author | haftmann |
Mon, 27 Nov 2006 13:42:46 +0100 | |
changeset 21550 | 7cc49399929a |
parent 21473 | 02054bf31c0e |
child 21621 | f9fd69d96c4e |
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 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 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 Trueprop_conv: (cterm -> thm) -> cterm -> thm |
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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 class_eq: string |
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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 mk_split: 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 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_binum: IntInf.int -> term |
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val bin_of : term -> int list |
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val listT : typ -> typ |
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val mk_list: ('a -> term) -> typ -> 'a list -> term |
15062 | 91 |
val dest_list: term -> term list |
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val charT : typ |
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val int_of_nibble : string -> int |
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val mk_char : string -> term |
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val dest_char : term -> int option |
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val print_char : string -> string |
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val stringT : typ |
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val mk_string : string -> term |
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val print_string : string -> string |
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end; |
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structure HOLogic: HOLOGIC = |
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struct |
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(* HOL syntax *) |
923 | 107 |
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val typeS: sort = ["HOL.type"]; |
de0f4a63baa5
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109 |
val typeT = TypeInfer.anyT typeS; |
de0f4a63baa5
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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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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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fun Trueprop_conv conv ct = (case term_of ct of |
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Const ("Trueprop", _) $ _ => |
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let val (ct1, ct2) = Thm.dest_comb ct |
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in Thm.combination (Thm.reflexive ct1) (conv ct2) end |
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| _ => raise TERM ("Trueprop_conv", [])); |
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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 (xs, t) = fold_rev (fn (x, T) => fn P => all_const T $ Abs (x, T, P)) xs t; |
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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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val class_eq = "Code_Generator.eq"; |
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fun mk_mem (x, A) = |
187 |
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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||
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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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212 |
if c = c' andalso (T=T' orelse T=dummyT) then (t, u) |
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else raise TERM ("dest_bin " ^ c, [tm]) |
214 |
| dest_bin c _ tm = raise TERM ("dest_bin " ^ c, [tm]); |
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(* unit *) |
218 |
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11604 | 219 |
val unitT = Type ("Product_Type.unit", []); |
4571 | 220 |
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11604 | 221 |
fun is_unitT (Type ("Product_Type.unit", [])) = true |
9362 | 222 |
| is_unitT _ = false; |
223 |
||
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val unit = Const ("Product_Type.Unity", unitT); |
4571 | 225 |
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11604 | 226 |
fun is_unit (Const ("Product_Type.Unity", _)) = true |
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| is_unit _ = false; |
228 |
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229 |
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(* prod *) |
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232 |
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)); |
238 |
||
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fun mk_prod (t1, t2) = |
240 |
let val T1 = fastype_of t1 and T2 = fastype_of t2 in |
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14048 | 241 |
pair_const T1 T2 $ t1 $ t2 |
4571 | 242 |
end; |
243 |
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244 |
fun dest_prod (Const ("Pair", _) $ t1 $ t2) = (t1, t2) |
|
245 |
| dest_prod t = raise TERM ("dest_prod", [t]); |
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246 |
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247 |
fun mk_fst p = |
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248 |
let val pT = fastype_of p in |
|
249 |
Const ("fst", pT --> fst (dest_prodT pT)) $ p |
|
250 |
end; |
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251 |
||
252 |
fun mk_snd p = |
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253 |
let val pT = fastype_of p in |
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254 |
Const ("snd", pT --> snd (dest_prodT pT)) $ p |
|
255 |
end; |
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256 |
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18285 | 257 |
fun split_const (A, B, C) = |
258 |
Const ("split", (A --> B --> C) --> mk_prodT (A, B) --> C); |
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259 |
||
260 |
fun mk_split t = |
|
261 |
(case Term.fastype_of t of |
|
262 |
T as (Type ("fun", [A, Type ("fun", [B, C])])) => |
|
263 |
Const ("split", T --> mk_prodT (A, B) --> C) $ t |
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264 |
| _ => raise TERM ("mk_split: bad body type", [t])); |
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266 |
(*Maps the type T1 * ... * Tn to [T1, ..., Tn], however nested*) |
84b00be693b4
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parents:
4571
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changeset
|
267 |
fun prodT_factors (Type ("*", [T1, T2])) = prodT_factors T1 @ prodT_factors T2 |
84b00be693b4
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parents:
4571
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changeset
|
268 |
| prodT_factors T = [T]; |
84b00be693b4
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berghofe
parents:
4571
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changeset
|
269 |
|
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berghofe
parents:
4571
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changeset
|
270 |
(*Makes a nested tuple from a list, following the product type structure*) |
16971 | 271 |
fun mk_tuple (Type ("*", [T1, T2])) tms = |
272 |
mk_prod (mk_tuple T1 tms, |
|
15570 | 273 |
mk_tuple T2 (Library.drop (length (prodT_factors T1), tms))) |
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parents:
4571
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|
274 |
| mk_tuple T (t::_) = t; |
4571 | 275 |
|
5207 | 276 |
|
277 |
(* nat *) |
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278 |
||
279 |
val natT = Type ("nat", []); |
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280 |
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281 |
val zero = Const ("HOL.zero", natT); |
5207 | 282 |
|
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|
283 |
fun is_zero (Const ("HOL.zero", _)) = true |
5207 | 284 |
| is_zero _ = false; |
285 |
||
286 |
fun mk_Suc t = Const ("Suc", natT --> natT) $ t; |
|
287 |
||
288 |
fun dest_Suc (Const ("Suc", _) $ t) = t |
|
289 |
| dest_Suc t = raise TERM ("dest_Suc", [t]); |
|
290 |
||
291 |
fun mk_nat 0 = zero |
|
292 |
| mk_nat n = mk_Suc (mk_nat (n - 1)); |
|
293 |
||
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|
294 |
fun dest_nat (Const ("HOL.zero", _)) = 0 |
5207 | 295 |
| dest_nat (Const ("Suc", _) $ t) = dest_nat t + 1 |
296 |
| dest_nat t = raise TERM ("dest_nat", [t]); |
|
297 |
||
298 |
||
20485 | 299 |
(* binary numerals and int *) |
7073 | 300 |
|
20485 | 301 |
val intT = Type ("IntDef.int", []); |
15620
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parents:
15595
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changeset
|
302 |
val bitT = Type ("Numeral.bit", []); |
8ccdc8bc66a2
replaced bool by a new datatype "bit" for binary numerals
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|
303 |
|
8ccdc8bc66a2
replaced bool by a new datatype "bit" for binary numerals
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|
304 |
val B0_const = Const ("Numeral.bit.B0", bitT); |
8ccdc8bc66a2
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parents:
15595
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changeset
|
305 |
val B1_const = Const ("Numeral.bit.B1", bitT); |
8ccdc8bc66a2
replaced bool by a new datatype "bit" for binary numerals
paulson
parents:
15595
diff
changeset
|
306 |
|
20485 | 307 |
val pls_const = Const ("Numeral.Pls", intT) |
308 |
and min_const = Const ("Numeral.Min", intT) |
|
309 |
and bit_const = Const ("Numeral.Bit", [intT, bitT] ---> intT); |
|
8768 | 310 |
|
20485 | 311 |
fun number_of_const T = Const ("Numeral.number_of", intT --> T); |
8739 | 312 |
|
16971 | 313 |
fun int_of [] = 0 |
15965
f422f8283491
Use of IntInf.int instead of int in most numeric simprocs; avoids
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parents:
15945
diff
changeset
|
314 |
| int_of (b :: bs) = IntInf.fromInt b + (2 * int_of bs); |
15595 | 315 |
|
15620
8ccdc8bc66a2
replaced bool by a new datatype "bit" for binary numerals
paulson
parents:
15595
diff
changeset
|
316 |
(*When called from a print translation, the Numeral qualifier will probably have |
21473 | 317 |
been removed from Bit, bit.B0, etc.*) (* FIXME !? *) |
15620
8ccdc8bc66a2
replaced bool by a new datatype "bit" for binary numerals
paulson
parents:
15595
diff
changeset
|
318 |
fun dest_bit (Const ("Numeral.bit.B0", _)) = 0 |
8ccdc8bc66a2
replaced bool by a new datatype "bit" for binary numerals
paulson
parents:
15595
diff
changeset
|
319 |
| dest_bit (Const ("Numeral.bit.B1", _)) = 1 |
8ccdc8bc66a2
replaced bool by a new datatype "bit" for binary numerals
paulson
parents:
15595
diff
changeset
|
320 |
| dest_bit (Const ("bit.B0", _)) = 0 |
8ccdc8bc66a2
replaced bool by a new datatype "bit" for binary numerals
paulson
parents:
15595
diff
changeset
|
321 |
| dest_bit (Const ("bit.B1", _)) = 1 |
7548
9e29a3af64ab
ROOT: Integ/bin_simprocs.ML now loaded in Integ/Bin.ML
nipkow
parents:
7163
diff
changeset
|
322 |
| 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
|
323 |
|
15013 | 324 |
fun bin_of (Const ("Numeral.Pls", _)) = [] |
325 |
| bin_of (Const ("Numeral.Min", _)) = [~1] |
|
326 |
| 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
|
327 |
| 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
|
328 |
| 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
|
329 |
|
9e29a3af64ab
ROOT: Integ/bin_simprocs.ML now loaded in Integ/Bin.ML
nipkow
parents:
7163
diff
changeset
|
330 |
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
|
331 |
|
19481
a6205c6203ea
renamed HOLogic.mk_bin to mk_binum for consistency with dest_binum
paulson
parents:
18285
diff
changeset
|
332 |
fun mk_binum n = |
16971 | 333 |
let |
334 |
fun mk_bit n = if n = 0 then B0_const else B1_const; |
|
335 |
fun bin_of n = |
|
336 |
if n = 0 then pls_const |
|
337 |
else if n = ~1 then min_const |
|
338 |
else |
|
339 |
let |
|
20713
823967ef47f1
renamed 0 and 1 to HOL.zero and HOL.one respectivly; introduced corresponding syntactic classes
haftmann
parents:
20485
diff
changeset
|
340 |
val (q,r) = IntInf.divMod (n, 2); |
16971 | 341 |
in bit_const $ bin_of q $ mk_bit r end; |
342 |
in bin_of n end; |
|
13755 | 343 |
|
20713
823967ef47f1
renamed 0 and 1 to HOL.zero and HOL.one respectivly; introduced corresponding syntactic classes
haftmann
parents:
20485
diff
changeset
|
344 |
fun mk_int 0 = Const ("HOL.zero", intT) |
823967ef47f1
renamed 0 and 1 to HOL.zero and HOL.one respectivly; introduced corresponding syntactic classes
haftmann
parents:
20485
diff
changeset
|
345 |
| mk_int 1 = Const ("HOL.one", intT) |
19481
a6205c6203ea
renamed HOLogic.mk_bin to mk_binum for consistency with dest_binum
paulson
parents:
18285
diff
changeset
|
346 |
| mk_int i = number_of_const intT $ mk_binum i; |
13755 | 347 |
|
348 |
||
349 |
(* real *) |
|
350 |
||
16971 | 351 |
val realT = Type ("RealDef.real", []); |
13755 | 352 |
|
353 |
||
354 |
(* list *) |
|
355 |
||
21455 | 356 |
fun listT T = Type ("List.list", [T]); |
17083 | 357 |
|
358 |
fun mk_list f T [] = Const ("List.list.Nil", listT T) |
|
13755 | 359 |
| mk_list f T (x :: xs) = Const ("List.list.Cons", |
17083 | 360 |
T --> listT T --> listT T) $ f x $ |
13755 | 361 |
mk_list f T xs; |
362 |
||
15062 | 363 |
fun dest_list (Const ("List.list.Nil", _)) = [] |
364 |
| dest_list (Const ("List.list.Cons", _) $ x $ xs) = x :: dest_list xs |
|
365 |
| dest_list t = raise TERM ("dest_list", [t]); |
|
366 |
||
21455 | 367 |
|
368 |
(* char *) |
|
369 |
||
370 |
val nibbleT = Type ("List.nibble", []); |
|
371 |
val charT = Type ("List.char", []); |
|
372 |
||
373 |
fun int_of_nibble h = |
|
374 |
if "0" <= h andalso h <= "9" then ord h - ord "0" |
|
375 |
else if "A" <= h andalso h <= "F" then ord h - ord "A" + 10 |
|
376 |
else raise Match; |
|
377 |
||
378 |
fun nibble_of_int i = |
|
379 |
if i <= 9 then chr (ord "0" + i) else chr (ord "A" + i - 10); |
|
380 |
||
381 |
fun mk_char c = |
|
382 |
Const ("List.char.Char", nibbleT --> nibbleT --> charT) $ |
|
383 |
Const ("List.nibble.Nibble" ^ nibble_of_int (ord c div 16), nibbleT) $ |
|
384 |
Const ("List.nibble.Nibble" ^ nibble_of_int (ord c mod 16), nibbleT); |
|
385 |
||
386 |
fun dest_char (Const ("List.char.Char", _) $ c1 $ c2) = |
|
387 |
let |
|
388 |
fun dest_nibble (Const (s, _)) = (int_of_nibble o unprefix "List.nibble.Nibble") s |
|
389 |
| dest_nibble _ = raise Match; |
|
390 |
in |
|
391 |
(SOME (dest_nibble c1 * 16 + dest_nibble c2) |
|
392 |
handle Fail _ => NONE | Match => NONE) |
|
393 |
end |
|
394 |
| dest_char _ = NONE; |
|
395 |
||
396 |
fun print_char c = |
|
397 |
let |
|
398 |
val i = ord c |
|
399 |
in if i < 32 |
|
400 |
then prefix "\\" (string_of_int i) |
|
401 |
else c |
|
402 |
end; |
|
403 |
||
404 |
||
405 |
(* string *) |
|
406 |
||
407 |
val stringT = Type ("List.string", []); |
|
408 |
||
409 |
fun mk_string s = |
|
410 |
let |
|
411 |
val ty_n = Type ("List.nibble", []); |
|
412 |
val ty_c = Type ("List.char", []); |
|
413 |
val ty_l = Type ("List.list", [ty_c]); |
|
414 |
fun mk_nib n = Const ("List.nibble.Nibble" ^ chr (n + (if n <= 9 then ord "0" else ord "A" - 10)), ty_n); |
|
415 |
fun mk_char c = |
|
416 |
if Symbol.is_ascii c andalso Symbol.is_printable c then |
|
417 |
Const ("List.char.Char", ty_n --> ty_n --> ty_c) $ mk_nib (ord c div 16) $ mk_nib (ord c mod 16) |
|
418 |
else error ("Printable ASCII character expected: " ^ quote c); |
|
419 |
fun mk_string c t = Const ("List.list.Cons", ty_c --> ty_l --> ty_l) |
|
420 |
$ mk_char c $ t; |
|
421 |
in fold_rev mk_string (explode s) (Const ("List.list.Nil", ty_l)) end; |
|
422 |
||
423 |
val print_string = quote; |
|
424 |
||
923 | 425 |
end; |