(* Title: HOL/hologic.ML
ID: $Id$
Author: Lawrence C Paulson and Markus Wenzel
Abstract syntax operations for HOL.
*)
signature HOLOGIC =
sig
val typeS: sort
val typeT: typ
val read_cterm: Sign.sg -> string -> cterm
val boolN: string
val boolT: typ
val false_const: term
val true_const: term
val not_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 Not: term
val mk_conj: term * term -> term
val mk_disj: term * term -> term
val mk_imp: term * term -> term
val dest_conj: term -> term list
val dest_imp: term -> term * term
val dest_not: term -> term
val dest_concls: term -> term list
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 list_all: (string * typ) list * 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_UNIV: typ -> 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 is_unitT: typ -> bool
val unit: term
val is_unit: term -> bool
val mk_prodT: typ * typ -> typ
val dest_prodT: typ -> typ * typ
val pair_const: typ -> typ -> term
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 mk_int: int -> term
val realT: typ
val bitT: typ
val B0_const: term
val B1_const: term
val binT: typ
val pls_const: term
val min_const: term
val bit_const: term
val number_of_const: typ -> term
val int_of: int list -> int
val intinf_of: int list -> IntInf.int
val dest_binum: term -> int
val mk_bin: int -> term
val mk_bin_from_intinf: IntInf.int -> term
val bin_of : term -> int list
val mk_list: ('a -> term) -> typ -> 'a list -> term
val dest_list: term -> term list
end;
structure HOLogic: HOLOGIC =
struct
(* HOL syntax *)
val typeS: sort = ["HOL.type"];
val typeT = TypeInfer.anyT typeS;
fun read_cterm sg s = Thm.read_cterm sg (s, typeT);
(* bool and set *)
val boolN = "bool";
val boolT = Type (boolN, []);
val true_const = Const ("True", boolT);
val false_const = Const ("False", boolT);
val not_const = Const ("Not", boolT --> 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)
and Not = Const ("Not", boolT --> boolT);
fun mk_conj (t1, t2) = conj $ t1 $ t2
and mk_disj (t1, t2) = disj $ t1 $ t2
and mk_imp (t1, t2) = imp $ t1 $ t2;
fun dest_conj (Const ("op &", _) $ t $ t') = t :: dest_conj t'
| dest_conj t = [t];
fun dest_imp (Const("op -->",_) $ A $ B) = (A, B)
| dest_imp t = raise TERM ("dest_imp", [t]);
fun dest_not (Const ("Not", _) $ t) = t
| dest_not t = raise TERM ("dest_not", [t]);
fun imp_concl_of t = imp_concl_of (#2 (dest_imp t)) handle TERM _ => t;
val dest_concls = map imp_concl_of o dest_conj o dest_Trueprop;
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 list_all (vs,x) = foldr (fn ((x, T), P) => all_const T $ Abs (x, T, P)) x vs;
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]);
fun mk_UNIV T = Const ("UNIV", mk_setT T);
(* binary operations 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;
(*destruct the application of a binary operator. The dummyT case is a crude
way of handling polymorphic operators.*)
fun dest_bin c T (tm as Const (c', Type ("fun", [T', _])) $ t $ u) =
if c = c' andalso (T=T' orelse T=dummyT) then (t, u)
else raise TERM ("dest_bin " ^ c, [tm])
| dest_bin c _ tm = raise TERM ("dest_bin " ^ c, [tm]);
(* unit *)
val unitT = Type ("Product_Type.unit", []);
fun is_unitT (Type ("Product_Type.unit", [])) = true
| is_unitT _ = false;
val unit = Const ("Product_Type.Unity", unitT);
fun is_unit (Const ("Product_Type.Unity", _)) = 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 pair_const T1 T2 = Const ("Pair", [T1, T2] ---> mk_prodT (T1, T2));
fun mk_prod (t1, t2) =
let val T1 = fastype_of t1 and T2 = fastype_of t2 in
pair_const 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 (Library.drop (length (prodT_factors T1), tms)))
| mk_tuple T (t::_) = t;
(* proper tuples *)
local (*currently unused*)
fun mk_tupleT Ts = foldr mk_prodT unitT Ts;
fun dest_tupleT (Type ("Product_Type.unit", [])) = []
| dest_tupleT (Type ("*", [T, U])) = T :: dest_tupleT U
| dest_tupleT T = raise TYPE ("dest_tupleT", [T], []);
fun mk_tuple ts = foldr mk_prod unit ts;
fun dest_tuple (Const ("Product_Type.Unity", _)) = []
| dest_tuple (Const ("Pair", _) $ t $ u) = t :: dest_tuple u
| dest_tuple t = raise TERM ("dest_tuple", [t]);
in val _ = unit end;
(* 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]);
(* binary numerals *)
val binT = Type ("Numeral.bin", []);
val bitT = Type ("Numeral.bit", []);
val B0_const = Const ("Numeral.bit.B0", bitT);
val B1_const = Const ("Numeral.bit.B1", bitT);
val pls_const = Const ("Numeral.Pls", binT)
and min_const = Const ("Numeral.Min", binT)
and bit_const = Const ("Numeral.Bit", [binT, bitT] ---> binT);
fun number_of_const T = Const ("Numeral.number_of", binT --> T);
fun int_of [] = 0
| int_of (b :: bs) = b + 2 * int_of bs;
fun intinf_of [] = IntInf.fromInt 0
| intinf_of (b :: bs) = IntInf.+ (IntInf.fromInt b, IntInf.*(IntInf.fromInt 2, intinf_of bs));
(*When called from a print translation, the Numeral qualifier will probably have
been removed from Bit, bin.B0, etc.*)
fun dest_bit (Const ("Numeral.bit.B0", _)) = 0
| dest_bit (Const ("Numeral.bit.B1", _)) = 1
| dest_bit (Const ("bit.B0", _)) = 0
| dest_bit (Const ("bit.B1", _)) = 1
| dest_bit t = raise TERM("dest_bit", [t]);
fun bin_of (Const ("Numeral.Pls", _)) = []
| bin_of (Const ("Numeral.Min", _)) = [~1]
| bin_of (Const ("Numeral.Bit", _) $ bs $ b) = dest_bit b :: bin_of bs
| bin_of (Const ("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;
fun mk_bit 0 = B0_const
| mk_bit 1 = B1_const
| mk_bit _ = sys_error "mk_bit";
fun mk_bin_from_intinf n =
let
val zero = IntInf.fromInt 0
val minus_one = IntInf.fromInt ~1
val two = IntInf.fromInt 2
fun mk_bit n = if n = zero then B0_const else B1_const
fun bin_of n =
if n = zero then pls_const
else if n = minus_one then min_const
else
let
(*val (q,r) = IntInf.divMod (n, two): doesn't work in SML 10.0.7, but in newer versions!*)
val q = IntInf.div (n, two)
val r = IntInf.mod (n, two)
in
bit_const $ bin_of q $ mk_bit r
end
in
bin_of n
end
val mk_bin = mk_bin_from_intinf o IntInf.fromInt;
(* int *)
val intT = Type ("IntDef.int", []);
fun mk_int 0 = Const ("0", intT)
| mk_int 1 = Const ("1", intT)
| mk_int i = number_of_const intT $ mk_bin i;
(* real *)
val realT = Type("RealDef.real", []);
(* list *)
fun mk_list f T [] = Const ("List.list.Nil", Type ("List.list", [T]))
| mk_list f T (x :: xs) = Const ("List.list.Cons",
T --> Type ("List.list", [T]) --> Type ("List.list", [T])) $ f x $
mk_list f T xs;
fun dest_list (Const ("List.list.Nil", _)) = []
| dest_list (Const ("List.list.Cons", _) $ x $ xs) = x :: dest_list xs
| dest_list t = raise TERM ("dest_list", [t]);
end;