftmann@22994
   442
  let
haftmann@22994
   443
    fun mk 0 = zero
wenzelm@23297
   444
      | mk n = mk_Suc (mk (n - 1));
wenzelm@23576
   445
  in if n < 0 then raise TERM ("mk_nat: negative number", []) else mk n end;
wenzelm@5207
   446
wenzelm@24630
   447
fun dest_nat (Const ("HOL.zero_class.zero", _)) = 0
wenzelm@23297
   448
  | dest_nat (Const ("Suc", _) $ t) = dest_nat t + 1
wenzelm@5207
   449
  | dest_nat t = raise TERM ("dest_nat", [t]);
wenzelm@5207
   450
haftmann@22994
   451
val class_size = "Nat.size";
haftmann@22994
   452
haftmann@22994
   453
fun size_const T = Const ("Nat.size_class.size", T --> natT);
haftmann@22994
   454
wenzelm@5207
   455
haftmann@26036
   456
(* index *)
haftmann@26036
   457
haftmann@26036
   458
val indexT = Type ("Code_Index.index", []);
haftmann@26036
   459
haftmann@26036
   460
wenzelm@21778
   461
(* binary numerals and int -- non-unique representation due to leading zeros/ones! *)
wenzelm@21778
   462
haftmann@25919
   463
val intT = Type ("Int.int", []);
wenzelm@21778
   464
haftmann@25919
   465
val pls_const = Const ("Int.Pls", intT)
haftmann@25919
   466
and min_const = Const ("Int.Min", intT)
huffman@26086
   467
and bit0_const = Const ("Int.Bit0", intT --> intT)
huffman@26086
   468
and bit1_const = Const ("Int.Bit1", intT --> intT);
huffman@26086
   469
huffman@26086
   470
fun mk_bit 0 = bit0_const
huffman@26086
   471
  | mk_bit 1 = bit1_const
huffman@26086
   472
  | mk_bit _ = raise TERM ("mk_bit", []);
huffman@26086
   473
huffman@26086
   474
fun dest_bit (Const ("Int.Bit0", _)) = 0
huffman@26086
   475
  | dest_bit (Const ("Int.Bit1", _)) = 1
huffman@26086
   476
  | dest_bit t = raise TERM ("dest_bit", [t]);
paulson@8768
   477
wenzelm@21829
   478
fun mk_numeral 0 = pls_const
wenzelm@21829
   479
  | mk_numeral ~1 = min_const
wenzelm@21829
   480
  | mk_numeral i =
wenzelm@24630
   481
      let val (q, r) = Integer.div_mod i 2;
huffman@26086
   482
      in mk_bit r $ mk_numeral q end;
berghofe@13755
   483
haftmann@25919
   484
fun dest_numeral (Const ("Int.Pls", _)) = 0
haftmann@25919
   485
  | dest_numeral (Const ("Int.Min", _)) = ~1
huffman@26086
   486
  | dest_numeral (Const ("Int.Bit0", _) $ bs) = 2 * dest_numeral bs
huffman@26086
   487
  | dest_numeral (Const ("Int.Bit1", _) $ bs) = 2 * dest_numeral bs + 1
wenzelm@21829
   488
  | dest_numeral t = raise TERM ("dest_numeral", [t]);
berghofe@13755
   489
haftmann@25919
   490
fun number_of_const T = Const ("Int.number_class.number_of", intT --> T);
haftmann@21820
   491
haftmann@25919
   492
fun add_numerals (Const ("Int.number_class.number_of", Type (_, [_, T])) $ t) = cons (t, T)
wenzelm@23269
   493
  | add_numerals (t $ u) = add_numerals t #> add_numerals u
wenzelm@23269
   494
  | add_numerals (Abs (_, _, t)) = add_numerals t
wenzelm@23269
   495
  | add_numerals _ = I;
haftmann@22391
   496
haftmann@22994
   497
fun mk_number T 0 = Const ("HOL.zero_class.zero", T)
haftmann@22994
   498
  | mk_number T 1 = Const ("HOL.one_class.one", T)
haftmann@21820
   499
  | mk_number T i = number_of_const T $ mk_numeral i;
haftmann@21820
   500
haftmann@22994
   501
fun dest_number (Const ("HOL.zero_class.zero", T)) = (T, 0)
haftmann@22994
   502
  | dest_number (Const ("HOL.one_class.one", T)) = (T, 1)
haftmann@25919
   503
  | dest_number (Const ("Int.number_class.number_of", Type ("fun", [_, T])) $ t) =
haftmann@22994
   504
      (T, dest_numeral t)
haftmann@21820
   505
  | dest_number t = raise TERM ("dest_number", [t]);
berghofe@13755
   506
wenzelm@21829
   507
berghofe@13755
   508
(* real *)
berghofe@13755
   509
wenzelm@16971
   510
val realT = Type ("RealDef.real", []);
berghofe@13755
   511
berghofe@13755
   512
wenzelm@21755
   513
(* nibble *)
wenzelm@21755
   514
wenzelm@21755
   515
val nibbleT = Type ("List.nibble", []);
berghofe@13755
   516
wenzelm@21755
   517
fun mk_nibble n =
wenzelm@21755
   518
  let val s =
wenzelm@21755
   519
    if 0 <= n andalso n <= 9 then chr (n + ord "0")
wenzelm@21755
   520
    else if 10 <= n andalso n <= 15 then chr (n + ord "A" - 10)
wenzelm@21755
   521
    else raise TERM ("mk_nibble", [])
wenzelm@21755
   522
  in Const ("List.nibble.Nibble" ^ s, nibbleT) end;
nipkow@17083
   523
wenzelm@21755
   524
fun dest_nibble t =
wenzelm@21755
   525
  let fun err () = raise TERM ("dest_nibble", [t]) in
wenzelm@21755
   526
    (case try (unprefix "List.nibble.Nibble" o fst o Term.dest_Const) t of
wenzelm@21755
   527
      NONE => err ()
wenzelm@21755
   528
    | SOME c =>
wenzelm@21755
   529
        if size c <> 1 then err ()
wenzelm@21755
   530
        else if "0" <= c andalso c <= "9" then ord c - ord "0"
wenzelm@21755
   531
        else if "A" <= c andalso c <= "F" then ord c - ord "A" + 10
wenzelm@21755
   532
        else err ())
wenzelm@21755
   533
  end;
berghofe@15062
   534
haftmann@21455
   535
haftmann@21455
   536
(* char *)
haftmann@21455
   537
haftmann@21455
   538
val charT = Type ("List.char", []);
haftmann@21455
   539
wenzelm@21755
   540
fun mk_char n =
wenzelm@21755
   541
  if 0 <= n andalso n <= 255 then
wenzelm@21755
   542
    Const ("List.char.Char", nibbleT --> nibbleT --> charT) $
wenzelm@21755
   543
      mk_nibble (n div 16) $ mk_nibble (n mod 16)
wenzelm@21755
   544
  else raise TERM ("mk_char", []);
haftmann@21455
   545
wenzelm@21755
   546
fun dest_char (Const ("List.char.Char", _) $ t $ u) =
wenzelm@21755
   547
      dest_nibble t * 16 + dest_nibble u
wenzelm@21755
   548
  | dest_char t = raise TERM ("dest_char", [t]);
haftmann@21455
   549
wenzelm@21755
   550
wenzelm@21755
   551
(* list *)
haftmann@21455
   552
wenzelm@21755
   553
fun listT T = Type ("List.list", [T]);
haftmann@21455
   554
berghofe@25887
   555
fun nil_const T = Const ("List.list.Nil", listT T);
berghofe@25887
   556
berghofe@25887
   557
fun cons_const T =
berghofe@25887
   558
  let val lT = listT T
berghofe@25887
   559
  in Const ("List.list.Cons", T --> lT --> lT) end;
berghofe@25887
   560
wenzelm@21755
   561
fun mk_list T ts =
haftmann@21455
   562
  let
wenzelm@21755
   563
    val lT = listT T;
wenzelm@21755
   564
    val Nil = Const ("List.list.Nil", lT);
wenzelm@21755
   565
    fun Cons t u = Const ("List.list.Cons", T --> lT --> lT) $ t $ u;
wenzelm@21755
   566
  in fold_rev Cons ts Nil end;
wenzelm@21755
   567
wenzelm@21755
   568
fun dest_list (Const ("List.list.Nil", _)) = []
wenzelm@21755
   569
  | dest_list (Const ("List.list.Cons", _) $ t $ u) = t :: dest_list u
wenzelm@21755
   570
  | dest_list t = raise TERM ("dest_list", [t]);
haftmann@21455
   571
haftmann@21455
   572
haftmann@21455
   573
(* string *)
haftmann@21455
   574
haftmann@21820
   575
val stringT = Type ("List.string", []);
haftmann@21455
   576
wenzelm@21755
   577
val mk_string = mk_list charT o map (mk_char o ord) o explode;
wenzelm@21755
   578
val dest_string = implode o map (chr o dest_char) o dest_list;
haftmann@21455
   579
clasohm@923
   580
end;