author | nipkow |
Tue, 09 Aug 2005 11:44:38 +0200 | |
changeset 17040 | 6682c93b7d9f |
parent 16971 | 968adbfbf93b |
child 17083 | 051b0897bc98 |
permissions | -rw-r--r-- |
923 | 1 |
(* 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 |
8275 | 12 |
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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923 | 16 |
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 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 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: IntInf.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 -> IntInf.int |
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val dest_binum: term -> IntInf.int |
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val mk_bin: 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 |
15062 | 88 |
val dest_list: term -> term list |
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end; |
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2510 | 91 |
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structure HOLogic: HOLOGIC = |
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struct |
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(* HOL syntax *) |
923 | 96 |
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val typeS: sort = ["HOL.type"]; |
de0f4a63baa5
renamed class "term" to "type" (actually "HOL.type");
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parents:
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|
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val typeT = TypeInfer.anyT typeS; |
de0f4a63baa5
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parents:
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923 | 100 |
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(* bool and set *) |
923 | 102 |
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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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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 (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 *) |
2510 | 180 |
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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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191 |
(*destruct the application of a binary operator. The dummyT case is a crude |
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192 |
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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194 |
if c = c' andalso (T=T' orelse T=dummyT) then (t, u) |
3794 | 195 |
else raise TERM ("dest_bin " ^ c, [tm]) |
196 |
| dest_bin c _ tm = raise TERM ("dest_bin " ^ c, [tm]); |
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2510 | 197 |
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4571 | 199 |
(* unit *) |
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11604 | 201 |
val unitT = Type ("Product_Type.unit", []); |
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11604 | 203 |
fun is_unitT (Type ("Product_Type.unit", [])) = true |
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| is_unitT _ = false; |
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11604 | 206 |
val unit = Const ("Product_Type.Unity", unitT); |
4571 | 207 |
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11604 | 208 |
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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14048 | 219 |
fun pair_const T1 T2 = Const ("Pair", [T1, T2] ---> mk_prodT (T1, T2)); |
220 |
||
4571 | 221 |
fun mk_prod (t1, t2) = |
222 |
let val T1 = fastype_of t1 and T2 = fastype_of t2 in |
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14048 | 223 |
pair_const T1 T2 $ t1 $ t2 |
4571 | 224 |
end; |
225 |
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226 |
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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||
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berghofe
parents:
4571
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changeset
|
239 |
(*Maps the type T1 * ... * Tn to [T1, ..., Tn], however nested*) |
84b00be693b4
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berghofe
parents:
4571
diff
changeset
|
240 |
fun prodT_factors (Type ("*", [T1, T2])) = prodT_factors T1 @ prodT_factors T2 |
84b00be693b4
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berghofe
parents:
4571
diff
changeset
|
241 |
| prodT_factors T = [T]; |
84b00be693b4
Moved most of the Prod_Syntax - stuff to HOLogic.
berghofe
parents:
4571
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changeset
|
242 |
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16971 | 243 |
fun split_const (Ta, Tb, Tc) = |
5096
84b00be693b4
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berghofe
parents:
4571
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changeset
|
244 |
Const ("split", [[Ta, Tb] ---> Tc, mk_prodT (Ta, Tb)] ---> Tc); |
84b00be693b4
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berghofe
parents:
4571
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changeset
|
245 |
|
84b00be693b4
Moved most of the Prod_Syntax - stuff to HOLogic.
berghofe
parents:
4571
diff
changeset
|
246 |
(*Makes a nested tuple from a list, following the product type structure*) |
16971 | 247 |
fun mk_tuple (Type ("*", [T1, T2])) tms = |
248 |
mk_prod (mk_tuple T1 tms, |
|
15570 | 249 |
mk_tuple T2 (Library.drop (length (prodT_factors T1), tms))) |
5096
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Moved most of the Prod_Syntax - stuff to HOLogic.
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parents:
4571
diff
changeset
|
250 |
| mk_tuple T (t::_) = t; |
4571 | 251 |
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5207 | 252 |
|
253 |
(* nat *) |
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254 |
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255 |
val natT = Type ("nat", []); |
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256 |
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257 |
val zero = Const ("0", natT); |
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258 |
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259 |
fun is_zero (Const ("0", _)) = true |
|
260 |
| is_zero _ = false; |
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261 |
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262 |
fun mk_Suc t = Const ("Suc", natT --> natT) $ t; |
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263 |
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264 |
fun dest_Suc (Const ("Suc", _) $ t) = t |
|
265 |
| dest_Suc t = raise TERM ("dest_Suc", [t]); |
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266 |
||
267 |
fun mk_nat 0 = zero |
|
268 |
| mk_nat n = mk_Suc (mk_nat (n - 1)); |
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269 |
||
270 |
fun dest_nat (Const ("0", _)) = 0 |
|
271 |
| dest_nat (Const ("Suc", _) $ t) = dest_nat t + 1 |
|
272 |
| dest_nat t = raise TERM ("dest_nat", [t]); |
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273 |
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274 |
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7073 | 275 |
(* binary numerals *) |
276 |
||
277 |
val binT = Type ("Numeral.bin", []); |
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278 |
||
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replaced bool by a new datatype "bit" for binary numerals
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parents:
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changeset
|
279 |
val bitT = Type ("Numeral.bit", []); |
8ccdc8bc66a2
replaced bool by a new datatype "bit" for binary numerals
paulson
parents:
15595
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changeset
|
280 |
|
8ccdc8bc66a2
replaced bool by a new datatype "bit" for binary numerals
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parents:
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changeset
|
281 |
val B0_const = Const ("Numeral.bit.B0", bitT); |
8ccdc8bc66a2
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parents:
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changeset
|
282 |
val B1_const = Const ("Numeral.bit.B1", bitT); |
8ccdc8bc66a2
replaced bool by a new datatype "bit" for binary numerals
paulson
parents:
15595
diff
changeset
|
283 |
|
15013 | 284 |
val pls_const = Const ("Numeral.Pls", binT) |
285 |
and min_const = Const ("Numeral.Min", binT) |
|
15620
8ccdc8bc66a2
replaced bool by a new datatype "bit" for binary numerals
paulson
parents:
15595
diff
changeset
|
286 |
and bit_const = Const ("Numeral.Bit", [binT, bitT] ---> binT); |
8768 | 287 |
|
288 |
fun number_of_const T = Const ("Numeral.number_of", binT --> T); |
|
8739 | 289 |
|
16971 | 290 |
fun int_of [] = 0 |
15965
f422f8283491
Use of IntInf.int instead of int in most numeric simprocs; avoids
paulson
parents:
15945
diff
changeset
|
291 |
| int_of (b :: bs) = IntInf.fromInt b + (2 * int_of bs); |
15595 | 292 |
|
15620
8ccdc8bc66a2
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parents:
15595
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changeset
|
293 |
(*When called from a print translation, the Numeral qualifier will probably have |
8ccdc8bc66a2
replaced bool by a new datatype "bit" for binary numerals
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parents:
15595
diff
changeset
|
294 |
been removed from Bit, bin.B0, etc.*) |
8ccdc8bc66a2
replaced bool by a new datatype "bit" for binary numerals
paulson
parents:
15595
diff
changeset
|
295 |
fun dest_bit (Const ("Numeral.bit.B0", _)) = 0 |
8ccdc8bc66a2
replaced bool by a new datatype "bit" for binary numerals
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parents:
15595
diff
changeset
|
296 |
| dest_bit (Const ("Numeral.bit.B1", _)) = 1 |
8ccdc8bc66a2
replaced bool by a new datatype "bit" for binary numerals
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parents:
15595
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changeset
|
297 |
| dest_bit (Const ("bit.B0", _)) = 0 |
8ccdc8bc66a2
replaced bool by a new datatype "bit" for binary numerals
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parents:
15595
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changeset
|
298 |
| dest_bit (Const ("bit.B1", _)) = 1 |
7548
9e29a3af64ab
ROOT: Integ/bin_simprocs.ML now loaded in Integ/Bin.ML
nipkow
parents:
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diff
changeset
|
299 |
| dest_bit t = raise TERM("dest_bit", [t]); |
9e29a3af64ab
ROOT: Integ/bin_simprocs.ML now loaded in Integ/Bin.ML
nipkow
parents:
7163
diff
changeset
|
300 |
|
15013 | 301 |
fun bin_of (Const ("Numeral.Pls", _)) = [] |
302 |
| bin_of (Const ("Numeral.Min", _)) = [~1] |
|
303 |
| bin_of (Const ("Numeral.Bit", _) $ bs $ b) = dest_bit b :: bin_of bs |
|
15620
8ccdc8bc66a2
replaced bool by a new datatype "bit" for binary numerals
paulson
parents:
15595
diff
changeset
|
304 |
| bin_of (Const ("Bit", _) $ bs $ b) = dest_bit b :: bin_of bs |
7548
9e29a3af64ab
ROOT: Integ/bin_simprocs.ML now loaded in Integ/Bin.ML
nipkow
parents:
7163
diff
changeset
|
305 |
| bin_of t = raise TERM("bin_of", [t]); |
9e29a3af64ab
ROOT: Integ/bin_simprocs.ML now loaded in Integ/Bin.ML
nipkow
parents:
7163
diff
changeset
|
306 |
|
9e29a3af64ab
ROOT: Integ/bin_simprocs.ML now loaded in Integ/Bin.ML
nipkow
parents:
7163
diff
changeset
|
307 |
val dest_binum = int_of o bin_of; |
9e29a3af64ab
ROOT: Integ/bin_simprocs.ML now loaded in Integ/Bin.ML
nipkow
parents:
7163
diff
changeset
|
308 |
|
15620
8ccdc8bc66a2
replaced bool by a new datatype "bit" for binary numerals
paulson
parents:
15595
diff
changeset
|
309 |
fun mk_bit 0 = B0_const |
8ccdc8bc66a2
replaced bool by a new datatype "bit" for binary numerals
paulson
parents:
15595
diff
changeset
|
310 |
| mk_bit 1 = B1_const |
10693 | 311 |
| mk_bit _ = sys_error "mk_bit"; |
312 |
||
15965
f422f8283491
Use of IntInf.int instead of int in most numeric simprocs; avoids
paulson
parents:
15945
diff
changeset
|
313 |
fun mk_bin n = |
16971 | 314 |
let |
315 |
fun mk_bit n = if n = 0 then B0_const else B1_const; |
|
316 |
||
317 |
fun bin_of n = |
|
318 |
if n = 0 then pls_const |
|
319 |
else if n = ~1 then min_const |
|
320 |
else |
|
321 |
let |
|
322 |
(*val (q,r) = IntInf.divMod (n, 2): doesn't work in SML 110.0.7, |
|
323 |
but in newer versions! FIXME: put this back after new SML released!*) |
|
324 |
val q = IntInf.div (n, 2); |
|
325 |
val r = IntInf.mod (n, 2); |
|
326 |
in bit_const $ bin_of q $ mk_bit r end; |
|
327 |
in bin_of n end; |
|
13755 | 328 |
|
15620
8ccdc8bc66a2
replaced bool by a new datatype "bit" for binary numerals
paulson
parents:
15595
diff
changeset
|
329 |
|
13755 | 330 |
(* int *) |
331 |
||
332 |
val intT = Type ("IntDef.int", []); |
|
333 |
||
14103
afd168fdcd3a
mk_int now produces specific constants for 0 and 1.
berghofe
parents:
14048
diff
changeset
|
334 |
fun mk_int 0 = Const ("0", intT) |
afd168fdcd3a
mk_int now produces specific constants for 0 and 1.
berghofe
parents:
14048
diff
changeset
|
335 |
| mk_int 1 = Const ("1", intT) |
afd168fdcd3a
mk_int now produces specific constants for 0 and 1.
berghofe
parents:
14048
diff
changeset
|
336 |
| mk_int i = number_of_const intT $ mk_bin i; |
13755 | 337 |
|
338 |
||
339 |
(* real *) |
|
340 |
||
16971 | 341 |
val realT = Type ("RealDef.real", []); |
13755 | 342 |
|
343 |
||
344 |
(* list *) |
|
345 |
||
346 |
fun mk_list f T [] = Const ("List.list.Nil", Type ("List.list", [T])) |
|
347 |
| mk_list f T (x :: xs) = Const ("List.list.Cons", |
|
348 |
T --> Type ("List.list", [T]) --> Type ("List.list", [T])) $ f x $ |
|
349 |
mk_list f T xs; |
|
350 |
||
15062 | 351 |
fun dest_list (Const ("List.list.Nil", _)) = [] |
352 |
| dest_list (Const ("List.list.Cons", _) $ x $ xs) = x :: dest_list xs |
|
353 |
| dest_list t = raise TERM ("dest_list", [t]); |
|
354 |
||
923 | 355 |
end; |