src/HOL/hologic.ML
author haftmann
Fri Mar 02 15:43:22 2007 +0100 (2007-03-02)
changeset 22391 56861fe9c22c
parent 21829 016eff9c5699
child 22994 02440636214f
permissions -rw-r--r--
added add_numerals_of
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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 Trueprop_conv: (cterm -> thm) -> cterm -> thm
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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 dest_imp: term -> term * term
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  val dest_not: term -> term
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  val dest_concls: term -> term list
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  val eq_const: typ -> term
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  val mk_eq: term * term -> term
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  val dest_eq: term -> term * term
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  val all_const: typ -> term
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  val mk_all: string * typ * term -> term
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  val list_all: (string * typ) list * term -> term
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  val exists_const: typ -> term
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  val mk_exists: string * typ * term -> term
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  val choice_const: typ -> term
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  val Collect_const: typ -> term
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  val mk_Collect: string * typ * term -> term
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  val class_eq: string
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  val mk_mem: term * term -> term
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  val dest_mem: term -> term * term
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  val mk_UNIV: typ -> term
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  val mk_binop: string -> term * term -> term
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  val mk_binrel: string -> term * term -> term
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  val dest_bin: string -> typ -> term -> term * term
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  val unitT: typ
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  val is_unitT: typ -> bool
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  val unit: term
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  val is_unit: term -> bool
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  val mk_prodT: typ * typ -> typ
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  val dest_prodT: typ -> typ * typ
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  val pair_const: typ -> typ -> term
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  val mk_prod: term * term -> term
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  val dest_prod: term -> term * term
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  val mk_fst: term -> term
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  val mk_snd: term -> term
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  val split_const: typ * typ * typ -> term
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  val mk_split: term -> term
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  val prodT_factors: typ -> typ list
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  val mk_tuple: typ -> term list -> term
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  val 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: IntInf.int -> term
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  val dest_nat: term -> IntInf.int
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  val bitT: typ
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  val B0_const: term
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  val B1_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 intT: typ
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  val pls_const: term
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  val min_const: term
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  val bit_const: term
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  val mk_numeral: IntInf.int -> term
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  val dest_numeral: term -> IntInf.int
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  val number_of_const: typ -> term
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  val add_numerals_of: term -> (term * typ) list -> (term * typ) list
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  val mk_number: typ -> IntInf.int -> term
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  val dest_number: term -> typ * IntInf.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 mk_list: typ -> term list -> term
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  val dest_list: term -> term list
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  val stringT: typ
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  val mk_string: string -> term
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  val dest_string: term -> string
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end;
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structure HOLogic: HOLOGIC =
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struct
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(* HOL syntax *)
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val typeS: sort = ["HOL.type"];
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val typeT = TypeInfer.anyT typeS;
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(* bool and set *)
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val boolN = "bool";
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val boolT = Type (boolN, []);
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val true_const =  Const ("True", boolT);
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val false_const = Const ("False", boolT);
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fun mk_setT T = Type ("set", [T]);
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fun dest_setT (Type ("set", [T])) = T
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  | dest_setT T = raise TYPE ("dest_setT: set type expected", [T], []);
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(* logic *)
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val Trueprop = Const ("Trueprop", boolT --> propT);
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fun mk_Trueprop P = Trueprop $ P;
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fun dest_Trueprop (Const ("Trueprop", _) $ P) = P
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  | dest_Trueprop t = raise TERM ("dest_Trueprop", [t]);
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fun Trueprop_conv conv ct = (case term_of ct of
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    Const ("Trueprop", _) $ _ =>
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      let val (ct1, ct2) = Thm.dest_comb ct
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      in Thm.combination (Thm.reflexive ct1) (conv ct2) end
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  | _ => raise TERM ("Trueprop_conv", []));
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val conj = Const ("op &", [boolT, boolT] ---> boolT)
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and disj = Const ("op |", [boolT, boolT] ---> boolT)
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and imp = Const ("op -->", [boolT, boolT] ---> boolT)
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and Not = Const ("Not", boolT --> boolT);
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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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fun dest_imp (Const("op -->",_) $ A $ B) = (A, B)
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  | dest_imp  t = raise TERM ("dest_imp", [t]);
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fun dest_not (Const ("Not", _) $ t) = t
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  | dest_not t = raise TERM ("dest_not", [t]);
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fun imp_concl_of t = imp_concl_of (#2 (dest_imp t)) handle TERM _ => t;
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val dest_concls = map imp_concl_of o dest_conj o dest_Trueprop;
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fun eq_const T = Const ("op =", [T, T] ---> boolT);
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fun mk_eq (t, u) = eq_const (fastype_of t) $ t $ u;
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fun dest_eq (Const ("op =", _) $ lhs $ rhs) = (lhs, rhs)
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  | dest_eq t = raise TERM ("dest_eq", [t])
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fun all_const T = Const ("All", [T --> boolT] ---> boolT);
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fun mk_all (x, T, P) = all_const T $ absfree (x, T, P);
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fun list_all (xs, t) = fold_rev (fn (x, T) => fn P => all_const T $ Abs (x, T, P)) xs t;
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fun exists_const T = Const ("Ex", [T --> boolT] ---> boolT);
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fun mk_exists (x, T, P) = exists_const T $ absfree (x, T, P);
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fun choice_const T = Const("Hilbert_Choice.Eps", (T --> boolT) --> T);
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fun Collect_const T = Const ("Collect", [T --> boolT] ---> mk_setT T);
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fun mk_Collect (a, T, t) = Collect_const T $ absfree (a, T, t);
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val class_eq = "Code_Generator.eq";
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fun mk_mem (x, A) =
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  let val setT = fastype_of A in
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    Const ("op :", [dest_setT setT, setT] ---> boolT) $ x $ A
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  end;
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fun dest_mem (Const ("op :", _) $ x $ A) = (x, A)
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  | dest_mem t = raise TERM ("dest_mem", [t]);
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fun mk_UNIV T = Const ("UNIV", mk_setT T);
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(* binary operations and relations *)
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fun mk_binop c (t, u) =
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  let val T = fastype_of t in
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    Const (c, [T, T] ---> T) $ t $ u
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  end;
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fun mk_binrel c (t, u) =
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  let val T = fastype_of t in
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    Const (c, [T, T] ---> boolT) $ t $ u
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  end;
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(*destruct the application of a binary operator. The dummyT case is a crude
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  way of handling polymorphic operators.*)
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fun dest_bin c T (tm as Const (c', Type ("fun", [T', _])) $ t $ u) =
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      if c = c' andalso (T=T' orelse T=dummyT) then (t, u)
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      else raise TERM ("dest_bin " ^ c, [tm])
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  | dest_bin c _ tm = raise TERM ("dest_bin " ^ c, [tm]);
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(* unit *)
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val unitT = Type ("Product_Type.unit", []);
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fun is_unitT (Type ("Product_Type.unit", [])) = true
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  | is_unitT _ = false;
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val unit = Const ("Product_Type.Unity", unitT);
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fun is_unit (Const ("Product_Type.Unity", _)) = true
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  | is_unit _ = false;
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(* prod *)
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fun mk_prodT (T1, T2) = Type ("*", [T1, T2]);
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fun dest_prodT (Type ("*", [T1, T2])) = (T1, T2)
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  | dest_prodT T = raise TYPE ("dest_prodT", [T], []);
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fun pair_const T1 T2 = Const ("Pair", [T1, T2] ---> mk_prodT (T1, T2));
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fun mk_prod (t1, t2) =
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  let val T1 = fastype_of t1 and T2 = fastype_of t2 in
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    pair_const T1 T2 $ t1 $ t2
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  end;
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fun dest_prod (Const ("Pair", _) $ t1 $ t2) = (t1, t2)
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  | dest_prod t = raise TERM ("dest_prod", [t]);
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fun mk_fst p =
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  let val pT = fastype_of p in
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    Const ("fst", pT --> fst (dest_prodT pT)) $ p
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  end;
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fun mk_snd p =
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  let val pT = fastype_of p in
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    Const ("snd", pT --> snd (dest_prodT pT)) $ p
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  end;
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fun split_const (A, B, C) =
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  Const ("split", (A --> B --> C) --> mk_prodT (A, B) --> C);
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fun mk_split t =
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  (case Term.fastype_of t of
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    T as (Type ("fun", [A, Type ("fun", [B, C])])) =>
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      Const ("split", T --> mk_prodT (A, B) --> C) $ t
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  | _ => raise TERM ("mk_split: bad body type", [t]));
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(*Maps the type T1 * ... * Tn to [T1, ..., Tn], however nested*)
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fun prodT_factors (Type ("*", [T1, T2])) = prodT_factors T1 @ prodT_factors T2
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  | prodT_factors T = [T];
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(*Makes a nested tuple from a list, following the product type structure*)
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fun mk_tuple (Type ("*", [T1, T2])) tms =
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        mk_prod (mk_tuple T1 tms,
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                 mk_tuple T2 (Library.drop (length (prodT_factors T1), tms)))
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  | mk_tuple T (t::_) = t;
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(* nat *)
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val natT = Type ("nat", []);
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val zero = Const ("HOL.zero", natT);
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fun is_zero (Const ("HOL.zero", _)) = true
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  | is_zero _ = false;
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fun mk_Suc t = Const ("Suc", natT --> natT) $ t;
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fun dest_Suc (Const ("Suc", _) $ t) = t
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  | dest_Suc t = raise TERM ("dest_Suc", [t]);
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val Suc_zero = mk_Suc zero;
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fun mk_nat 0 = zero
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  | mk_nat n = mk_Suc (mk_nat (IntInf.- (n, 1)));
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fun dest_nat (Const ("HOL.zero", _)) = 0
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  | dest_nat (Const ("Suc", _) $ t) = IntInf.+ (dest_nat t, 1)
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  | dest_nat t = raise TERM ("dest_nat", [t]);
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(* bit *)
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val bitT = Type ("Numeral.bit", []);
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val B0_const = Const ("Numeral.bit.B0", bitT);
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val B1_const =  Const ("Numeral.bit.B1", bitT);
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fun mk_bit 0 = B0_const
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  | mk_bit 1 = B1_const
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  | mk_bit _ = raise TERM ("mk_bit", []);
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fun dest_bit (Const ("Numeral.bit.B0", _)) = 0
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  | dest_bit (Const ("Numeral.bit.B1", _)) = 1
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  | dest_bit t = raise TERM ("dest_bit", [t]);
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(* binary numerals and int -- non-unique representation due to leading zeros/ones! *)
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val intT = Type ("IntDef.int", []);
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val pls_const = Const ("Numeral.Pls", intT)
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and min_const = Const ("Numeral.Min", intT)
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and bit_const = Const ("Numeral.Bit", [intT, bitT] ---> intT);
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fun mk_numeral 0 = pls_const
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  | mk_numeral ~1 = min_const
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  | mk_numeral i =
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      let val (q, r) = IntInf.divMod (i, 2)
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      in bit_const $ mk_numeral q $ mk_bit (IntInf.toInt r) end;
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fun dest_numeral (Const ("Numeral.Pls", _)) = 0
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  | dest_numeral (Const ("Numeral.Min", _)) = ~1
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  | dest_numeral (Const ("Numeral.Bit", _) $ bs $ b) =
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      2 * dest_numeral bs + IntInf.fromInt (dest_bit b)
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   338
  | dest_numeral t = raise TERM ("dest_numeral", [t]);
berghofe@13755
   339
wenzelm@21829
   340
fun number_of_const T = Const ("Numeral.number_of", intT --> T);
haftmann@21820
   341
haftmann@22391
   342
fun add_numerals_of (Const _) =
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   343
      I
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  | add_numerals_of (Var _) =
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   345
      I
haftmann@22391
   346
  | add_numerals_of (Free _) =
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   347
      I
haftmann@22391
   348
  | add_numerals_of (Bound _) =
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   349
      I
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   350
  | add_numerals_of (Abs (_, _, t)) =
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   351
      add_numerals_of t
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   352
  | add_numerals_of (t as _ $ _) =
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   353
      case strip_comb t
haftmann@22391
   354
       of (Const ("Numeral.number_of",
haftmann@22391
   355
           Type (_, [_, T])), ts) => fold (cons o rpair T) ts
haftmann@22391
   356
        | (t', ts) => add_numerals_of t' #> fold add_numerals_of ts;
haftmann@22391
   357
haftmann@21820
   358
fun mk_number T 0 = Const ("HOL.zero", T)
haftmann@21820
   359
  | mk_number T 1 = Const ("HOL.one", T)
haftmann@21820
   360
  | mk_number T i = number_of_const T $ mk_numeral i;
haftmann@21820
   361
haftmann@21820
   362
fun dest_number (Const ("HOL.zero", T)) = (T, 0)
haftmann@21820
   363
  | dest_number (Const ("HOL.one", T)) = (T, 1)
haftmann@21820
   364
  | dest_number (Const ("Numeral.number_of", Type ("fun", [_, T])) $ t) = (T, dest_numeral t)
haftmann@21820
   365
  | dest_number t = raise TERM ("dest_number", [t]);
berghofe@13755
   366
wenzelm@21829
   367
berghofe@13755
   368
(* real *)
berghofe@13755
   369
wenzelm@16971
   370
val realT = Type ("RealDef.real", []);
berghofe@13755
   371
berghofe@13755
   372
wenzelm@21755
   373
(* nibble *)
wenzelm@21755
   374
wenzelm@21755
   375
val nibbleT = Type ("List.nibble", []);
berghofe@13755
   376
wenzelm@21755
   377
fun mk_nibble n =
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   378
  let val s =
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   379
    if 0 <= n andalso n <= 9 then chr (n + ord "0")
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   380
    else if 10 <= n andalso n <= 15 then chr (n + ord "A" - 10)
wenzelm@21755
   381
    else raise TERM ("mk_nibble", [])
wenzelm@21755
   382
  in Const ("List.nibble.Nibble" ^ s, nibbleT) end;
nipkow@17083
   383
wenzelm@21755
   384
fun dest_nibble t =
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   385
  let fun err () = raise TERM ("dest_nibble", [t]) in
wenzelm@21755
   386
    (case try (unprefix "List.nibble.Nibble" o fst o Term.dest_Const) t of
wenzelm@21755
   387
      NONE => err ()
wenzelm@21755
   388
    | SOME c =>
wenzelm@21755
   389
        if size c <> 1 then err ()
wenzelm@21755
   390
        else if "0" <= c andalso c <= "9" then ord c - ord "0"
wenzelm@21755
   391
        else if "A" <= c andalso c <= "F" then ord c - ord "A" + 10
wenzelm@21755
   392
        else err ())
wenzelm@21755
   393
  end;
berghofe@15062
   394
haftmann@21455
   395
haftmann@21455
   396
(* char *)
haftmann@21455
   397
haftmann@21455
   398
val charT = Type ("List.char", []);
haftmann@21455
   399
wenzelm@21755
   400
fun mk_char n =
wenzelm@21755
   401
  if 0 <= n andalso n <= 255 then
wenzelm@21755
   402
    Const ("List.char.Char", nibbleT --> nibbleT --> charT) $
wenzelm@21755
   403
      mk_nibble (n div 16) $ mk_nibble (n mod 16)
wenzelm@21755
   404
  else raise TERM ("mk_char", []);
haftmann@21455
   405
wenzelm@21755
   406
fun dest_char (Const ("List.char.Char", _) $ t $ u) =
wenzelm@21755
   407
      dest_nibble t * 16 + dest_nibble u
wenzelm@21755
   408
  | dest_char t = raise TERM ("dest_char", [t]);
haftmann@21455
   409
wenzelm@21755
   410
wenzelm@21755
   411
(* list *)
haftmann@21455
   412
wenzelm@21755
   413
fun listT T = Type ("List.list", [T]);
haftmann@21455
   414
wenzelm@21755
   415
fun mk_list T ts =
haftmann@21455
   416
  let
wenzelm@21755
   417
    val lT = listT T;
wenzelm@21755
   418
    val Nil = Const ("List.list.Nil", lT);
wenzelm@21755
   419
    fun Cons t u = Const ("List.list.Cons", T --> lT --> lT) $ t $ u;
wenzelm@21755
   420
  in fold_rev Cons ts Nil end;
wenzelm@21755
   421
wenzelm@21755
   422
fun dest_list (Const ("List.list.Nil", _)) = []
wenzelm@21755
   423
  | dest_list (Const ("List.list.Cons", _) $ t $ u) = t :: dest_list u
wenzelm@21755
   424
  | dest_list t = raise TERM ("dest_list", [t]);
haftmann@21455
   425
haftmann@21455
   426
haftmann@21455
   427
(* string *)
haftmann@21455
   428
haftmann@21820
   429
val stringT = Type ("List.string", []);
haftmann@21455
   430
wenzelm@21755
   431
val mk_string = mk_list charT o map (mk_char o ord) o explode;
wenzelm@21755
   432
val dest_string = implode o map (chr o dest_char) o dest_list;
haftmann@21455
   433
clasohm@923
   434
end;