author  wenzelm 
Fri, 07 Oct 2005 18:49:20 +0200  
changeset 17777  05f5532a8289 
parent 17756  d4a35f82fbb4 
child 17786  f06d6498ebf0 
permissions  rwrr 
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(* Title: Pure/term.ML 
0  2 
ID: $Id$ 
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory 
0  4 
Copyright Cambridge University 1992 
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4444  6 
Simply typed lambdacalculus: types, terms, and basic operations. 
0  7 
*) 
8 

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infix 9 $; 
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infixr 5 >; 
4444  11 
infixr >; 
12 
infix aconv; 

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4444  14 
signature BASIC_TERM = 
15 
sig 

16 
type indexname 

17 
type class 

18 
type sort 

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type arity 
4444  20 
datatype typ = 
21 
Type of string * typ list  

22 
TFree of string * sort  

23 
TVar of indexname * sort 

16537  24 
datatype term = 
25 
Const of string * typ  

26 
Free of string * typ  

27 
Var of indexname * typ  

28 
Bound of int  

29 
Abs of string * typ * term  

17756  30 
$ of term * term 
16537  31 
exception TYPE of string * typ list * term list 
32 
exception TERM of string * term list 

16710  33 
val dummyT: typ 
34 
val no_dummyT: typ > typ 

4444  35 
val > : typ * typ > typ 
36 
val > : typ list * typ > typ 

16710  37 
val dest_Type: typ > string * typ list 
38 
val dest_TVar: typ > indexname * sort 

39 
val dest_TFree: typ > string * sort 

40 
val is_Bound: term > bool 

41 
val is_Const: term > bool 

42 
val is_Free: term > bool 

43 
val is_Var: term > bool 

4444  44 
val is_TVar: typ > bool 
15573  45 
val is_funtype: typ > bool 
16710  46 
val dest_Const: term > string * typ 
47 
val dest_Free: term > string * typ 

48 
val dest_Var: term > indexname * typ 

4444  49 
val domain_type: typ > typ 
4480  50 
val range_type: typ > typ 
4444  51 
val binder_types: typ > typ list 
52 
val body_type: typ > typ 

53 
val strip_type: typ > typ list * typ 

16710  54 
val type_of1: typ list * term > typ 
4444  55 
val type_of: term > typ 
16710  56 
val fastype_of1: typ list * term > typ 
4444  57 
val fastype_of: term > typ 
10806  58 
val list_abs: (string * typ) list * term > term 
4444  59 
val strip_abs_body: term > term 
60 
val strip_abs_vars: term > (string * typ) list 

61 
val strip_qnt_body: string > term > term 

62 
val strip_qnt_vars: string > term > (string * typ) list 

63 
val list_comb: term * term list > term 

64 
val strip_comb: term > term * term list 

65 
val head_of: term > term 

66 
val size_of_term: term > int 

67 
val map_type_tvar: (indexname * sort > typ) > typ > typ 

68 
val map_type_tfree: (string * sort > typ) > typ > typ 

69 
val map_term_types: (typ > typ) > term > term 

70 
val it_term_types: (typ * 'a > 'a) > term * 'a > 'a 

16943  71 
val fold_atyps: (typ > 'a > 'a) > typ > 'a > 'a 
72 
val fold_aterms: (term > 'a > 'a) > term > 'a > 'a 

73 
val fold_term_types: (term > typ > 'a > 'a) > term > 'a > 'a 

74 
val fold_types: (typ > 'a > 'a) > term > 'a > 'a 

75 
val add_term_names: term * string list > string list 

76 
val add_term_varnames: term > indexname list > indexname list 

77 
val term_varnames: term > indexname list 

16710  78 
val aconv: term * term > bool 
79 
val aconvs: term list * term list > bool 

16537  80 
structure Vartab: TABLE 
81 
structure Typtab: TABLE 

82 
structure Termtab: TABLE 

4444  83 
val itselfT: typ > typ 
84 
val a_itselfT: typ 

85 
val propT: typ 

86 
val implies: term 

87 
val all: typ > term 

88 
val equals: typ > term 

89 
val strip_all_body: term > term 

90 
val strip_all_vars: term > (string * typ) list 

91 
val incr_bv: int * int * term > term 

92 
val incr_boundvars: int > term > term 

93 
val add_loose_bnos: term * int * int list > int list 

94 
val loose_bnos: term > int list 

95 
val loose_bvar: term * int > bool 

96 
val loose_bvar1: term * int > bool 

97 
val subst_bounds: term list * term > term 

98 
val subst_bound: term * term > term 

99 
val betapply: term * term > term 

100 
val eq_ix: indexname * indexname > bool 

101 
val ins_ix: indexname * indexname list > indexname list 

102 
val mem_ix: indexname * indexname list > bool 

103 
val mem_term: term * term list > bool 

104 
val subset_term: term list * term list > bool 

105 
val eq_set_term: term list * term list > bool 

106 
val ins_term: term * term list > term list 

107 
val union_term: term list * term list > term list 

5585  108 
val inter_term: term list * term list > term list 
4444  109 
val could_unify: term * term > bool 
110 
val subst_free: (term * term) list > term > term 

111 
val xless: (string * int) * indexname > bool 

112 
val abstract_over: term * term > term 

11922  113 
val lambda: term > term > term 
4444  114 
val absfree: string * typ * term > term 
115 
val list_abs_free: (string * typ) list * term > term 

116 
val list_all_free: (string * typ) list * term > term 

117 
val list_all: (string * typ) list * term > term 

16710  118 
val subst_atomic: (term * term) list > term > term 
119 
val typ_subst_atomic: (typ * typ) list > typ > typ 

120 
val subst_atomic_types: (typ * typ) list > term > term 

121 
val typ_subst_TVars: (indexname * typ) list > typ > typ 

122 
val subst_TVars: (indexname * typ) list > term > term 

123 
val subst_Vars: (indexname * term) list > term > term 

124 
val subst_vars: (indexname * typ) list * (indexname * term) list > term > term 

125 
val is_first_order: string list > term > bool 

4444  126 
val maxidx_of_typ: typ > int 
127 
val maxidx_of_typs: typ list > int 

128 
val maxidx_of_term: term > int 

129 
val variant: string list > string > string 

130 
val variantlist: string list * string list > string list 

16537  131 
(*note reversed order of args wrt. variant!*) 
4444  132 
val add_typ_classes: typ * class list > class list 
133 
val add_typ_tycons: typ * string list > string list 

134 
val add_term_classes: term * class list > class list 

16710  135 
val add_term_tycons: term * string list > string list 
4444  136 
val add_term_consts: term * string list > string list 
13646  137 
val term_consts: term > string list 
16943  138 
val exists_subterm: (term > bool) > term > bool 
16710  139 
val exists_Const: (string * typ > bool) > term > bool 
140 
val add_term_free_names: term * string list > string list 

141 
val add_typ_tvars: typ * (indexname * sort) list > (indexname * sort) list 

142 
val add_typ_tfree_names: typ * string list > string list 

143 
val add_typ_tfrees: typ * (string * sort) list > (string * sort) list 

144 
val add_typ_varnames: typ * string list > string list 

145 
val add_term_tvars: term * (indexname * sort) list > (indexname * sort) list 

146 
val add_term_tfrees: term * (string * sort) list > (string * sort) list 

147 
val add_term_tfree_names: term * string list > string list 

148 
val add_term_tvarnames: term * string list > string list 

149 
val typ_tfrees: typ > (string * sort) list 

150 
val typ_tvars: typ > (indexname * sort) list 

151 
val term_tfrees: term > (string * sort) list 

152 
val term_tvars: term > (indexname * sort) list 

153 
val add_typ_ixns: indexname list * typ > indexname list 

154 
val add_term_tvar_ixns: term * indexname list > indexname list 

155 
val add_term_vars: term * term list > term list 

156 
val term_vars: term > term list 

4444  157 
val add_term_frees: term * term list > term list 
158 
val term_frees: term > term list 

16710  159 
val variant_abs: string * typ * term > string * term 
160 
val rename_wrt_term: term > (string * typ) list > (string * typ) list 

15986  161 
val show_question_marks: bool ref 
4444  162 
end; 
0  163 

4444  164 
signature TERM = 
165 
sig 

166 
include BASIC_TERM 

16710  167 
val argument_type_of: term > typ 
16943  168 
val add_tvarsT: typ > (indexname * sort) list > (indexname * sort) list 
169 
val add_tvars: term > (indexname * sort) list > (indexname * sort) list 

170 
val add_vars: term > (indexname * typ) list > (indexname * typ) list 

171 
val add_tfreesT: typ > (string * sort) list > (string * sort) list 

172 
val add_tfrees: term > (string * sort) list > (string * sort) list 

173 
val add_frees: term > (string * typ) list > (string * typ) list 

16678  174 
val fast_indexname_ord: indexname * indexname > order 
16537  175 
val indexname_ord: indexname * indexname > order 
176 
val sort_ord: sort * sort > order 

177 
val typ_ord: typ * typ > order 

16678  178 
val fast_term_ord: term * term > order 
16537  179 
val term_ord: term * term > order 
180 
val hd_ord: term * term > order 

181 
val termless: term * term > bool 

16570  182 
val term_lpo: (string > int) > term * term > order 
12981  183 
val match_bvars: (term * term) * (string * string) list > (string * string) list 
184 
val rename_abs: term > term > term > term option 

16943  185 
val eq_tvar: (indexname * sort) * (indexname * sort) > bool 
16882  186 
val eq_var: (indexname * typ) * (indexname * typ) > bool 
16943  187 
val tvar_ord: (indexname * sort) * (indexname * sort) > order 
188 
val var_ord: (indexname * typ) * (indexname * typ) > order 

16882  189 
val instantiate: ((indexname * sort) * typ) list * ((indexname * typ) * term) list 
190 
> term > term 

191 
val instantiateT: ((indexname * sort) * typ) list > typ > typ 

16710  192 
val maxidx_typ: typ > int > int 
193 
val maxidx_typs: typ list > int > int 

194 
val maxidx_term: term > int > int 

12499  195 
val invent_names: string list > string > int > string list 
16338  196 
val map_typ: (string > string) > (string > string) > typ > typ 
197 
val map_term: (string > string) > (string > string) > (string > string) > term > term 

16710  198 
val dest_abs: string * typ * term > string * term 
16990  199 
val bound: int > string 
200 
val is_bound: string > bool 

16943  201 
val zero_var_indexesT: typ > typ 
202 
val zero_var_indexes: term > term 

203 
val zero_var_indexes_inst: term > 

204 
((indexname * sort) * typ) list * ((indexname * typ) * term) list 

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val dummy_patternN: string 
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val no_dummy_patterns: term > term 
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val replace_dummy_patterns: int * term > int * term 
10552  208 
val is_replaced_dummy_pattern: indexname > bool 
16035  209 
val show_dummy_patterns: term > term 
13484  210 
val adhoc_freeze_vars: term > term * string list 
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val string_of_vname: indexname > string 
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val string_of_vname': indexname > string 
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val str_of_term: term > string 
4444  214 
end; 
215 

216 
structure Term: TERM = 

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struct 
0  218 

219 
(*Indexnames can be quickly renamed by adding an offset to the integer part, 

220 
for resolution.*) 

16537  221 
type indexname = string * int; 
0  222 

4626  223 
(* Types are classified by sorts. *) 
0  224 
type class = string; 
225 
type sort = class list; 

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type arity = string * sort list * sort; 
0  227 

228 
(* The sorts attached to TFrees and TVars specify the sort of that variable *) 

229 
datatype typ = Type of string * typ list 

230 
 TFree of string * sort 

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 TVar of indexname * sort; 
0  232 

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(*Terms. Bound variables are indicated by depth number. 
0  234 
Free variables, (scheme) variables and constants have names. 
4626  235 
An term is "closed" if every bound variable of level "lev" 
13000  236 
is enclosed by at least "lev" abstractions. 
0  237 

238 
It is possible to create meaningless terms containing loose bound vars 

239 
or type mismatches. But such terms are not allowed in rules. *) 

240 

13000  241 
datatype term = 
0  242 
Const of string * typ 
13000  243 
 Free of string * typ 
0  244 
 Var of indexname * typ 
245 
 Bound of int 

246 
 Abs of string*typ*term 

3965  247 
 op $ of term*term; 
0  248 

16537  249 
(*Errors involving type mismatches*) 
0  250 
exception TYPE of string * typ list * term list; 
251 

16537  252 
(*Errors errors involving terms*) 
0  253 
exception TERM of string * term list; 
254 

255 
(*Note variable naming conventions! 

256 
a,b,c: string 

257 
f,g,h: functions (including terms of function type) 

258 
i,j,m,n: int 

259 
t,u: term 

260 
v,w: indexnames 

261 
x,y: any 

262 
A,B,C: term (denoting formulae) 

263 
T,U: typ 

264 
*) 

265 

266 

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(** Types **) 
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268 

16537  269 
(*dummy type for parsing and printing etc.*) 
270 
val dummyT = Type ("dummy", []); 

271 

272 
fun no_dummyT typ = 

273 
let 

274 
fun check (T as Type ("dummy", _)) = 

275 
raise TYPE ("Illegal occurrence of '_' dummy type", [T], []) 

276 
 check (Type (_, Ts)) = List.app check Ts 

277 
 check _ = (); 

278 
in check typ; typ end; 

279 

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fun S > T = Type("fun",[S,T]); 
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(*handy for multiple args: [T1,...,Tn]>T gives T1>(T2> ... >T)*) 
15570  283 
val op > = Library.foldr (op >); 
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fun dest_Type (Type x) = x 
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 dest_Type T = raise TYPE ("dest_Type", [T], []); 
15914  287 
fun dest_TVar (TVar x) = x 
288 
 dest_TVar T = raise TYPE ("dest_TVar", [T], []); 

289 
fun dest_TFree (TFree x) = x 

290 
 dest_TFree T = raise TYPE ("dest_TFree", [T], []); 

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291 

16537  292 

0  293 
(** Discriminators **) 
294 

7318  295 
fun is_Bound (Bound _) = true 
296 
 is_Bound _ = false; 

297 

0  298 
fun is_Const (Const _) = true 
299 
 is_Const _ = false; 

300 

301 
fun is_Free (Free _) = true 

302 
 is_Free _ = false; 

303 

304 
fun is_Var (Var _) = true 

305 
 is_Var _ = false; 

306 

307 
fun is_TVar (TVar _) = true 

308 
 is_TVar _ = false; 

309 

15573  310 
(*Differs from proofterm/is_fun in its treatment of TVar*) 
311 
fun is_funtype (Type("fun",[_,_])) = true 

312 
 is_funtype _ = false; 

313 

16537  314 

0  315 
(** Destructors **) 
316 

317 
fun dest_Const (Const x) = x 

318 
 dest_Const t = raise TERM("dest_Const", [t]); 

319 

320 
fun dest_Free (Free x) = x 

321 
 dest_Free t = raise TERM("dest_Free", [t]); 

322 

323 
fun dest_Var (Var x) = x 

324 
 dest_Var t = raise TERM("dest_Var", [t]); 

325 

326 

4464  327 
fun domain_type (Type("fun", [T,_])) = T 
328 
and range_type (Type("fun", [_,T])) = T; 

4064  329 

0  330 
(* maps [T1,...,Tn]>T to the list [T1,T2,...,Tn]*) 
331 
fun binder_types (Type("fun",[S,T])) = S :: binder_types T 

332 
 binder_types _ = []; 

333 

334 
(* maps [T1,...,Tn]>T to T*) 

335 
fun body_type (Type("fun",[S,T])) = body_type T 

336 
 body_type T = T; 

337 

338 
(* maps [T1,...,Tn]>T to ([T1,T2,...,Tn], T) *) 

339 
fun strip_type T : typ list * typ = 

340 
(binder_types T, body_type T); 

341 

342 

343 
(*Compute the type of the term, checking that combinations are welltyped 

344 
Ts = [T0,T1,...] holds types of bound variables 0, 1, ...*) 

345 
fun type_of1 (Ts, Const (_,T)) = T 

346 
 type_of1 (Ts, Free (_,T)) = T 

15570  347 
 type_of1 (Ts, Bound i) = (List.nth (Ts,i) 
348 
handle Subscript => raise TYPE("type_of: bound variable", [], [Bound i])) 

0  349 
 type_of1 (Ts, Var (_,T)) = T 
350 
 type_of1 (Ts, Abs (_,T,body)) = T > type_of1(T::Ts, body) 

13000  351 
 type_of1 (Ts, f$u) = 
0  352 
let val U = type_of1(Ts,u) 
353 
and T = type_of1(Ts,f) 

354 
in case T of 

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Type("fun",[T1,T2]) => 
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if T1=U then T2 else raise TYPE 
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357 
("type_of: type mismatch in application", [T1,U], [f$u]) 
13000  358 
 _ => raise TYPE 
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("type_of: function type is expected in application", 
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[T,U], [f$u]) 
0  361 
end; 
362 

363 
fun type_of t : typ = type_of1 ([],t); 

364 

365 
(*Determines the type of a term, with minimal checking*) 

13000  366 
fun fastype_of1 (Ts, f$u) = 
61  367 
(case fastype_of1 (Ts,f) of 
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Type("fun",[_,T]) => T 
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 _ => raise TERM("fastype_of: expected function type", [f$u])) 
61  370 
 fastype_of1 (_, Const (_,T)) = T 
371 
 fastype_of1 (_, Free (_,T)) = T 

15570  372 
 fastype_of1 (Ts, Bound i) = (List.nth(Ts,i) 
373 
handle Subscript => raise TERM("fastype_of: Bound", [Bound i])) 

13000  374 
 fastype_of1 (_, Var (_,T)) = T 
61  375 
 fastype_of1 (Ts, Abs (_,T,u)) = T > fastype_of1 (T::Ts, u); 
376 

377 
fun fastype_of t : typ = fastype_of1 ([],t); 

0  378 

16678  379 
(*Determine the argument type of a function*) 
380 
fun argument_type_of tm = 

381 
let 

382 
fun argT i (Type ("fun", [T, U])) = if i = 0 then T else argT (i  1) U 

383 
 argT _ T = raise TYPE ("argument_type_of", [T], []); 

384 

385 
fun arg 0 _ (Abs (_, T, _)) = T 

386 
 arg i Ts (Abs (_, T, t)) = arg (i  1) (T :: Ts) t 

387 
 arg i Ts (t $ _) = arg (i + 1) Ts t 

388 
 arg i Ts a = argT i (fastype_of1 (Ts, a)); 

389 
in arg 0 [] tm end; 

390 

0  391 

15570  392 
val list_abs = Library.foldr (fn ((x, T), t) => Abs (x, T, t)); 
10806  393 

0  394 
(* maps (x1,...,xn)t to t *) 
13000  395 
fun strip_abs_body (Abs(_,_,t)) = strip_abs_body t 
0  396 
 strip_abs_body u = u; 
397 

398 
(* maps (x1,...,xn)t to [x1, ..., xn] *) 

13000  399 
fun strip_abs_vars (Abs(a,T,t)) = (a,T) :: strip_abs_vars t 
0  400 
 strip_abs_vars u = [] : (string*typ) list; 
401 

402 

403 
fun strip_qnt_body qnt = 

404 
let fun strip(tm as Const(c,_)$Abs(_,_,t)) = if c=qnt then strip t else tm 

405 
 strip t = t 

406 
in strip end; 

407 

408 
fun strip_qnt_vars qnt = 

409 
let fun strip(Const(c,_)$Abs(a,T,t)) = if c=qnt then (a,T)::strip t else [] 

410 
 strip t = [] : (string*typ) list 

411 
in strip end; 

412 

413 

414 
(* maps (f, [t1,...,tn]) to f(t1,...,tn) *) 

15570  415 
val list_comb : term * term list > term = Library.foldl (op $); 
0  416 

417 

418 
(* maps f(t1,...,tn) to (f, [t1,...,tn]) ; naturally tailrecursive*) 

13000  419 
fun strip_comb u : term * term list = 
0  420 
let fun stripc (f$t, ts) = stripc (f, t::ts) 
13000  421 
 stripc x = x 
0  422 
in stripc(u,[]) end; 
423 

424 

425 
(* maps f(t1,...,tn) to f , which is never a combination *) 

426 
fun head_of (f$t) = head_of f 

427 
 head_of u = u; 

428 

429 

16599  430 
(*number of atoms and abstractions in a term*) 
431 
fun size_of_term tm = 

432 
let 

16678  433 
fun add_size (t $ u, n) = add_size (t, add_size (u, n)) 
434 
 add_size (Abs (_ ,_, t), n) = add_size (t, n + 1) 

435 
 add_size (_, n) = n + 1; 

436 
in add_size (tm, 0) end; 

0  437 

16678  438 
fun map_type_tvar f = 
439 
let 

440 
fun map_aux (Type (a, Ts)) = Type (a, map map_aux Ts) 

441 
 map_aux (TVar x) = f x 

442 
 map_aux T = T; 

443 
in map_aux end; 

949
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset

444 

16678  445 
fun map_type_tfree f = 
446 
let 

447 
fun map_aux (Type (a, Ts)) = Type (a, map map_aux Ts) 

448 
 map_aux (TFree x) = f x 

449 
 map_aux T = T; 

450 
in map_aux end; 

949
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset

451 

0  452 
fun map_term_types f = 
16678  453 
let 
454 
fun map_aux (Const (a, T)) = Const (a, f T) 

455 
 map_aux (Free (a, T)) = Free (a, f T) 

456 
 map_aux (Var (v, T)) = Var (v, f T) 

457 
 map_aux (t as Bound _) = t 

458 
 map_aux (Abs (a, T, t)) = Abs (a, f T, map_aux t) 

459 
 map_aux (t $ u) = map_aux t $ map_aux u; 

460 
in map_aux end; 

0  461 

462 
(* iterate a function over all types in a term *) 

463 
fun it_term_types f = 

464 
let fun iter(Const(_,T), a) = f(T,a) 

465 
 iter(Free(_,T), a) = f(T,a) 

466 
 iter(Var(_,T), a) = f(T,a) 

467 
 iter(Abs(_,T,t), a) = iter(t,f(T,a)) 

468 
 iter(f$u, a) = iter(f, iter(u, a)) 

469 
 iter(Bound _, a) = a 

470 
in iter end 

471 

472 

16943  473 
(* fold types and terms *) 
474 

475 
(*fold atoms of type*) 

476 
fun fold_atyps f (Type (_, Ts)) = fold (fold_atyps f) Ts 

477 
 fold_atyps f T = f T; 

478 

479 
(*fold atoms of term*) 

480 
fun fold_aterms f (t $ u) = fold_aterms f t #> fold_aterms f u 

481 
 fold_aterms f (Abs (_, _, t)) = fold_aterms f t 

482 
 fold_aterms f a = f a; 

483 

484 
(*fold types of term*) 

485 
fun fold_term_types f (t as Const (_, T)) = f t T 

486 
 fold_term_types f (t as Free (_, T)) = f t T 

487 
 fold_term_types f (t as Var (_, T)) = f t T 

488 
 fold_term_types f (Bound _) = I 

489 
 fold_term_types f (t as Abs (_, T, b)) = f t T #> fold_term_types f b 

490 
 fold_term_types f (t $ u) = fold_term_types f t #> fold_term_types f u; 

491 

492 
fun fold_types f = fold_term_types (K f); 

493 

494 
(*collect variables*) 

495 
val add_tvarsT = fold_atyps (fn TVar v => insert (op =) v  _ => I); 

496 
val add_tvars = fold_types add_tvarsT; 

497 
val add_vars = fold_aterms (fn Var v => insert (op =) v  _ => I); 

498 
val add_tfreesT = fold_atyps (fn TFree v => insert (op =) v  _ => I); 

499 
val add_tfrees = fold_types add_tfreesT; 

500 
val add_frees = fold_aterms (fn Free v => insert (op =) v  _ => I); 

501 

502 
(*collect variable names*) 

503 
val add_term_varnames = fold_aterms (fn Var (xi, _) => insert (op =) xi  _ => I); 

504 
fun term_varnames t = add_term_varnames t []; 

505 

506 

16678  507 
(** Comparing terms, types, sorts etc. **) 
16537  508 

16678  509 
(* fast syntactic comparison *) 
510 

511 
fun fast_indexname_ord ((x, i), (y, j)) = 

512 
(case int_ord (i, j) of EQUAL => fast_string_ord (x, y)  ord => ord); 

16537  513 

16599  514 
fun sort_ord SS = 
515 
if pointer_eq SS then EQUAL 

16990  516 
else dict_ord fast_string_ord SS; 
16678  517 

518 
local 

16537  519 

16678  520 
fun cons_nr (TVar _) = 0 
521 
 cons_nr (TFree _) = 1 

522 
 cons_nr (Type _) = 2; 

16537  523 

16678  524 
in 
16537  525 

526 
fun typ_ord TU = 

527 
if pointer_eq TU then EQUAL 

528 
else 

529 
(case TU of 

16678  530 
(Type (a, Ts), Type (b, Us)) => 
16990  531 
(case fast_string_ord (a, b) of EQUAL => dict_ord typ_ord (Ts, Us)  ord => ord) 
16678  532 
 (TFree (a, S), TFree (b, S')) => 
533 
(case fast_string_ord (a, b) of EQUAL => sort_ord (S, S')  ord => ord) 

534 
 (TVar (xi, S), TVar (yj, S')) => 

535 
(case fast_indexname_ord (xi, yj) of EQUAL => sort_ord (S, S')  ord => ord) 

536 
 (T, U) => int_ord (cons_nr T, cons_nr U)); 

537 

538 
end; 

539 

540 
local 

541 

542 
fun cons_nr (Const _) = 0 

543 
 cons_nr (Free _) = 1 

544 
 cons_nr (Var _) = 2 

545 
 cons_nr (Bound _) = 3 

546 
 cons_nr (Abs _) = 4 

547 
 cons_nr (_ $ _) = 5; 

548 

549 
fun struct_ord (Abs (_, _, t), Abs (_, _, u)) = struct_ord (t, u) 

550 
 struct_ord (t1 $ t2, u1 $ u2) = 

551 
(case struct_ord (t1, u1) of EQUAL => struct_ord (t2, u2)  ord => ord) 

552 
 struct_ord (t, u) = int_ord (cons_nr t, cons_nr u); 

553 

554 
fun atoms_ord (Abs (_, _, t), Abs (_, _, u)) = atoms_ord (t, u) 

555 
 atoms_ord (t1 $ t2, u1 $ u2) = 

556 
(case atoms_ord (t1, u1) of EQUAL => atoms_ord (t2, u2)  ord => ord) 

557 
 atoms_ord (Const (a, _), Const (b, _)) = fast_string_ord (a, b) 

558 
 atoms_ord (Free (x, _), Free (y, _)) = fast_string_ord (x, y) 

559 
 atoms_ord (Var (xi, _), Var (yj, _)) = fast_indexname_ord (xi, yj) 

560 
 atoms_ord (Bound i, Bound j) = int_ord (i, j) 

561 
 atoms_ord _ = sys_error "atoms_ord"; 

562 

563 
fun types_ord (Abs (_, T, t), Abs (_, U, u)) = 

564 
(case typ_ord (T, U) of EQUAL => types_ord (t, u)  ord => ord) 

565 
 types_ord (t1 $ t2, u1 $ u2) = 

566 
(case types_ord (t1, u1) of EQUAL => types_ord (t2, u2)  ord => ord) 

567 
 types_ord (Const (_, T), Const (_, U)) = typ_ord (T, U) 

568 
 types_ord (Free (_, T), Free (_, U)) = typ_ord (T, U) 

569 
 types_ord (Var (_, T), Var (_, U)) = typ_ord (T, U) 

570 
 types_ord (Bound _, Bound _) = EQUAL 

571 
 types_ord _ = sys_error "types_ord"; 

572 

573 
in 

574 

575 
fun fast_term_ord tu = 

576 
if pointer_eq tu then EQUAL 

577 
else 

578 
(case struct_ord tu of 

579 
EQUAL => (case atoms_ord tu of EQUAL => types_ord tu  ord => ord) 

580 
 ord => ord); 

581 

582 
fun op aconv tu = (fast_term_ord tu = EQUAL); 

583 
fun aconvs ts_us = (list_ord fast_term_ord ts_us = EQUAL); 

584 

585 
structure Vartab = TableFun(type key = indexname val ord = fast_indexname_ord); 

586 
structure Typtab = TableFun(type key = typ val ord = typ_ord); 

587 
structure Termtab = TableFun(type key = term val ord = fast_term_ord); 

588 

589 
end; 

16537  590 

591 

592 
(* term_ord *) 

593 

594 
(*a linear wellfounded ACcompatible ordering for terms: 

595 
s < t <=> 1. size(s) < size(t) or 

596 
2. size(s) = size(t) and s=f(...) and t=g(...) and f<g or 

597 
3. size(s) = size(t) and s=f(s1..sn) and t=f(t1..tn) and 

598 
(s1..sn) < (t1..tn) (lexicographically)*) 

16678  599 

600 
fun indexname_ord ((x, i), (y, j)) = 

601 
(case int_ord (i, j) of EQUAL => string_ord (x, y)  ord => ord); 

602 

16667  603 
local 
604 

605 
fun hd_depth (t $ _, n) = hd_depth (t, n + 1) 

606 
 hd_depth p = p; 

16537  607 

608 
fun dest_hd (Const (a, T)) = (((a, 0), T), 0) 

609 
 dest_hd (Free (a, T)) = (((a, 0), T), 1) 

610 
 dest_hd (Var v) = (v, 2) 

611 
 dest_hd (Bound i) = ((("", i), dummyT), 3) 

612 
 dest_hd (Abs (_, T, _)) = ((("", 0), T), 4); 

613 

16667  614 
in 
615 

16537  616 
fun term_ord tu = 
617 
if pointer_eq tu then EQUAL 

618 
else 

619 
(case tu of 

620 
(Abs (_, T, t), Abs(_, U, u)) => 

621 
(case term_ord (t, u) of EQUAL => typ_ord (T, U)  ord => ord) 

16667  622 
 (t, u) => 
16537  623 
(case int_ord (size_of_term t, size_of_term u) of 
624 
EQUAL => 

16943  625 
(case prod_ord hd_ord int_ord (hd_depth (t, 0), hd_depth (u, 0)) of 
626 
EQUAL => args_ord (t, u)  ord => ord) 

16537  627 
 ord => ord)) 
628 
and hd_ord (f, g) = 

629 
prod_ord (prod_ord indexname_ord typ_ord) int_ord (dest_hd f, dest_hd g) 

16667  630 
and args_ord (f $ t, g $ u) = 
631 
(case args_ord (f, g) of EQUAL => term_ord (t, u)  ord => ord) 

632 
 args_ord _ = EQUAL; 

16537  633 

634 
fun termless tu = (term_ord tu = LESS); 

635 

16667  636 
end; 
637 

638 

639 
(** Lexicographic path order on terms **) 

640 

641 
(* 

16570  642 
See Baader & Nipkow, Term rewriting, CUP 1998. 
643 
Without variables. Const, Var, Bound, Free and Abs are treated all as 

644 
constants. 

645 

646 
f_ord maps strings to integers and serves two purposes: 

647 
 Predicate on constant symbols. Those that are not recognised by f_ord 

648 
must be mapped to ~1. 

649 
 Order on the recognised symbols. These must be mapped to distinct 

650 
integers >= 0. 

651 

16667  652 
*) 
16570  653 

654 
local 

16667  655 
fun dest_hd f_ord (Const (a, T)) = 
16570  656 
let val ord = f_ord a in 
657 
if ord = ~1 then ((1, ((a, 0), T)), 0) else ((0, (("", ord), T)), 0) 

658 
end 

659 
 dest_hd _ (Free (a, T)) = ((1, ((a, 0), T)), 0) 

660 
 dest_hd _ (Var v) = ((1, v), 1) 

661 
 dest_hd _ (Bound i) = ((1, (("", i), dummyT)), 2) 

662 
 dest_hd _ (Abs (_, T, _)) = ((1, (("", 0), T)), 3); 

663 

664 
fun term_lpo f_ord (s, t) = 

665 
let val (f, ss) = strip_comb s and (g, ts) = strip_comb t in 

666 
if forall (fn si => term_lpo f_ord (si, t) = LESS) ss 

667 
then case hd_ord f_ord (f, g) of 

16667  668 
GREATER => 
669 
if forall (fn ti => term_lpo f_ord (s, ti) = GREATER) ts 

670 
then GREATER else LESS 

16570  671 
 EQUAL => 
16667  672 
if forall (fn ti => term_lpo f_ord (s, ti) = GREATER) ts 
673 
then list_ord (term_lpo f_ord) (ss, ts) 

674 
else LESS 

16570  675 
 LESS => LESS 
676 
else GREATER 

677 
end 

678 
and hd_ord f_ord (f, g) = case (f, g) of 

679 
(Abs (_, T, t), Abs (_, U, u)) => 

680 
(case term_lpo f_ord (t, u) of EQUAL => typ_ord (T, U)  ord => ord) 

681 
 (_, _) => prod_ord (prod_ord int_ord 

682 
(prod_ord indexname_ord typ_ord)) int_ord 

683 
(dest_hd f_ord f, dest_hd f_ord g) 

684 
in 

685 
val term_lpo = term_lpo 

686 
end; 

687 

16537  688 

0  689 
(** Connectives of higher order logic **) 
690 

375  691 
fun itselfT ty = Type ("itself", [ty]); 
14854  692 
val a_itselfT = itselfT (TFree ("'a", [])); 
375  693 

0  694 
val propT : typ = Type("prop",[]); 
695 

696 
val implies = Const("==>", propT>propT>propT); 

697 

698 
fun all T = Const("all", (T>propT)>propT); 

699 

700 
fun equals T = Const("==", T>T>propT); 

701 

702 
(* maps !!x1...xn. t to t *) 

13000  703 
fun strip_all_body (Const("all",_)$Abs(_,_,t)) = strip_all_body t 
0  704 
 strip_all_body t = t; 
705 

706 
(* maps !!x1...xn. t to [x1, ..., xn] *) 

707 
fun strip_all_vars (Const("all",_)$Abs(a,T,t)) = 

13000  708 
(a,T) :: strip_all_vars t 
0  709 
 strip_all_vars t = [] : (string*typ) list; 
710 

711 
(*increments a term's nonlocal bound variables 

712 
required when moving a term within abstractions 

713 
inc is increment for bound variables 

714 
lev is level at which a bound variable is considered 'loose'*) 

13000  715 
fun incr_bv (inc, lev, u as Bound i) = if i>=lev then Bound(i+inc) else u 
0  716 
 incr_bv (inc, lev, Abs(a,T,body)) = 
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset

717 
Abs(a, T, incr_bv(inc,lev+1,body)) 
13000  718 
 incr_bv (inc, lev, f$t) = 
0  719 
incr_bv(inc,lev,f) $ incr_bv(inc,lev,t) 
720 
 incr_bv (inc, lev, u) = u; 

721 

722 
fun incr_boundvars 0 t = t 

723 
 incr_boundvars inc t = incr_bv(inc,0,t); 

724 

12981  725 
(*Scan a pair of terms; while they are similar, 
726 
accumulate corresponding bound vars in "al"*) 

727 
fun match_bvs(Abs(x,_,s),Abs(y,_,t), al) = 

728 
match_bvs(s, t, if x="" orelse y="" then al 

729 
else (x,y)::al) 

730 
 match_bvs(f$s, g$t, al) = match_bvs(f,g,match_bvs(s,t,al)) 

731 
 match_bvs(_,_,al) = al; 

732 

733 
(* strip abstractions created by parameters *) 

734 
fun match_bvars((s,t),al) = match_bvs(strip_abs_body s, strip_abs_body t, al); 

735 

736 
fun rename_abs pat obj t = 

737 
let 

738 
val ren = match_bvs (pat, obj, []); 

739 
fun ren_abs (Abs (x, T, b)) = 

17271  740 
Abs (if_none (AList.lookup (op =) ren x) x, T, ren_abs b) 
12981  741 
 ren_abs (f $ t) = ren_abs f $ ren_abs t 
742 
 ren_abs t = t 

15531  743 
in if null ren then NONE else SOME (ren_abs t) end; 
0  744 

745 
(*Accumulate all 'loose' bound vars referring to level 'lev' or beyond. 

746 
(Bound 0) is loose at level 0 *) 

13000  747 
fun add_loose_bnos (Bound i, lev, js) = 
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset

748 
if i<lev then js else (ilev) ins_int js 
0  749 
 add_loose_bnos (Abs (_,_,t), lev, js) = add_loose_bnos (t, lev+1, js) 
750 
 add_loose_bnos (f$t, lev, js) = 

13000  751 
add_loose_bnos (f, lev, add_loose_bnos (t, lev, js)) 
0  752 
 add_loose_bnos (_, _, js) = js; 
753 

754 
fun loose_bnos t = add_loose_bnos (t, 0, []); 

755 

756 
(* loose_bvar(t,k) iff t contains a 'loose' bound variable referring to 

757 
level k or beyond. *) 

758 
fun loose_bvar(Bound i,k) = i >= k 

759 
 loose_bvar(f$t, k) = loose_bvar(f,k) orelse loose_bvar(t,k) 

760 
 loose_bvar(Abs(_,_,t),k) = loose_bvar(t,k+1) 

761 
 loose_bvar _ = false; 

762 

2792  763 
fun loose_bvar1(Bound i,k) = i = k 
764 
 loose_bvar1(f$t, k) = loose_bvar1(f,k) orelse loose_bvar1(t,k) 

765 
 loose_bvar1(Abs(_,_,t),k) = loose_bvar1(t,k+1) 

766 
 loose_bvar1 _ = false; 

0  767 

768 
(*Substitute arguments for loose bound variables. 

769 
Betareduction of arg(n1)...arg0 into t replacing (Bound i) with (argi). 

4626  770 
Note that for ((%x y. c) a b), the bound vars in c are x=1 and y=0 
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset

771 
and the appropriate call is subst_bounds([b,a], c) . 
0  772 
Loose bound variables >=n are reduced by "n" to 
773 
compensate for the disappearance of lambdas. 

774 
*) 

13000  775 
fun subst_bounds (args: term list, t) : term = 
0  776 
let val n = length args; 
777 
fun subst (t as Bound i, lev) = 

9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset

778 
(if i<lev then t (*var is locally bound*) 
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset

779 
else incr_boundvars lev (List.nth(args, ilev)) 
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset

780 
handle Subscript => Bound(in) (*loose: change it*)) 
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset

781 
 subst (Abs(a,T,body), lev) = Abs(a, T, subst(body,lev+1)) 
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset

782 
 subst (f$t, lev) = subst(f,lev) $ subst(t,lev) 
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset

783 
 subst (t,lev) = t 
0  784 
in case args of [] => t  _ => subst (t,0) end; 
785 

2192
3bf092b5310b
Optimizations: removal of polymorphic equality; oneargument case
paulson
parents:
2182
diff
changeset

786 
(*Special case: one argument*) 
13000  787 
fun subst_bound (arg, t) : term = 
2192
3bf092b5310b
Optimizations: removal of polymorphic equality; oneargument case
paulson
parents:
2182
diff
changeset

788 
let fun subst (t as Bound i, lev) = 
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset

789 
if i<lev then t (*var is locally bound*) 
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset

790 
else if i=lev then incr_boundvars lev arg 
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset

791 
else Bound(i1) (*loose: change it*) 
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset

792 
 subst (Abs(a,T,body), lev) = Abs(a, T, subst(body,lev+1)) 
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset

793 
 subst (f$t, lev) = subst(f,lev) $ subst(t,lev) 
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset

794 
 subst (t,lev) = t 
2192
3bf092b5310b
Optimizations: removal of polymorphic equality; oneargument case
paulson
parents:
2182
diff
changeset

795 
in subst (t,0) end; 
3bf092b5310b
Optimizations: removal of polymorphic equality; oneargument case
paulson
parents:
2182
diff
changeset

796 

0  797 
(*betareduce if possible, else form application*) 
2192
3bf092b5310b
Optimizations: removal of polymorphic equality; oneargument case
paulson
parents:
2182
diff
changeset

798 
fun betapply (Abs(_,_,t), u) = subst_bound (u,t) 
0  799 
 betapply (f,u) = f$u; 
800 

14786
24a7bc97a27a
moved some sort ops to sorts.ML; added string_of_vname (from Syntax module);
wenzelm
parents:
14695
diff
changeset

801 

16882  802 
(** Specialized equality, membership, insertion etc. **) 
2192
3bf092b5310b
Optimizations: removal of polymorphic equality; oneargument case
paulson
parents:
2182
diff
changeset

803 

16882  804 
(* indexnames *) 
805 

16724  806 
fun eq_ix ((x, i): indexname, (y, j)) = i = j andalso x = y; 
2192
3bf092b5310b
Optimizations: removal of polymorphic equality; oneargument case
paulson
parents:
2182
diff
changeset

807 

2959  808 
fun mem_ix (_, []) = false 
16882  809 
 mem_ix (x, y :: ys) = eq_ix (x, y) orelse mem_ix (x, ys); 
2192
3bf092b5310b
Optimizations: removal of polymorphic equality; oneargument case
paulson
parents:
2182
diff
changeset

810 

16882  811 
fun ins_ix (x, xs) = if mem_ix (x, xs) then xs else x :: xs; 
2192
3bf092b5310b
Optimizations: removal of polymorphic equality; oneargument case
paulson
parents:
2182
diff
changeset

812 

0  813 

16882  814 
(* variables *) 
815 

16943  816 
fun eq_tvar ((xi, S: sort), (xi', S')) = eq_ix (xi, xi') andalso S = S'; 
817 
fun eq_var ((xi, T: typ), (xi', T')) = eq_ix (xi, xi') andalso T = T'; 

818 

819 
val tvar_ord = prod_ord indexname_ord sort_ord; 

820 
val var_ord = prod_ord indexname_ord typ_ord; 

16882  821 

822 

823 
(* terms *) 

2176  824 

825 
fun mem_term (_, []) = false 

16882  826 
 mem_term (t, t'::ts) = t aconv t' orelse mem_term (t, ts); 
2176  827 

2182
29e56f003599
Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
parents:
2176
diff
changeset

828 
fun subset_term ([], ys) = true 
29e56f003599
Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
parents:
2176
diff
changeset

829 
 subset_term (x :: xs, ys) = mem_term (x, ys) andalso subset_term(xs, ys); 
29e56f003599
Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
parents:
2176
diff
changeset

830 

29e56f003599
Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
parents:
2176
diff
changeset

831 
fun eq_set_term (xs, ys) = 
29e56f003599
Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
parents:
2176
diff
changeset

832 
xs = ys orelse (subset_term (xs, ys) andalso subset_term (ys, xs)); 
29e56f003599
Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
parents:
2176
diff
changeset

833 

2176  834 
fun ins_term(t,ts) = if mem_term(t,ts) then ts else t :: ts; 
835 

836 
fun union_term (xs, []) = xs 

837 
 union_term ([], ys) = ys 

838 
 union_term ((x :: xs), ys) = union_term (xs, ins_term (x, ys)); 

839 

5585  840 
fun inter_term ([], ys) = [] 
841 
 inter_term (x::xs, ys) = 

842 
if mem_term (x,ys) then x :: inter_term(xs,ys) else inter_term(xs,ys); 

843 

16882  844 

13000  845 
(*A fast unification filter: true unless the two terms cannot be unified. 
0  846 
Terms must be NORMAL. Treats all Vars as distinct. *) 
847 
fun could_unify (t,u) = 

848 
let fun matchrands (f$t, g$u) = could_unify(t,u) andalso matchrands(f,g) 

9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset

849 
 matchrands _ = true 
0  850 
in case (head_of t , head_of u) of 
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset

851 
(_, Var _) => true 
0  852 
 (Var _, _) => true 
853 
 (Const(a,_), Const(b,_)) => a=b andalso matchrands(t,u) 

854 
 (Free(a,_), Free(b,_)) => a=b andalso matchrands(t,u) 

855 
 (Bound i, Bound j) => i=j andalso matchrands(t,u) 

856 
 (Abs _, _) => true (*because of possible eta equality*) 

857 
 (_, Abs _) => true 

858 
 _ => false 

859 
end; 

860 

861 
(*Substitute new for free occurrences of old in a term*) 

862 
fun subst_free [] = (fn t=>t) 

863 
 subst_free pairs = 

13000  864 
let fun substf u = 
17314  865 
case AList.lookup (op aconv) pairs u of 
15531  866 
SOME u' => u' 
867 
 NONE => (case u of Abs(a,T,t) => Abs(a, T, substf t) 

9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset

868 
 t$u' => substf t $ substf u' 
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset

869 
 _ => u) 
0  870 
in substf end; 
871 

872 
(*a total, irreflexive ordering on index names*) 

873 
fun xless ((a,i), (b,j): indexname) = i<j orelse (i=j andalso a<b); 

874 

875 

13000  876 
(*Abstraction of the term "body" over its occurrences of v, 
0  877 
which must contain no loose bound variables. 
878 
The resulting term is ready to become the body of an Abs.*) 

16882  879 
fun abstract_over (v, body) = 
880 
let 

16990  881 
exception SAME; 
882 
fun abs lev tm = 

883 
if v aconv tm then Bound lev 

16882  884 
else 
16990  885 
(case tm of 
886 
Abs (a, T, t) => Abs (a, T, abs (lev + 1) t) 

887 
 t $ u => (abs lev t $ (abs lev u handle SAME => u) handle SAME => t $ abs lev u) 

888 
 _ => raise SAME); 

889 
in abs 0 body handle SAME => body end; 

0  890 

13665  891 
fun lambda (v as Free (x, T)) t = Abs (x, T, abstract_over (v, t)) 
892 
 lambda (v as Var ((x, _), T)) t = Abs (x, T, abstract_over (v, t)) 

893 
 lambda v t = raise TERM ("lambda", [v, t]); 

0  894 

895 
(*Form an abstraction over a free variable.*) 

896 
fun absfree (a,T,body) = Abs(a, T, abstract_over (Free(a,T), body)); 

897 

898 
(*Abstraction over a list of free variables*) 

899 
fun list_abs_free ([ ] , t) = t 

13000  900 
 list_abs_free ((a,T)::vars, t) = 
0  901 
absfree(a, T, list_abs_free(vars,t)); 
902 

903 
(*Quantification over a list of free variables*) 

904 
fun list_all_free ([], t: term) = t 

13000  905 
 list_all_free ((a,T)::vars, t) = 
0  906 
(all T) $ (absfree(a, T, list_all_free(vars,t))); 
907 

908 
(*Quantification over a list of variables (already bound in body) *) 

909 
fun list_all ([], t) = t 

13000  910 
 list_all ((a,T)::vars, t) = 
0  911 
(all T) $ (Abs(a, T, list_all(vars,t))); 
912 

16678  913 
(*Replace the ATOMIC term ti by ui; inst = [(t1,u1), ..., (tn,un)]. 
0  914 
A simultaneous substitution: [ (a,b), (b,a) ] swaps a and b. *) 
16678  915 
fun subst_atomic [] tm = tm 
916 
 subst_atomic inst tm = 

917 
let 

918 
fun subst (Abs (a, T, body)) = Abs (a, T, subst body) 

919 
 subst (t $ u) = subst t $ subst u 

17314  920 
 subst t = if_none (AList.lookup (op aconv) inst t) t; 
16678  921 
in subst tm end; 
0  922 

16678  923 
(*Replace the ATOMIC type Ti by Ui; inst = [(T1,U1), ..., (Tn,Un)].*) 
924 
fun typ_subst_atomic [] ty = ty 

925 
 typ_subst_atomic inst ty = 

926 
let 

927 
fun subst (Type (a, Ts)) = Type (a, map subst Ts) 

17314  928 
 subst T = if_none (AList.lookup (op = : typ * typ > bool) inst T) T; 
16678  929 
in subst ty end; 
15797  930 

16678  931 
fun subst_atomic_types [] tm = tm 
932 
 subst_atomic_types inst tm = map_term_types (typ_subst_atomic inst) tm; 

933 

934 
fun typ_subst_TVars [] ty = ty 

935 
 typ_subst_TVars inst ty = 

936 
let 

937 
fun subst (Type (a, Ts)) = Type (a, map subst Ts) 

17271  938 
 subst (T as TVar (xi, _)) = if_none (AList.lookup (op =) inst xi) T 
16678  939 
 subst T = T; 
940 
in subst ty end; 

0  941 

16678  942 
fun subst_TVars [] tm = tm 
943 
 subst_TVars inst tm = map_term_types (typ_subst_TVars inst) tm; 

0  944 

16678  945 
(*see also Envir.norm_term*) 
946 
fun subst_Vars [] tm = tm 

947 
 subst_Vars inst tm = 

948 
let 

17271  949 
fun subst (t as Var (xi, _)) = if_none (AList.lookup (op =) inst xi) t 
16678  950 
 subst (Abs (a, T, t)) = Abs (a, T, subst t) 
951 
 subst (t $ u) = subst t $ subst u 

952 
 subst t = t; 

953 
in subst tm end; 

0  954 

16678  955 
(*see also Envir.norm_term*) 
956 
fun subst_vars ([], []) tm = tm 

957 
 subst_vars ([], inst) tm = subst_Vars inst tm 

958 
 subst_vars (instT, inst) tm = 

959 
let 

960 
fun subst (Const (a, T)) = Const (a, typ_subst_TVars instT T) 

961 
 subst (Free (a, T)) = Free (a, typ_subst_TVars instT T) 

962 
 subst (t as Var (xi, T)) = 

17271  963 
(case AList.lookup (op =) inst xi of 
16678  964 
NONE => Var (xi, typ_subst_TVars instT T) 
965 
 SOME t => t) 

966 
 subst (t as Bound _) = t 

967 
 subst (Abs (a, T, t)) = Abs (a, typ_subst_TVars instT T, subst t) 

968 
 subst (t $ u) = subst t $ subst u; 

969 
in subst tm end; 

0  970 

971 

16943  972 
(* instantiation of schematic variables (types before terms) *) 
16882  973 

974 
local exception SAME in 

975 

16943  976 
fun instantiateT_same [] _ = raise SAME 
977 
 instantiateT_same instT ty = 

16882  978 
let 
979 
fun subst_typ (Type (a, Ts)) = Type (a, subst_typs Ts) 

980 
 subst_typ (TVar v) = 

17314  981 
(case AList.lookup eq_tvar instT v of 
16882  982 
SOME T => T 
983 
 NONE => raise SAME) 

984 
 subst_typ _ = raise SAME 

985 
and subst_typs (T :: Ts) = 

986 
(subst_typ T :: (subst_typs Ts handle SAME => Ts) 

987 
handle SAME => T :: subst_typs Ts) 

988 
 subst_typs [] = raise SAME; 

989 
in subst_typ ty end; 

990 

991 
fun instantiate ([], []) tm = tm 

992 
 instantiate (instT, inst) tm = 

993 
let 

16943  994 
val substT = instantiateT_same instT; 
995 
fun subst (Const (c, T)) = Const (c, substT T) 

996 
 subst (Free (x, T)) = Free (x, substT T) 

16882  997 
 subst (Var (xi, T)) = 
16943  998 
let val (T', same) = (substT T, false) handle SAME => (T, true) in 
17314  999 
(case AList.lookup eq_var inst (xi, T') of 
16882  1000 
SOME t => t 
1001 
 NONE => if same then raise SAME else Var (xi, T')) 

1002 
end 

1003 
 subst (Bound _) = raise SAME 

1004 
 subst (Abs (x, T, t)) = 

16943  1005 
(Abs (x, substT T, subst t handle SAME => t) 
16882  1006 
handle SAME => Abs (x, T, subst t)) 
1007 
 subst (t $ u) = (subst t $ (subst u handle SAME => u) handle SAME => t $ subst u); 

1008 
in subst tm handle SAME => tm end; 

1009 

1010 
fun instantiateT instT ty = 

16943  1011 
instantiateT_same instT ty handle SAME => ty; 
16882  1012 

1013 
end; 

1014 

1015 

15573  1016 
(** Identifying firstorder terms **) 
1017 

1018 
(*Argument Ts is a reverse list of binder types, needed if term t contains Bound vars*) 

1019 
fun has_not_funtype Ts t = not (is_funtype (fastype_of1 (Ts,t))); 

1020 

16537  1021 
(*First order means in all terms of the form f(t1,...,tn) no argument has a 
16589  1022 
function type. The supplied quantifiers are excluded: their argument always 
1023 
has a function type through a recursive call into its body.*) 

16667  1024 
fun is_first_order quants = 
16589  1025 
let fun first_order1 Ts (Abs (_,T,body)) = first_order1 (T::Ts) body 
16667  1026 
 first_order1 Ts (Const(q,_) $ Abs(a,T,body)) = 
1027 
q mem_string quants andalso (*it is a known quantifier*) 

16589  1028 
not (is_funtype T) andalso first_order1 (T::Ts) body 
16667  1029 
 first_order1 Ts t = 
1030 
case strip_comb t of 

1031 
(Var _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts 

1032 
 (Free _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts 

1033 
 (Const _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts 

1034 
 (Bound _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts 

1035 
 (Abs _, ts) => false (*not in betanormal form*) 

1036 
 _ => error "first_order: unexpected case" 

16589  1037 
in first_order1 [] end; 
15573  1038 

16710  1039 

16990  1040 
(* maximum index of typs and terms *) 
0  1041 

16710  1042 
fun maxidx_typ (TVar ((_, j), _)) i = Int.max (i, j) 
1043 
 maxidx_typ (Type (_, Ts)) i = maxidx_typs Ts i 

1044 
 maxidx_typ (TFree _) i = i 

1045 
and maxidx_typs [] i = i 

1046 
 maxidx_typs (T :: Ts) i = maxidx_typs Ts (maxidx_typ T i); 

0  1047 

16710  1048 
fun maxidx_term (Var ((_, j), T)) i = maxidx_typ T (Int.max (i, j)) 
1049 
 maxidx_term (Const (_, T)) i = maxidx_typ T i 

1050 
 maxidx_term (Free (_, T)) i = maxidx_typ T i 

1051 
 maxidx_term (Bound _) i = i 

1052 
 maxidx_term (Abs (_, T, t)) i = maxidx_term t (maxidx_typ T i) 

1053 
 maxidx_term (t $ u) i = maxidx_term u (maxidx_term t i); 

0  1054 

16710  1055 
fun maxidx_of_typ T = maxidx_typ T ~1; 
1056 
fun maxidx_of_typs Ts = maxidx_typs Ts ~1; 

1057 
fun maxidx_of_term t = maxidx_term t ~1; 

13665  1058 

0  1059 

1060 

1061 
(**** Syntaxrelated declarations ****) 

1062 

1063 
(*** Printing ***) 

1064 

16943  1065 
(*Makes a variant of a name distinct from the names in 'used'. 
14676  1066 
First attaches the suffix and then increments this; 
12306
749a04f0cfb0
variant: preserve suffix of underscores (for skolem/internal names etc.);
wenzelm
parents:
11922
diff
changeset

1067 
preserves a suffix of underscores "_". *) 
16943  1068 
fun variant used name = 
12306
749a04f0cfb0
variant: preserve suffix of underscores (for skolem/internal names etc.);
wenzelm
parents:
11922
diff
changeset

1069 
let 
749a04f0cfb0
variant: preserve suffix of underscores (for skolem/internal names etc.);
wenzelm
parents:
11922
diff
changeset

1070 
val (c, u) = pairself implode (Library.take_suffix (equal "_") (Symbol.explode name)); 
16943  1071 
fun vary2 c = if ((c ^ u) mem_string used) then vary2 (Symbol.bump_string c) else c; 
1072 
fun vary1 c = if ((c ^ u) mem_string used) then vary2 (Symbol.bump_init c) else c; 

12306
749a04f0cfb0
variant: preserve suffix of underscores (for skolem/internal names etc.);
wenzelm
parents:
11922
diff
changeset

1073 
in vary1 (if c = "" then "u" else c) ^ u end; 
0  1074 

1075 
(*Create variants of the list of names, with priority to the first ones*) 

1076 
fun variantlist ([], used) = [] 

13000  1077 
 variantlist(b::bs, used) = 
0  1078 
let val b' = variant used b 
1079 
in b' :: variantlist (bs, b'::used) end; 

1080 

14695  1081 
(*Invent fresh names*) 
1082 
fun invent_names _ _ 0 = [] 

1083 
 invent_names used a n = 

1084 
let val b = Symbol.bump_string a in 

1085 
if a mem_string used then invent_names used b n 

1086 
else a :: invent_names used b (n  1) 

1087 
end; 

11353  1088 

16537  1089 

4017
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset

1090 
(** Consts etc. **) 
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset

1091 

15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15573
diff
changeset

1092 
fun add_typ_classes (Type (_, Ts), cs) = foldr add_typ_classes cs Ts 
4017
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset

1093 
 add_typ_classes (TFree (_, S), cs) = S union cs 
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset

1094 
 add_typ_classes (TVar (_, S), cs) = S union cs; 
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset

1095 

16294  1096 
fun add_typ_tycons (Type (c, Ts), cs) = foldr add_typ_tycons (c ins_string cs) Ts 
4017
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset

1097 
 add_typ_tycons (_, cs) = cs; 
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset

1098 

63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset

1099 
val add_term_classes = it_term_types add_typ_classes; 
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset

1100 
val add_term_tycons = it_term_types add_typ_tycons; 
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset

1101 

9319  1102 
fun add_term_consts (Const (c, _), cs) = c ins_string cs 
4017
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset

1103 
 add_term_consts (t $ u, cs) = add_term_consts (t, add_term_consts (u, cs)) 
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset

1104 
 add_term_consts (Abs (_, _, t), cs) = add_term_consts (t, cs) 
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset

1105 
 add_term_consts (_, cs) = cs; 
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset

1106 

13646  1107 
fun term_consts t = add_term_consts(t,[]); 
1108 

16943  1109 
fun exists_subterm P = 
1110 
let 

1111 
fun ex tm = P tm orelse 

1112 
(case tm of 

1113 
t $ u => ex t orelse ex u 

1114 
 Abs (_, _, t) => ex t 

1115 
 _ => false); 

1116 
in ex end; 

16108
cf468b93a02e
Implement cyclefree overloading, so that definitions cannot harm consistency any more (except of course via interaction with axioms).
obua
parents:
16035
diff
changeset

1117 

16943  1118 
fun exists_Const P = exists_subterm (fn Const c => P c  _ => false); 
4631  1119 

4017
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset

1120 
(*map classes, tycons*) 
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset

1121 
fun map_typ f g (Type (c, Ts)) = Type (g c, map (map_typ f g) Ts) 
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset

1122 
 map_typ f _ (TFree (x, S)) = TFree (x, map f S) 
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset

1123 
 map_typ f _ (TVar (xi, S)) = TVar (xi, map f S); 
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset

1124 

63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset

1125 
(*map classes, tycons, consts*) 
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset

1126 
fun map_term f g h (Const (c, T)) = Const (h c, map_typ f g T) 
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset

1127 
 map_term f g _ (Free (x, T)) = Free (x, map_typ f g T) 
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset

1128 
 map_term f g _ (Var (xi, T)) = Var (xi, map_typ f g T) 
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset

1129 
 map_term _ _ _ (t as Bound _) = t 
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset

1130 
 map_term f g h (Abs (x, T, t)) = Abs (x, map_typ f g T, map_term f g h t) 
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset

1131 
 map_term f g h (t $ u) = map_term f g h t $ map_term f g h u; 
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset

1132 

63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset

1133 

0  1134 
(** TFrees and TVars **) 
1135 

12802
c69bd9754473
added add_term_free_names (more precise/efficient than add_term_names);
wenzelm
parents:
12499
diff
changeset

1136 
(*Accumulates the names of Frees in the term, suppressing duplicates.*) 
c69bd9754473
added add_term_free_names (more precise/efficient than add_term_names);
wenzelm
parents:
12499
diff
changeset

1137 
fun add_term_free_names (Free(a,_), bs) = a ins_string bs 
c69bd9754473
added add_term_free_names (more precise/efficient than add_term_names);
wenzelm
parents:
12499
diff
changeset

1138 
 add_term_free_names (f$u, bs) = add_term_free_names (f, add_term_free_names(u, bs)) 
c69bd9754473
added add_term_free_names (more precise/efficient than add_term_names);
wenzelm
parents:
12499
diff
changeset

1139 
 add_term_free_names (Abs(_,_,t), bs) = add_term_free_names(t,bs) 
c69bd9754473
added add_term_free_names (more precise/efficient than add_term_names);
wenzelm
parents:
12499
diff
changeset

1140 
 add_term_free_names (_, bs) = bs; 
c69bd9754473
added add_term_free_names (more precise/efficient than add_term_names);
wenzelm
parents:
12499
diff
changeset

1141 

0  1142 
(*Accumulates the names in the term, suppressing duplicates. 
1143 
Includes Frees and Consts. For choosing unambiguous bound var names.*) 

10666  1144 
fun add_term_names (Const(a,_), bs) = NameSpace.base a ins_string bs 
2176  1145 
 add_term_names (Free(a,_), bs) = a ins_string bs 
0  1146 
 add_term_names (f$u, bs) = add_term_names (f, add_term_names(u, bs)) 
1147 
 add_term_names (Abs(_,_,t), bs) = add_term_names(t,bs) 

1148 
 add_term_names (_, bs) = bs; 

1149 

1150 
(*Accumulates the TVars in a type, suppressing duplicates. *) 

15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15573
diff
changeset

1151 
fun add_typ_tvars(Type(_,Ts),vs) = foldr add_typ_tvars vs Ts 
0  1152 
 add_typ_tvars(TFree(_),vs) = vs 
16294  1153 
 add_typ_tvars(TVar(v),vs) = insert (op =) v vs; 
0  1154 

1155 
(*Accumulates the TFrees in a type, suppressing duplicates. *) 

15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15573
diff
changeset

1156 
fun add_typ_tfree_names(Type(_,Ts),fs) = foldr add_typ_tfree_names fs Ts 
2176  1157 
 add_typ_tfree_names(TFree(f,_),fs) = f ins_string fs 
0  1158 
 add_typ_tfree_names(TVar(_),fs) = fs; 
1159 

15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15573
diff
changeset

1160 
fun add_typ_tfrees(Type(_,Ts),fs) = foldr add_typ_tfrees fs Ts 
16294  1161 
 add_typ_tfrees(TFree(f),fs) = insert (op =) f fs 
0  1162 
 add_typ_tfrees(TVar(_),fs) = fs; 
1163 

15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15573
diff
changeset

1164 
fun add_typ_varnames(Type(_,Ts),nms) = foldr add_typ_varnames nms Ts 
2176  1165 
 add_typ_varnames(TFree(nm,_),nms) = nm ins_string nms 
1166 
 add_typ_varnames(TVar((nm,_),_),nms) = nm ins_string nms; 

949
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset

1167 

0  1168 
(*Accumulates the TVars in a term, suppressing duplicates. *) 
1169 
val add_term_tvars = it_term_types add_typ_tvars; 

1170 

1171 
(*Accumulates the TFrees in a term, suppressing duplicates. *) 

1172 
val add_term_tfrees = it_term_types add_typ_tfrees; 

1173 
val add_term_tfree_names = it_term_types add_typ_tfree_names; 

1174 

949
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset

1175 
val add_term_tvarnames = it_term_types add_typ_varnames; 
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset

1176 

0  1177 
(*Nonlist versions*) 
1178 
fun typ_tfrees T = add_typ_tfrees(T,[]); 

1179 
fun typ_tvars T = add_typ_tvars(T,[]); 

1180 
fun term_tfrees t = add_term_tfrees(t,[]); 

1181 
fun term_tvars t = add_term_tvars(t,[]); 

1182 

949
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset

1183 
(*special code to enforce lefttoright collection of TVarindexnames*) 
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset

1184 

15570  1185 
fun add_typ_ixns(ixns,Type(_,Ts)) = Library.foldl add_typ_ixns (ixns,Ts) 
13000  1186 
 add_typ_ixns(ixns,TVar(ixn,_)) = if mem_ix (ixn, ixns) then ixns 
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset

1187 
else ixns@[ixn] 
949
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset

1188 
 add_typ_ixns(ixns,TFree(_)) = ixns; 
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset

1189 

83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset

1190 
fun add_term_tvar_ixns(Const(_,T),ixns) = add_typ_ixns(ixns,T) 
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset

1191 
 add_term_tvar_ixns(Free(_,T),ixns) = add_typ_ixns(ixns,T) 
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset

1192 
 add_term_tvar_ixns(Var(_,T),ixns) = add_typ_ixns(ixns,T) 
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset

1193 
 add_term_tvar_ixns(Bound _,ixns) = ixns 
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset

1194 
 add_term_tvar_ixns(Abs(_,T,t),ixns) = 
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset

1195 
add_term_tvar_ixns(t,add_typ_ixns(ixns,T)) 
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset

1196 
 add_term_tvar_ixns(f$t,ixns) = 
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset

1197 
add_term_tvar_ixns(t,add_term_tvar_ixns(f,ixns)); 
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset

1198 

16537  1199 

0  1200 
(** Frees and Vars **) 
1201 

1202 
(*Accumulates the Vars in the term, suppressing duplicates*) 

1203 
fun add_term_vars (t, vars: term list) = case t of 

16990  1204 
Var _ => OrdList.insert term_ord t vars 
0  1205 
 Abs (_,_,body) => add_term_vars(body,vars) 
1206 
 f$t => add_term_vars (f, add_term_vars(t, vars)) 

1207 
 _ => vars; 

1208 

1209 
fun term_vars t = add_term_vars(t,[]); 

1210 

1211 
(*Accumulates the Frees in the term, suppressing duplicates*) 

1212 
fun add_term_frees (t, frees: term list) = case t of 

16990  1213 
Free _ => OrdList.insert term_ord t frees 
0  1214 
 Abs (_,_,body) => add_term_frees(body,frees) 
1215 
 f$t => add_term_frees (f, add_term_frees(t, frees)) 

1216 
 _ => frees; 

1217 

1218 
fun term_frees t = add_term_frees(t,[]); 

1219 

1220 
(*Given an abstraction over P, replaces the bound variable by a Free variable 

16678  1221 
having a unique name*) 
0  1222 
fun variant_abs (a,T,P) = 
1223 
let val b = variant (add_term_names(P,[])) a 

2192
3bf092b5310b
Optimizations: removal of polymorphic equality; oneargument case
paulson
parents:
2182
diff
changeset

1224 
in (b, subst_bound (Free(b,T), P)) end; 
0  1225 

16678  1226 
fun dest_abs (x, T, body) = 
1227 
let 

1228 
fun name_clash (Free (y, _)) = (x = y) 

1229 
 name_clash (t $ u) = name_clash t orelse name_clash u 

1230 
 name_clash (Abs (_, _, t)) = name_clash t 

1231 
 name_clash _ = false; 

1232 
in 

1233 
if name_clash body then 

1234 
dest_abs (variant [x] x, T, body) (*potentially slow, but rarely happens*) 

1235 
else (x, subst_bound (Free (x, T), body)) 

1236 
end; 

1237 

16990  1238 
(*names for numbered variables  
1239 
preserves order wrt. int_ord vs. string_ord, avoids allocating new strings*) 

1240 
local 

1241 
val small_int = Vector.tabulate (1000, fn i => 

1242 
let val leading = if i < 10 then "00" else if i < 100 then "0" else "" 

1243 
in ":" ^ leading ^ string_of_int i end); 

1244 
in 

1245 
fun bound n = 

1246 
if n < 1000 then Vector.sub (small_int, n) 

1247 
else ":" ^ bound (n div 1000) ^ Vector.sub (small_int, n mod 1000); 

1248 
end; 

1249 

1250 
val is_bound = String.isPrefix ":"; 

16943  1251 

0  1252 
(* renames and reverses the strings in vars away from names *) 
1253 
fun rename_aTs names vars : (string*typ)list = 

1254 
let fun rename_aT (vars,(a,T)) = 

9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset

1255 
(variant (map #1 vars @ names) a, T) :: vars 
15570  1256 
in Library.foldl rename_aT ([],vars) end; 
0  1257 

1258 
fun rename_wrt_term t = rename_aTs (add_term_names(t,[])); 

1364
8ea1a962ad72
files now define a structure to allow SML/NJ to optimize the code
clasohm
parents:
1029
diff
changeset

1259 

1417  1260 

16943  1261 
(* zero var indexes *) 
4286
a09e3e6da2de
added foldl_atyps: ('a * typ > 'a) > 'a * typ > 'a;
wenzelm
parents:
4188
diff
changeset

1262 

16943  1263 
fun zero_var_inst vars = 
1264 
fold (fn v as ((x, i), X) => fn (used, inst) => 

1265 
let 

17642  1266 
val x' = variant used (if is_bound x then "u" else x); 
16943  1267 
val used' = x' :: used; 
1268 
in if x = x' andalso i = 0 then (used', inst) else (used', (v, ((x', 0), X)) :: inst) end) 

1269 
vars ([], []) > #2; 

4286
a09e3e6da2de
added foldl_atyps: ('a * typ > 'a) > 'a * typ > 'a;
wenzelm
parents:
4188
diff
changeset

1270 

16943  1271 
fun zero_var_indexesT ty = 
1272 
instantiateT (map (apsnd TVar) (zero_var_inst (sort tvar_ord (add_tvarsT ty [])))) ty; 

16790  1273 

16943  1274 
fun zero_var_indexes_inst tm = 
1275 
let 

1276 
val instT = map (apsnd TVar) (zero_var_inst (sort tvar_ord (fold_types add_tvarsT tm []))); 

1277 
val inst = 

1278 
add_vars tm [] > map (apsnd (instantiateT instT)) 

1279 
> sort var_ord > zero_var_inst > map (apsnd Var); 

1280 
in (instT, inst) end; 

12499  1281 

16943  1282 
fun zero_var_indexes tm = instantiate (zero_var_indexes_inst tm) tm; 
4286
a09e3e6da2de
added foldl_atyps: ('a * typ > 'a) > 'a * typ > 'a;
wenzelm
parents:
4188
diff
changeset

1283 

1417  1284 

9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset

1285 
(* dummy patterns *) 
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset

1286 

b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset

1287 
val dummy_patternN = "dummy_pattern"; 
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset

1288 

b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset

1289 
fun is_dummy_pattern (Const ("dummy_pattern", _)) = true 
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset

1290 
 is_dummy_pattern _ = false; 
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset

1291 

b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset

1292 
fun no_dummy_patterns tm = 
16787  1293 
if not (fold_aterms (fn t => fn b => b orelse is_dummy_pattern t) tm false) then tm 
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset

1294 
else raise TERM ("Illegal occurrence of '_' dummy pattern", [tm]); 
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset

1295 

11903  1296 
fun replace_dummy Ts (i, Const ("dummy_pattern", T)) = 
1297 
(i + 1, list_comb (Var (("_dummy_", i), Ts > T), map Bound (0 upto length Ts  1))) 

1298 
 replace_dummy Ts (i, Abs (x, T, t)) = 

1299 
let val (i', t') = replace_dummy (T :: Ts) (i, t) 

1300 
in (i', Abs (x, T, t')) end 

1301 
 replace_dummy Ts (i, t $ u) = 

1302 
let val (i', t') = replace_dummy Ts (i, t); val (i'', u') = replace_dummy Ts (i', u) 

1303 
in (i'', t' $ u') end 

1304 
 replace_dummy _ (i, a) = (i, a); 

1305 

1306 
val replace_dummy_patterns = replace_dummy []; 

9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset

1307 

10552  1308 
fun is_replaced_dummy_pattern ("_dummy_", _) = true 
1309 
 is_replaced_dummy_pattern _ = false; 

9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset

1310 

16035  1311 
fun show_dummy_patterns (Var (("_dummy_", _), T)) = Const ("dummy_pattern", T) 
1312 
 show_dummy_patterns (t $ u) = show_dummy_patterns t $ show_dummy_patterns u 

1313 
 show_dummy_patterns (Abs (x, T, t)) = Abs (x, T, show_dummy_patterns t) 

1314 
 show_dummy_patterns a = a; 

1315 

13484  1316 

1317 
(* adhoc freezing *) 

1318 

1319 
fun adhoc_freeze_vars tm = 

1320 
let 

1321 
fun mk_inst (var as Var ((a, i), T)) = 

1322 
let val x = a ^ Library.gensym "_" ^ string_of_int i 

1323 
in ((var, Free(x, T)), x) end; 

1324 
val (insts, xs) = split_list (map mk_inst (term_vars tm)); 

1325 
in (subst_atomic insts tm, xs) end; 

1326 

1327 

14786
24a7bc97a27a
moved some sort ops to sorts.ML; added string_of_vname (from Syntax module);
wenzelm
parents:
14695
diff
changeset

1328 
(* string_of_vname *) 
24a7bc97a27a
moved some sort ops to sorts.ML; added string_of_vname (from Syntax module);
wenzelm
parents:
14695
diff
changeset

1329 

15986  1330 
val show_question_marks = ref true; 
15472  1331 

14786
24a7bc97a27a
moved some sort ops to sorts.ML; added string_of_vname (from Syntax module);
wenzelm
parents:
14695
diff
changeset

1332 
fun string_of_vname (x, i) = 
24a7bc97a27a
moved some sort ops to sorts.ML; added string_of_vname (from Syntax module);
wenzelm
parents:
14695
diff
changeset

1333 
let 
15986  1334 
val question_mark = if ! show_question_marks then "?" else ""; 
1335 
val idx = string_of_int i; 

1336 
val dot = 

1337 
(case rev (Symbol.explode x) of 

1338 
_ :: "\\<^isub>" :: _ => false 

1339 
 _ :: "\\<^isup>" :: _ => false 

1340 
 c :: _ => Symbol.is_digit c 

1341 
 _ => true); 

14786
24a7bc97a27a
moved some sort ops to sorts.ML; added string_of_vname (from Syntax module);
wenzelm
parents:
14695
diff
changeset

1342 
in 
15986  1343 
if dot then question_mark ^ x ^ "." ^ idx 
1344 
else if i <> 0 then question_mark ^ x ^ idx 

1345 
else question_mark ^ x 

14786
24a7bc97a27a
moved some sort ops to sorts.ML; added string_of_vname (from Syntax module);
wenzelm
parents:
14695
diff
changeset

1346 
end; 
24a7bc97a27a
moved some sort ops to sorts.ML; added string_of_vname (from Syntax module);
wenzelm
parents:
14695
diff
changeset

1347 

24a7bc97a27a
moved some sort ops to sorts.ML; added string_of_vname (from Syntax module);
wenzelm
parents:
14695
diff
changeset

1348 
fun string_of_vname' (x, ~1) = x 
24a7bc97a27a
moved some sort ops to sorts.ML; added string_of_vname (from Syntax module);
wenzelm
parents:
14695
diff
changeset

1349 
 string_of_vname' xi = string_of_vname xi; 
24a7bc97a27a
moved some sort ops to sorts.ML; added string_of_vname (from Syntax module);
wenzelm
parents:
14695
diff
changeset

1350 

17777
05f5532a8289
added str_of_term (from HOL/Tools/ATP/recon_translate_proof.ML);
wenzelm
parents:
17756
diff
changeset

1351 

05f5532a8289
added str_of_term (from HOL/Tools/ATP/recon_translate_proof.ML);
wenzelm
parents:
17756
diff
changeset

1352 
(* str_of_term *) 
05f5532a8289
added str_of_term (from HOL/Tools/ATP/recon_translate_proof.ML);
wenzelm
parents:
17756
diff
changeset

1353 

05f5532a8289
added str_of_term (from HOL/Tools/ATP/recon_translate_proof.ML);
wenzelm
parents:
17756
diff
changeset

1354 
fun str_of_term (Const (c, _)) = c 
05f5532a8289
added str_of_term (from HOL/Tools/ATP/recon_translate_proof.ML);
wenzelm
parents:
17756
diff
changeset

1355 
 str_of_term (Free (x, _)) = x 
05f5532a8289
added str_of_term (from HOL/Tools/ATP/recon_translate_proof.ML);
wenzelm
parents:
17756
diff
changeset

1356 
 str_of_term (Var (xi, _)) = string_of_vname xi 
05f5532a8289
added str_of_term (from HOL/Tools/ATP/recon_translate_proof.ML);
wenzelm
parents:
17756
diff
changeset

1357 
 str_of_term (Bound i) = string_of_int i 
05f5532a8289
added str_of_term (from HOL/Tools/ATP/recon_translate_proof.ML);
wenzelm
parents:
17756
diff
changeset

1358 
 str_of_term (Abs (x, _, t)) = "%" ^ x ^ ". " ^ str_of_term t 
05f5532a8289
added str_of_term (from HOL/Tools/ATP/recon_translate_proof.ML);
wenzelm
parents:
17756
diff
changeset

1359 
 str_of_term (t $ u) = "(" ^ str_of_term t ^ " " ^ str_of_term u ^ ")"; 
05f5532a8289
added str_of_term (from HOL/Tools/ATP/recon_translate_proof.ML);
wenzelm
parents:
17756
diff
changeset

1360 

1364
8ea1a962ad72
files now define a structure to allow SML/NJ to optimize the code
clasohm
parents:
1029
diff
changeset

1361 
end; 
8ea1a962ad72
files now define a structure to allow SML/NJ to optimize the code
clasohm
parents:
1029
diff
changeset

1362 

4444  1363 
structure BasicTerm: BASIC_TERM = Term; 
1364 
open BasicTerm; 