author | paulson |
Fri, 29 Oct 2004 15:16:02 +0200 | |
changeset 15270 | 8b3f707a78a7 |
parent 15151 | 429666b09783 |
child 15570 | 8d8c70b41bab |
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 |
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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_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 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 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 dest_binum: term -> int |
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val mk_bin: int -> term |
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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_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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val list_all = foldr (fn ((x, T), P) => all_const T $ Abs (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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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]) |
187 |
| 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) = |
213 |
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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230 |
(*Maps the type T1 * ... * Tn to [T1, ..., Tn], however nested*) |
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231 |
fun prodT_factors (Type ("*", [T1, T2])) = prodT_factors T1 @ prodT_factors T2 |
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232 |
| prodT_factors T = [T]; |
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233 |
|
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234 |
fun split_const (Ta, Tb, Tc) = |
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235 |
Const ("split", [[Ta, Tb] ---> Tc, mk_prodT (Ta, Tb)] ---> Tc); |
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236 |
|
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237 |
(*Makes a nested tuple from a list, following the product type structure*) |
84b00be693b4
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238 |
fun mk_tuple (Type ("*", [T1, T2])) tms = |
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239 |
mk_prod (mk_tuple T1 tms, |
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240 |
mk_tuple T2 (drop (length (prodT_factors T1), tms))) |
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241 |
| mk_tuple T (t::_) = t; |
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5207 | 243 |
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244 |
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9362 | 245 |
(* proper tuples *) |
246 |
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247 |
local (*currently unused*) |
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248 |
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249 |
fun mk_tupleT Ts = foldr mk_prodT (Ts, unitT); |
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250 |
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11604 | 251 |
fun dest_tupleT (Type ("Product_Type.unit", [])) = [] |
9362 | 252 |
| dest_tupleT (Type ("*", [T, U])) = T :: dest_tupleT U |
253 |
| dest_tupleT T = raise TYPE ("dest_tupleT", [T], []); |
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254 |
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255 |
fun mk_tuple ts = foldr mk_prod (ts, unit); |
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256 |
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11604 | 257 |
fun dest_tuple (Const ("Product_Type.Unity", _)) = [] |
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| dest_tuple (Const ("Pair", _) $ t $ u) = t :: dest_tuple u |
259 |
| dest_tuple t = raise TERM ("dest_tuple", [t]); |
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260 |
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261 |
in val _ = unit end; |
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262 |
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263 |
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5207 | 264 |
(* nat *) |
265 |
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266 |
val natT = Type ("nat", []); |
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267 |
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268 |
val zero = Const ("0", natT); |
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269 |
||
270 |
fun is_zero (Const ("0", _)) = true |
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271 |
| is_zero _ = false; |
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272 |
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273 |
fun mk_Suc t = Const ("Suc", natT --> natT) $ t; |
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274 |
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275 |
fun dest_Suc (Const ("Suc", _) $ t) = t |
|
276 |
| dest_Suc t = raise TERM ("dest_Suc", [t]); |
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277 |
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278 |
fun mk_nat 0 = zero |
|
279 |
| mk_nat n = mk_Suc (mk_nat (n - 1)); |
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280 |
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281 |
fun dest_nat (Const ("0", _)) = 0 |
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282 |
| dest_nat (Const ("Suc", _) $ t) = dest_nat t + 1 |
|
283 |
| dest_nat t = raise TERM ("dest_nat", [t]); |
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284 |
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285 |
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7073 | 286 |
(* binary numerals *) |
287 |
||
288 |
val binT = Type ("Numeral.bin", []); |
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289 |
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15013 | 290 |
val pls_const = Const ("Numeral.Pls", binT) |
291 |
and min_const = Const ("Numeral.Min", binT) |
|
292 |
and bit_const = Const ("Numeral.Bit", [binT, boolT] ---> binT); |
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8768 | 293 |
|
294 |
fun number_of_const T = Const ("Numeral.number_of", binT --> T); |
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8739 | 295 |
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7073 | 296 |
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fun int_of [] = 0 |
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298 |
| int_of (b :: bs) = b + 2 * int_of bs; |
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|
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300 |
fun dest_bit (Const ("False", _)) = 0 |
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301 |
| dest_bit (Const ("True", _)) = 1 |
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302 |
| dest_bit t = raise TERM("dest_bit", [t]); |
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303 |
|
15013 | 304 |
fun bin_of (Const ("Numeral.Pls", _)) = [] |
305 |
| bin_of (Const ("Numeral.Min", _)) = [~1] |
|
306 |
| bin_of (Const ("Numeral.Bit", _) $ bs $ b) = dest_bit b :: bin_of bs |
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307 |
| bin_of t = raise TERM("bin_of", [t]); |
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309 |
val dest_binum = int_of o bin_of; |
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310 |
|
10693 | 311 |
fun mk_bit 0 = false_const |
312 |
| mk_bit 1 = true_const |
|
313 |
| mk_bit _ = sys_error "mk_bit"; |
|
314 |
||
315 |
fun mk_bin n = |
|
316 |
let |
|
317 |
fun bin_of 0 = [] |
|
318 |
| bin_of ~1 = [~1] |
|
319 |
| bin_of n = (n mod 2) :: bin_of (n div 2); |
|
320 |
||
321 |
fun term_of [] = pls_const |
|
322 |
| term_of [~1] = min_const |
|
323 |
| term_of (b :: bs) = bit_const $ term_of bs $ mk_bit b; |
|
324 |
in term_of (bin_of n) end; |
|
325 |
||
13755 | 326 |
|
327 |
(* int *) |
|
328 |
||
329 |
val intT = Type ("IntDef.int", []); |
|
330 |
||
14103
afd168fdcd3a
mk_int now produces specific constants for 0 and 1.
berghofe
parents:
14048
diff
changeset
|
331 |
fun mk_int 0 = Const ("0", intT) |
afd168fdcd3a
mk_int now produces specific constants for 0 and 1.
berghofe
parents:
14048
diff
changeset
|
332 |
| mk_int 1 = Const ("1", intT) |
afd168fdcd3a
mk_int now produces specific constants for 0 and 1.
berghofe
parents:
14048
diff
changeset
|
333 |
| mk_int i = number_of_const intT $ mk_bin i; |
13755 | 334 |
|
335 |
||
336 |
(* real *) |
|
337 |
||
338 |
val realT = Type("RealDef.real", []); |
|
339 |
||
340 |
||
341 |
(* list *) |
|
342 |
||
343 |
fun mk_list f T [] = Const ("List.list.Nil", Type ("List.list", [T])) |
|
344 |
| mk_list f T (x :: xs) = Const ("List.list.Cons", |
|
345 |
T --> Type ("List.list", [T]) --> Type ("List.list", [T])) $ f x $ |
|
346 |
mk_list f T xs; |
|
347 |
||
15062 | 348 |
fun dest_list (Const ("List.list.Nil", _)) = [] |
349 |
| dest_list (Const ("List.list.Cons", _) $ x $ xs) = x :: dest_list xs |
|
350 |
| dest_list t = raise TERM ("dest_list", [t]); |
|
351 |
||
923 | 352 |
end; |