src/HOL/hologic.ML
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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 termC: class
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  val termS: sort
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  val termTVar: typ
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  val boolT: typ
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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 dest_imp: term -> term * term
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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 Collect_const: typ -> term
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  val mk_eq: term * term -> term
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  val mk_all: string * typ * 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 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 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 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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end;
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structure HOLogic: HOLOGIC =
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struct
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(* basics *)
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val termC: class = "term";
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val termS: sort = [termC];
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val termTVar = TVar (("'a", 0), termS);
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(* bool and set *)
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val boolT = Type ("bool", []);
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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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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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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 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 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 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 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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(* binary oprations 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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fun dest_bin c T (tm as Const (c', Type ("fun", [T', _])) $ t $ u) =
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      if c = c' andalso T = T' 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 ("unit", []);
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val unit = Const ("()", unitT);
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fun is_unit (Const ("()", _)) = 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 mk_prod (t1, t2) =
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  let val T1 = fastype_of t1 and T2 = fastype_of t2 in
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    Const ("Pair", [T1, T2] ---> mk_prodT (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 (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 ("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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end;