author | wenzelm |
Fri, 07 Oct 2005 23:29:00 +0200 | |
changeset 17789 | ccba4e900023 |
parent 17786 | f06d6498ebf0 |
child 17851 | 2fa4f9b54761 |
permissions | -rw-r--r-- |
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1 |
(* Title: Pure/term.ML |
0 | 2 |
ID: $Id$ |
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3 |
Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
0 | 4 |
Copyright Cambridge University 1992 |
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5 |
|
4444 | 6 |
Simply typed lambda-calculus: types, terms, and basic operations. |
0 | 7 |
*) |
8 |
||
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9 |
infix 9 $; |
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10 |
infixr 5 -->; |
4444 | 11 |
infixr --->; |
12 |
infix aconv; |
|
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13 |
|
4444 | 14 |
signature BASIC_TERM = |
15 |
sig |
|
16 |
type indexname |
|
17 |
type class |
|
18 |
type sort |
|
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19 |
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 |
17786 | 115 |
val absdummy: typ * term -> term |
4444 | 116 |
val list_abs_free: (string * typ) list * term -> term |
117 |
val list_all_free: (string * typ) list * term -> term |
|
118 |
val list_all: (string * typ) list * term -> term |
|
16710 | 119 |
val subst_atomic: (term * term) list -> term -> term |
120 |
val typ_subst_atomic: (typ * typ) list -> typ -> typ |
|
121 |
val subst_atomic_types: (typ * typ) list -> term -> term |
|
122 |
val typ_subst_TVars: (indexname * typ) list -> typ -> typ |
|
123 |
val subst_TVars: (indexname * typ) list -> term -> term |
|
124 |
val subst_Vars: (indexname * term) list -> term -> term |
|
125 |
val subst_vars: (indexname * typ) list * (indexname * term) list -> term -> term |
|
126 |
val is_first_order: string list -> term -> bool |
|
4444 | 127 |
val maxidx_of_typ: typ -> int |
128 |
val maxidx_of_typs: typ list -> int |
|
129 |
val maxidx_of_term: term -> int |
|
130 |
val variant: string list -> string -> string |
|
131 |
val variantlist: string list * string list -> string list |
|
16537 | 132 |
(*note reversed order of args wrt. variant!*) |
4444 | 133 |
val add_typ_classes: typ * class list -> class list |
134 |
val add_typ_tycons: typ * string list -> string list |
|
135 |
val add_term_classes: term * class list -> class list |
|
16710 | 136 |
val add_term_tycons: term * string list -> string list |
4444 | 137 |
val add_term_consts: term * string list -> string list |
13646 | 138 |
val term_consts: term -> string list |
16943 | 139 |
val exists_subterm: (term -> bool) -> term -> bool |
16710 | 140 |
val exists_Const: (string * typ -> bool) -> term -> bool |
141 |
val add_term_free_names: term * string list -> string list |
|
142 |
val add_typ_tvars: typ * (indexname * sort) list -> (indexname * sort) list |
|
143 |
val add_typ_tfree_names: typ * string list -> string list |
|
144 |
val add_typ_tfrees: typ * (string * sort) list -> (string * sort) list |
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145 |
val add_typ_varnames: typ * string list -> string list |
|
146 |
val add_term_tvars: term * (indexname * sort) list -> (indexname * sort) list |
|
147 |
val add_term_tfrees: term * (string * sort) list -> (string * sort) list |
|
148 |
val add_term_tfree_names: term * string list -> string list |
|
149 |
val add_term_tvarnames: term * string list -> string list |
|
150 |
val typ_tfrees: typ -> (string * sort) list |
|
151 |
val typ_tvars: typ -> (indexname * sort) list |
|
152 |
val term_tfrees: term -> (string * sort) list |
|
153 |
val term_tvars: term -> (indexname * sort) list |
|
154 |
val add_typ_ixns: indexname list * typ -> indexname list |
|
155 |
val add_term_tvar_ixns: term * indexname list -> indexname list |
|
156 |
val add_term_vars: term * term list -> term list |
|
157 |
val term_vars: term -> term list |
|
4444 | 158 |
val add_term_frees: term * term list -> term list |
159 |
val term_frees: term -> term list |
|
16710 | 160 |
val variant_abs: string * typ * term -> string * term |
161 |
val rename_wrt_term: term -> (string * typ) list -> (string * typ) list |
|
15986 | 162 |
val show_question_marks: bool ref |
4444 | 163 |
end; |
0 | 164 |
|
4444 | 165 |
signature TERM = |
166 |
sig |
|
167 |
include BASIC_TERM |
|
16710 | 168 |
val argument_type_of: term -> typ |
16943 | 169 |
val add_tvarsT: typ -> (indexname * sort) list -> (indexname * sort) list |
170 |
val add_tvars: term -> (indexname * sort) list -> (indexname * sort) list |
|
171 |
val add_vars: term -> (indexname * typ) list -> (indexname * typ) list |
|
172 |
val add_tfreesT: typ -> (string * sort) list -> (string * sort) list |
|
173 |
val add_tfrees: term -> (string * sort) list -> (string * sort) list |
|
174 |
val add_frees: term -> (string * typ) list -> (string * typ) list |
|
16678 | 175 |
val fast_indexname_ord: indexname * indexname -> order |
16537 | 176 |
val indexname_ord: indexname * indexname -> order |
177 |
val sort_ord: sort * sort -> order |
|
178 |
val typ_ord: typ * typ -> order |
|
16678 | 179 |
val fast_term_ord: term * term -> order |
16537 | 180 |
val term_ord: term * term -> order |
181 |
val hd_ord: term * term -> order |
|
182 |
val termless: term * term -> bool |
|
16570 | 183 |
val term_lpo: (string -> int) -> term * term -> order |
12981 | 184 |
val match_bvars: (term * term) * (string * string) list -> (string * string) list |
185 |
val rename_abs: term -> term -> term -> term option |
|
16943 | 186 |
val eq_tvar: (indexname * sort) * (indexname * sort) -> bool |
16882 | 187 |
val eq_var: (indexname * typ) * (indexname * typ) -> bool |
16943 | 188 |
val tvar_ord: (indexname * sort) * (indexname * sort) -> order |
189 |
val var_ord: (indexname * typ) * (indexname * typ) -> order |
|
16882 | 190 |
val instantiate: ((indexname * sort) * typ) list * ((indexname * typ) * term) list |
191 |
-> term -> term |
|
192 |
val instantiateT: ((indexname * sort) * typ) list -> typ -> typ |
|
16710 | 193 |
val maxidx_typ: typ -> int -> int |
194 |
val maxidx_typs: typ list -> int -> int |
|
195 |
val maxidx_term: term -> int -> int |
|
12499 | 196 |
val invent_names: string list -> string -> int -> string list |
16338 | 197 |
val map_typ: (string -> string) -> (string -> string) -> typ -> typ |
198 |
val map_term: (string -> string) -> (string -> string) -> (string -> string) -> term -> term |
|
16710 | 199 |
val dest_abs: string * typ * term -> string * term |
16990 | 200 |
val bound: int -> string |
201 |
val is_bound: string -> bool |
|
16943 | 202 |
val zero_var_indexesT: typ -> typ |
203 |
val zero_var_indexes: term -> term |
|
204 |
val zero_var_indexes_inst: term -> |
|
205 |
((indexname * sort) * typ) list * ((indexname * typ) * term) list |
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val dummy_patternN: string |
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207 |
val no_dummy_patterns: term -> term |
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208 |
val replace_dummy_patterns: int * term -> int * term |
10552 | 209 |
val is_replaced_dummy_pattern: indexname -> bool |
16035 | 210 |
val show_dummy_patterns: term -> term |
13484 | 211 |
val adhoc_freeze_vars: term -> term * string list |
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val string_of_vname: indexname -> string |
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213 |
val string_of_vname': indexname -> string |
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214 |
val str_of_term: term -> string |
4444 | 215 |
end; |
216 |
||
217 |
structure Term: TERM = |
|
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218 |
struct |
0 | 219 |
|
220 |
(*Indexnames can be quickly renamed by adding an offset to the integer part, |
|
221 |
for resolution.*) |
|
16537 | 222 |
type indexname = string * int; |
0 | 223 |
|
4626 | 224 |
(* Types are classified by sorts. *) |
0 | 225 |
type class = string; |
226 |
type sort = class list; |
|
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227 |
type arity = string * sort list * sort; |
0 | 228 |
|
229 |
(* The sorts attached to TFrees and TVars specify the sort of that variable *) |
|
230 |
datatype typ = Type of string * typ list |
|
231 |
| TFree of string * sort |
|
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232 |
| TVar of indexname * sort; |
0 | 233 |
|
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234 |
(*Terms. Bound variables are indicated by depth number. |
0 | 235 |
Free variables, (scheme) variables and constants have names. |
4626 | 236 |
An term is "closed" if every bound variable of level "lev" |
13000 | 237 |
is enclosed by at least "lev" abstractions. |
0 | 238 |
|
239 |
It is possible to create meaningless terms containing loose bound vars |
|
240 |
or type mismatches. But such terms are not allowed in rules. *) |
|
241 |
||
13000 | 242 |
datatype term = |
0 | 243 |
Const of string * typ |
13000 | 244 |
| Free of string * typ |
0 | 245 |
| Var of indexname * typ |
246 |
| Bound of int |
|
247 |
| Abs of string*typ*term |
|
3965 | 248 |
| op $ of term*term; |
0 | 249 |
|
16537 | 250 |
(*Errors involving type mismatches*) |
0 | 251 |
exception TYPE of string * typ list * term list; |
252 |
||
16537 | 253 |
(*Errors errors involving terms*) |
0 | 254 |
exception TERM of string * term list; |
255 |
||
256 |
(*Note variable naming conventions! |
|
257 |
a,b,c: string |
|
258 |
f,g,h: functions (including terms of function type) |
|
259 |
i,j,m,n: int |
|
260 |
t,u: term |
|
261 |
v,w: indexnames |
|
262 |
x,y: any |
|
263 |
A,B,C: term (denoting formulae) |
|
264 |
T,U: typ |
|
265 |
*) |
|
266 |
||
267 |
||
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268 |
(** Types **) |
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269 |
|
16537 | 270 |
(*dummy type for parsing and printing etc.*) |
271 |
val dummyT = Type ("dummy", []); |
|
272 |
||
273 |
fun no_dummyT typ = |
|
274 |
let |
|
275 |
fun check (T as Type ("dummy", _)) = |
|
276 |
raise TYPE ("Illegal occurrence of '_' dummy type", [T], []) |
|
277 |
| check (Type (_, Ts)) = List.app check Ts |
|
278 |
| check _ = (); |
|
279 |
in check typ; typ end; |
|
280 |
||
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281 |
fun S --> T = Type("fun",[S,T]); |
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282 |
|
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283 |
(*handy for multiple args: [T1,...,Tn]--->T gives T1-->(T2--> ... -->T)*) |
15570 | 284 |
val op ---> = Library.foldr (op -->); |
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285 |
|
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|
286 |
fun dest_Type (Type x) = x |
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|
287 |
| dest_Type T = raise TYPE ("dest_Type", [T], []); |
15914 | 288 |
fun dest_TVar (TVar x) = x |
289 |
| dest_TVar T = raise TYPE ("dest_TVar", [T], []); |
|
290 |
fun dest_TFree (TFree x) = x |
|
291 |
| dest_TFree T = raise TYPE ("dest_TFree", [T], []); |
|
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292 |
|
16537 | 293 |
|
0 | 294 |
(** Discriminators **) |
295 |
||
7318 | 296 |
fun is_Bound (Bound _) = true |
297 |
| is_Bound _ = false; |
|
298 |
||
0 | 299 |
fun is_Const (Const _) = true |
300 |
| is_Const _ = false; |
|
301 |
||
302 |
fun is_Free (Free _) = true |
|
303 |
| is_Free _ = false; |
|
304 |
||
305 |
fun is_Var (Var _) = true |
|
306 |
| is_Var _ = false; |
|
307 |
||
308 |
fun is_TVar (TVar _) = true |
|
309 |
| is_TVar _ = false; |
|
310 |
||
15573 | 311 |
(*Differs from proofterm/is_fun in its treatment of TVar*) |
312 |
fun is_funtype (Type("fun",[_,_])) = true |
|
313 |
| is_funtype _ = false; |
|
314 |
||
16537 | 315 |
|
0 | 316 |
(** Destructors **) |
317 |
||
318 |
fun dest_Const (Const x) = x |
|
319 |
| dest_Const t = raise TERM("dest_Const", [t]); |
|
320 |
||
321 |
fun dest_Free (Free x) = x |
|
322 |
| dest_Free t = raise TERM("dest_Free", [t]); |
|
323 |
||
324 |
fun dest_Var (Var x) = x |
|
325 |
| dest_Var t = raise TERM("dest_Var", [t]); |
|
326 |
||
327 |
||
4464 | 328 |
fun domain_type (Type("fun", [T,_])) = T |
329 |
and range_type (Type("fun", [_,T])) = T; |
|
4064 | 330 |
|
0 | 331 |
(* maps [T1,...,Tn]--->T to the list [T1,T2,...,Tn]*) |
332 |
fun binder_types (Type("fun",[S,T])) = S :: binder_types T |
|
333 |
| binder_types _ = []; |
|
334 |
||
335 |
(* maps [T1,...,Tn]--->T to T*) |
|
336 |
fun body_type (Type("fun",[S,T])) = body_type T |
|
337 |
| body_type T = T; |
|
338 |
||
339 |
(* maps [T1,...,Tn]--->T to ([T1,T2,...,Tn], T) *) |
|
340 |
fun strip_type T : typ list * typ = |
|
341 |
(binder_types T, body_type T); |
|
342 |
||
343 |
||
344 |
(*Compute the type of the term, checking that combinations are well-typed |
|
345 |
Ts = [T0,T1,...] holds types of bound variables 0, 1, ...*) |
|
346 |
fun type_of1 (Ts, Const (_,T)) = T |
|
347 |
| type_of1 (Ts, Free (_,T)) = T |
|
15570 | 348 |
| type_of1 (Ts, Bound i) = (List.nth (Ts,i) |
349 |
handle Subscript => raise TYPE("type_of: bound variable", [], [Bound i])) |
|
0 | 350 |
| type_of1 (Ts, Var (_,T)) = T |
351 |
| type_of1 (Ts, Abs (_,T,body)) = T --> type_of1(T::Ts, body) |
|
13000 | 352 |
| type_of1 (Ts, f$u) = |
0 | 353 |
let val U = type_of1(Ts,u) |
354 |
and T = type_of1(Ts,f) |
|
355 |
in case T of |
|
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
356 |
Type("fun",[T1,T2]) => |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
357 |
if T1=U then T2 else raise TYPE |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
358 |
("type_of: type mismatch in application", [T1,U], [f$u]) |
13000 | 359 |
| _ => raise TYPE |
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
360 |
("type_of: function type is expected in application", |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
361 |
[T,U], [f$u]) |
0 | 362 |
end; |
363 |
||
364 |
fun type_of t : typ = type_of1 ([],t); |
|
365 |
||
366 |
(*Determines the type of a term, with minimal checking*) |
|
13000 | 367 |
fun fastype_of1 (Ts, f$u) = |
61 | 368 |
(case fastype_of1 (Ts,f) of |
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
369 |
Type("fun",[_,T]) => T |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
370 |
| _ => raise TERM("fastype_of: expected function type", [f$u])) |
61 | 371 |
| fastype_of1 (_, Const (_,T)) = T |
372 |
| fastype_of1 (_, Free (_,T)) = T |
|
15570 | 373 |
| fastype_of1 (Ts, Bound i) = (List.nth(Ts,i) |
374 |
handle Subscript => raise TERM("fastype_of: Bound", [Bound i])) |
|
13000 | 375 |
| fastype_of1 (_, Var (_,T)) = T |
61 | 376 |
| fastype_of1 (Ts, Abs (_,T,u)) = T --> fastype_of1 (T::Ts, u); |
377 |
||
378 |
fun fastype_of t : typ = fastype_of1 ([],t); |
|
0 | 379 |
|
16678 | 380 |
(*Determine the argument type of a function*) |
381 |
fun argument_type_of tm = |
|
382 |
let |
|
383 |
fun argT i (Type ("fun", [T, U])) = if i = 0 then T else argT (i - 1) U |
|
384 |
| argT _ T = raise TYPE ("argument_type_of", [T], []); |
|
385 |
||
386 |
fun arg 0 _ (Abs (_, T, _)) = T |
|
387 |
| arg i Ts (Abs (_, T, t)) = arg (i - 1) (T :: Ts) t |
|
388 |
| arg i Ts (t $ _) = arg (i + 1) Ts t |
|
389 |
| arg i Ts a = argT i (fastype_of1 (Ts, a)); |
|
390 |
in arg 0 [] tm end; |
|
391 |
||
0 | 392 |
|
15570 | 393 |
val list_abs = Library.foldr (fn ((x, T), t) => Abs (x, T, t)); |
10806 | 394 |
|
0 | 395 |
(* maps (x1,...,xn)t to t *) |
13000 | 396 |
fun strip_abs_body (Abs(_,_,t)) = strip_abs_body t |
0 | 397 |
| strip_abs_body u = u; |
398 |
||
399 |
(* maps (x1,...,xn)t to [x1, ..., xn] *) |
|
13000 | 400 |
fun strip_abs_vars (Abs(a,T,t)) = (a,T) :: strip_abs_vars t |
0 | 401 |
| strip_abs_vars u = [] : (string*typ) list; |
402 |
||
403 |
||
404 |
fun strip_qnt_body qnt = |
|
405 |
let fun strip(tm as Const(c,_)$Abs(_,_,t)) = if c=qnt then strip t else tm |
|
406 |
| strip t = t |
|
407 |
in strip end; |
|
408 |
||
409 |
fun strip_qnt_vars qnt = |
|
410 |
let fun strip(Const(c,_)$Abs(a,T,t)) = if c=qnt then (a,T)::strip t else [] |
|
411 |
| strip t = [] : (string*typ) list |
|
412 |
in strip end; |
|
413 |
||
414 |
||
415 |
(* maps (f, [t1,...,tn]) to f(t1,...,tn) *) |
|
15570 | 416 |
val list_comb : term * term list -> term = Library.foldl (op $); |
0 | 417 |
|
418 |
||
419 |
(* maps f(t1,...,tn) to (f, [t1,...,tn]) ; naturally tail-recursive*) |
|
13000 | 420 |
fun strip_comb u : term * term list = |
0 | 421 |
let fun stripc (f$t, ts) = stripc (f, t::ts) |
13000 | 422 |
| stripc x = x |
0 | 423 |
in stripc(u,[]) end; |
424 |
||
425 |
||
426 |
(* maps f(t1,...,tn) to f , which is never a combination *) |
|
427 |
fun head_of (f$t) = head_of f |
|
428 |
| head_of u = u; |
|
429 |
||
430 |
||
16599 | 431 |
(*number of atoms and abstractions in a term*) |
432 |
fun size_of_term tm = |
|
433 |
let |
|
16678 | 434 |
fun add_size (t $ u, n) = add_size (t, add_size (u, n)) |
435 |
| add_size (Abs (_ ,_, t), n) = add_size (t, n + 1) |
|
436 |
| add_size (_, n) = n + 1; |
|
437 |
in add_size (tm, 0) end; |
|
0 | 438 |
|
16678 | 439 |
fun map_type_tvar f = |
440 |
let |
|
441 |
fun map_aux (Type (a, Ts)) = Type (a, map map_aux Ts) |
|
442 |
| map_aux (TVar x) = f x |
|
443 |
| map_aux T = T; |
|
444 |
in map_aux end; |
|
949
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
445 |
|
16678 | 446 |
fun map_type_tfree f = |
447 |
let |
|
448 |
fun map_aux (Type (a, Ts)) = Type (a, map map_aux Ts) |
|
449 |
| map_aux (TFree x) = f x |
|
450 |
| map_aux T = T; |
|
451 |
in map_aux end; |
|
949
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
452 |
|
0 | 453 |
fun map_term_types f = |
16678 | 454 |
let |
455 |
fun map_aux (Const (a, T)) = Const (a, f T) |
|
456 |
| map_aux (Free (a, T)) = Free (a, f T) |
|
457 |
| map_aux (Var (v, T)) = Var (v, f T) |
|
458 |
| map_aux (t as Bound _) = t |
|
459 |
| map_aux (Abs (a, T, t)) = Abs (a, f T, map_aux t) |
|
460 |
| map_aux (t $ u) = map_aux t $ map_aux u; |
|
461 |
in map_aux end; |
|
0 | 462 |
|
463 |
(* iterate a function over all types in a term *) |
|
464 |
fun it_term_types f = |
|
465 |
let fun iter(Const(_,T), a) = f(T,a) |
|
466 |
| iter(Free(_,T), a) = f(T,a) |
|
467 |
| iter(Var(_,T), a) = f(T,a) |
|
468 |
| iter(Abs(_,T,t), a) = iter(t,f(T,a)) |
|
469 |
| iter(f$u, a) = iter(f, iter(u, a)) |
|
470 |
| iter(Bound _, a) = a |
|
471 |
in iter end |
|
472 |
||
473 |
||
16943 | 474 |
(* fold types and terms *) |
475 |
||
476 |
(*fold atoms of type*) |
|
477 |
fun fold_atyps f (Type (_, Ts)) = fold (fold_atyps f) Ts |
|
478 |
| fold_atyps f T = f T; |
|
479 |
||
480 |
(*fold atoms of term*) |
|
481 |
fun fold_aterms f (t $ u) = fold_aterms f t #> fold_aterms f u |
|
482 |
| fold_aterms f (Abs (_, _, t)) = fold_aterms f t |
|
483 |
| fold_aterms f a = f a; |
|
484 |
||
485 |
(*fold types of term*) |
|
486 |
fun fold_term_types f (t as Const (_, T)) = f t T |
|
487 |
| fold_term_types f (t as Free (_, T)) = f t T |
|
488 |
| fold_term_types f (t as Var (_, T)) = f t T |
|
489 |
| fold_term_types f (Bound _) = I |
|
490 |
| fold_term_types f (t as Abs (_, T, b)) = f t T #> fold_term_types f b |
|
491 |
| fold_term_types f (t $ u) = fold_term_types f t #> fold_term_types f u; |
|
492 |
||
493 |
fun fold_types f = fold_term_types (K f); |
|
494 |
||
495 |
(*collect variables*) |
|
496 |
val add_tvarsT = fold_atyps (fn TVar v => insert (op =) v | _ => I); |
|
497 |
val add_tvars = fold_types add_tvarsT; |
|
498 |
val add_vars = fold_aterms (fn Var v => insert (op =) v | _ => I); |
|
499 |
val add_tfreesT = fold_atyps (fn TFree v => insert (op =) v | _ => I); |
|
500 |
val add_tfrees = fold_types add_tfreesT; |
|
501 |
val add_frees = fold_aterms (fn Free v => insert (op =) v | _ => I); |
|
502 |
||
503 |
(*collect variable names*) |
|
504 |
val add_term_varnames = fold_aterms (fn Var (xi, _) => insert (op =) xi | _ => I); |
|
505 |
fun term_varnames t = add_term_varnames t []; |
|
506 |
||
507 |
||
16678 | 508 |
(** Comparing terms, types, sorts etc. **) |
16537 | 509 |
|
16678 | 510 |
(* fast syntactic comparison *) |
511 |
||
512 |
fun fast_indexname_ord ((x, i), (y, j)) = |
|
513 |
(case int_ord (i, j) of EQUAL => fast_string_ord (x, y) | ord => ord); |
|
16537 | 514 |
|
16599 | 515 |
fun sort_ord SS = |
516 |
if pointer_eq SS then EQUAL |
|
16990 | 517 |
else dict_ord fast_string_ord SS; |
16678 | 518 |
|
519 |
local |
|
16537 | 520 |
|
16678 | 521 |
fun cons_nr (TVar _) = 0 |
522 |
| cons_nr (TFree _) = 1 |
|
523 |
| cons_nr (Type _) = 2; |
|
16537 | 524 |
|
16678 | 525 |
in |
16537 | 526 |
|
527 |
fun typ_ord TU = |
|
528 |
if pointer_eq TU then EQUAL |
|
529 |
else |
|
530 |
(case TU of |
|
16678 | 531 |
(Type (a, Ts), Type (b, Us)) => |
16990 | 532 |
(case fast_string_ord (a, b) of EQUAL => dict_ord typ_ord (Ts, Us) | ord => ord) |
16678 | 533 |
| (TFree (a, S), TFree (b, S')) => |
534 |
(case fast_string_ord (a, b) of EQUAL => sort_ord (S, S') | ord => ord) |
|
535 |
| (TVar (xi, S), TVar (yj, S')) => |
|
536 |
(case fast_indexname_ord (xi, yj) of EQUAL => sort_ord (S, S') | ord => ord) |
|
537 |
| (T, U) => int_ord (cons_nr T, cons_nr U)); |
|
538 |
||
539 |
end; |
|
540 |
||
541 |
local |
|
542 |
||
543 |
fun cons_nr (Const _) = 0 |
|
544 |
| cons_nr (Free _) = 1 |
|
545 |
| cons_nr (Var _) = 2 |
|
546 |
| cons_nr (Bound _) = 3 |
|
547 |
| cons_nr (Abs _) = 4 |
|
548 |
| cons_nr (_ $ _) = 5; |
|
549 |
||
550 |
fun struct_ord (Abs (_, _, t), Abs (_, _, u)) = struct_ord (t, u) |
|
551 |
| struct_ord (t1 $ t2, u1 $ u2) = |
|
552 |
(case struct_ord (t1, u1) of EQUAL => struct_ord (t2, u2) | ord => ord) |
|
553 |
| struct_ord (t, u) = int_ord (cons_nr t, cons_nr u); |
|
554 |
||
555 |
fun atoms_ord (Abs (_, _, t), Abs (_, _, u)) = atoms_ord (t, u) |
|
556 |
| atoms_ord (t1 $ t2, u1 $ u2) = |
|
557 |
(case atoms_ord (t1, u1) of EQUAL => atoms_ord (t2, u2) | ord => ord) |
|
558 |
| atoms_ord (Const (a, _), Const (b, _)) = fast_string_ord (a, b) |
|
559 |
| atoms_ord (Free (x, _), Free (y, _)) = fast_string_ord (x, y) |
|
560 |
| atoms_ord (Var (xi, _), Var (yj, _)) = fast_indexname_ord (xi, yj) |
|
561 |
| atoms_ord (Bound i, Bound j) = int_ord (i, j) |
|
562 |
| atoms_ord _ = sys_error "atoms_ord"; |
|
563 |
||
564 |
fun types_ord (Abs (_, T, t), Abs (_, U, u)) = |
|
565 |
(case typ_ord (T, U) of EQUAL => types_ord (t, u) | ord => ord) |
|
566 |
| types_ord (t1 $ t2, u1 $ u2) = |
|
567 |
(case types_ord (t1, u1) of EQUAL => types_ord (t2, u2) | ord => ord) |
|
568 |
| types_ord (Const (_, T), Const (_, U)) = typ_ord (T, U) |
|
569 |
| types_ord (Free (_, T), Free (_, U)) = typ_ord (T, U) |
|
570 |
| types_ord (Var (_, T), Var (_, U)) = typ_ord (T, U) |
|
571 |
| types_ord (Bound _, Bound _) = EQUAL |
|
572 |
| types_ord _ = sys_error "types_ord"; |
|
573 |
||
574 |
in |
|
575 |
||
576 |
fun fast_term_ord tu = |
|
577 |
if pointer_eq tu then EQUAL |
|
578 |
else |
|
579 |
(case struct_ord tu of |
|
580 |
EQUAL => (case atoms_ord tu of EQUAL => types_ord tu | ord => ord) |
|
581 |
| ord => ord); |
|
582 |
||
583 |
fun op aconv tu = (fast_term_ord tu = EQUAL); |
|
584 |
fun aconvs ts_us = (list_ord fast_term_ord ts_us = EQUAL); |
|
585 |
||
586 |
structure Vartab = TableFun(type key = indexname val ord = fast_indexname_ord); |
|
587 |
structure Typtab = TableFun(type key = typ val ord = typ_ord); |
|
588 |
structure Termtab = TableFun(type key = term val ord = fast_term_ord); |
|
589 |
||
590 |
end; |
|
16537 | 591 |
|
592 |
||
593 |
(* term_ord *) |
|
594 |
||
595 |
(*a linear well-founded AC-compatible ordering for terms: |
|
596 |
s < t <=> 1. size(s) < size(t) or |
|
597 |
2. size(s) = size(t) and s=f(...) and t=g(...) and f<g or |
|
598 |
3. size(s) = size(t) and s=f(s1..sn) and t=f(t1..tn) and |
|
599 |
(s1..sn) < (t1..tn) (lexicographically)*) |
|
16678 | 600 |
|
601 |
fun indexname_ord ((x, i), (y, j)) = |
|
602 |
(case int_ord (i, j) of EQUAL => string_ord (x, y) | ord => ord); |
|
603 |
||
16667 | 604 |
local |
605 |
||
606 |
fun hd_depth (t $ _, n) = hd_depth (t, n + 1) |
|
607 |
| hd_depth p = p; |
|
16537 | 608 |
|
609 |
fun dest_hd (Const (a, T)) = (((a, 0), T), 0) |
|
610 |
| dest_hd (Free (a, T)) = (((a, 0), T), 1) |
|
611 |
| dest_hd (Var v) = (v, 2) |
|
612 |
| dest_hd (Bound i) = ((("", i), dummyT), 3) |
|
613 |
| dest_hd (Abs (_, T, _)) = ((("", 0), T), 4); |
|
614 |
||
16667 | 615 |
in |
616 |
||
16537 | 617 |
fun term_ord tu = |
618 |
if pointer_eq tu then EQUAL |
|
619 |
else |
|
620 |
(case tu of |
|
621 |
(Abs (_, T, t), Abs(_, U, u)) => |
|
622 |
(case term_ord (t, u) of EQUAL => typ_ord (T, U) | ord => ord) |
|
16667 | 623 |
| (t, u) => |
16537 | 624 |
(case int_ord (size_of_term t, size_of_term u) of |
625 |
EQUAL => |
|
16943 | 626 |
(case prod_ord hd_ord int_ord (hd_depth (t, 0), hd_depth (u, 0)) of |
627 |
EQUAL => args_ord (t, u) | ord => ord) |
|
16537 | 628 |
| ord => ord)) |
629 |
and hd_ord (f, g) = |
|
630 |
prod_ord (prod_ord indexname_ord typ_ord) int_ord (dest_hd f, dest_hd g) |
|
16667 | 631 |
and args_ord (f $ t, g $ u) = |
632 |
(case args_ord (f, g) of EQUAL => term_ord (t, u) | ord => ord) |
|
633 |
| args_ord _ = EQUAL; |
|
16537 | 634 |
|
635 |
fun termless tu = (term_ord tu = LESS); |
|
636 |
||
16667 | 637 |
end; |
638 |
||
639 |
||
640 |
(** Lexicographic path order on terms **) |
|
641 |
||
642 |
(* |
|
16570 | 643 |
See Baader & Nipkow, Term rewriting, CUP 1998. |
644 |
Without variables. Const, Var, Bound, Free and Abs are treated all as |
|
645 |
constants. |
|
646 |
||
647 |
f_ord maps strings to integers and serves two purposes: |
|
648 |
- Predicate on constant symbols. Those that are not recognised by f_ord |
|
649 |
must be mapped to ~1. |
|
650 |
- Order on the recognised symbols. These must be mapped to distinct |
|
651 |
integers >= 0. |
|
652 |
||
16667 | 653 |
*) |
16570 | 654 |
|
655 |
local |
|
16667 | 656 |
fun dest_hd f_ord (Const (a, T)) = |
16570 | 657 |
let val ord = f_ord a in |
658 |
if ord = ~1 then ((1, ((a, 0), T)), 0) else ((0, (("", ord), T)), 0) |
|
659 |
end |
|
660 |
| dest_hd _ (Free (a, T)) = ((1, ((a, 0), T)), 0) |
|
661 |
| dest_hd _ (Var v) = ((1, v), 1) |
|
662 |
| dest_hd _ (Bound i) = ((1, (("", i), dummyT)), 2) |
|
663 |
| dest_hd _ (Abs (_, T, _)) = ((1, (("", 0), T)), 3); |
|
664 |
||
665 |
fun term_lpo f_ord (s, t) = |
|
666 |
let val (f, ss) = strip_comb s and (g, ts) = strip_comb t in |
|
667 |
if forall (fn si => term_lpo f_ord (si, t) = LESS) ss |
|
668 |
then case hd_ord f_ord (f, g) of |
|
16667 | 669 |
GREATER => |
670 |
if forall (fn ti => term_lpo f_ord (s, ti) = GREATER) ts |
|
671 |
then GREATER else LESS |
|
16570 | 672 |
| EQUAL => |
16667 | 673 |
if forall (fn ti => term_lpo f_ord (s, ti) = GREATER) ts |
674 |
then list_ord (term_lpo f_ord) (ss, ts) |
|
675 |
else LESS |
|
16570 | 676 |
| LESS => LESS |
677 |
else GREATER |
|
678 |
end |
|
679 |
and hd_ord f_ord (f, g) = case (f, g) of |
|
680 |
(Abs (_, T, t), Abs (_, U, u)) => |
|
681 |
(case term_lpo f_ord (t, u) of EQUAL => typ_ord (T, U) | ord => ord) |
|
682 |
| (_, _) => prod_ord (prod_ord int_ord |
|
683 |
(prod_ord indexname_ord typ_ord)) int_ord |
|
684 |
(dest_hd f_ord f, dest_hd f_ord g) |
|
685 |
in |
|
686 |
val term_lpo = term_lpo |
|
687 |
end; |
|
688 |
||
16537 | 689 |
|
0 | 690 |
(** Connectives of higher order logic **) |
691 |
||
375 | 692 |
fun itselfT ty = Type ("itself", [ty]); |
14854 | 693 |
val a_itselfT = itselfT (TFree ("'a", [])); |
375 | 694 |
|
0 | 695 |
val propT : typ = Type("prop",[]); |
696 |
||
697 |
val implies = Const("==>", propT-->propT-->propT); |
|
698 |
||
699 |
fun all T = Const("all", (T-->propT)-->propT); |
|
700 |
||
701 |
fun equals T = Const("==", T-->T-->propT); |
|
702 |
||
703 |
(* maps !!x1...xn. t to t *) |
|
13000 | 704 |
fun strip_all_body (Const("all",_)$Abs(_,_,t)) = strip_all_body t |
0 | 705 |
| strip_all_body t = t; |
706 |
||
707 |
(* maps !!x1...xn. t to [x1, ..., xn] *) |
|
708 |
fun strip_all_vars (Const("all",_)$Abs(a,T,t)) = |
|
13000 | 709 |
(a,T) :: strip_all_vars t |
0 | 710 |
| strip_all_vars t = [] : (string*typ) list; |
711 |
||
712 |
(*increments a term's non-local bound variables |
|
713 |
required when moving a term within abstractions |
|
714 |
inc is increment for bound variables |
|
715 |
lev is level at which a bound variable is considered 'loose'*) |
|
13000 | 716 |
fun incr_bv (inc, lev, u as Bound i) = if i>=lev then Bound(i+inc) else u |
0 | 717 |
| incr_bv (inc, lev, Abs(a,T,body)) = |
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
718 |
Abs(a, T, incr_bv(inc,lev+1,body)) |
13000 | 719 |
| incr_bv (inc, lev, f$t) = |
0 | 720 |
incr_bv(inc,lev,f) $ incr_bv(inc,lev,t) |
721 |
| incr_bv (inc, lev, u) = u; |
|
722 |
||
723 |
fun incr_boundvars 0 t = t |
|
724 |
| incr_boundvars inc t = incr_bv(inc,0,t); |
|
725 |
||
12981 | 726 |
(*Scan a pair of terms; while they are similar, |
727 |
accumulate corresponding bound vars in "al"*) |
|
728 |
fun match_bvs(Abs(x,_,s),Abs(y,_,t), al) = |
|
729 |
match_bvs(s, t, if x="" orelse y="" then al |
|
730 |
else (x,y)::al) |
|
731 |
| match_bvs(f$s, g$t, al) = match_bvs(f,g,match_bvs(s,t,al)) |
|
732 |
| match_bvs(_,_,al) = al; |
|
733 |
||
734 |
(* strip abstractions created by parameters *) |
|
735 |
fun match_bvars((s,t),al) = match_bvs(strip_abs_body s, strip_abs_body t, al); |
|
736 |
||
737 |
fun rename_abs pat obj t = |
|
738 |
let |
|
739 |
val ren = match_bvs (pat, obj, []); |
|
740 |
fun ren_abs (Abs (x, T, b)) = |
|
17271 | 741 |
Abs (if_none (AList.lookup (op =) ren x) x, T, ren_abs b) |
12981 | 742 |
| ren_abs (f $ t) = ren_abs f $ ren_abs t |
743 |
| ren_abs t = t |
|
15531 | 744 |
in if null ren then NONE else SOME (ren_abs t) end; |
0 | 745 |
|
746 |
(*Accumulate all 'loose' bound vars referring to level 'lev' or beyond. |
|
747 |
(Bound 0) is loose at level 0 *) |
|
13000 | 748 |
fun add_loose_bnos (Bound i, lev, js) = |
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
749 |
if i<lev then js else (i-lev) ins_int js |
0 | 750 |
| add_loose_bnos (Abs (_,_,t), lev, js) = add_loose_bnos (t, lev+1, js) |
751 |
| add_loose_bnos (f$t, lev, js) = |
|
13000 | 752 |
add_loose_bnos (f, lev, add_loose_bnos (t, lev, js)) |
0 | 753 |
| add_loose_bnos (_, _, js) = js; |
754 |
||
755 |
fun loose_bnos t = add_loose_bnos (t, 0, []); |
|
756 |
||
757 |
(* loose_bvar(t,k) iff t contains a 'loose' bound variable referring to |
|
758 |
level k or beyond. *) |
|
759 |
fun loose_bvar(Bound i,k) = i >= k |
|
760 |
| loose_bvar(f$t, k) = loose_bvar(f,k) orelse loose_bvar(t,k) |
|
761 |
| loose_bvar(Abs(_,_,t),k) = loose_bvar(t,k+1) |
|
762 |
| loose_bvar _ = false; |
|
763 |
||
2792 | 764 |
fun loose_bvar1(Bound i,k) = i = k |
765 |
| loose_bvar1(f$t, k) = loose_bvar1(f,k) orelse loose_bvar1(t,k) |
|
766 |
| loose_bvar1(Abs(_,_,t),k) = loose_bvar1(t,k+1) |
|
767 |
| loose_bvar1 _ = false; |
|
0 | 768 |
|
769 |
(*Substitute arguments for loose bound variables. |
|
770 |
Beta-reduction of arg(n-1)...arg0 into t replacing (Bound i) with (argi). |
|
4626 | 771 |
Note that for ((%x y. c) a b), the bound vars in c are x=1 and y=0 |
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
772 |
and the appropriate call is subst_bounds([b,a], c) . |
0 | 773 |
Loose bound variables >=n are reduced by "n" to |
774 |
compensate for the disappearance of lambdas. |
|
775 |
*) |
|
13000 | 776 |
fun subst_bounds (args: term list, t) : term = |
0 | 777 |
let val n = length args; |
778 |
fun subst (t as Bound i, lev) = |
|
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
779 |
(if i<lev then t (*var is locally bound*) |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
780 |
else incr_boundvars lev (List.nth(args, i-lev)) |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
781 |
handle Subscript => Bound(i-n) (*loose: change it*)) |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
782 |
| subst (Abs(a,T,body), lev) = Abs(a, T, subst(body,lev+1)) |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
783 |
| subst (f$t, lev) = subst(f,lev) $ subst(t,lev) |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
784 |
| subst (t,lev) = t |
0 | 785 |
in case args of [] => t | _ => subst (t,0) end; |
786 |
||
2192
3bf092b5310b
Optimizations: removal of polymorphic equality; one-argument case
paulson
parents:
2182
diff
changeset
|
787 |
(*Special case: one argument*) |
13000 | 788 |
fun subst_bound (arg, t) : term = |
2192
3bf092b5310b
Optimizations: removal of polymorphic equality; one-argument case
paulson
parents:
2182
diff
changeset
|
789 |
let fun subst (t as Bound i, lev) = |
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
790 |
if i<lev then t (*var is locally bound*) |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
791 |
else if i=lev then incr_boundvars lev arg |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
792 |
else Bound(i-1) (*loose: change it*) |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
793 |
| 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
|
794 |
| 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
|
795 |
| subst (t,lev) = t |
2192
3bf092b5310b
Optimizations: removal of polymorphic equality; one-argument case
paulson
parents:
2182
diff
changeset
|
796 |
in subst (t,0) end; |
3bf092b5310b
Optimizations: removal of polymorphic equality; one-argument case
paulson
parents:
2182
diff
changeset
|
797 |
|
0 | 798 |
(*beta-reduce if possible, else form application*) |
2192
3bf092b5310b
Optimizations: removal of polymorphic equality; one-argument case
paulson
parents:
2182
diff
changeset
|
799 |
fun betapply (Abs(_,_,t), u) = subst_bound (u,t) |
0 | 800 |
| betapply (f,u) = f$u; |
801 |
||
14786
24a7bc97a27a
moved some sort ops to sorts.ML; added string_of_vname (from Syntax module);
wenzelm
parents:
14695
diff
changeset
|
802 |
|
16882 | 803 |
(** Specialized equality, membership, insertion etc. **) |
2192
3bf092b5310b
Optimizations: removal of polymorphic equality; one-argument case
paulson
parents:
2182
diff
changeset
|
804 |
|
16882 | 805 |
(* indexnames *) |
806 |
||
16724 | 807 |
fun eq_ix ((x, i): indexname, (y, j)) = i = j andalso x = y; |
2192
3bf092b5310b
Optimizations: removal of polymorphic equality; one-argument case
paulson
parents:
2182
diff
changeset
|
808 |
|
2959 | 809 |
fun mem_ix (_, []) = false |
16882 | 810 |
| mem_ix (x, y :: ys) = eq_ix (x, y) orelse mem_ix (x, ys); |
2192
3bf092b5310b
Optimizations: removal of polymorphic equality; one-argument case
paulson
parents:
2182
diff
changeset
|
811 |
|
16882 | 812 |
fun ins_ix (x, xs) = if mem_ix (x, xs) then xs else x :: xs; |
2192
3bf092b5310b
Optimizations: removal of polymorphic equality; one-argument case
paulson
parents:
2182
diff
changeset
|
813 |
|
0 | 814 |
|
16882 | 815 |
(* variables *) |
816 |
||
16943 | 817 |
fun eq_tvar ((xi, S: sort), (xi', S')) = eq_ix (xi, xi') andalso S = S'; |
818 |
fun eq_var ((xi, T: typ), (xi', T')) = eq_ix (xi, xi') andalso T = T'; |
|
819 |
||
820 |
val tvar_ord = prod_ord indexname_ord sort_ord; |
|
821 |
val var_ord = prod_ord indexname_ord typ_ord; |
|
16882 | 822 |
|
823 |
||
824 |
(* terms *) |
|
2176 | 825 |
|
826 |
fun mem_term (_, []) = false |
|
16882 | 827 |
| mem_term (t, t'::ts) = t aconv t' orelse mem_term (t, ts); |
2176 | 828 |
|
2182
29e56f003599
Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
parents:
2176
diff
changeset
|
829 |
fun subset_term ([], ys) = true |
29e56f003599
Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
parents:
2176
diff
changeset
|
830 |
| 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
|
831 |
|
29e56f003599
Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
parents:
2176
diff
changeset
|
832 |
fun eq_set_term (xs, ys) = |
29e56f003599
Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
parents:
2176
diff
changeset
|
833 |
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
|
834 |
|
2176 | 835 |
fun ins_term(t,ts) = if mem_term(t,ts) then ts else t :: ts; |
836 |
||
837 |
fun union_term (xs, []) = xs |
|
838 |
| union_term ([], ys) = ys |
|
839 |
| union_term ((x :: xs), ys) = union_term (xs, ins_term (x, ys)); |
|
840 |
||
5585 | 841 |
fun inter_term ([], ys) = [] |
842 |
| inter_term (x::xs, ys) = |
|
843 |
if mem_term (x,ys) then x :: inter_term(xs,ys) else inter_term(xs,ys); |
|
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 |
|
13665 | 892 |
fun lambda (v as Free (x, T)) t = Abs (x, T, abstract_over (v, t)) |
893 |
| lambda (v as Var ((x, _), T)) t = Abs (x, T, abstract_over (v, t)) |
|
894 |
| lambda v t = raise TERM ("lambda", [v, t]); |
|
0 | 895 |
|
896 |
(*Form an abstraction over a free variable.*) |
|
897 |
fun absfree (a,T,body) = Abs(a, T, abstract_over (Free(a,T), body)); |
|
17786 | 898 |
fun absdummy (T, body) = Abs ("uu", T, body); |
0 | 899 |
|
900 |
(*Abstraction over a list of free variables*) |
|
901 |
fun list_abs_free ([ ] , t) = t |
|
13000 | 902 |
| list_abs_free ((a,T)::vars, t) = |
0 | 903 |
absfree(a, T, list_abs_free(vars,t)); |
904 |
||
905 |
(*Quantification over a list of free variables*) |
|
906 |
fun list_all_free ([], t: term) = t |
|
13000 | 907 |
| list_all_free ((a,T)::vars, t) = |
0 | 908 |
(all T) $ (absfree(a, T, list_all_free(vars,t))); |
909 |
||
910 |
(*Quantification over a list of variables (already bound in body) *) |
|
911 |
fun list_all ([], t) = t |
|
13000 | 912 |
| list_all ((a,T)::vars, t) = |
0 | 913 |
(all T) $ (Abs(a, T, list_all(vars,t))); |
914 |
||
16678 | 915 |
(*Replace the ATOMIC term ti by ui; inst = [(t1,u1), ..., (tn,un)]. |
0 | 916 |
A simultaneous substitution: [ (a,b), (b,a) ] swaps a and b. *) |
16678 | 917 |
fun subst_atomic [] tm = tm |
918 |
| subst_atomic inst tm = |
|
919 |
let |
|
920 |
fun subst (Abs (a, T, body)) = Abs (a, T, subst body) |
|
921 |
| subst (t $ u) = subst t $ subst u |
|
17314 | 922 |
| subst t = if_none (AList.lookup (op aconv) inst t) t; |
16678 | 923 |
in subst tm end; |
0 | 924 |
|
16678 | 925 |
(*Replace the ATOMIC type Ti by Ui; inst = [(T1,U1), ..., (Tn,Un)].*) |
926 |
fun typ_subst_atomic [] ty = ty |
|
927 |
| typ_subst_atomic inst ty = |
|
928 |
let |
|
929 |
fun subst (Type (a, Ts)) = Type (a, map subst Ts) |
|
17314 | 930 |
| subst T = if_none (AList.lookup (op = : typ * typ -> bool) inst T) T; |
16678 | 931 |
in subst ty end; |
15797 | 932 |
|
16678 | 933 |
fun subst_atomic_types [] tm = tm |
934 |
| subst_atomic_types inst tm = map_term_types (typ_subst_atomic inst) tm; |
|
935 |
||
936 |
fun typ_subst_TVars [] ty = ty |
|
937 |
| typ_subst_TVars inst ty = |
|
938 |
let |
|
939 |
fun subst (Type (a, Ts)) = Type (a, map subst Ts) |
|
17271 | 940 |
| subst (T as TVar (xi, _)) = if_none (AList.lookup (op =) inst xi) T |
16678 | 941 |
| subst T = T; |
942 |
in subst ty end; |
|
0 | 943 |
|
16678 | 944 |
fun subst_TVars [] tm = tm |
945 |
| subst_TVars inst tm = map_term_types (typ_subst_TVars inst) tm; |
|
0 | 946 |
|
16678 | 947 |
(*see also Envir.norm_term*) |
948 |
fun subst_Vars [] tm = tm |
|
949 |
| subst_Vars inst tm = |
|
950 |
let |
|
17271 | 951 |
fun subst (t as Var (xi, _)) = if_none (AList.lookup (op =) inst xi) t |
16678 | 952 |
| subst (Abs (a, T, t)) = Abs (a, T, subst t) |
953 |
| subst (t $ u) = subst t $ subst u |
|
954 |
| subst t = t; |
|
955 |
in subst tm end; |
|
0 | 956 |
|
16678 | 957 |
(*see also Envir.norm_term*) |
958 |
fun subst_vars ([], []) tm = tm |
|
959 |
| subst_vars ([], inst) tm = subst_Vars inst tm |
|
960 |
| subst_vars (instT, inst) tm = |
|
961 |
let |
|
962 |
fun subst (Const (a, T)) = Const (a, typ_subst_TVars instT T) |
|
963 |
| subst (Free (a, T)) = Free (a, typ_subst_TVars instT T) |
|
964 |
| subst (t as Var (xi, T)) = |
|
17271 | 965 |
(case AList.lookup (op =) inst xi of |
16678 | 966 |
NONE => Var (xi, typ_subst_TVars instT T) |
967 |
| SOME t => t) |
|
968 |
| subst (t as Bound _) = t |
|
969 |
| subst (Abs (a, T, t)) = Abs (a, typ_subst_TVars instT T, subst t) |
|
970 |
| subst (t $ u) = subst t $ subst u; |
|
971 |
in subst tm end; |
|
0 | 972 |
|
973 |
||
16943 | 974 |
(* instantiation of schematic variables (types before terms) *) |
16882 | 975 |
|
976 |
local exception SAME in |
|
977 |
||
16943 | 978 |
fun instantiateT_same [] _ = raise SAME |
979 |
| instantiateT_same instT ty = |
|
16882 | 980 |
let |
981 |
fun subst_typ (Type (a, Ts)) = Type (a, subst_typs Ts) |
|
982 |
| subst_typ (TVar v) = |
|
17314 | 983 |
(case AList.lookup eq_tvar instT v of |
16882 | 984 |
SOME T => T |
985 |
| NONE => raise SAME) |
|
986 |
| subst_typ _ = raise SAME |
|
987 |
and subst_typs (T :: Ts) = |
|
988 |
(subst_typ T :: (subst_typs Ts handle SAME => Ts) |
|
989 |
handle SAME => T :: subst_typs Ts) |
|
990 |
| subst_typs [] = raise SAME; |
|
991 |
in subst_typ ty end; |
|
992 |
||
993 |
fun instantiate ([], []) tm = tm |
|
994 |
| instantiate (instT, inst) tm = |
|
995 |
let |
|
16943 | 996 |
val substT = instantiateT_same instT; |
997 |
fun subst (Const (c, T)) = Const (c, substT T) |
|
998 |
| subst (Free (x, T)) = Free (x, substT T) |
|
16882 | 999 |
| subst (Var (xi, T)) = |
16943 | 1000 |
let val (T', same) = (substT T, false) handle SAME => (T, true) in |
17314 | 1001 |
(case AList.lookup eq_var inst (xi, T') of |
16882 | 1002 |
SOME t => t |
1003 |
| NONE => if same then raise SAME else Var (xi, T')) |
|
1004 |
end |
|
1005 |
| subst (Bound _) = raise SAME |
|
1006 |
| subst (Abs (x, T, t)) = |
|
16943 | 1007 |
(Abs (x, substT T, subst t handle SAME => t) |
16882 | 1008 |
handle SAME => Abs (x, T, subst t)) |
1009 |
| subst (t $ u) = (subst t $ (subst u handle SAME => u) handle SAME => t $ subst u); |
|
1010 |
in subst tm handle SAME => tm end; |
|
1011 |
||
1012 |
fun instantiateT instT ty = |
|
16943 | 1013 |
instantiateT_same instT ty handle SAME => ty; |
16882 | 1014 |
|
1015 |
end; |
|
1016 |
||
1017 |
||
15573 | 1018 |
(** Identifying first-order terms **) |
1019 |
||
1020 |
(*Argument Ts is a reverse list of binder types, needed if term t contains Bound vars*) |
|
1021 |
fun has_not_funtype Ts t = not (is_funtype (fastype_of1 (Ts,t))); |
|
1022 |
||
16537 | 1023 |
(*First order means in all terms of the form f(t1,...,tn) no argument has a |
16589 | 1024 |
function type. The supplied quantifiers are excluded: their argument always |
1025 |
has a function type through a recursive call into its body.*) |
|
16667 | 1026 |
fun is_first_order quants = |
16589 | 1027 |
let fun first_order1 Ts (Abs (_,T,body)) = first_order1 (T::Ts) body |
16667 | 1028 |
| first_order1 Ts (Const(q,_) $ Abs(a,T,body)) = |
1029 |
q mem_string quants andalso (*it is a known quantifier*) |
|
16589 | 1030 |
not (is_funtype T) andalso first_order1 (T::Ts) body |
16667 | 1031 |
| first_order1 Ts t = |
1032 |
case strip_comb t of |
|
1033 |
(Var _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts |
|
1034 |
| (Free _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts |
|
1035 |
| (Const _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts |
|
1036 |
| (Bound _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts |
|
1037 |
| (Abs _, ts) => false (*not in beta-normal form*) |
|
1038 |
| _ => error "first_order: unexpected case" |
|
16589 | 1039 |
in first_order1 [] end; |
15573 | 1040 |
|
16710 | 1041 |
|
16990 | 1042 |
(* maximum index of typs and terms *) |
0 | 1043 |
|
16710 | 1044 |
fun maxidx_typ (TVar ((_, j), _)) i = Int.max (i, j) |
1045 |
| maxidx_typ (Type (_, Ts)) i = maxidx_typs Ts i |
|
1046 |
| maxidx_typ (TFree _) i = i |
|
1047 |
and maxidx_typs [] i = i |
|
1048 |
| maxidx_typs (T :: Ts) i = maxidx_typs Ts (maxidx_typ T i); |
|
0 | 1049 |
|
16710 | 1050 |
fun maxidx_term (Var ((_, j), T)) i = maxidx_typ T (Int.max (i, j)) |
1051 |
| maxidx_term (Const (_, T)) i = maxidx_typ T i |
|
1052 |
| maxidx_term (Free (_, T)) i = maxidx_typ T i |
|
1053 |
| maxidx_term (Bound _) i = i |
|
1054 |
| maxidx_term (Abs (_, T, t)) i = maxidx_term t (maxidx_typ T i) |
|
1055 |
| maxidx_term (t $ u) i = maxidx_term u (maxidx_term t i); |
|
0 | 1056 |
|
16710 | 1057 |
fun maxidx_of_typ T = maxidx_typ T ~1; |
1058 |
fun maxidx_of_typs Ts = maxidx_typs Ts ~1; |
|
1059 |
fun maxidx_of_term t = maxidx_term t ~1; |
|
13665 | 1060 |
|
0 | 1061 |
|
1062 |
||
1063 |
(**** Syntax-related declarations ****) |
|
1064 |
||
1065 |
(*** Printing ***) |
|
1066 |
||
16943 | 1067 |
(*Makes a variant of a name distinct from the names in 'used'. |
14676 | 1068 |
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
|
1069 |
preserves a suffix of underscores "_". *) |
16943 | 1070 |
fun variant used name = |
12306
749a04f0cfb0
variant: preserve suffix of underscores (for skolem/internal names etc.);
wenzelm
parents:
11922
diff
changeset
|
1071 |
let |
749a04f0cfb0
variant: preserve suffix of underscores (for skolem/internal names etc.);
wenzelm
parents:
11922
diff
changeset
|
1072 |
val (c, u) = pairself implode (Library.take_suffix (equal "_") (Symbol.explode name)); |
16943 | 1073 |
fun vary2 c = if ((c ^ u) mem_string used) then vary2 (Symbol.bump_string c) else c; |
1074 |
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
|
1075 |
in vary1 (if c = "" then "u" else c) ^ u end; |
0 | 1076 |
|
1077 |
(*Create variants of the list of names, with priority to the first ones*) |
|
1078 |
fun variantlist ([], used) = [] |
|
13000 | 1079 |
| variantlist(b::bs, used) = |
0 | 1080 |
let val b' = variant used b |
1081 |
in b' :: variantlist (bs, b'::used) end; |
|
1082 |
||
14695 | 1083 |
(*Invent fresh names*) |
1084 |
fun invent_names _ _ 0 = [] |
|
1085 |
| invent_names used a n = |
|
1086 |
let val b = Symbol.bump_string a in |
|
1087 |
if a mem_string used then invent_names used b n |
|
1088 |
else a :: invent_names used b (n - 1) |
|
1089 |
end; |
|
11353 | 1090 |
|
16537 | 1091 |
|
4017
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset
|
1092 |
(** Consts etc. **) |
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset
|
1093 |
|
15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15573
diff
changeset
|
1094 |
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
|
1095 |
| 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
|
1096 |
| 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
|
1097 |
|
16294 | 1098 |
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
|
1099 |
| add_typ_tycons (_, cs) = cs; |
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset
|
1100 |
|
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset
|
1101 |
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
|
1102 |
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
|
1103 |
|
9319 | 1104 |
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
|
1105 |
| 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
|
1106 |
| 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
|
1107 |
| add_term_consts (_, cs) = cs; |
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset
|
1108 |
|
13646 | 1109 |
fun term_consts t = add_term_consts(t,[]); |
1110 |
||
16943 | 1111 |
fun exists_subterm P = |
1112 |
let |
|
1113 |
fun ex tm = P tm orelse |
|
1114 |
(case tm of |
|
1115 |
t $ u => ex t orelse ex u |
|
1116 |
| Abs (_, _, t) => ex t |
|
1117 |
| _ => false); |
|
1118 |
in ex end; |
|
16108
cf468b93a02e
Implement cycle-free overloading, so that definitions cannot harm consistency any more (except of course via interaction with axioms).
obua
parents:
16035
diff
changeset
|
1119 |
|
16943 | 1120 |
fun exists_Const P = exists_subterm (fn Const c => P c | _ => false); |
4631 | 1121 |
|
4017
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset
|
1122 |
(*map classes, tycons*) |
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset
|
1123 |
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
|
1124 |
| 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
|
1125 |
| 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
|
1126 |
|
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset
|
1127 |
(*map classes, tycons, consts*) |
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset
|
1128 |
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
|
1129 |
| 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
|
1130 |
| 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
|
1131 |
| map_term _ _ _ (t as Bound _) = t |
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset
|
1132 |
| 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
|
1133 |
| 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
|
1134 |
|
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset
|
1135 |
|
0 | 1136 |
(** TFrees and TVars **) |
1137 |
||
12802
c69bd9754473
added add_term_free_names (more precise/efficient than add_term_names);
wenzelm
parents:
12499
diff
changeset
|
1138 |
(*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
|
1139 |
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
|
1140 |
| add_term_free_names (f$u, bs) = add_term_free_names (f, add_term_free_names(u, bs)) |
c69bd9754473
added add_term_free_names (more precise/efficient than add_term_names);
wenzelm
parents:
12499
diff
changeset
|
1141 |
| add_term_free_names (Abs(_,_,t), bs) = add_term_free_names(t,bs) |
c69bd9754473
added add_term_free_names (more precise/efficient than add_term_names);
wenzelm
parents:
12499
diff
changeset
|
1142 |
| add_term_free_names (_, bs) = bs; |
c69bd9754473
added add_term_free_names (more precise/efficient than add_term_names);
wenzelm
parents:
12499
diff
changeset
|
1143 |
|
0 | 1144 |
(*Accumulates the names in the term, suppressing duplicates. |
1145 |
Includes Frees and Consts. For choosing unambiguous bound var names.*) |
|
10666 | 1146 |
fun add_term_names (Const(a,_), bs) = NameSpace.base a ins_string bs |
2176 | 1147 |
| add_term_names (Free(a,_), bs) = a ins_string bs |
0 | 1148 |
| add_term_names (f$u, bs) = add_term_names (f, add_term_names(u, bs)) |
1149 |
| add_term_names (Abs(_,_,t), bs) = add_term_names(t,bs) |
|
1150 |
| add_term_names (_, bs) = bs; |
|
1151 |
||
1152 |
(*Accumulates the TVars in a type, suppressing duplicates. *) |
|
15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15573
diff
changeset
|
1153 |
fun add_typ_tvars(Type(_,Ts),vs) = foldr add_typ_tvars vs Ts |
0 | 1154 |
| add_typ_tvars(TFree(_),vs) = vs |
16294 | 1155 |
| add_typ_tvars(TVar(v),vs) = insert (op =) v vs; |
0 | 1156 |
|
1157 |
(*Accumulates the TFrees in a type, suppressing duplicates. *) |
|
15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15573
diff
changeset
|
1158 |
fun add_typ_tfree_names(Type(_,Ts),fs) = foldr add_typ_tfree_names fs Ts |
2176 | 1159 |
| add_typ_tfree_names(TFree(f,_),fs) = f ins_string fs |
0 | 1160 |
| add_typ_tfree_names(TVar(_),fs) = fs; |
1161 |
||
15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15573
diff
changeset
|
1162 |
fun add_typ_tfrees(Type(_,Ts),fs) = foldr add_typ_tfrees fs Ts |
16294 | 1163 |
| add_typ_tfrees(TFree(f),fs) = insert (op =) f fs |
0 | 1164 |
| add_typ_tfrees(TVar(_),fs) = fs; |
1165 |
||
15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15573
diff
changeset
|
1166 |
fun add_typ_varnames(Type(_,Ts),nms) = foldr add_typ_varnames nms Ts |
2176 | 1167 |
| add_typ_varnames(TFree(nm,_),nms) = nm ins_string nms |
1168 |
| 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
|
1169 |
|
0 | 1170 |
(*Accumulates the TVars in a term, suppressing duplicates. *) |
1171 |
val add_term_tvars = it_term_types add_typ_tvars; |
|
1172 |
||
1173 |
(*Accumulates the TFrees in a term, suppressing duplicates. *) |
|
1174 |
val add_term_tfrees = it_term_types add_typ_tfrees; |
|
1175 |
val add_term_tfree_names = it_term_types add_typ_tfree_names; |
|
1176 |
||
949
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
1177 |
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
|
1178 |
|
0 | 1179 |
(*Non-list versions*) |
1180 |
fun typ_tfrees T = add_typ_tfrees(T,[]); |
|
1181 |
fun typ_tvars T = add_typ_tvars(T,[]); |
|
1182 |
fun term_tfrees t = add_term_tfrees(t,[]); |
|
1183 |
fun term_tvars t = add_term_tvars(t,[]); |
|
1184 |
||
949
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
1185 |
(*special code to enforce left-to-right collection of TVar-indexnames*) |
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
1186 |
|
15570 | 1187 |
fun add_typ_ixns(ixns,Type(_,Ts)) = Library.foldl add_typ_ixns (ixns,Ts) |
13000 | 1188 |
| 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
|
1189 |
else ixns@[ixn] |
949
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
1190 |
| add_typ_ixns(ixns,TFree(_)) = ixns; |
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
1191 |
|
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
1192 |
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
|
1193 |
| 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
|
1194 |
| 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
|
1195 |
| add_term_tvar_ixns(Bound _,ixns) = ixns |
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
1196 |
| add_term_tvar_ixns(Abs(_,T,t),ixns) = |
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
1197 |
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
|
1198 |
| add_term_tvar_ixns(f$t,ixns) = |
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
1199 |
add_term_tvar_ixns(t,add_term_tvar_ixns(f,ixns)); |
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
1200 |
|
16537 | 1201 |
|
0 | 1202 |
(** Frees and Vars **) |
1203 |
||
1204 |
(*Accumulates the Vars in the term, suppressing duplicates*) |
|
1205 |
fun add_term_vars (t, vars: term list) = case t of |
|
16990 | 1206 |
Var _ => OrdList.insert term_ord t vars |
0 | 1207 |
| Abs (_,_,body) => add_term_vars(body,vars) |
1208 |
| f$t => add_term_vars (f, add_term_vars(t, vars)) |
|
1209 |
| _ => vars; |
|
1210 |
||
1211 |
fun term_vars t = add_term_vars(t,[]); |
|
1212 |
||
1213 |
(*Accumulates the Frees in the term, suppressing duplicates*) |
|
1214 |
fun add_term_frees (t, frees: term list) = case t of |
|
16990 | 1215 |
Free _ => OrdList.insert term_ord t frees |
0 | 1216 |
| Abs (_,_,body) => add_term_frees(body,frees) |
1217 |
| f$t => add_term_frees (f, add_term_frees(t, frees)) |
|
1218 |
| _ => frees; |
|
1219 |
||
1220 |
fun term_frees t = add_term_frees(t,[]); |
|
1221 |
||
1222 |
(*Given an abstraction over P, replaces the bound variable by a Free variable |
|
16678 | 1223 |
having a unique name*) |
0 | 1224 |
fun variant_abs (a,T,P) = |
1225 |
let val b = variant (add_term_names(P,[])) a |
|
2192
3bf092b5310b
Optimizations: removal of polymorphic equality; one-argument case
paulson
parents:
2182
diff
changeset
|
1226 |
in (b, subst_bound (Free(b,T), P)) end; |
0 | 1227 |
|
16678 | 1228 |
fun dest_abs (x, T, body) = |
1229 |
let |
|
1230 |
fun name_clash (Free (y, _)) = (x = y) |
|
1231 |
| name_clash (t $ u) = name_clash t orelse name_clash u |
|
1232 |
| name_clash (Abs (_, _, t)) = name_clash t |
|
1233 |
| name_clash _ = false; |
|
1234 |
in |
|
1235 |
if name_clash body then |
|
1236 |
dest_abs (variant [x] x, T, body) (*potentially slow, but rarely happens*) |
|
1237 |
else (x, subst_bound (Free (x, T), body)) |
|
1238 |
end; |
|
1239 |
||
16990 | 1240 |
(*names for numbered variables -- |
1241 |
preserves order wrt. int_ord vs. string_ord, avoids allocating new strings*) |
|
1242 |
local |
|
1243 |
val small_int = Vector.tabulate (1000, fn i => |
|
1244 |
let val leading = if i < 10 then "00" else if i < 100 then "0" else "" |
|
1245 |
in ":" ^ leading ^ string_of_int i end); |
|
1246 |
in |
|
1247 |
fun bound n = |
|
1248 |
if n < 1000 then Vector.sub (small_int, n) |
|
1249 |
else ":" ^ bound (n div 1000) ^ Vector.sub (small_int, n mod 1000); |
|
1250 |
end; |
|
1251 |
||
1252 |
val is_bound = String.isPrefix ":"; |
|
16943 | 1253 |
|
0 | 1254 |
(* renames and reverses the strings in vars away from names *) |
1255 |
fun rename_aTs names vars : (string*typ)list = |
|
1256 |
let fun rename_aT (vars,(a,T)) = |
|
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
1257 |
(variant (map #1 vars @ names) a, T) :: vars |
15570 | 1258 |
in Library.foldl rename_aT ([],vars) end; |
0 | 1259 |
|
1260 |
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
|
1261 |
|
1417 | 1262 |
|
16943 | 1263 |
(* zero var indexes *) |
4286
a09e3e6da2de
added foldl_atyps: ('a * typ -> 'a) -> 'a * typ -> 'a;
wenzelm
parents:
4188
diff
changeset
|
1264 |
|
16943 | 1265 |
fun zero_var_inst vars = |
1266 |
fold (fn v as ((x, i), X) => fn (used, inst) => |
|
1267 |
let |
|
17642 | 1268 |
val x' = variant used (if is_bound x then "u" else x); |
16943 | 1269 |
val used' = x' :: used; |
1270 |
in if x = x' andalso i = 0 then (used', inst) else (used', (v, ((x', 0), X)) :: inst) end) |
|
1271 |
vars ([], []) |> #2; |
|
4286
a09e3e6da2de
added foldl_atyps: ('a * typ -> 'a) -> 'a * typ -> 'a;
wenzelm
parents:
4188
diff
changeset
|
1272 |
|
16943 | 1273 |
fun zero_var_indexesT ty = |
1274 |
instantiateT (map (apsnd TVar) (zero_var_inst (sort tvar_ord (add_tvarsT ty [])))) ty; |
|
16790 | 1275 |
|
16943 | 1276 |
fun zero_var_indexes_inst tm = |
1277 |
let |
|
1278 |
val instT = map (apsnd TVar) (zero_var_inst (sort tvar_ord (fold_types add_tvarsT tm []))); |
|
1279 |
val inst = |
|
1280 |
add_vars tm [] |> map (apsnd (instantiateT instT)) |
|
1281 |
|> sort var_ord |> zero_var_inst |> map (apsnd Var); |
|
1282 |
in (instT, inst) end; |
|
12499 | 1283 |
|
16943 | 1284 |
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
|
1285 |
|
1417 | 1286 |
|
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
1287 |
(* dummy patterns *) |
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 |
val dummy_patternN = "dummy_pattern"; |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
1290 |
|
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
1291 |
fun is_dummy_pattern (Const ("dummy_pattern", _)) = true |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
1292 |
| is_dummy_pattern _ = false; |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
1293 |
|
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
1294 |
fun no_dummy_patterns tm = |
16787 | 1295 |
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
|
1296 |
else raise TERM ("Illegal occurrence of '_' dummy pattern", [tm]); |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
1297 |
|
11903 | 1298 |
fun replace_dummy Ts (i, Const ("dummy_pattern", T)) = |
1299 |
(i + 1, list_comb (Var (("_dummy_", i), Ts ---> T), map Bound (0 upto length Ts - 1))) |
|
1300 |
| replace_dummy Ts (i, Abs (x, T, t)) = |
|
1301 |
let val (i', t') = replace_dummy (T :: Ts) (i, t) |
|
1302 |
in (i', Abs (x, T, t')) end |
|
1303 |
| replace_dummy Ts (i, t $ u) = |
|
1304 |
let val (i', t') = replace_dummy Ts (i, t); val (i'', u') = replace_dummy Ts (i', u) |
|
1305 |
in (i'', t' $ u') end |
|
1306 |
| replace_dummy _ (i, a) = (i, a); |
|
1307 |
||
1308 |
val replace_dummy_patterns = replace_dummy []; |
|
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
1309 |
|
10552 | 1310 |
fun is_replaced_dummy_pattern ("_dummy_", _) = true |
1311 |
| is_replaced_dummy_pattern _ = false; |
|
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
1312 |
|
16035 | 1313 |
fun show_dummy_patterns (Var (("_dummy_", _), T)) = Const ("dummy_pattern", T) |
1314 |
| show_dummy_patterns (t $ u) = show_dummy_patterns t $ show_dummy_patterns u |
|
1315 |
| show_dummy_patterns (Abs (x, T, t)) = Abs (x, T, show_dummy_patterns t) |
|
1316 |
| show_dummy_patterns a = a; |
|
1317 |
||
13484 | 1318 |
|
1319 |
(* adhoc freezing *) |
|
1320 |
||
1321 |
fun adhoc_freeze_vars tm = |
|
1322 |
let |
|
1323 |
fun mk_inst (var as Var ((a, i), T)) = |
|
1324 |
let val x = a ^ Library.gensym "_" ^ string_of_int i |
|
1325 |
in ((var, Free(x, T)), x) end; |
|
1326 |
val (insts, xs) = split_list (map mk_inst (term_vars tm)); |
|
1327 |
in (subst_atomic insts tm, xs) end; |
|
1328 |
||
1329 |
||
14786
24a7bc97a27a
moved some sort ops to sorts.ML; added string_of_vname (from Syntax module);
wenzelm
parents:
14695
diff
changeset
|
1330 |
(* string_of_vname *) |
24a7bc97a27a
moved some sort ops to sorts.ML; added string_of_vname (from Syntax module);
wenzelm
parents:
14695
diff
changeset
|
1331 |
|
15986 | 1332 |
val show_question_marks = ref true; |
15472 | 1333 |
|
14786
24a7bc97a27a
moved some sort ops to sorts.ML; added string_of_vname (from Syntax module);
wenzelm
parents:
14695
diff
changeset
|
1334 |
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
|
1335 |
let |
15986 | 1336 |
val question_mark = if ! show_question_marks then "?" else ""; |
1337 |
val idx = string_of_int i; |
|
1338 |
val dot = |
|
1339 |
(case rev (Symbol.explode x) of |
|
1340 |
_ :: "\\<^isub>" :: _ => false |
|
1341 |
| _ :: "\\<^isup>" :: _ => false |
|
1342 |
| c :: _ => Symbol.is_digit c |
|
1343 |
| _ => true); |
|
14786
24a7bc97a27a
moved some sort ops to sorts.ML; added string_of_vname (from Syntax module);
wenzelm
parents:
14695
diff
changeset
|
1344 |
in |
15986 | 1345 |
if dot then question_mark ^ x ^ "." ^ idx |
1346 |
else if i <> 0 then question_mark ^ x ^ idx |
|
1347 |
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
|
1348 |
end; |
24a7bc97a27a
moved some sort ops to sorts.ML; added string_of_vname (from Syntax module);
wenzelm
parents:
14695
diff
changeset
|
1349 |
|
24a7bc97a27a
moved some sort ops to sorts.ML; added string_of_vname (from Syntax module);
wenzelm
parents:
14695
diff
changeset
|
1350 |
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
|
1351 |
| 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
|
1352 |
|
17777
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 |
(* str_of_term *) |
05f5532a8289
added str_of_term (from HOL/Tools/ATP/recon_translate_proof.ML);
wenzelm
parents:
17756
diff
changeset
|
1355 |
|
05f5532a8289
added str_of_term (from HOL/Tools/ATP/recon_translate_proof.ML);
wenzelm
parents:
17756
diff
changeset
|
1356 |
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
|
1357 |
| str_of_term (Free (x, _)) = x |
05f5532a8289
added str_of_term (from HOL/Tools/ATP/recon_translate_proof.ML);
wenzelm
parents:
17756
diff
changeset
|
1358 |
| 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
|
1359 |
| 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
|
1360 |
| 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
|
1361 |
| 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
|
1362 |
|
1364
8ea1a962ad72
files now define a structure to allow SML/NJ to optimize the code
clasohm
parents:
1029
diff
changeset
|
1363 |
end; |
8ea1a962ad72
files now define a structure to allow SML/NJ to optimize the code
clasohm
parents:
1029
diff
changeset
|
1364 |
|
4444 | 1365 |
structure BasicTerm: BASIC_TERM = Term; |
1366 |
open BasicTerm; |