src/HOL/Tools/hologic.ML
author wenzelm
Sun, 01 Mar 2009 23:36:12 +0100
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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 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 = 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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(* 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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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;
4571
6b02fc8a97f6 added unit and prod stuff;
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parents: 4466
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   309
23745
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berghofe
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   310
fun dest_tuple (Const ("Pair", _) $ t $ u) = dest_tuple t @ dest_tuple u
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berghofe
parents: 23576
diff changeset
   311
  | dest_tuple t = [t];
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berghofe
parents: 23576
diff changeset
   312
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berghofe
parents: 23576
diff changeset
   313
(*In ap_split S T u, term u expects separate arguments for the factors of S,
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   314
  with result type T.  The call creates a new term expecting one argument
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   315
  of type S.*)
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berghofe
parents: 23576
diff changeset
   316
fun ap_split T T3 u =
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berghofe
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   317
  let
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berghofe
parents: 23576
diff changeset
   318
    fun ap (T :: Ts) =
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berghofe
parents: 23576
diff changeset
   319
          (case T of
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berghofe
parents: 23576
diff changeset
   320
             Type ("*", [T1, T2]) =>
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berghofe
parents: 23576
diff changeset
   321
               split_const (T1, T2, Ts ---> T3) $ ap (T1 :: T2 :: Ts)
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berghofe
parents: 23576
diff changeset
   322
           | _ => Abs ("x", T, ap Ts))
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berghofe
parents: 23576
diff changeset
   323
      | ap [] =
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berghofe
parents: 23576
diff changeset
   324
          let val k = length (prodT_factors T)
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   325
          in list_comb (incr_boundvars k u, map Bound (k - 1 downto 0)) end
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   326
  in ap [T] end;
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berghofe
parents: 23576
diff changeset
   327
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   328
25172
ad25033f9ca4 tuned comments;
wenzelm
parents: 24958
diff changeset
   329
(* operations on tuples with specific arities *)
ad25033f9ca4 tuned comments;
wenzelm
parents: 24958
diff changeset
   330
(*
ad25033f9ca4 tuned comments;
wenzelm
parents: 24958
diff changeset
   331
  an "arity" of a tuple is a list of lists of integers
ad25033f9ca4 tuned comments;
wenzelm
parents: 24958
diff changeset
   332
  ("factors"), denoting paths to subterms that are pairs
ad25033f9ca4 tuned comments;
wenzelm
parents: 24958
diff changeset
   333
*)
23745
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berghofe
parents: 23576
diff changeset
   334
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   335
fun prod_err s = raise TERM (s ^ ": inconsistent use of products", []);
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berghofe
parents: 23576
diff changeset
   336
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   337
fun prod_factors t =
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berghofe
parents: 23576
diff changeset
   338
  let
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   339
    fun factors p (Const ("Pair", _) $ t $ u) =
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berghofe
parents: 23576
diff changeset
   340
          p :: factors (1::p) t @ factors (2::p) u
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   341
      | factors p _ = []
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   342
  in factors [] t end;
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   343
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   344
fun dest_tuple' ps =
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berghofe
parents: 23576
diff changeset
   345
  let
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berghofe
parents: 23576
diff changeset
   346
    fun dest p t = if p mem ps then (case t of
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   347
        Const ("Pair", _) $ t $ u =>
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berghofe
parents: 23576
diff changeset
   348
          dest (1::p) t @ dest (2::p) u
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   349
      | _ => prod_err "dest_tuple'") else [t]
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   350
  in dest [] end;
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   351
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   352
fun prodT_factors' ps =
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berghofe
parents: 23576
diff changeset
   353
  let
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   354
    fun factors p T = if p mem ps then (case T of
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   355
        Type ("*", [T1, T2]) =>
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berghofe
parents: 23576
diff changeset
   356
          factors (1::p) T1 @ factors (2::p) T2
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   357
      | _ => prod_err "prodT_factors'") else [T]
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   358
  in factors [] end;
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   359
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   360
(*In ap_split' ps S T u, term u expects separate arguments for the factors of S,
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   361
  with result type T.  The call creates a new term expecting one argument
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   362
  of type S.*)
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   363
fun ap_split' ps T T3 u =
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berghofe
parents: 23576
diff changeset
   364
  let
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   365
    fun ap ((p, T) :: pTs) =
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   366
          if p mem ps then (case T of
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   367
              Type ("*", [T1, T2]) =>
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berghofe
parents: 23576
diff changeset
   368
                split_const (T1, T2, map snd pTs ---> T3) $
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   369
                  ap ((1::p, T1) :: (2::p, T2) :: pTs)
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   370
            | _ => prod_err "ap_split'")
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   371
          else Abs ("x", T, ap pTs)
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   372
      | ap [] =
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   373
          let val k = length ps
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   374
          in list_comb (incr_boundvars (k + 1) u, map Bound (k downto 0)) end
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   375
  in ap [([], T)] end;
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   376
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   377
fun mk_tuple' ps =
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   378
  let
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   379
    fun mk p T ts =
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   380
      if p mem ps then (case T of
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   381
          Type ("*", [T1, T2]) =>
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   382
            let
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   383
              val (t, ts') = mk (1::p) T1 ts;
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   384
              val (u, ts'') = mk (2::p) T2 ts'
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   385
            in (pair_const T1 T2 $ t $ u, ts'') end
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   386
        | _ => prod_err "mk_tuple'")
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   387
      else (hd ts, tl ts)
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   388
  in fst oo mk [] end;
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   389
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   390
fun mk_tupleT ps =
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   391
  let
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   392
    fun mk p Ts =
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   393
      if p mem ps then
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   394
        let
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   395
          val (T, Ts') = mk (1::p) Ts;
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   396
          val (U, Ts'') = mk (2::p) Ts'
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   397
        in (mk_prodT (T, U), Ts'') end
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   398
      else (hd Ts, tl Ts)
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   399
  in fst o mk [] end;
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   400
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   401
fun strip_split t =
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   402
  let
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   403
    fun strip [] qs Ts t = (t, Ts, qs)
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   404
      | strip (p :: ps) qs Ts (Const ("split", _) $ t) =
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   405
          strip ((1 :: p) :: (2 :: p) :: ps) (p :: qs) Ts t
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   406
      | strip (p :: ps) qs Ts (Abs (s, T, t)) = strip ps qs (T :: Ts) t
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   407
      | strip (p :: ps) qs Ts t = strip ps qs
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   408
          (hd (binder_types (fastype_of1 (Ts, t))) :: Ts)
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   409
          (incr_boundvars 1 t $ Bound 0)
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   410
  in strip [[]] [] [] t end;
28df61d931e2 New operations on tuples with specific arities.
berghofe
parents: 23576
diff changeset
   411
5207
wenzelm
parents: 5096
diff changeset
   412
wenzelm
parents: 5096
diff changeset
   413
(* nat *)
wenzelm
parents: 5096
diff changeset
   414
wenzelm
parents: 5096
diff changeset
   415
val natT = Type ("nat", []);
wenzelm
parents: 5096
diff changeset
   416
22994
02440636214f abstract size function in hologic.ML
haftmann
parents: 22391
diff changeset
   417
val zero = Const ("HOL.zero_class.zero", natT);
5207
wenzelm
parents: 5096
diff changeset
   418
22994
02440636214f abstract size function in hologic.ML
haftmann
parents: 22391
diff changeset
   419
fun is_zero (Const ("HOL.zero_class.zero", _)) = true
5207
wenzelm
parents: 5096
diff changeset
   420
  | is_zero _ = false;
wenzelm
parents: 5096
diff changeset
   421
wenzelm
parents: 5096
diff changeset
   422
fun mk_Suc t = Const ("Suc", natT --> natT) $ t;
wenzelm
parents: 5096
diff changeset
   423
wenzelm
parents: 5096
diff changeset
   424
fun dest_Suc (Const ("Suc", _) $ t) = t
wenzelm
parents: 5096
diff changeset
   425
  | dest_Suc t = raise TERM ("dest_Suc", [t]);
wenzelm
parents: 5096
diff changeset
   426
21621
f9fd69d96c4e slight cleanup in hologic.ML
haftmann
parents: 21550
diff changeset
   427
val Suc_zero = mk_Suc zero;
f9fd69d96c4e slight cleanup in hologic.ML
haftmann
parents: 21550
diff changeset
   428
24630
351a308ab58d simplified type int (eliminated IntInf.int, integer);
wenzelm
parents: 23745
diff changeset
   429
fun mk_nat n =
22994
02440636214f abstract size function in hologic.ML
haftmann
parents: 22391
diff changeset
   430
  let
02440636214f abstract size function in hologic.ML
haftmann
parents: 22391
diff changeset
   431
    fun mk 0 = zero
23297
06f108974fa1 simplified type integer;
wenzelm
parents: 23269
diff changeset
   432
      | mk n = mk_Suc (mk (n - 1));
23576
1ffe739e5ee0 removed dest_cTrueprop (cf. ObjectLogic.dest_judgment);
wenzelm
parents: 23566
diff changeset
   433
  in if n < 0 then raise TERM ("mk_nat: negative number", []) else mk n end;
5207
wenzelm
parents: 5096
diff changeset
   434
24630
351a308ab58d simplified type int (eliminated IntInf.int, integer);
wenzelm
parents: 23745
diff changeset
   435
fun dest_nat (Const ("HOL.zero_class.zero", _)) = 0
23297
06f108974fa1 simplified type integer;
wenzelm
parents: 23269
diff changeset
   436
  | dest_nat (Const ("Suc", _) $ t) = dest_nat t + 1
5207
wenzelm
parents: 5096
diff changeset
   437
  | dest_nat t = raise TERM ("dest_nat", [t]);
wenzelm
parents: 5096
diff changeset
   438
22994
02440636214f abstract size function in hologic.ML
haftmann
parents: 22391
diff changeset
   439
val class_size = "Nat.size";
02440636214f abstract size function in hologic.ML
haftmann
parents: 22391
diff changeset
   440
02440636214f abstract size function in hologic.ML
haftmann
parents: 22391
diff changeset
   441
fun size_const T = Const ("Nat.size_class.size", T --> natT);
02440636214f abstract size function in hologic.ML
haftmann
parents: 22391
diff changeset
   442
5207
wenzelm
parents: 5096
diff changeset
   443
26036
f9e779f11949 added indexT
haftmann
parents: 25919
diff changeset
   444
(* index *)
f9e779f11949 added indexT
haftmann
parents: 25919
diff changeset
   445
f9e779f11949 added indexT
haftmann
parents: 25919
diff changeset
   446
val indexT = Type ("Code_Index.index", []);
f9e779f11949 added indexT
haftmann
parents: 25919
diff changeset
   447
f9e779f11949 added indexT
haftmann
parents: 25919
diff changeset
   448
21778
66440bf72cdc binary numerals: restricted to actual abstract syntax;
wenzelm
parents: 21755
diff changeset
   449
(* binary numerals and int -- non-unique representation due to leading zeros/ones! *)
66440bf72cdc binary numerals: restricted to actual abstract syntax;
wenzelm
parents: 21755
diff changeset
   450
25919
8b1c0d434824 joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents: 25887
diff changeset
   451
val intT = Type ("Int.int", []);
21778
66440bf72cdc binary numerals: restricted to actual abstract syntax;
wenzelm
parents: 21755
diff changeset
   452
25919
8b1c0d434824 joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents: 25887
diff changeset
   453
val pls_const = Const ("Int.Pls", intT)
8b1c0d434824 joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents: 25887
diff changeset
   454
and min_const = Const ("Int.Min", intT)
26086
3c243098b64a New simpler representation of numerals, using Bit0 and Bit1 instead of BIT, B0, and B1
huffman
parents: 26036
diff changeset
   455
and bit0_const = Const ("Int.Bit0", intT --> intT)
3c243098b64a New simpler representation of numerals, using Bit0 and Bit1 instead of BIT, B0, and B1
huffman
parents: 26036
diff changeset
   456
and bit1_const = Const ("Int.Bit1", intT --> intT);
3c243098b64a New simpler representation of numerals, using Bit0 and Bit1 instead of BIT, B0, and B1
huffman
parents: 26036
diff changeset
   457
3c243098b64a New simpler representation of numerals, using Bit0 and Bit1 instead of BIT, B0, and B1
huffman
parents: 26036
diff changeset
   458
fun mk_bit 0 = bit0_const
3c243098b64a New simpler representation of numerals, using Bit0 and Bit1 instead of BIT, B0, and B1
huffman
parents: 26036
diff changeset
   459
  | mk_bit 1 = bit1_const
3c243098b64a New simpler representation of numerals, using Bit0 and Bit1 instead of BIT, B0, and B1
huffman
parents: 26036
diff changeset
   460
  | mk_bit _ = raise TERM ("mk_bit", []);
3c243098b64a New simpler representation of numerals, using Bit0 and Bit1 instead of BIT, B0, and B1
huffman
parents: 26036
diff changeset
   461
3c243098b64a New simpler representation of numerals, using Bit0 and Bit1 instead of BIT, B0, and B1
huffman
parents: 26036
diff changeset
   462
fun dest_bit (Const ("Int.Bit0", _)) = 0
3c243098b64a New simpler representation of numerals, using Bit0 and Bit1 instead of BIT, B0, and B1
huffman
parents: 26036
diff changeset
   463
  | dest_bit (Const ("Int.Bit1", _)) = 1
3c243098b64a New simpler representation of numerals, using Bit0 and Bit1 instead of BIT, B0, and B1
huffman
parents: 26036
diff changeset
   464
  | dest_bit t = raise TERM ("dest_bit", [t]);
8768
9f18aba48519 number_of now takes a type arg
paulson
parents: 8739
diff changeset
   465
21829
016eff9c5699 simplified mk/dest_numeral (cf. mk/dest_binum of 1.65);
wenzelm
parents: 21820
diff changeset
   466
fun mk_numeral 0 = pls_const
016eff9c5699 simplified mk/dest_numeral (cf. mk/dest_binum of 1.65);
wenzelm
parents: 21820
diff changeset
   467
  | mk_numeral ~1 = min_const
016eff9c5699 simplified mk/dest_numeral (cf. mk/dest_binum of 1.65);
wenzelm
parents: 21820
diff changeset
   468
  | mk_numeral i =
24630
351a308ab58d simplified type int (eliminated IntInf.int, integer);
wenzelm
parents: 23745
diff changeset
   469
      let val (q, r) = Integer.div_mod i 2;
26086
3c243098b64a New simpler representation of numerals, using Bit0 and Bit1 instead of BIT, B0, and B1
huffman
parents: 26036
diff changeset
   470
      in mk_bit r $ mk_numeral q end;
13755
a9bb54a3cfb7 Added mk_int and mk_list.
berghofe
parents: 13743
diff changeset
   471
25919
8b1c0d434824 joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents: 25887
diff changeset
   472
fun dest_numeral (Const ("Int.Pls", _)) = 0
8b1c0d434824 joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents: 25887
diff changeset
   473
  | dest_numeral (Const ("Int.Min", _)) = ~1
26086
3c243098b64a New simpler representation of numerals, using Bit0 and Bit1 instead of BIT, B0, and B1
huffman
parents: 26036
diff changeset
   474
  | dest_numeral (Const ("Int.Bit0", _) $ bs) = 2 * dest_numeral bs
3c243098b64a New simpler representation of numerals, using Bit0 and Bit1 instead of BIT, B0, and B1
huffman
parents: 26036
diff changeset
   475
  | dest_numeral (Const ("Int.Bit1", _) $ bs) = 2 * dest_numeral bs + 1
21829
016eff9c5699 simplified mk/dest_numeral (cf. mk/dest_binum of 1.65);
wenzelm
parents: 21820
diff changeset
   476
  | dest_numeral t = raise TERM ("dest_numeral", [t]);
13755
a9bb54a3cfb7 Added mk_int and mk_list.
berghofe
parents: 13743
diff changeset
   477
25919
8b1c0d434824 joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents: 25887
diff changeset
   478
fun number_of_const T = Const ("Int.number_class.number_of", intT --> T);
21820
2f2b6a965ccc introduced mk/dest_numeral/number for mk/dest_binum etc.
haftmann
parents: 21788
diff changeset
   479
25919
8b1c0d434824 joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents: 25887
diff changeset
   480
fun add_numerals (Const ("Int.number_class.number_of", Type (_, [_, T])) $ t) = cons (t, T)
23269
851b8ea067ac simplified/renamed add_numerals;
wenzelm
parents: 23247
diff changeset
   481
  | add_numerals (t $ u) = add_numerals t #> add_numerals u
851b8ea067ac simplified/renamed add_numerals;
wenzelm
parents: 23247
diff changeset
   482
  | add_numerals (Abs (_, _, t)) = add_numerals t
851b8ea067ac simplified/renamed add_numerals;
wenzelm
parents: 23247
diff changeset
   483
  | add_numerals _ = I;
22391
56861fe9c22c added add_numerals_of
haftmann
parents: 21829
diff changeset
   484
22994
02440636214f abstract size function in hologic.ML
haftmann
parents: 22391
diff changeset
   485
fun mk_number T 0 = Const ("HOL.zero_class.zero", T)
02440636214f abstract size function in hologic.ML
haftmann
parents: 22391
diff changeset
   486
  | mk_number T 1 = Const ("HOL.one_class.one", T)
21820
2f2b6a965ccc introduced mk/dest_numeral/number for mk/dest_binum etc.
haftmann
parents: 21788
diff changeset
   487
  | mk_number T i = number_of_const T $ mk_numeral i;
2f2b6a965ccc introduced mk/dest_numeral/number for mk/dest_binum etc.
haftmann
parents: 21788
diff changeset
   488
22994
02440636214f abstract size function in hologic.ML
haftmann
parents: 22391
diff changeset
   489
fun dest_number (Const ("HOL.zero_class.zero", T)) = (T, 0)
02440636214f abstract size function in hologic.ML
haftmann
parents: 22391
diff changeset
   490
  | dest_number (Const ("HOL.one_class.one", T)) = (T, 1)
25919
8b1c0d434824 joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents: 25887
diff changeset
   491
  | dest_number (Const ("Int.number_class.number_of", Type ("fun", [_, T])) $ t) =
22994
02440636214f abstract size function in hologic.ML
haftmann
parents: 22391
diff changeset
   492
      (T, dest_numeral t)
21820
2f2b6a965ccc introduced mk/dest_numeral/number for mk/dest_binum etc.
haftmann
parents: 21788
diff changeset
   493
  | dest_number t = raise TERM ("dest_number", [t]);
13755
a9bb54a3cfb7 Added mk_int and mk_list.
berghofe
parents: 13743
diff changeset
   494
21829
016eff9c5699 simplified mk/dest_numeral (cf. mk/dest_binum of 1.65);
wenzelm
parents: 21820
diff changeset
   495
13755
a9bb54a3cfb7 Added mk_int and mk_list.
berghofe
parents: 13743
diff changeset
   496
(* real *)
a9bb54a3cfb7 Added mk_int and mk_list.
berghofe
parents: 13743
diff changeset
   497
16971
968adbfbf93b removed read_cterm;
wenzelm
parents: 16835
diff changeset
   498
val realT = Type ("RealDef.real", []);
13755
a9bb54a3cfb7 Added mk_int and mk_list.
berghofe
parents: 13743
diff changeset
   499
a9bb54a3cfb7 Added mk_int and mk_list.
berghofe
parents: 13743
diff changeset
   500
21755
22dd32812116 misc cleanup -- removed non-HOL operations;
wenzelm
parents: 21621
diff changeset
   501
(* nibble *)
22dd32812116 misc cleanup -- removed non-HOL operations;
wenzelm
parents: 21621
diff changeset
   502
22dd32812116 misc cleanup -- removed non-HOL operations;
wenzelm
parents: 21621
diff changeset
   503
val nibbleT = Type ("List.nibble", []);
13755
a9bb54a3cfb7 Added mk_int and mk_list.
berghofe
parents: 13743
diff changeset
   504
21755
22dd32812116 misc cleanup -- removed non-HOL operations;
wenzelm
parents: 21621
diff changeset
   505
fun mk_nibble n =
22dd32812116 misc cleanup -- removed non-HOL operations;
wenzelm
parents: 21621
diff changeset
   506
  let val s =
22dd32812116 misc cleanup -- removed non-HOL operations;
wenzelm
parents: 21621
diff changeset
   507
    if 0 <= n andalso n <= 9 then chr (n + ord "0")
22dd32812116 misc cleanup -- removed non-HOL operations;
wenzelm
parents: 21621
diff changeset
   508
    else if 10 <= n andalso n <= 15 then chr (n + ord "A" - 10)
22dd32812116 misc cleanup -- removed non-HOL operations;
wenzelm
parents: 21621
diff changeset
   509
    else raise TERM ("mk_nibble", [])
22dd32812116 misc cleanup -- removed non-HOL operations;
wenzelm
parents: 21621
diff changeset
   510
  in Const ("List.nibble.Nibble" ^ s, nibbleT) end;
17083
051b0897bc98 added listT
nipkow
parents: 16971
diff changeset
   511
21755
22dd32812116 misc cleanup -- removed non-HOL operations;
wenzelm
parents: 21621
diff changeset
   512
fun dest_nibble t =
22dd32812116 misc cleanup -- removed non-HOL operations;
wenzelm
parents: 21621
diff changeset
   513
  let fun err () = raise TERM ("dest_nibble", [t]) in
22dd32812116 misc cleanup -- removed non-HOL operations;
wenzelm
parents: 21621
diff changeset
   514
    (case try (unprefix "List.nibble.Nibble" o fst o Term.dest_Const) t of
22dd32812116 misc cleanup -- removed non-HOL operations;
wenzelm
parents: 21621
diff changeset
   515
      NONE => err ()
22dd32812116 misc cleanup -- removed non-HOL operations;
wenzelm
parents: 21621
diff changeset
   516
    | SOME c =>
22dd32812116 misc cleanup -- removed non-HOL operations;
wenzelm
parents: 21621
diff changeset
   517
        if size c <> 1 then err ()
22dd32812116 misc cleanup -- removed non-HOL operations;
wenzelm
parents: 21621
diff changeset
   518
        else if "0" <= c andalso c <= "9" then ord c - ord "0"
22dd32812116 misc cleanup -- removed non-HOL operations;
wenzelm
parents: 21621
diff changeset
   519
        else if "A" <= c andalso c <= "F" then ord c - ord "A" + 10
22dd32812116 misc cleanup -- removed non-HOL operations;
wenzelm
parents: 21621
diff changeset
   520
        else err ())
22dd32812116 misc cleanup -- removed non-HOL operations;
wenzelm
parents: 21621
diff changeset
   521
  end;
15062
8049f217428e Added function dest_list.
berghofe
parents: 15013
diff changeset
   522
21455
b6be1d1b66c5 incorporated structure HOList into HOLogic
haftmann
parents: 21219
diff changeset
   523
b6be1d1b66c5 incorporated structure HOList into HOLogic
haftmann
parents: 21219
diff changeset
   524
(* char *)
b6be1d1b66c5 incorporated structure HOList into HOLogic
haftmann
parents: 21219
diff changeset
   525
b6be1d1b66c5 incorporated structure HOList into HOLogic
haftmann
parents: 21219
diff changeset
   526
val charT = Type ("List.char", []);
b6be1d1b66c5 incorporated structure HOList into HOLogic
haftmann
parents: 21219
diff changeset
   527
21755
22dd32812116 misc cleanup -- removed non-HOL operations;
wenzelm
parents: 21621
diff changeset
   528
fun mk_char n =
22dd32812116 misc cleanup -- removed non-HOL operations;
wenzelm
parents: 21621
diff changeset
   529
  if 0 <= n andalso n <= 255 then
22dd32812116 misc cleanup -- removed non-HOL operations;
wenzelm
parents: 21621
diff changeset
   530
    Const ("List.char.Char", nibbleT --> nibbleT --> charT) $
22dd32812116 misc cleanup -- removed non-HOL operations;
wenzelm
parents: 21621
diff changeset
   531
      mk_nibble (n div 16) $ mk_nibble (n mod 16)
22dd32812116 misc cleanup -- removed non-HOL operations;
wenzelm
parents: 21621
diff changeset
   532
  else raise TERM ("mk_char", []);
21455
b6be1d1b66c5 incorporated structure HOList into HOLogic
haftmann
parents: 21219
diff changeset
   533
21755
22dd32812116 misc cleanup -- removed non-HOL operations;
wenzelm
parents: 21621
diff changeset
   534
fun dest_char (Const ("List.char.Char", _) $ t $ u) =
22dd32812116 misc cleanup -- removed non-HOL operations;
wenzelm
parents: 21621
diff changeset
   535
      dest_nibble t * 16 + dest_nibble u
22dd32812116 misc cleanup -- removed non-HOL operations;
wenzelm
parents: 21621
diff changeset
   536
  | dest_char t = raise TERM ("dest_char", [t]);
21455
b6be1d1b66c5 incorporated structure HOList into HOLogic
haftmann
parents: 21219
diff changeset
   537
21755
22dd32812116 misc cleanup -- removed non-HOL operations;
wenzelm
parents: 21621
diff changeset
   538
22dd32812116 misc cleanup -- removed non-HOL operations;
wenzelm
parents: 21621
diff changeset
   539
(* list *)
21455
b6be1d1b66c5 incorporated structure HOList into HOLogic
haftmann
parents: 21219
diff changeset
   540
21755
22dd32812116 misc cleanup -- removed non-HOL operations;
wenzelm
parents: 21621
diff changeset
   541
fun listT T = Type ("List.list", [T]);
21455
b6be1d1b66c5 incorporated structure HOList into HOLogic
haftmann
parents: 21219
diff changeset
   542
25887
5dcc3c257922 Added nil_const and cons_const.
berghofe
parents: 25172
diff changeset
   543
fun nil_const T = Const ("List.list.Nil", listT T);
5dcc3c257922 Added nil_const and cons_const.
berghofe
parents: 25172
diff changeset
   544
5dcc3c257922 Added nil_const and cons_const.
berghofe
parents: 25172
diff changeset
   545
fun cons_const T =
5dcc3c257922 Added nil_const and cons_const.
berghofe
parents: 25172
diff changeset
   546
  let val lT = listT T
5dcc3c257922 Added nil_const and cons_const.
berghofe
parents: 25172
diff changeset
   547
  in Const ("List.list.Cons", T --> lT --> lT) end;
5dcc3c257922 Added nil_const and cons_const.
berghofe
parents: 25172
diff changeset
   548
21755
22dd32812116 misc cleanup -- removed non-HOL operations;
wenzelm
parents: 21621
diff changeset
   549
fun mk_list T ts =
21455
b6be1d1b66c5 incorporated structure HOList into HOLogic
haftmann
parents: 21219
diff changeset
   550
  let
21755
22dd32812116 misc cleanup -- removed non-HOL operations;
wenzelm
parents: 21621
diff changeset
   551
    val lT = listT T;
22dd32812116 misc cleanup -- removed non-HOL operations;
wenzelm
parents: 21621
diff changeset
   552
    val Nil = Const ("List.list.Nil", lT);
22dd32812116 misc cleanup -- removed non-HOL operations;
wenzelm
parents: 21621
diff changeset
   553
    fun Cons t u = Const ("List.list.Cons", T --> lT --> lT) $ t $ u;
22dd32812116 misc cleanup -- removed non-HOL operations;
wenzelm
parents: 21621
diff changeset
   554
  in fold_rev Cons ts Nil end;
22dd32812116 misc cleanup -- removed non-HOL operations;
wenzelm
parents: 21621
diff changeset
   555
22dd32812116 misc cleanup -- removed non-HOL operations;
wenzelm
parents: 21621
diff changeset
   556
fun dest_list (Const ("List.list.Nil", _)) = []
22dd32812116 misc cleanup -- removed non-HOL operations;
wenzelm
parents: 21621
diff changeset
   557
  | dest_list (Const ("List.list.Cons", _) $ t $ u) = t :: dest_list u
22dd32812116 misc cleanup -- removed non-HOL operations;
wenzelm
parents: 21621
diff changeset
   558
  | dest_list t = raise TERM ("dest_list", [t]);
21455
b6be1d1b66c5 incorporated structure HOList into HOLogic
haftmann
parents: 21219
diff changeset
   559
b6be1d1b66c5 incorporated structure HOList into HOLogic
haftmann
parents: 21219
diff changeset
   560
b6be1d1b66c5 incorporated structure HOList into HOLogic
haftmann
parents: 21219
diff changeset
   561
(* string *)
b6be1d1b66c5 incorporated structure HOList into HOLogic
haftmann
parents: 21219
diff changeset
   562
21820
2f2b6a965ccc introduced mk/dest_numeral/number for mk/dest_binum etc.
haftmann
parents: 21788
diff changeset
   563
val stringT = Type ("List.string", []);
21455
b6be1d1b66c5 incorporated structure HOList into HOLogic
haftmann
parents: 21219
diff changeset
   564
21755
22dd32812116 misc cleanup -- removed non-HOL operations;
wenzelm
parents: 21621
diff changeset
   565
val mk_string = mk_list charT o map (mk_char o ord) o explode;
22dd32812116 misc cleanup -- removed non-HOL operations;
wenzelm
parents: 21621
diff changeset
   566
val dest_string = implode o map (chr o dest_char) o dest_list;
21455
b6be1d1b66c5 incorporated structure HOList into HOLogic
haftmann
parents: 21219
diff changeset
   567
923
ff1574a81019 new version of HOL with curried function application
clasohm
parents:
diff changeset
   568
end;