author  wenzelm 
Thu, 16 Feb 2006 00:09:46 +0100  
changeset 19065  82e2d66f995b 
parent 19014  f70ced571ba8 
child 19394  9f69613362c1 
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 
18927  59 
val strip_abs: term > (string * typ) list * term 
4444  60 
val strip_abs_body: term > term 
61 
val strip_abs_vars: term > (string * typ) list 

62 
val strip_qnt_body: string > term > term 

63 
val strip_qnt_vars: string > term > (string * typ) list 

64 
val list_comb: term * term list > term 

65 
val strip_comb: term > term * term list 

66 
val head_of: term > term 

67 
val size_of_term: term > int 

18847  68 
val map_atyps: (typ > typ) > typ > typ 
69 
val map_aterms: (term > term) > term > term 

4444  70 
val map_type_tvar: (indexname * sort > typ) > typ > typ 
71 
val map_type_tfree: (string * sort > typ) > typ > typ 

72 
val map_term_types: (typ > typ) > term > term 

16943  73 
val fold_atyps: (typ > 'a > 'a) > typ > 'a > 'a 
74 
val fold_aterms: (term > 'a > 'a) > term > 'a > 'a 

75 
val fold_term_types: (term > typ > 'a > 'a) > term > 'a > 'a 

76 
val fold_types: (typ > 'a > 'a) > term > 'a > 'a 

18927  77 
val it_term_types: (typ * 'a > 'a) > term * 'a > 'a 
16943  78 
val add_term_names: term * string list > string list 
79 
val add_term_varnames: term > indexname list > indexname list 

80 
val term_varnames: term > indexname list 

18149  81 
val find_free: term > string > term option 
16710  82 
val aconv: term * term > bool 
83 
val aconvs: term list * term list > bool 

16537  84 
structure Vartab: TABLE 
85 
structure Typtab: TABLE 

86 
structure Termtab: TABLE 

4444  87 
val itselfT: typ > typ 
88 
val a_itselfT: typ 

89 
val propT: typ 

90 
val implies: term 

91 
val all: typ > term 

92 
val equals: typ > term 

93 
val strip_all_body: term > term 

94 
val strip_all_vars: term > (string * typ) list 

95 
val incr_bv: int * int * term > term 

96 
val incr_boundvars: int > term > term 

97 
val add_loose_bnos: term * int * int list > int list 

98 
val loose_bnos: term > int list 

99 
val loose_bvar: term * int > bool 

100 
val loose_bvar1: term * int > bool 

101 
val subst_bounds: term list * term > term 

102 
val subst_bound: term * term > term 

103 
val betapply: term * term > term 

18183  104 
val betapplys: term * term list > term 
4444  105 
val eq_ix: indexname * indexname > bool 
106 
val ins_ix: indexname * indexname list > indexname list 

107 
val mem_ix: indexname * indexname list > bool 

108 
val mem_term: term * term list > bool 

109 
val ins_term: term * term list > term list 

110 
val could_unify: term * term > bool 

111 
val subst_free: (term * term) list > term > term 

112 
val xless: (string * int) * indexname > bool 

113 
val abstract_over: term * term > term 

11922  114 
val lambda: term > term > term 
4444  115 
val absfree: string * typ * term > term 
17786  116 
val absdummy: typ * term > term 
4444  117 
val list_abs_free: (string * typ) list * term > term 
118 
val list_all_free: (string * typ) list * term > term 

119 
val list_all: (string * typ) list * term > term 

16710  120 
val subst_atomic: (term * term) list > term > term 
121 
val typ_subst_atomic: (typ * typ) list > typ > typ 

122 
val subst_atomic_types: (typ * typ) list > term > term 

123 
val typ_subst_TVars: (indexname * typ) list > typ > typ 

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

125 
val subst_Vars: (indexname * term) list > term > term 

126 
val subst_vars: (indexname * typ) list * (indexname * term) list > term > term 

127 
val is_first_order: string list > term > bool 

4444  128 
val maxidx_of_typ: typ > int 
129 
val maxidx_of_typs: typ list > int 

130 
val maxidx_of_term: term > int 

131 
val variant: string list > string > string 

132 
val variantlist: string list * string list > string list 

16537  133 
(*note reversed order of args wrt. variant!*) 
4444  134 
val add_term_consts: term * string list > string list 
13646  135 
val term_consts: term > string list 
16943  136 
val exists_subterm: (term > bool) > term > bool 
16710  137 
val exists_Const: (string * typ > bool) > term > bool 
138 
val add_term_free_names: term * string list > string list 

139 
val add_typ_tvars: typ * (indexname * sort) list > (indexname * sort) list 

140 
val add_typ_tfree_names: typ * string list > string list 

141 
val add_typ_tfrees: typ * (string * sort) list > (string * sort) list 

142 
val add_typ_varnames: typ * string list > string list 

143 
val add_term_tvars: term * (indexname * sort) list > (indexname * sort) list 

144 
val add_term_tfrees: term * (string * sort) list > (string * sort) list 

145 
val add_term_tfree_names: term * string list > string list 

146 
val add_term_tvarnames: term * string list > string list 

147 
val typ_tfrees: typ > (string * sort) list 

148 
val typ_tvars: typ > (indexname * sort) list 

149 
val term_tfrees: term > (string * sort) list 

150 
val term_tvars: term > (indexname * sort) list 

151 
val add_typ_ixns: indexname list * typ > indexname list 

152 
val add_term_tvar_ixns: term * indexname list > indexname list 

153 
val add_term_vars: term * term list > term list 

154 
val term_vars: term > term list 

4444  155 
val add_term_frees: term * term list > term list 
156 
val term_frees: term > term list 

16710  157 
val variant_abs: string * typ * term > string * term 
158 
val rename_wrt_term: term > (string * typ) list > (string * typ) list 

15986  159 
val show_question_marks: bool ref 
4444  160 
end; 
0  161 

4444  162 
signature TERM = 
163 
sig 

164 
include BASIC_TERM 

16710  165 
val argument_type_of: term > typ 
16943  166 
val add_tvarsT: typ > (indexname * sort) list > (indexname * sort) list 
167 
val add_tvars: term > (indexname * sort) list > (indexname * sort) list 

168 
val add_vars: term > (indexname * typ) list > (indexname * typ) list 

169 
val add_tfreesT: typ > (string * sort) list > (string * sort) list 

170 
val add_tfrees: term > (string * sort) list > (string * sort) list 

171 
val add_frees: term > (string * typ) list > (string * typ) list 

16678  172 
val fast_indexname_ord: indexname * indexname > order 
16537  173 
val indexname_ord: indexname * indexname > order 
174 
val sort_ord: sort * sort > order 

175 
val typ_ord: typ * typ > order 

16678  176 
val fast_term_ord: term * term > order 
16537  177 
val term_ord: term * term > order 
178 
val hd_ord: term * term > order 

179 
val termless: term * term > bool 

16570  180 
val term_lpo: (string > int) > term * term > order 
12981  181 
val match_bvars: (term * term) * (string * string) list > (string * string) list 
182 
val rename_abs: term > term > term > term option 

16943  183 
val eq_tvar: (indexname * sort) * (indexname * sort) > bool 
16882  184 
val eq_var: (indexname * typ) * (indexname * typ) > bool 
16943  185 
val tvar_ord: (indexname * sort) * (indexname * sort) > order 
186 
val var_ord: (indexname * typ) * (indexname * typ) > order 

16882  187 
val instantiate: ((indexname * sort) * typ) list * ((indexname * typ) * term) list 
188 
> term > term 

189 
val instantiateT: ((indexname * sort) * typ) list > typ > typ 

16710  190 
val maxidx_typ: typ > int > int 
191 
val maxidx_typs: typ list > int > int 

192 
val maxidx_term: term > int > int 

19014  193 
val variant_name: (string > bool) > string > string 
12499  194 
val invent_names: string list > string > int > string list 
16710  195 
val dest_abs: string * typ * term > string * term 
16990  196 
val bound: int > string 
197 
val is_bound: string > bool 

16943  198 
val zero_var_indexesT: typ > typ 
199 
val zero_var_indexes: term > term 

200 
val zero_var_indexes_inst: term > 

201 
((indexname * sort) * typ) list * ((indexname * typ) * term) list 

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val dummy_patternN: string 
18253  203 
val dummy_pattern: typ > term 
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val no_dummy_patterns: term > term 
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val replace_dummy_patterns: int * term > int * term 
10552  206 
val is_replaced_dummy_pattern: indexname > bool 
16035  207 
val show_dummy_patterns: term > term 
13484  208 
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  212 
end; 
213 

214 
structure Term: TERM = 

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struct 
0  216 

217 
(*Indexnames can be quickly renamed by adding an offset to the integer part, 

218 
for resolution.*) 

16537  219 
type indexname = string * int; 
0  220 

4626  221 
(* Types are classified by sorts. *) 
0  222 
type class = string; 
223 
type sort = class list; 

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type arity = string * sort list * sort; 
0  225 

226 
(* The sorts attached to TFrees and TVars specify the sort of that variable *) 

227 
datatype typ = Type of string * typ list 

228 
 TFree of string * sort 

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 TVar of indexname * sort; 
0  230 

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(*Terms. Bound variables are indicated by depth number. 
0  232 
Free variables, (scheme) variables and constants have names. 
4626  233 
An term is "closed" if every bound variable of level "lev" 
13000  234 
is enclosed by at least "lev" abstractions. 
0  235 

236 
It is possible to create meaningless terms containing loose bound vars 

237 
or type mismatches. But such terms are not allowed in rules. *) 

238 

13000  239 
datatype term = 
0  240 
Const of string * typ 
13000  241 
 Free of string * typ 
0  242 
 Var of indexname * typ 
243 
 Bound of int 

244 
 Abs of string*typ*term 

3965  245 
 op $ of term*term; 
0  246 

16537  247 
(*Errors involving type mismatches*) 
0  248 
exception TYPE of string * typ list * term list; 
249 

16537  250 
(*Errors errors involving terms*) 
0  251 
exception TERM of string * term list; 
252 

253 
(*Note variable naming conventions! 

254 
a,b,c: string 

255 
f,g,h: functions (including terms of function type) 

256 
i,j,m,n: int 

257 
t,u: term 

258 
v,w: indexnames 

259 
x,y: any 

260 
A,B,C: term (denoting formulae) 

261 
T,U: typ 

262 
*) 

263 

264 

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(** Types **) 
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16537  267 
(*dummy type for parsing and printing etc.*) 
268 
val dummyT = Type ("dummy", []); 

269 

270 
fun no_dummyT typ = 

271 
let 

272 
fun check (T as Type ("dummy", _)) = 

273 
raise TYPE ("Illegal occurrence of '_' dummy type", [T], []) 

274 
 check (Type (_, Ts)) = List.app check Ts 

275 
 check _ = (); 

276 
in check typ; typ end; 

277 

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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  281 
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  285 
fun dest_TVar (TVar x) = x 
286 
 dest_TVar T = raise TYPE ("dest_TVar", [T], []); 

287 
fun dest_TFree (TFree x) = x 

288 
 dest_TFree T = raise TYPE ("dest_TFree", [T], []); 

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289 

16537  290 

0  291 
(** Discriminators **) 
292 

7318  293 
fun is_Bound (Bound _) = true 
294 
 is_Bound _ = false; 

295 

0  296 
fun is_Const (Const _) = true 
297 
 is_Const _ = false; 

298 

299 
fun is_Free (Free _) = true 

300 
 is_Free _ = false; 

301 

302 
fun is_Var (Var _) = true 

303 
 is_Var _ = false; 

304 

305 
fun is_TVar (TVar _) = true 

306 
 is_TVar _ = false; 

307 

15573  308 
(*Differs from proofterm/is_fun in its treatment of TVar*) 
309 
fun is_funtype (Type("fun",[_,_])) = true 

310 
 is_funtype _ = false; 

311 

16537  312 

0  313 
(** Destructors **) 
314 

315 
fun dest_Const (Const x) = x 

316 
 dest_Const t = raise TERM("dest_Const", [t]); 

317 

318 
fun dest_Free (Free x) = x 

319 
 dest_Free t = raise TERM("dest_Free", [t]); 

320 

321 
fun dest_Var (Var x) = x 

322 
 dest_Var t = raise TERM("dest_Var", [t]); 

323 

324 

4464  325 
fun domain_type (Type("fun", [T,_])) = T 
326 
and range_type (Type("fun", [_,T])) = T; 

4064  327 

0  328 
(* maps [T1,...,Tn]>T to the list [T1,T2,...,Tn]*) 
329 
fun binder_types (Type("fun",[S,T])) = S :: binder_types T 

330 
 binder_types _ = []; 

331 

332 
(* maps [T1,...,Tn]>T to T*) 

333 
fun body_type (Type("fun",[S,T])) = body_type T 

334 
 body_type T = T; 

335 

336 
(* maps [T1,...,Tn]>T to ([T1,T2,...,Tn], T) *) 

337 
fun strip_type T : typ list * typ = 

338 
(binder_types T, body_type T); 

339 

340 

341 
(*Compute the type of the term, checking that combinations are welltyped 

342 
Ts = [T0,T1,...] holds types of bound variables 0, 1, ...*) 

343 
fun type_of1 (Ts, Const (_,T)) = T 

344 
 type_of1 (Ts, Free (_,T)) = T 

15570  345 
 type_of1 (Ts, Bound i) = (List.nth (Ts,i) 
346 
handle Subscript => raise TYPE("type_of: bound variable", [], [Bound i])) 

0  347 
 type_of1 (Ts, Var (_,T)) = T 
348 
 type_of1 (Ts, Abs (_,T,body)) = T > type_of1(T::Ts, body) 

13000  349 
 type_of1 (Ts, f$u) = 
0  350 
let val U = type_of1(Ts,u) 
351 
and T = type_of1(Ts,f) 

352 
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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("type_of: type mismatch in application", [T1,U], [f$u]) 
13000  356 
 _ => raise TYPE 
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("type_of: function type is expected in application", 
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[T,U], [f$u]) 
0  359 
end; 
360 

361 
fun type_of t : typ = type_of1 ([],t); 

362 

363 
(*Determines the type of a term, with minimal checking*) 

13000  364 
fun fastype_of1 (Ts, f$u) = 
61  365 
(case fastype_of1 (Ts,f) of 
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Type("fun",[_,T]) => T 
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 _ => raise TERM("fastype_of: expected function type", [f$u])) 
61  368 
 fastype_of1 (_, Const (_,T)) = T 
369 
 fastype_of1 (_, Free (_,T)) = T 

15570  370 
 fastype_of1 (Ts, Bound i) = (List.nth(Ts,i) 
371 
handle Subscript => raise TERM("fastype_of: Bound", [Bound i])) 

13000  372 
 fastype_of1 (_, Var (_,T)) = T 
61  373 
 fastype_of1 (Ts, Abs (_,T,u)) = T > fastype_of1 (T::Ts, u); 
374 

375 
fun fastype_of t : typ = fastype_of1 ([],t); 

0  376 

16678  377 
(*Determine the argument type of a function*) 
378 
fun argument_type_of tm = 

379 
let 

380 
fun argT i (Type ("fun", [T, U])) = if i = 0 then T else argT (i  1) U 

381 
 argT _ T = raise TYPE ("argument_type_of", [T], []); 

382 

383 
fun arg 0 _ (Abs (_, T, _)) = T 

384 
 arg i Ts (Abs (_, T, t)) = arg (i  1) (T :: Ts) t 

385 
 arg i Ts (t $ _) = arg (i + 1) Ts t 

386 
 arg i Ts a = argT i (fastype_of1 (Ts, a)); 

387 
in arg 0 [] tm end; 

388 

0  389 

15570  390 
val list_abs = Library.foldr (fn ((x, T), t) => Abs (x, T, t)); 
10806  391 

18927  392 
fun strip_abs (Abs (a, T, t)) = 
393 
let val (a', t') = strip_abs t 

394 
in ((a, T) :: a', t') end 

395 
 strip_abs t = ([], t); 

396 

0  397 
(* maps (x1,...,xn)t to t *) 
13000  398 
fun strip_abs_body (Abs(_,_,t)) = strip_abs_body t 
0  399 
 strip_abs_body u = u; 
400 

401 
(* maps (x1,...,xn)t to [x1, ..., xn] *) 

13000  402 
fun strip_abs_vars (Abs(a,T,t)) = (a,T) :: strip_abs_vars t 
0  403 
 strip_abs_vars u = [] : (string*typ) list; 
404 

405 

406 
fun strip_qnt_body qnt = 

407 
let fun strip(tm as Const(c,_)$Abs(_,_,t)) = if c=qnt then strip t else tm 

408 
 strip t = t 

409 
in strip end; 

410 

411 
fun strip_qnt_vars qnt = 

412 
let fun strip(Const(c,_)$Abs(a,T,t)) = if c=qnt then (a,T)::strip t else [] 

413 
 strip t = [] : (string*typ) list 

414 
in strip end; 

415 

416 

417 
(* maps (f, [t1,...,tn]) to f(t1,...,tn) *) 

15570  418 
val list_comb : term * term list > term = Library.foldl (op $); 
0  419 

420 

421 
(* maps f(t1,...,tn) to (f, [t1,...,tn]) ; naturally tailrecursive*) 

13000  422 
fun strip_comb u : term * term list = 
0  423 
let fun stripc (f$t, ts) = stripc (f, t::ts) 
13000  424 
 stripc x = x 
0  425 
in stripc(u,[]) end; 
426 

427 

428 
(* maps f(t1,...,tn) to f , which is never a combination *) 

429 
fun head_of (f$t) = head_of f 

430 
 head_of u = u; 

431 

432 

16599  433 
(*number of atoms and abstractions in a term*) 
434 
fun size_of_term tm = 

435 
let 

16678  436 
fun add_size (t $ u, n) = add_size (t, add_size (u, n)) 
437 
 add_size (Abs (_ ,_, t), n) = add_size (t, n + 1) 

438 
 add_size (_, n) = n + 1; 

439 
in add_size (tm, 0) end; 

0  440 

18847  441 
fun map_atyps f (Type (a, Ts)) = Type (a, map (map_atyps f) Ts) 
18976
4efb82669880
fixed the most silly bug conceivable in map_atyps
haftmann
parents:
18975
diff
changeset

442 
 map_atyps f T = f T; 
18847  443 

444 
fun map_aterms f (t $ u) = map_aterms f t $ map_aterms f u 

445 
 map_aterms f (Abs (a, T, t)) = Abs (a, T, map_aterms f t) 

446 
 map_aterms f t = f t; 

447 

18981  448 
fun map_type_tvar f = map_atyps (fn TVar x => f x  T => T); 
449 
fun map_type_tfree f = map_atyps (fn TFree x => f x  T => T); 

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

450 

0  451 
fun map_term_types f = 
16678  452 
let 
453 
fun map_aux (Const (a, T)) = Const (a, f T) 

454 
 map_aux (Free (a, T)) = Free (a, f T) 

455 
 map_aux (Var (v, T)) = Var (v, f T) 

456 
 map_aux (t as Bound _) = t 

457 
 map_aux (Abs (a, T, t)) = Abs (a, f T, map_aux t) 

458 
 map_aux (t $ u) = map_aux t $ map_aux u; 

459 
in map_aux end; 

0  460 

461 
(* iterate a function over all types in a term *) 

462 
fun it_term_types f = 

463 
let fun iter(Const(_,T), a) = f(T,a) 

464 
 iter(Free(_,T), a) = f(T,a) 

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

466 
 iter(Abs(_,T,t), a) = iter(t,f(T,a)) 

467 
 iter(f$u, a) = iter(f, iter(u, a)) 

468 
 iter(Bound _, a) = a 

469 
in iter end 

470 

471 

16943  472 
(* fold types and terms *) 
473 

474 
(*fold atoms of type*) 

475 
fun fold_atyps f (Type (_, Ts)) = fold (fold_atyps f) Ts 

476 
 fold_atyps f T = f T; 

477 

478 
(*fold atoms of term*) 

479 
fun fold_aterms f (t $ u) = fold_aterms f t #> fold_aterms f u 

480 
 fold_aterms f (Abs (_, _, t)) = fold_aterms f t 

481 
 fold_aterms f a = f a; 

482 

483 
(*fold types of term*) 

484 
fun fold_term_types f (t as Const (_, T)) = f t T 

485 
 fold_term_types f (t as Free (_, T)) = f t T 

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

487 
 fold_term_types f (Bound _) = I 

488 
 fold_term_types f (t as Abs (_, T, b)) = f t T #> fold_term_types f b 

489 
 fold_term_types f (t $ u) = fold_term_types f t #> fold_term_types f u; 

490 

491 
fun fold_types f = fold_term_types (K f); 

492 

493 
(*collect variables*) 

494 
val add_tvarsT = fold_atyps (fn TVar v => insert (op =) v  _ => I); 

495 
val add_tvars = fold_types add_tvarsT; 

496 
val add_vars = fold_aterms (fn Var v => insert (op =) v  _ => I); 

497 
val add_tfreesT = fold_atyps (fn TFree v => insert (op =) v  _ => I); 

498 
val add_tfrees = fold_types add_tfreesT; 

499 
val add_frees = fold_aterms (fn Free v => insert (op =) v  _ => I); 

500 

501 
(*collect variable names*) 

502 
val add_term_varnames = fold_aterms (fn Var (xi, _) => insert (op =) xi  _ => I); 

503 
fun term_varnames t = add_term_varnames t []; 

504 

18149  505 
fun find_free t x = 
506 
let 

507 
exception Found of term; 

508 
fun find (t as Free (x', _)) = if x = x' then raise Found t else I 

509 
 find _ = I; 

510 
in (fold_aterms find t (); NONE) handle Found v => SOME v end; 

511 

512 

16943  513 

16678  514 
(** Comparing terms, types, sorts etc. **) 
16537  515 

16678  516 
(* fast syntactic comparison *) 
517 

518 
fun fast_indexname_ord ((x, i), (y, j)) = 

519 
(case int_ord (i, j) of EQUAL => fast_string_ord (x, y)  ord => ord); 

16537  520 

16599  521 
fun sort_ord SS = 
522 
if pointer_eq SS then EQUAL 

16990  523 
else dict_ord fast_string_ord SS; 
16678  524 

525 
local 

16537  526 

16678  527 
fun cons_nr (TVar _) = 0 
528 
 cons_nr (TFree _) = 1 

529 
 cons_nr (Type _) = 2; 

16537  530 

16678  531 
in 
16537  532 

533 
fun typ_ord TU = 

534 
if pointer_eq TU then EQUAL 

535 
else 

536 
(case TU of 

16678  537 
(Type (a, Ts), Type (b, Us)) => 
16990  538 
(case fast_string_ord (a, b) of EQUAL => dict_ord typ_ord (Ts, Us)  ord => ord) 
16678  539 
 (TFree (a, S), TFree (b, S')) => 
540 
(case fast_string_ord (a, b) of EQUAL => sort_ord (S, S')  ord => ord) 

541 
 (TVar (xi, S), TVar (yj, S')) => 

542 
(case fast_indexname_ord (xi, yj) of EQUAL => sort_ord (S, S')  ord => ord) 

543 
 (T, U) => int_ord (cons_nr T, cons_nr U)); 

544 

545 
end; 

546 

547 
local 

548 

549 
fun cons_nr (Const _) = 0 

550 
 cons_nr (Free _) = 1 

551 
 cons_nr (Var _) = 2 

552 
 cons_nr (Bound _) = 3 

553 
 cons_nr (Abs _) = 4 

554 
 cons_nr (_ $ _) = 5; 

555 

556 
fun struct_ord (Abs (_, _, t), Abs (_, _, u)) = struct_ord (t, u) 

557 
 struct_ord (t1 $ t2, u1 $ u2) = 

558 
(case struct_ord (t1, u1) of EQUAL => struct_ord (t2, u2)  ord => ord) 

559 
 struct_ord (t, u) = int_ord (cons_nr t, cons_nr u); 

560 

561 
fun atoms_ord (Abs (_, _, t), Abs (_, _, u)) = atoms_ord (t, u) 

562 
 atoms_ord (t1 $ t2, u1 $ u2) = 

563 
(case atoms_ord (t1, u1) of EQUAL => atoms_ord (t2, u2)  ord => ord) 

564 
 atoms_ord (Const (a, _), Const (b, _)) = fast_string_ord (a, b) 

565 
 atoms_ord (Free (x, _), Free (y, _)) = fast_string_ord (x, y) 

566 
 atoms_ord (Var (xi, _), Var (yj, _)) = fast_indexname_ord (xi, yj) 

567 
 atoms_ord (Bound i, Bound j) = int_ord (i, j) 

568 
 atoms_ord _ = sys_error "atoms_ord"; 

569 

570 
fun types_ord (Abs (_, T, t), Abs (_, U, u)) = 

571 
(case typ_ord (T, U) of EQUAL => types_ord (t, u)  ord => ord) 

572 
 types_ord (t1 $ t2, u1 $ u2) = 

573 
(case types_ord (t1, u1) of EQUAL => types_ord (t2, u2)  ord => ord) 

574 
 types_ord (Const (_, T), Const (_, U)) = typ_ord (T, U) 

575 
 types_ord (Free (_, T), Free (_, U)) = typ_ord (T, U) 

576 
 types_ord (Var (_, T), Var (_, U)) = typ_ord (T, U) 

577 
 types_ord (Bound _, Bound _) = EQUAL 

578 
 types_ord _ = sys_error "types_ord"; 

579 

580 
in 

581 

582 
fun fast_term_ord tu = 

583 
if pointer_eq tu then EQUAL 

584 
else 

585 
(case struct_ord tu of 

586 
EQUAL => (case atoms_ord tu of EQUAL => types_ord tu  ord => ord) 

587 
 ord => ord); 

588 

589 
fun op aconv tu = (fast_term_ord tu = EQUAL); 

590 
fun aconvs ts_us = (list_ord fast_term_ord ts_us = EQUAL); 

591 

592 
structure Vartab = TableFun(type key = indexname val ord = fast_indexname_ord); 

593 
structure Typtab = TableFun(type key = typ val ord = typ_ord); 

594 
structure Termtab = TableFun(type key = term val ord = fast_term_ord); 

595 

596 
end; 

16537  597 

598 

599 
(* term_ord *) 

600 

601 
(*a linear wellfounded ACcompatible ordering for terms: 

602 
s < t <=> 1. size(s) < size(t) or 

603 
2. size(s) = size(t) and s=f(...) and t=g(...) and f<g or 

604 
3. size(s) = size(t) and s=f(s1..sn) and t=f(t1..tn) and 

605 
(s1..sn) < (t1..tn) (lexicographically)*) 

16678  606 

607 
fun indexname_ord ((x, i), (y, j)) = 

608 
(case int_ord (i, j) of EQUAL => string_ord (x, y)  ord => ord); 

609 

16667  610 
local 
611 

612 
fun hd_depth (t $ _, n) = hd_depth (t, n + 1) 

613 
 hd_depth p = p; 

16537  614 

615 
fun dest_hd (Const (a, T)) = (((a, 0), T), 0) 

616 
 dest_hd (Free (a, T)) = (((a, 0), T), 1) 

617 
 dest_hd (Var v) = (v, 2) 

618 
 dest_hd (Bound i) = ((("", i), dummyT), 3) 

619 
 dest_hd (Abs (_, T, _)) = ((("", 0), T), 4); 

620 

16667  621 
in 
622 

16537  623 
fun term_ord tu = 
624 
if pointer_eq tu then EQUAL 

625 
else 

626 
(case tu of 

627 
(Abs (_, T, t), Abs(_, U, u)) => 

628 
(case term_ord (t, u) of EQUAL => typ_ord (T, U)  ord => ord) 

16667  629 
 (t, u) => 
16537  630 
(case int_ord (size_of_term t, size_of_term u) of 
631 
EQUAL => 

16943  632 
(case prod_ord hd_ord int_ord (hd_depth (t, 0), hd_depth (u, 0)) of 
633 
EQUAL => args_ord (t, u)  ord => ord) 

16537  634 
 ord => ord)) 
635 
and hd_ord (f, g) = 

636 
prod_ord (prod_ord indexname_ord typ_ord) int_ord (dest_hd f, dest_hd g) 

16667  637 
and args_ord (f $ t, g $ u) = 
638 
(case args_ord (f, g) of EQUAL => term_ord (t, u)  ord => ord) 

639 
 args_ord _ = EQUAL; 

16537  640 

641 
fun termless tu = (term_ord tu = LESS); 

642 

16667  643 
end; 
644 

645 

646 
(** Lexicographic path order on terms **) 

647 

648 
(* 

16570  649 
See Baader & Nipkow, Term rewriting, CUP 1998. 
650 
Without variables. Const, Var, Bound, Free and Abs are treated all as 

651 
constants. 

652 

653 
f_ord maps strings to integers and serves two purposes: 

654 
 Predicate on constant symbols. Those that are not recognised by f_ord 

655 
must be mapped to ~1. 

656 
 Order on the recognised symbols. These must be mapped to distinct 

657 
integers >= 0. 

658 

16667  659 
*) 
16570  660 

661 
local 

16667  662 
fun dest_hd f_ord (Const (a, T)) = 
16570  663 
let val ord = f_ord a in 
664 
if ord = ~1 then ((1, ((a, 0), T)), 0) else ((0, (("", ord), T)), 0) 

665 
end 

666 
 dest_hd _ (Free (a, T)) = ((1, ((a, 0), T)), 0) 

667 
 dest_hd _ (Var v) = ((1, v), 1) 

668 
 dest_hd _ (Bound i) = ((1, (("", i), dummyT)), 2) 

669 
 dest_hd _ (Abs (_, T, _)) = ((1, (("", 0), T)), 3); 

670 

671 
fun term_lpo f_ord (s, t) = 

672 
let val (f, ss) = strip_comb s and (g, ts) = strip_comb t in 

673 
if forall (fn si => term_lpo f_ord (si, t) = LESS) ss 

674 
then case hd_ord f_ord (f, g) of 

16667  675 
GREATER => 
676 
if forall (fn ti => term_lpo f_ord (s, ti) = GREATER) ts 

677 
then GREATER else LESS 

16570  678 
 EQUAL => 
16667  679 
if forall (fn ti => term_lpo f_ord (s, ti) = GREATER) ts 
680 
then list_ord (term_lpo f_ord) (ss, ts) 

681 
else LESS 

16570  682 
 LESS => LESS 
683 
else GREATER 

684 
end 

685 
and hd_ord f_ord (f, g) = case (f, g) of 

686 
(Abs (_, T, t), Abs (_, U, u)) => 

687 
(case term_lpo f_ord (t, u) of EQUAL => typ_ord (T, U)  ord => ord) 

688 
 (_, _) => prod_ord (prod_ord int_ord 

689 
(prod_ord indexname_ord typ_ord)) int_ord 

690 
(dest_hd f_ord f, dest_hd f_ord g) 

691 
in 

692 
val term_lpo = term_lpo 

693 
end; 

694 

16537  695 

0  696 
(** Connectives of higher order logic **) 
697 

375  698 
fun itselfT ty = Type ("itself", [ty]); 
14854  699 
val a_itselfT = itselfT (TFree ("'a", [])); 
375  700 

0  701 
val propT : typ = Type("prop",[]); 
702 

703 
val implies = Const("==>", propT>propT>propT); 

704 

705 
fun all T = Const("all", (T>propT)>propT); 

706 

707 
fun equals T = Const("==", T>T>propT); 

708 

709 
(* maps !!x1...xn. t to t *) 

13000  710 
fun strip_all_body (Const("all",_)$Abs(_,_,t)) = strip_all_body t 
0  711 
 strip_all_body t = t; 
712 

713 
(* maps !!x1...xn. t to [x1, ..., xn] *) 

714 
fun strip_all_vars (Const("all",_)$Abs(a,T,t)) = 

13000  715 
(a,T) :: strip_all_vars t 
0  716 
 strip_all_vars t = [] : (string*typ) list; 
717 

718 
(*increments a term's nonlocal bound variables 

719 
required when moving a term within abstractions 

720 
inc is increment for bound variables 

721 
lev is level at which a bound variable is considered 'loose'*) 

13000  722 
fun incr_bv (inc, lev, u as Bound i) = if i>=lev then Bound(i+inc) else u 
0  723 
 incr_bv (inc, lev, Abs(a,T,body)) = 
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset

724 
Abs(a, T, incr_bv(inc,lev+1,body)) 
13000  725 
 incr_bv (inc, lev, f$t) = 
0  726 
incr_bv(inc,lev,f) $ incr_bv(inc,lev,t) 
727 
 incr_bv (inc, lev, u) = u; 

728 

729 
fun incr_boundvars 0 t = t 

730 
 incr_boundvars inc t = incr_bv(inc,0,t); 

731 

12981  732 
(*Scan a pair of terms; while they are similar, 
733 
accumulate corresponding bound vars in "al"*) 

734 
fun match_bvs(Abs(x,_,s),Abs(y,_,t), al) = 

735 
match_bvs(s, t, if x="" orelse y="" then al 

736 
else (x,y)::al) 

737 
 match_bvs(f$s, g$t, al) = match_bvs(f,g,match_bvs(s,t,al)) 

738 
 match_bvs(_,_,al) = al; 

739 

740 
(* strip abstractions created by parameters *) 

741 
fun match_bvars((s,t),al) = match_bvs(strip_abs_body s, strip_abs_body t, al); 

742 

743 
fun rename_abs pat obj t = 

744 
let 

745 
val ren = match_bvs (pat, obj, []); 

746 
fun ren_abs (Abs (x, T, b)) = 

18942  747 
Abs (the_default x (AList.lookup (op =) ren x), T, ren_abs b) 
12981  748 
 ren_abs (f $ t) = ren_abs f $ ren_abs t 
749 
 ren_abs t = t 

15531  750 
in if null ren then NONE else SOME (ren_abs t) end; 
0  751 

752 
(*Accumulate all 'loose' bound vars referring to level 'lev' or beyond. 

753 
(Bound 0) is loose at level 0 *) 

13000  754 
fun add_loose_bnos (Bound i, lev, js) = 
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset

755 
if i<lev then js else (ilev) ins_int js 
0  756 
 add_loose_bnos (Abs (_,_,t), lev, js) = add_loose_bnos (t, lev+1, js) 
757 
 add_loose_bnos (f$t, lev, js) = 

13000  758 
add_loose_bnos (f, lev, add_loose_bnos (t, lev, js)) 
0  759 
 add_loose_bnos (_, _, js) = js; 
760 

761 
fun loose_bnos t = add_loose_bnos (t, 0, []); 

762 

763 
(* loose_bvar(t,k) iff t contains a 'loose' bound variable referring to 

764 
level k or beyond. *) 

765 
fun loose_bvar(Bound i,k) = i >= k 

766 
 loose_bvar(f$t, k) = loose_bvar(f,k) orelse loose_bvar(t,k) 

767 
 loose_bvar(Abs(_,_,t),k) = loose_bvar(t,k+1) 

768 
 loose_bvar _ = false; 

769 

2792  770 
fun loose_bvar1(Bound i,k) = i = k 
771 
 loose_bvar1(f$t, k) = loose_bvar1(f,k) orelse loose_bvar1(t,k) 

772 
 loose_bvar1(Abs(_,_,t),k) = loose_bvar1(t,k+1) 

773 
 loose_bvar1 _ = false; 

0  774 

775 
(*Substitute arguments for loose bound variables. 

776 
Betareduction of arg(n1)...arg0 into t replacing (Bound i) with (argi). 

4626  777 
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

778 
and the appropriate call is subst_bounds([b,a], c) . 
0  779 
Loose bound variables >=n are reduced by "n" to 
780 
compensate for the disappearance of lambdas. 

781 
*) 

13000  782 
fun subst_bounds (args: term list, t) : term = 
19065  783 
let 
784 
exception SAME; 

785 
val n = length args; 

786 
fun subst (t as Bound i, lev) = 

787 
(if i < lev then raise SAME (*var is locally bound*) 

788 
else incr_boundvars lev (List.nth (args, i  lev)) 

789 
handle Subscript => Bound (i  n)) (*loose: change it*) 

790 
 subst (Abs (a, T, body), lev) = Abs (a, T, subst (body, lev + 1)) 

791 
 subst (f $ t, lev) = 

792 
(subst (f, lev) $ (subst (t, lev) handle SAME => t) handle SAME => f $ subst (t, lev)) 

793 
 subst _ = raise SAME; 

794 
in case args of [] => t  _ => (subst (t, 0) handle SAME => t) end; 

0  795 

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

796 
(*Special case: one argument*) 
13000  797 
fun subst_bound (arg, t) : term = 
19065  798 
let 
799 
exception SAME; 

800 
fun subst (Bound i, lev) = 

801 
if i < lev then raise SAME (*var is locally bound*) 

802 
else if i = lev then incr_boundvars lev arg 

803 
else Bound (i  1) (*loose: change it*) 

804 
 subst (Abs (a, T, body), lev) = Abs (a, T, subst (body, lev + 1)) 

805 
 subst (f $ t, lev) = 

806 
(subst (f, lev) $ (subst (t, lev) handle SAME => t) handle SAME => f $ subst (t, lev)) 

807 
 subst _ = raise SAME; 

808 
in subst (t, 0) handle SAME => t end; 

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

809 

0  810 
(*betareduce if possible, else form application*) 
2192
3bf092b5310b
Optimizations: removal of polymorphic equality; oneargument case
paulson
parents:
2182
diff
changeset

811 
fun betapply (Abs(_,_,t), u) = subst_bound (u,t) 
0  812 
 betapply (f,u) = f$u; 
813 

18183  814 
val betapplys = Library.foldl betapply; 
815 

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

816 

16882  817 
(** Specialized equality, membership, insertion etc. **) 
2192
3bf092b5310b
Optimizations: removal of polymorphic equality; oneargument case
paulson
parents:
2182
diff
changeset

818 

16882  819 
(* indexnames *) 
820 

16724  821 
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

822 

2959  823 
fun mem_ix (_, []) = false 
16882  824 
 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

825 

16882  826 
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

827 

0  828 

16882  829 
(* variables *) 
830 

16943  831 
fun eq_tvar ((xi, S: sort), (xi', S')) = eq_ix (xi, xi') andalso S = S'; 
832 
fun eq_var ((xi, T: typ), (xi', T')) = eq_ix (xi, xi') andalso T = T'; 

833 

834 
val tvar_ord = prod_ord indexname_ord sort_ord; 

835 
val var_ord = prod_ord indexname_ord typ_ord; 

16882  836 

837 

838 
(* terms *) 

2176  839 

840 
fun mem_term (_, []) = false 

16882  841 
 mem_term (t, t'::ts) = t aconv t' orelse mem_term (t, ts); 
2176  842 

843 
fun ins_term(t,ts) = if mem_term(t,ts) then ts else t :: ts; 

844 

16882  845 

13000  846 
(*A fast unification filter: true unless the two terms cannot be unified. 
0  847 
Terms must be NORMAL. Treats all Vars as distinct. *) 
848 
fun could_unify (t,u) = 

849 
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

850 
 matchrands _ = true 
0  851 
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

852 
(_, Var _) => true 
0  853 
 (Var _, _) => true 
854 
 (Const(a,_), Const(b,_)) => a=b andalso matchrands(t,u) 

855 
 (Free(a,_), Free(b,_)) => a=b andalso matchrands(t,u) 

856 
 (Bound i, Bound j) => i=j andalso matchrands(t,u) 

857 
 (Abs _, _) => true (*because of possible eta equality*) 

858 
 (_, Abs _) => true 

859 
 _ => false 

860 
end; 

861 

862 
(*Substitute new for free occurrences of old in a term*) 

863 
fun subst_free [] = (fn t=>t) 

864 
 subst_free pairs = 

13000  865 
let fun substf u = 
17314  866 
case AList.lookup (op aconv) pairs u of 
15531  867 
SOME u' => u' 
868 
 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

869 
 t$u' => substf t $ substf u' 
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset

870 
 _ => u) 
0  871 
in substf end; 
872 

873 
(*a total, irreflexive ordering on index names*) 

874 
fun xless ((a,i), (b,j): indexname) = i<j orelse (i=j andalso a<b); 

875 

876 

13000  877 
(*Abstraction of the term "body" over its occurrences of v, 
0  878 
which must contain no loose bound variables. 
879 
The resulting term is ready to become the body of an Abs.*) 

16882  880 
fun abstract_over (v, body) = 
881 
let 

16990  882 
exception SAME; 
883 
fun abs lev tm = 

884 
if v aconv tm then Bound lev 

16882  885 
else 
16990  886 
(case tm of 
887 
Abs (a, T, t) => Abs (a, T, abs (lev + 1) t) 

888 
 t $ u => (abs lev t $ (abs lev u handle SAME => u) handle SAME => t $ abs lev u) 

889 
 _ => raise SAME); 

890 
in abs 0 body handle SAME => body end; 

0  891 

18975  892 
fun lambda (v as Const (x, T)) t = Abs (NameSpace.base x, T, abstract_over (v, t)) 
18942  893 
 lambda (v as Free (x, T)) t = Abs (x, T, abstract_over (v, t)) 
13665  894 
 lambda (v as Var ((x, _), T)) t = Abs (x, T, abstract_over (v, t)) 
895 
 lambda v t = raise TERM ("lambda", [v, t]); 

0  896 

897 
(*Form an abstraction over a free variable.*) 

898 
fun absfree (a,T,body) = Abs(a, T, abstract_over (Free(a,T), body)); 

17786  899 
fun absdummy (T, body) = Abs ("uu", T, body); 
0  900 

901 
(*Abstraction over a list of free variables*) 

902 
fun list_abs_free ([ ] , t) = t 

13000  903 
 list_abs_free ((a,T)::vars, t) = 
0  904 
absfree(a, T, list_abs_free(vars,t)); 
905 

906 
(*Quantification over a list of free variables*) 

907 
fun list_all_free ([], t: term) = t 

13000  908 
 list_all_free ((a,T)::vars, t) = 
0  909 
(all T) $ (absfree(a, T, list_all_free(vars,t))); 
910 

911 
(*Quantification over a list of variables (already bound in body) *) 

912 
fun list_all ([], t) = t 

13000  913 
 list_all ((a,T)::vars, t) = 
0  914 
(all T) $ (Abs(a, T, list_all(vars,t))); 
915 

16678  916 
(*Replace the ATOMIC term ti by ui; inst = [(t1,u1), ..., (tn,un)]. 
0  917 
A simultaneous substitution: [ (a,b), (b,a) ] swaps a and b. *) 
16678  918 
fun subst_atomic [] tm = tm 
919 
 subst_atomic inst tm = 

920 
let 

921 
fun subst (Abs (a, T, body)) = Abs (a, T, subst body) 

922 
 subst (t $ u) = subst t $ subst u 

18942  923 
 subst t = the_default t (AList.lookup (op aconv) inst t); 
16678  924 
in subst tm end; 
0  925 

16678  926 
(*Replace the ATOMIC type Ti by Ui; inst = [(T1,U1), ..., (Tn,Un)].*) 
927 
fun typ_subst_atomic [] ty = ty 

928 
 typ_subst_atomic inst ty = 

929 
let 

930 
fun subst (Type (a, Ts)) = Type (a, map subst Ts) 

18942  931 
 subst T = the_default T (AList.lookup (op = : typ * typ > bool) inst T); 
16678  932 
in subst ty end; 
15797  933 

16678  934 
fun subst_atomic_types [] tm = tm 
935 
 subst_atomic_types inst tm = map_term_types (typ_subst_atomic inst) tm; 

936 

937 
fun typ_subst_TVars [] ty = ty 

938 
 typ_subst_TVars inst ty = 

939 
let 

940 
fun subst (Type (a, Ts)) = Type (a, map subst Ts) 

18942  941 
 subst (T as TVar (xi, _)) = the_default T (AList.lookup (op =) inst xi) 
16678  942 
 subst T = T; 
943 
in subst ty end; 

0  944 

16678  945 
fun subst_TVars [] tm = tm 
946 
 subst_TVars inst tm = map_term_types (typ_subst_TVars inst) tm; 

0  947 

16678  948 
(*see also Envir.norm_term*) 
949 
fun subst_Vars [] tm = tm 

950 
 subst_Vars inst tm = 

951 
let 

18942  952 
fun subst (t as Var (xi, _)) = the_default t (AList.lookup (op =) inst xi) 
16678  953 
 subst (Abs (a, T, t)) = Abs (a, T, subst t) 
954 
 subst (t $ u) = subst t $ subst u 

955 
 subst t = t; 

956 
in subst tm end; 

0  957 

16678  958 
(*see also Envir.norm_term*) 
959 
fun subst_vars ([], []) tm = tm 

960 
 subst_vars ([], inst) tm = subst_Vars inst tm 

961 
 subst_vars (instT, inst) tm = 

962 
let 

963 
fun subst (Const (a, T)) = Const (a, typ_subst_TVars instT T) 

964 
 subst (Free (a, T)) = Free (a, typ_subst_TVars instT T) 

965 
 subst (t as Var (xi, T)) = 

17271  966 
(case AList.lookup (op =) inst xi of 
16678  967 
NONE => Var (xi, typ_subst_TVars instT T) 
968 
 SOME t => t) 

969 
 subst (t as Bound _) = t 

970 
 subst (Abs (a, T, t)) = Abs (a, typ_subst_TVars instT T, subst t) 

971 
 subst (t $ u) = subst t $ subst u; 

972 
in subst tm end; 

0  973 

974 

16943  975 
(* instantiation of schematic variables (types before terms) *) 
16882  976 

977 
local exception SAME in 

978 

16943  979 
fun instantiateT_same [] _ = raise SAME 
980 
 instantiateT_same instT ty = 

16882  981 
let 
982 
fun subst_typ (Type (a, Ts)) = Type (a, subst_typs Ts) 

983 
 subst_typ (TVar v) = 

17314  984 
(case AList.lookup eq_tvar instT v of 
16882  985 
SOME T => T 
986 
 NONE => raise SAME) 

987 
 subst_typ _ = raise SAME 

988 
and subst_typs (T :: Ts) = 

989 
(subst_typ T :: (subst_typs Ts handle SAME => Ts) 

990 
handle SAME => T :: subst_typs Ts) 

991 
 subst_typs [] = raise SAME; 

992 
in subst_typ ty end; 

993 

994 
fun instantiate ([], []) tm = tm 

995 
 instantiate (instT, inst) tm = 

996 
let 

16943  997 
val substT = instantiateT_same instT; 
998 
fun subst (Const (c, T)) = Const (c, substT T) 

999 
 subst (Free (x, T)) = Free (x, substT T) 

16882  1000 
 subst (Var (xi, T)) = 
16943  1001 
let val (T', same) = (substT T, false) handle SAME => (T, true) in 
17314  1002 
(case AList.lookup eq_var inst (xi, T') of 
16882  1003 
SOME t => t 
1004 
 NONE => if same then raise SAME else Var (xi, T')) 

1005 
end 

1006 
 subst (Bound _) = raise SAME 

1007 
 subst (Abs (x, T, t)) = 

16943  1008 
(Abs (x, substT T, subst t handle SAME => t) 
16882  1009 
handle SAME => Abs (x, T, subst t)) 
1010 
 subst (t $ u) = (subst t $ (subst u handle SAME => u) handle SAME => t $ subst u); 

1011 
in subst tm handle SAME => tm end; 

1012 

1013 
fun instantiateT instT ty = 

16943  1014 
instantiateT_same instT ty handle SAME => ty; 
16882  1015 

1016 
end; 

1017 

1018 

15573  1019 
(** Identifying firstorder terms **) 
1020 

1021 
(*Argument Ts is a reverse list of binder types, needed if term t contains Bound vars*) 

1022 
fun has_not_funtype Ts t = not (is_funtype (fastype_of1 (Ts,t))); 

1023 

16537  1024 
(*First order means in all terms of the form f(t1,...,tn) no argument has a 
16589  1025 
function type. The supplied quantifiers are excluded: their argument always 
1026 
has a function type through a recursive call into its body.*) 

16667  1027 
fun is_first_order quants = 
16589  1028 
let fun first_order1 Ts (Abs (_,T,body)) = first_order1 (T::Ts) body 
16667  1029 
 first_order1 Ts (Const(q,_) $ Abs(a,T,body)) = 
1030 
q mem_string quants andalso (*it is a known quantifier*) 

16589  1031 
not (is_funtype T) andalso first_order1 (T::Ts) body 
16667  1032 
 first_order1 Ts t = 
1033 
case strip_comb t of 

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

1035 
 (Free _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts 

1036 
 (Const _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts 

1037 
 (Bound _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts 

1038 
 (Abs _, ts) => false (*not in betanormal form*) 

1039 
 _ => error "first_order: unexpected case" 

16589  1040 
in first_order1 [] end; 
15573  1041 

16710  1042 

16990  1043 
(* maximum index of typs and terms *) 
0  1044 

16710  1045 
fun maxidx_typ (TVar ((_, j), _)) i = Int.max (i, j) 
1046 
 maxidx_typ (Type (_, Ts)) i = maxidx_typs Ts i 

1047 
 maxidx_typ (TFree _) i = i 

1048 
and maxidx_typs [] i = i 

1049 
 maxidx_typs (T :: Ts) i = maxidx_typs Ts (maxidx_typ T i); 

0  1050 

16710  1051 
fun maxidx_term (Var ((_, j), T)) i = maxidx_typ T (Int.max (i, j)) 
1052 
 maxidx_term (Const (_, T)) i = maxidx_typ T i 

1053 
 maxidx_term (Free (_, T)) i = maxidx_typ T i 

1054 
 maxidx_term (Bound _) i = i 

1055 
 maxidx_term (Abs (_, T, t)) i = maxidx_term t (maxidx_typ T i) 

1056 
 maxidx_term (t $ u) i = maxidx_term u (maxidx_term t i); 

0  1057 

16710  1058 
fun maxidx_of_typ T = maxidx_typ T ~1; 
1059 
fun maxidx_of_typs Ts = maxidx_typs Ts ~1; 

1060 
fun maxidx_of_term t = maxidx_term t ~1; 

13665  1061 

0  1062 

1063 

1064 
(**** Syntaxrelated declarations ****) 

1065 

1066 
(*** Printing ***) 

1067 

19014  1068 
(*Makes a variant of a name distinct from already used names. First 
1069 
attaches the suffix and then increments this; preserves a suffix of 

1070 
underscores "_". *) 

1071 
fun variant_name used name = 

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

1072 
let 
19014  1073 
val (c, u) = pairself implode (Library.take_suffix (fn s => s = "_") (Symbol.explode name)); 
1074 
fun vary2 c = if used (c ^ u) then vary2 (Symbol.bump_string c) else c; 

1075 
fun vary1 c = if used (c ^ u) 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

1076 
in vary1 (if c = "" then "u" else c) ^ u end; 
0  1077 

19014  1078 
fun variant used_names = variant_name (member (op =) used_names); 
1079 

0  1080 
(*Create variants of the list of names, with priority to the first ones*) 
1081 
fun variantlist ([], used) = [] 

13000  1082 
 variantlist(b::bs, used) = 
0  1083 
let val b' = variant used b 
1084 
in b' :: variantlist (bs, b'::used) end; 

1085 

14695  1086 
(*Invent fresh names*) 
1087 
fun invent_names _ _ 0 = [] 

1088 
 invent_names used a n = 

1089 
let val b = Symbol.bump_string a in 

1090 
if a mem_string used then invent_names used b n 

1091 
else a :: invent_names used b (n  1) 

1092 
end; 

11353  1093 

16537  1094 

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

1095 
(** Consts etc. **) 
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset

1096 

18995  1097 
fun add_term_consts (Const (c, _), cs) = insert (op =) c cs 
4017
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset

1098 
 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

1099 
 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

1100 
 add_term_consts (_, cs) = cs; 
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset

1101 

13646  1102 
fun term_consts t = add_term_consts(t,[]); 
1103 

16943  1104 
fun exists_subterm P = 
1105 
let 

1106 
fun ex tm = P tm orelse 

1107 
(case tm of 

1108 
t $ u => ex t orelse ex u 

1109 
 Abs (_, _, t) => ex t 

1110 
 _ => false); 

1111 
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

1112 

16943  1113 
fun exists_Const P = exists_subterm (fn Const c => P c  _ => false); 
4631  1114 

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

1115 

0  1116 
(** TFrees and TVars **) 
1117 

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

1118 
(*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

1119 
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

1120 
 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

1121 
 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

1122 
 add_term_free_names (_, bs) = bs; 
c69bd9754473
added add_term_free_names (more precise/efficient than add_term_names);
wenzelm
parents:
12499
diff
changeset

1123 

0  1124 
(*Accumulates the names in the term, suppressing duplicates. 
1125 
Includes Frees and Consts. For choosing unambiguous bound var names.*) 

10666  1126 
fun add_term_names (Const(a,_), bs) = NameSpace.base a ins_string bs 
2176  1127 
 add_term_names (Free(a,_), bs) = a ins_string bs 
0  1128 
 add_term_names (f$u, bs) = add_term_names (f, add_term_names(u, bs)) 
1129 
 add_term_names (Abs(_,_,t), bs) = add_term_names(t,bs) 

1130 
 add_term_names (_, bs) = bs; 

1131 

1132 
(*Accumulates the TVars in a type, suppressing duplicates. *) 

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

1133 
fun add_typ_tvars(Type(_,Ts),vs) = foldr add_typ_tvars vs Ts 
0  1134 
 add_typ_tvars(TFree(_),vs) = vs 
16294  1135 
 add_typ_tvars(TVar(v),vs) = insert (op =) v vs; 
0  1136 

1137 
(*Accumulates the TFrees in a type, suppressing duplicates. *) 

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

1138 
fun add_typ_tfree_names(Type(_,Ts),fs) = foldr add_typ_tfree_names fs Ts 
2176  1139 
 add_typ_tfree_names(TFree(f,_),fs) = f ins_string fs 
0  1140 
 add_typ_tfree_names(TVar(_),fs) = fs; 
1141 

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

1142 
fun add_typ_tfrees(Type(_,Ts),fs) = foldr add_typ_tfrees fs Ts 
16294  1143 
 add_typ_tfrees(TFree(f),fs) = insert (op =) f fs 
0  1144 
 add_typ_tfrees(TVar(_),fs) = fs; 
1145 

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

1146 
fun add_typ_varnames(Type(_,Ts),nms) = foldr add_typ_varnames nms Ts 
2176  1147 
 add_typ_varnames(TFree(nm,_),nms) = nm ins_string nms 
1148 
 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

1149 

0  1150 
(*Accumulates the TVars in a term, suppressing duplicates. *) 
1151 
val add_term_tvars = it_term_types add_typ_tvars; 

1152 

1153 
(*Accumulates the TFrees in a term, suppressing duplicates. *) 

1154 
val add_term_tfrees = it_term_types add_typ_tfrees; 

1155 
val add_term_tfree_names = it_term_types add_typ_tfree_names; 

1156 

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

1157 
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

1158 

0  1159 
(*Nonlist versions*) 
1160 
fun typ_tfrees T = add_typ_tfrees(T,[]); 

1161 
fun typ_tvars T = add_typ_tvars(T,[]); 

1162 
fun term_tfrees t = add_term_tfrees(t,[]); 

1163 
fun term_tvars t = add_term_tvars(t,[]); 

1164 

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

1165 
(*special code to enforce lefttoright collection of TVarindexnames*) 
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset

1166 

15570  1167 
fun add_typ_ixns(ixns,Type(_,Ts)) = Library.foldl add_typ_ixns (ixns,Ts) 
13000  1168 
 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

1169 
else ixns@[ixn] 
949
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset

1170 
 add_typ_ixns(ixns,TFree(_)) = ixns; 
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset

1171 

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

1172 
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

1173 
 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

1174 
 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

1175 
 add_term_tvar_ixns(Bound _,ixns) = ixns 
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset

1176 
 add_term_tvar_ixns(Abs(_,T,t),ixns) = 
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset

1177 
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

1178 
 add_term_tvar_ixns(f$t,ixns) = 
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset

1179 
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

1180 

16537  1181 

0  1182 
(** Frees and Vars **) 
1183 

1184 
(*Accumulates the Vars in the term, suppressing duplicates*) 

1185 
fun add_term_vars (t, vars: term list) = case t of 

16990  1186 
Var _ => OrdList.insert term_ord t vars 
0  1187 
 Abs (_,_,body) => add_term_vars(body,vars) 
1188 
 f$t => add_term_vars (f, add_term_vars(t, vars)) 

1189 
 _ => vars; 

1190 

1191 
fun term_vars t = add_term_vars(t,[]); 

1192 

1193 
(*Accumulates the Frees in the term, suppressing duplicates*) 

1194 
fun add_term_frees (t, frees: term list) = case t of 

16990  1195 
Free _ => OrdList.insert term_ord t frees 
0  1196 
 Abs (_,_,body) => add_term_frees(body,frees) 
1197 
 f$t => add_term_frees (f, add_term_frees(t, frees)) 

1198 
 _ => frees; 

1199 

1200 
fun term_frees t = add_term_frees(t,[]); 

1201 

1202 
(*Given an abstraction over P, replaces the bound variable by a Free variable 

17851  1203 
having a unique name  SLOW!*) 
0  1204 
fun variant_abs (a,T,P) = 
1205 
let val b = variant (add_term_names(P,[])) a 

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

1206 
in (b, subst_bound (Free(b,T), P)) end; 
0  1207 

16678  1208 
fun dest_abs (x, T, body) = 
1209 
let 

1210 
fun name_clash (Free (y, _)) = (x = y) 

1211 
 name_clash (t $ u) = name_clash t orelse name_clash u 

1212 
 name_clash (Abs (_, _, t)) = name_clash t 

1213 
 name_clash _ = false; 

1214 
in 

1215 
if name_clash body then 

1216 
dest_abs (variant [x] x, T, body) (*potentially slow, but rarely happens*) 

1217 
else (x, subst_bound (Free (x, T), body)) 

1218 
end; 

1219 

16990  1220 
(*names for numbered variables  
1221 
preserves order wrt. int_ord vs. string_ord, avoids allocating new strings*) 

1222 
local 

1223 
val small_int = Vector.tabulate (1000, fn i => 

1224 
let val leading = if i < 10 then "00" else if i < 100 then "0" else "" 

1225 
in ":" ^ leading ^ string_of_int i end); 

1226 
in 

1227 
fun bound n = 

1228 
if n < 1000 then Vector.sub (small_int, n) 

1229 
else ":" ^ bound (n div 1000) ^ Vector.sub (small_int, n mod 1000); 

1230 
end; 

1231 

1232 
val is_bound = String.isPrefix ":"; 

16943  1233 

0  1234 
(* renames and reverses the strings in vars away from names *) 
1235 
fun rename_aTs names vars : (string*typ)list = 

1236 
let fun rename_aT (vars,(a,T)) = 

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

1237 
(variant (map #1 vars @ names) a, T) :: vars 
15570  1238 
in Library.foldl rename_aT ([],vars) end; 
0  1239 

1240 
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

1241 

1417  1242 

16943  1243 
(* zero var indexes *) 
4286
a09e3e6da2de
added foldl_atyps: ('a * typ > 'a) > 'a * typ > 'a;
wenzelm
parents:
4188
diff
changeset

1244 

16943  1245 
fun zero_var_inst vars = 
1246 
fold (fn v as ((x, i), X) => fn (used, inst) => 

1247 
let 

17642  1248 
val x' = variant used (if is_bound x then "u" else x); 
16943  1249 
val used' = x' :: used; 
1250 
in if x = x' andalso i = 0 then (used', inst) else (used', (v, ((x', 0), X)) :: inst) end) 

1251 
vars ([], []) > #2; 

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

1252 

16943  1253 
fun zero_var_indexesT ty = 
1254 
instantiateT (map (apsnd TVar) (zero_var_inst (sort tvar_ord (add_tvarsT ty [])))) ty; 

16790  1255 

16943  1256 
fun zero_var_indexes_inst tm = 
1257 
let 

1258 
val instT = map (apsnd TVar) (zero_var_inst (sort tvar_ord (fold_types add_tvarsT tm []))); 

1259 
val inst = 

1260 
add_vars tm [] > map (apsnd (instantiateT instT)) 

1261 
> sort var_ord > zero_var_inst > map (apsnd Var); 

1262 
in (instT, inst) end; 

12499  1263 

16943  1264 
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

1265 

1417  1266 

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

1267 
(* dummy patterns *) 
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset

1268 

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

1269 
val dummy_patternN = "dummy_pattern"; 
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset

1270 

18253  1271 
fun dummy_pattern T = Const (dummy_patternN, T); 
1272 

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

1273 
fun is_dummy_pattern (Const ("dummy_pattern", _)) = true 
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset

1274 
 is_dummy_pattern _ = false; 
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset

1275 

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

1276 
fun no_dummy_patterns tm = 
16787  1277 
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

1278 
else raise TERM ("Illegal occurrence of '_' dummy pattern", [tm]); 
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset

1279 

11903  1280 
fun replace_dummy Ts (i, Const ("dummy_pattern", T)) = 
1281 
(i + 1, list_comb (Var (("_dummy_", i), Ts > T), map Bound (0 upto length Ts  1))) 

1282 
 replace_dummy Ts (i, Abs (x, T, t)) = 

1283 
let val (i', t') = replace_dummy (T :: Ts) (i, t) 

1284 
in (i', Abs (x, T, t')) end 

1285 
 replace_dummy Ts (i, t $ u) = 

1286 
let val (i', t') = replace_dummy Ts (i, t); val (i'', u') = replace_dummy Ts (i', u) 

1287 
in (i'', t' $ u') end 

1288 
 replace_dummy _ (i, a) = (i, a); 

1289 

1290 
val replace_dummy_patterns = replace_dummy []; 

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

1291 

10552  1292 
fun is_replaced_dummy_pattern ("_dummy_", _) = true 
1293 
 is_replaced_dummy_pattern _ = false; 

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

1294 

16035  1295 
fun show_dummy_patterns (Var (("_dummy_", _), T)) = Const ("dummy_pattern", T) 
1296 
 show_dummy_patterns (t $ u) = show_dummy_patterns t $ show_dummy_patterns u 

1297 
 show_dummy_patterns (Abs (x, T, t)) = Abs (x, T, show_dummy_patterns t) 

1298 
 show_dummy_patterns a = a; 

1299 

13484  1300 

1301 
(* adhoc freezing *) 

1302 

1303 
fun adhoc_freeze_vars tm = 

1304 
let 

1305 
fun mk_inst (var as Var ((a, i), T)) = 

1306 
let val x = a ^ Library.gensym "_" ^ string_of_int i 

1307 
in ((var, Free(x, T)), x) end; 

1308 
val (insts, xs) = split_list (map mk_inst (term_vars tm)); 

1309 
in (subst_atomic insts tm, xs) end; 

1310 

1311 

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

1312 
(* string_of_vname *) 
24a7bc97a27a
moved some sort ops to sorts.ML; added string_of_vname (from Syntax module);
wenzelm
parents:
14695
diff
changeset

1313 

15986  1314 
val show_question_marks = ref true; 
15472  1315 

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

1316 
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

1317 
let 
15986  1318 
val question_mark = if ! show_question_marks then "?" else ""; 
1319 
val idx = string_of_int i; 

1320 
val dot = 

1321 
(case rev (Symbol.explode x) of 

1322 
_ :: "\\<^isub>" :: _ => false 

1323 
 _ :: "\\<^isup>" :: _ => false 

1324 
 c :: _ => Symbol.is_digit c 

1325 
 _ => true); 

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

1326 
in 
15986  1327 
if dot then question_mark ^ x ^ "." ^ idx 
1328 
else if i <> 0 then question_mark ^ x ^ idx 

1329 
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

1330 
end; 
24a7bc97a27a
moved some sort ops to sorts.ML; added string_of_vname (from Syntax module);
wenzelm
parents:
14695
diff
changeset

1331 

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

1333 
 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

1334 

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

1335 

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

1336 
(* str_of_term *) 
05f5532a8289
added str_of_term (from HOL/Tools/ATP/recon_translate_proof.ML);
wenzelm
parents:
17756
diff
changeset

1337 

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

1338 
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

1339 
 str_of_term (Free (x, _)) = x 
05f5532a8289
added str_of_term (from HOL/Tools/ATP/recon_translate_proof.ML);
wenzelm
parents:
17756
diff
changeset

1340 
 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

1341 
 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

1342 
 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

1343 
 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

1344 

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

1345 
end; 
8ea1a962ad72
files now define a structure to allow SML/NJ to optimize the code
clasohm
parents:
1029
diff
changeset

1346 

4444  1347 
structure BasicTerm: BASIC_TERM = Term; 
1348 
open BasicTerm; 