(* Title: HOL/hologic.ML
ID: $Id$
Author: Lawrence C Paulson and Markus Wenzel
Abstract syntax operations for HOL.
*)
signature HOLOGIC =
sig
val termC: class
val termS: sort
val termTVar: typ
val boolT: typ
val false_const: term
val true_const: term
val mk_setT: typ -> typ
val dest_setT: typ -> typ
val mk_Trueprop: term -> term
val dest_Trueprop: term -> term
val conj: term
val disj: term
val imp: term
val dest_imp: term -> term * term
val eq_const: typ -> term
val all_const: typ -> term
val exists_const: typ -> term
val Collect_const: typ -> term
val mk_eq: term * term -> term
val dest_eq: term -> term * term
val mk_all: string * typ * term -> term
val mk_exists: string * typ * term -> term
val mk_Collect: string * typ * term -> term
val mk_mem: term * term -> term
val dest_mem: term -> term * term
val mk_binop: string -> term * term -> term
val mk_binrel: string -> term * term -> term
val dest_bin: string -> typ -> term -> term * term
val unitT: typ
val unit: term
val is_unit: term -> bool
val mk_prodT: typ * typ -> typ
val dest_prodT: typ -> typ * typ
val mk_prod: term * term -> term
val dest_prod: term -> term * term
val mk_fst: term -> term
val mk_snd: term -> term
val prodT_factors: typ -> typ list
val split_const: typ * typ * typ -> term
val mk_tuple: typ -> term list -> term
val natT: typ
val zero: term
val is_zero: term -> bool
val mk_Suc: term -> term
val dest_Suc: term -> term
val mk_nat: int -> term
val dest_nat: term -> int
val intT: typ
val realT: typ
val binT: typ
val pls_const: term
val min_const: term
val bit_const: term
val int_of: int list -> int
val dest_binum: term -> int
end;
structure HOLogic: HOLOGIC =
struct
(* basics *)
val termC: class = "term";
val termS: sort = [termC];
val termTVar = TVar (("'a", 0), termS);
(* bool and set *)
val boolT = Type ("bool", []);
val true_const = Const ("True", boolT)
and false_const = Const ("False", boolT);
fun mk_setT T = Type ("set", [T]);
fun dest_setT (Type ("set", [T])) = T
| dest_setT T = raise TYPE ("dest_setT: set type expected", [T], []);
(* logic *)
val Trueprop = Const ("Trueprop", boolT --> propT);
fun mk_Trueprop P = Trueprop $ P;
fun dest_Trueprop (Const ("Trueprop", _) $ P) = P
| dest_Trueprop t = raise TERM ("dest_Trueprop", [t]);
val conj = Const ("op &", [boolT, boolT] ---> boolT)
and disj = Const ("op |", [boolT, boolT] ---> boolT)
and imp = Const ("op -->", [boolT, boolT] ---> boolT);
fun dest_imp (Const("op -->",_) $ A $ B) = (A, B)
| dest_imp t = raise TERM ("dest_imp", [t]);
fun eq_const T = Const ("op =", [T, T] ---> boolT);
fun mk_eq (t, u) = eq_const (fastype_of t) $ t $ u;
fun dest_eq (Const ("op =", _) $ lhs $ rhs) = (lhs, rhs)
| dest_eq t = raise TERM ("dest_eq", [t])
fun all_const T = Const ("All", [T --> boolT] ---> boolT);
fun mk_all (x, T, P) = all_const T $ absfree (x, T, P);
fun exists_const T = Const ("Ex", [T --> boolT] ---> boolT);
fun mk_exists (x, T, P) = exists_const T $ absfree (x, T, P);
fun Collect_const T = Const ("Collect", [T --> boolT] ---> mk_setT T);
fun mk_Collect (a, T, t) = Collect_const T $ absfree (a, T, t);
fun mk_mem (x, A) =
let val setT = fastype_of A in
Const ("op :", [dest_setT setT, setT] ---> boolT) $ x $ A
end;
fun dest_mem (Const ("op :", _) $ x $ A) = (x, A)
| dest_mem t = raise TERM ("dest_mem", [t]);
(* binary oprations and relations *)
fun mk_binop c (t, u) =
let val T = fastype_of t in
Const (c, [T, T] ---> T) $ t $ u
end;
fun mk_binrel c (t, u) =
let val T = fastype_of t in
Const (c, [T, T] ---> boolT) $ t $ u
end;
fun dest_bin c T (tm as Const (c', Type ("fun", [T', _])) $ t $ u) =
if c = c' andalso T = T' then (t, u)
else raise TERM ("dest_bin " ^ c, [tm])
| dest_bin c _ tm = raise TERM ("dest_bin " ^ c, [tm]);
(* unit *)
val unitT = Type ("unit", []);
val unit = Const ("()", unitT);
fun is_unit (Const ("()", _)) = true
| is_unit _ = false;
(* prod *)
fun mk_prodT (T1, T2) = Type ("*", [T1, T2]);
fun dest_prodT (Type ("*", [T1, T2])) = (T1, T2)
| dest_prodT T = raise TYPE ("dest_prodT", [T], []);
fun mk_prod (t1, t2) =
let val T1 = fastype_of t1 and T2 = fastype_of t2 in
Const ("Pair", [T1, T2] ---> mk_prodT (T1, T2)) $ t1 $ t2
end;
fun dest_prod (Const ("Pair", _) $ t1 $ t2) = (t1, t2)
| dest_prod t = raise TERM ("dest_prod", [t]);
fun mk_fst p =
let val pT = fastype_of p in
Const ("fst", pT --> fst (dest_prodT pT)) $ p
end;
fun mk_snd p =
let val pT = fastype_of p in
Const ("snd", pT --> snd (dest_prodT pT)) $ p
end;
(*Maps the type T1 * ... * Tn to [T1, ..., Tn], however nested*)
fun prodT_factors (Type ("*", [T1, T2])) = prodT_factors T1 @ prodT_factors T2
| prodT_factors T = [T];
fun split_const (Ta, Tb, Tc) =
Const ("split", [[Ta, Tb] ---> Tc, mk_prodT (Ta, Tb)] ---> Tc);
(*Makes a nested tuple from a list, following the product type structure*)
fun mk_tuple (Type ("*", [T1, T2])) tms =
mk_prod (mk_tuple T1 tms,
mk_tuple T2 (drop (length (prodT_factors T1), tms)))
| mk_tuple T (t::_) = t;
(* nat *)
val natT = Type ("nat", []);
val zero = Const ("0", natT);
fun is_zero (Const ("0", _)) = true
| is_zero _ = false;
fun mk_Suc t = Const ("Suc", natT --> natT) $ t;
fun dest_Suc (Const ("Suc", _) $ t) = t
| dest_Suc t = raise TERM ("dest_Suc", [t]);
fun mk_nat 0 = zero
| mk_nat n = mk_Suc (mk_nat (n - 1));
fun dest_nat (Const ("0", _)) = 0
| dest_nat (Const ("Suc", _) $ t) = dest_nat t + 1
| dest_nat t = raise TERM ("dest_nat", [t]);
val intT = Type ("IntDef.int", []);
val realT = Type("RealDef.real",[]);
(* binary numerals *)
val binT = Type ("Numeral.bin", []);
val pls_const = Const ("Numeral.bin.Pls", binT)
and min_const = Const ("Numeral.bin.Min", binT)
and bit_const = Const ("Numeral.bin.Bit", [binT, boolT] ---> binT);
fun int_of [] = 0
| int_of (b :: bs) = b + 2 * int_of bs;
fun dest_bit (Const ("False", _)) = 0
| dest_bit (Const ("True", _)) = 1
| dest_bit t = raise TERM("dest_bit", [t]);
fun bin_of (Const ("Numeral.bin.Pls", _)) = []
| bin_of (Const ("Numeral.bin.Min", _)) = [~1]
| bin_of (Const ("Numeral.bin.Bit", _) $ bs $ b) = dest_bit b :: bin_of bs
| bin_of t = raise TERM("bin_of", [t]);
val dest_binum = int_of o bin_of;
end;