src/HOL/hologic.ML
author paulson
Mon, 09 May 2005 16:40:11 +0200
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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 read_cterm: Sign.sg -> string -> cterm
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  val boolN: string
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  val boolT: typ
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  val false_const: term
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  val true_const: term
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  val not_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 mk_Trueprop: term -> term
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  val dest_Trueprop: term -> term
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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 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 all_const: typ -> term
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  val exists_const: typ -> 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_eq: term * term -> term
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  val dest_eq: term -> term * 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 mk_exists: string * typ * term -> 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_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 prodT_factors: typ -> typ list
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  val split_const: typ * typ * typ -> term
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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 mk_nat: int -> term
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  val dest_nat: term -> int
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  val intT: typ
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  val mk_int: int -> term
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  val realT: typ
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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 binT: 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 number_of_const: typ -> term
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  val int_of: int list -> int
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  val intinf_of: int list -> IntInf.int
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  val dest_binum: term -> int
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  val mk_bin: int -> term
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  val mk_bin_from_intinf: IntInf.int -> term
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  val bin_of : term -> int list
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  val mk_list: ('a -> term) -> typ -> 'a list -> term
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  val dest_list: term -> term list
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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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fun read_cterm sg s = Thm.read_cterm sg (s, typeT);
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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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val not_const = Const ("Not", boolT --> 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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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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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 (vs,x) = foldr (fn ((x, T), P) => all_const T $ Abs (x, T, P)) x vs;
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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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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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(*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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fun split_const (Ta, Tb, Tc) = 
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    Const ("split", [[Ta, Tb] ---> Tc, mk_prodT (Ta, Tb)] ---> Tc);
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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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(* proper tuples *)
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local  (*currently unused*)
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fun mk_tupleT Ts = foldr mk_prodT unitT Ts;
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fun dest_tupleT (Type ("Product_Type.unit", [])) = []
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  | dest_tupleT (Type ("*", [T, U])) = T :: dest_tupleT U
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  | dest_tupleT T = raise TYPE ("dest_tupleT", [T], []);
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fun mk_tuple ts = foldr mk_prod unit ts;
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fun dest_tuple (Const ("Product_Type.Unity", _)) = []
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  | dest_tuple (Const ("Pair", _) $ t $ u) = t :: dest_tuple u
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  | dest_tuple t = raise TERM ("dest_tuple", [t]);
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in val _ = unit end;
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(* nat *)
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val natT = Type ("nat", []);
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val zero = Const ("0", natT);
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fun is_zero (Const ("0", _)) = 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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fun mk_nat 0 = zero
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  | mk_nat n = mk_Suc (mk_nat (n - 1));
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fun dest_nat (Const ("0", _)) = 0
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  | dest_nat (Const ("Suc", _) $ t) = dest_nat t + 1
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  | dest_nat t = raise TERM ("dest_nat", [t]);
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(* binary numerals *)
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val binT = Type ("Numeral.bin", []);
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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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val pls_const = Const ("Numeral.Pls", binT)
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and min_const = Const ("Numeral.Min", binT)
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and bit_const = Const ("Numeral.Bit", [binT, bitT] ---> binT);
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fun number_of_const T = Const ("Numeral.number_of", binT --> T);
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fun int_of [] = 0
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  | int_of (b :: bs) = b + 2 * int_of bs;
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fun intinf_of [] = IntInf.fromInt 0
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  | intinf_of (b :: bs) = IntInf.+ (IntInf.fromInt b, IntInf.*(IntInf.fromInt 2, intinf_of bs));
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(*When called from a print translation, the Numeral qualifier will probably have
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  been removed from Bit, bin.B0, etc.*)
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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 (Const ("bit.B0", _)) = 0
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  | dest_bit (Const ("bit.B1", _)) = 1
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  | dest_bit t = raise TERM("dest_bit", [t]);
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fun bin_of (Const ("Numeral.Pls", _)) = []
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  | bin_of (Const ("Numeral.Min", _)) = [~1]
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  | bin_of (Const ("Numeral.Bit", _) $ bs $ b) = dest_bit b :: bin_of bs
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  | bin_of (Const ("Bit", _) $ bs $ b) = dest_bit b :: bin_of bs
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  | bin_of t = raise TERM("bin_of", [t]);
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val dest_binum = int_of o bin_of;
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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 _ = sys_error "mk_bit";
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fun mk_bin_from_intinf  n =
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    let
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	val zero = IntInf.fromInt 0
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	val minus_one = IntInf.fromInt ~1
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	val two = IntInf.fromInt 2
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	fun mk_bit n = if n = zero then B0_const else B1_const
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	fun bin_of n = 
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	    if n = zero then pls_const
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	    else if n = minus_one then min_const
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	    else 
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		let 
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		    (*val (q,r) = IntInf.divMod (n, two): doesn't work in SML 10.0.7, but in newer versions!*)
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	            val q = IntInf.div (n, two)
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		    val r = IntInf.mod (n, two)
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		in
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		    bit_const $ bin_of q $ mk_bit r
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		end
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    in 
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	bin_of n
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    end
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val mk_bin = mk_bin_from_intinf o IntInf.fromInt;
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(* int *)
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val intT = Type ("IntDef.int", []);
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fun mk_int 0 = Const ("0", intT)
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  | mk_int 1 = Const ("1", intT)
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  | mk_int i = number_of_const intT $ mk_bin i;
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(* real *)
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val realT = Type("RealDef.real", []);
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   381
(* list *)
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fun mk_list f T [] = Const ("List.list.Nil", Type ("List.list", [T]))
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  | mk_list f T (x :: xs) = Const ("List.list.Cons",
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      T --> Type ("List.list", [T]) --> Type ("List.list", [T])) $ f x $
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        mk_list f T xs;
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fun dest_list (Const ("List.list.Nil", _)) = []
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  | dest_list (Const ("List.list.Cons", _) $ x $ xs) = x :: dest_list xs
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  | dest_list t = raise TERM ("dest_list", [t]);
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end;