author | wenzelm |
Thu, 03 Aug 2006 17:30:38 +0200 | |
changeset 20330 | 6192478fdba5 |
parent 20239 | 620a3f297072 |
child 20331 | ccdd1592f5ff |
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 |
|
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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 |
16710 | 45 |
val dest_Const: term -> string * typ |
46 |
val dest_Free: term -> string * typ |
|
47 |
val dest_Var: term -> indexname * typ |
|
4444 | 48 |
val domain_type: typ -> typ |
4480 | 49 |
val range_type: typ -> typ |
4444 | 50 |
val binder_types: typ -> typ list |
51 |
val body_type: typ -> typ |
|
52 |
val strip_type: typ -> typ list * typ |
|
16710 | 53 |
val type_of1: typ list * term -> typ |
4444 | 54 |
val type_of: term -> typ |
16710 | 55 |
val fastype_of1: typ list * term -> typ |
4444 | 56 |
val fastype_of: term -> typ |
10806 | 57 |
val list_abs: (string * typ) list * term -> term |
18927 | 58 |
val strip_abs: term -> (string * typ) list * 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 |
|
18847 | 67 |
val map_atyps: (typ -> typ) -> typ -> typ |
68 |
val map_aterms: (term -> term) -> term -> term |
|
4444 | 69 |
val map_type_tvar: (indexname * sort -> typ) -> typ -> typ |
70 |
val map_type_tfree: (string * sort -> typ) -> typ -> typ |
|
71 |
val map_term_types: (typ -> typ) -> term -> term |
|
16943 | 72 |
val fold_atyps: (typ -> 'a -> 'a) -> typ -> 'a -> 'a |
73 |
val fold_aterms: (term -> 'a -> 'a) -> term -> 'a -> 'a |
|
74 |
val fold_term_types: (term -> typ -> 'a -> 'a) -> term -> 'a -> 'a |
|
75 |
val fold_types: (typ -> 'a -> 'a) -> term -> 'a -> 'a |
|
18927 | 76 |
val it_term_types: (typ * 'a -> 'a) -> term * 'a -> 'a |
16943 | 77 |
val add_term_names: term * string list -> string 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 propT: typ |
84 |
val implies: term |
|
85 |
val all: typ -> term |
|
86 |
val equals: typ -> term |
|
87 |
val strip_all_body: term -> term |
|
88 |
val strip_all_vars: term -> (string * typ) list |
|
89 |
val incr_bv: int * int * term -> term |
|
90 |
val incr_boundvars: int -> term -> term |
|
91 |
val add_loose_bnos: term * int * int list -> int list |
|
92 |
val loose_bnos: term -> int list |
|
93 |
val loose_bvar: term * int -> bool |
|
94 |
val loose_bvar1: term * int -> bool |
|
95 |
val subst_bounds: term list * term -> term |
|
96 |
val subst_bound: term * term -> term |
|
97 |
val betapply: term * term -> term |
|
18183 | 98 |
val betapplys: term * term list -> term |
4444 | 99 |
val eq_ix: indexname * indexname -> bool |
100 |
val could_unify: term * term -> bool |
|
101 |
val subst_free: (term * term) list -> term -> term |
|
102 |
val abstract_over: term * term -> term |
|
11922 | 103 |
val lambda: term -> term -> term |
4444 | 104 |
val absfree: string * typ * term -> term |
17786 | 105 |
val absdummy: typ * term -> term |
4444 | 106 |
val list_abs_free: (string * typ) list * term -> term |
107 |
val list_all_free: (string * typ) list * term -> term |
|
108 |
val list_all: (string * typ) list * term -> term |
|
16710 | 109 |
val subst_atomic: (term * term) list -> term -> term |
110 |
val typ_subst_atomic: (typ * typ) list -> typ -> typ |
|
111 |
val subst_atomic_types: (typ * typ) list -> term -> term |
|
112 |
val typ_subst_TVars: (indexname * typ) list -> typ -> typ |
|
113 |
val subst_TVars: (indexname * typ) list -> term -> term |
|
114 |
val subst_Vars: (indexname * term) list -> term -> term |
|
115 |
val subst_vars: (indexname * typ) list * (indexname * term) list -> term -> term |
|
116 |
val is_first_order: string list -> term -> bool |
|
4444 | 117 |
val maxidx_of_typ: typ -> int |
118 |
val maxidx_of_typs: typ list -> int |
|
119 |
val maxidx_of_term: term -> int |
|
120 |
val add_term_consts: term * string list -> string list |
|
13646 | 121 |
val term_consts: term -> string list |
19909 | 122 |
val exists_subtype: (typ -> bool) -> typ -> bool |
16943 | 123 |
val exists_subterm: (term -> bool) -> term -> bool |
16710 | 124 |
val exists_Const: (string * typ -> bool) -> term -> bool |
125 |
val add_term_free_names: term * string list -> string list |
|
126 |
val add_typ_tvars: typ * (indexname * sort) list -> (indexname * sort) list |
|
127 |
val add_typ_tfree_names: typ * string list -> string list |
|
128 |
val add_typ_tfrees: typ * (string * sort) list -> (string * sort) list |
|
129 |
val add_typ_varnames: typ * string list -> string list |
|
130 |
val add_term_tvars: term * (indexname * sort) list -> (indexname * sort) list |
|
131 |
val add_term_tfrees: term * (string * sort) list -> (string * sort) list |
|
132 |
val add_term_tfree_names: term * string list -> string list |
|
133 |
val add_term_tvarnames: term * string list -> string list |
|
134 |
val typ_tfrees: typ -> (string * sort) list |
|
135 |
val typ_tvars: typ -> (indexname * sort) list |
|
136 |
val term_tfrees: term -> (string * sort) list |
|
137 |
val term_tvars: term -> (indexname * sort) list |
|
138 |
val add_typ_ixns: indexname list * typ -> indexname list |
|
139 |
val add_term_tvar_ixns: term * indexname list -> indexname list |
|
140 |
val add_term_vars: term * term list -> term list |
|
141 |
val term_vars: term -> term list |
|
4444 | 142 |
val add_term_frees: term * term list -> term list |
143 |
val term_frees: term -> term list |
|
20160 | 144 |
val rename_wrt_term: term -> (string * 'a) list -> (string * 'a) list |
15986 | 145 |
val show_question_marks: bool ref |
4444 | 146 |
end; |
0 | 147 |
|
4444 | 148 |
signature TERM = |
149 |
sig |
|
150 |
include BASIC_TERM |
|
19394 | 151 |
val aT: sort -> typ |
152 |
val itselfT: typ -> typ |
|
153 |
val a_itselfT: typ |
|
16710 | 154 |
val argument_type_of: term -> typ |
16943 | 155 |
val add_tvarsT: typ -> (indexname * sort) list -> (indexname * sort) list |
156 |
val add_tvars: term -> (indexname * sort) list -> (indexname * sort) list |
|
157 |
val add_vars: term -> (indexname * typ) list -> (indexname * typ) list |
|
158 |
val add_tfreesT: typ -> (string * sort) list -> (string * sort) list |
|
159 |
val add_tfrees: term -> (string * sort) list -> (string * sort) list |
|
160 |
val add_frees: term -> (string * typ) list -> (string * typ) list |
|
20199 | 161 |
val add_varnames: term -> indexname list -> indexname list |
20109 | 162 |
val strip_abs_eta: int -> term -> (string * typ) list * term |
16678 | 163 |
val fast_indexname_ord: indexname * indexname -> order |
16537 | 164 |
val indexname_ord: indexname * indexname -> order |
165 |
val sort_ord: sort * sort -> order |
|
166 |
val typ_ord: typ * typ -> order |
|
16678 | 167 |
val fast_term_ord: term * term -> order |
16537 | 168 |
val term_ord: term * term -> order |
169 |
val hd_ord: term * term -> order |
|
170 |
val termless: term * term -> bool |
|
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171 |
val term_lpo: (term -> int) -> term * term -> order |
12981 | 172 |
val match_bvars: (term * term) * (string * string) list -> (string * string) list |
173 |
val rename_abs: term -> term -> term -> term option |
|
16943 | 174 |
val eq_tvar: (indexname * sort) * (indexname * sort) -> bool |
16882 | 175 |
val eq_var: (indexname * typ) * (indexname * typ) -> bool |
16943 | 176 |
val tvar_ord: (indexname * sort) * (indexname * sort) -> order |
177 |
val var_ord: (indexname * typ) * (indexname * typ) -> order |
|
19909 | 178 |
val generalize: string list * string list -> int -> term -> term |
179 |
val generalizeT: string list -> int -> typ -> typ |
|
20001 | 180 |
val generalize_option: string list * string list -> int -> term -> term option |
181 |
val generalizeT_option: string list -> int -> typ -> typ option |
|
16882 | 182 |
val instantiate: ((indexname * sort) * typ) list * ((indexname * typ) * term) list |
183 |
-> term -> term |
|
184 |
val instantiateT: ((indexname * sort) * typ) list -> typ -> typ |
|
20001 | 185 |
val instantiate_option: ((indexname * sort) * typ) list * ((indexname * typ) * term) list |
186 |
-> term -> term option |
|
187 |
val instantiateT_option: ((indexname * sort) * typ) list -> typ -> typ option |
|
16710 | 188 |
val maxidx_typ: typ -> int -> int |
189 |
val maxidx_typs: typ list -> int -> int |
|
190 |
val maxidx_term: term -> int -> int |
|
20239 | 191 |
val dest_abs: string * typ * term -> string * term |
20148 | 192 |
val declare_term_names: term -> Name.context -> Name.context |
20160 | 193 |
val variant_frees: term -> (string * 'a) list -> (string * 'a) list |
16943 | 194 |
val zero_var_indexes: term -> term |
195 |
val zero_var_indexes_inst: term -> |
|
196 |
((indexname * sort) * typ) list * ((indexname * typ) * term) list |
|
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197 |
val dummy_patternN: string |
18253 | 198 |
val dummy_pattern: typ -> term |
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199 |
val no_dummy_patterns: term -> term |
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200 |
val replace_dummy_patterns: int * term -> int * term |
10552 | 201 |
val is_replaced_dummy_pattern: indexname -> bool |
16035 | 202 |
val show_dummy_patterns: term -> term |
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203 |
val string_of_vname: indexname -> string |
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204 |
val string_of_vname': indexname -> string |
4444 | 205 |
end; |
206 |
||
207 |
structure Term: TERM = |
|
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208 |
struct |
0 | 209 |
|
210 |
(*Indexnames can be quickly renamed by adding an offset to the integer part, |
|
211 |
for resolution.*) |
|
16537 | 212 |
type indexname = string * int; |
0 | 213 |
|
4626 | 214 |
(* Types are classified by sorts. *) |
0 | 215 |
type class = string; |
216 |
type sort = class list; |
|
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217 |
type arity = string * sort list * sort; |
0 | 218 |
|
219 |
(* The sorts attached to TFrees and TVars specify the sort of that variable *) |
|
220 |
datatype typ = Type of string * typ list |
|
221 |
| TFree of string * sort |
|
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222 |
| TVar of indexname * sort; |
0 | 223 |
|
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224 |
(*Terms. Bound variables are indicated by depth number. |
0 | 225 |
Free variables, (scheme) variables and constants have names. |
4626 | 226 |
An term is "closed" if every bound variable of level "lev" |
13000 | 227 |
is enclosed by at least "lev" abstractions. |
0 | 228 |
|
229 |
It is possible to create meaningless terms containing loose bound vars |
|
230 |
or type mismatches. But such terms are not allowed in rules. *) |
|
231 |
||
13000 | 232 |
datatype term = |
0 | 233 |
Const of string * typ |
13000 | 234 |
| Free of string * typ |
0 | 235 |
| Var of indexname * typ |
236 |
| Bound of int |
|
237 |
| Abs of string*typ*term |
|
3965 | 238 |
| op $ of term*term; |
0 | 239 |
|
16537 | 240 |
(*Errors involving type mismatches*) |
0 | 241 |
exception TYPE of string * typ list * term list; |
242 |
||
16537 | 243 |
(*Errors errors involving terms*) |
0 | 244 |
exception TERM of string * term list; |
245 |
||
246 |
(*Note variable naming conventions! |
|
247 |
a,b,c: string |
|
248 |
f,g,h: functions (including terms of function type) |
|
249 |
i,j,m,n: int |
|
250 |
t,u: term |
|
251 |
v,w: indexnames |
|
252 |
x,y: any |
|
253 |
A,B,C: term (denoting formulae) |
|
254 |
T,U: typ |
|
255 |
*) |
|
256 |
||
257 |
||
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258 |
(** Types **) |
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259 |
|
16537 | 260 |
(*dummy type for parsing and printing etc.*) |
261 |
val dummyT = Type ("dummy", []); |
|
262 |
||
263 |
fun no_dummyT typ = |
|
264 |
let |
|
265 |
fun check (T as Type ("dummy", _)) = |
|
266 |
raise TYPE ("Illegal occurrence of '_' dummy type", [T], []) |
|
267 |
| check (Type (_, Ts)) = List.app check Ts |
|
268 |
| check _ = (); |
|
269 |
in check typ; typ end; |
|
270 |
||
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271 |
fun S --> T = Type("fun",[S,T]); |
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272 |
|
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273 |
(*handy for multiple args: [T1,...,Tn]--->T gives T1-->(T2--> ... -->T)*) |
15570 | 274 |
val op ---> = Library.foldr (op -->); |
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275 |
|
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276 |
fun dest_Type (Type x) = x |
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277 |
| dest_Type T = raise TYPE ("dest_Type", [T], []); |
15914 | 278 |
fun dest_TVar (TVar x) = x |
279 |
| dest_TVar T = raise TYPE ("dest_TVar", [T], []); |
|
280 |
fun dest_TFree (TFree x) = x |
|
281 |
| dest_TFree T = raise TYPE ("dest_TFree", [T], []); |
|
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282 |
|
16537 | 283 |
|
0 | 284 |
(** Discriminators **) |
285 |
||
7318 | 286 |
fun is_Bound (Bound _) = true |
287 |
| is_Bound _ = false; |
|
288 |
||
0 | 289 |
fun is_Const (Const _) = true |
290 |
| is_Const _ = false; |
|
291 |
||
292 |
fun is_Free (Free _) = true |
|
293 |
| is_Free _ = false; |
|
294 |
||
295 |
fun is_Var (Var _) = true |
|
296 |
| is_Var _ = false; |
|
297 |
||
298 |
fun is_TVar (TVar _) = true |
|
299 |
| is_TVar _ = false; |
|
300 |
||
16537 | 301 |
|
0 | 302 |
(** Destructors **) |
303 |
||
304 |
fun dest_Const (Const x) = x |
|
305 |
| dest_Const t = raise TERM("dest_Const", [t]); |
|
306 |
||
307 |
fun dest_Free (Free x) = x |
|
308 |
| dest_Free t = raise TERM("dest_Free", [t]); |
|
309 |
||
310 |
fun dest_Var (Var x) = x |
|
311 |
| dest_Var t = raise TERM("dest_Var", [t]); |
|
312 |
||
313 |
||
4464 | 314 |
fun domain_type (Type("fun", [T,_])) = T |
315 |
and range_type (Type("fun", [_,T])) = T; |
|
4064 | 316 |
|
0 | 317 |
(* maps [T1,...,Tn]--->T to the list [T1,T2,...,Tn]*) |
318 |
fun binder_types (Type("fun",[S,T])) = S :: binder_types T |
|
319 |
| binder_types _ = []; |
|
320 |
||
321 |
(* maps [T1,...,Tn]--->T to T*) |
|
322 |
fun body_type (Type("fun",[S,T])) = body_type T |
|
323 |
| body_type T = T; |
|
324 |
||
325 |
(* maps [T1,...,Tn]--->T to ([T1,T2,...,Tn], T) *) |
|
326 |
fun strip_type T : typ list * typ = |
|
327 |
(binder_types T, body_type T); |
|
328 |
||
329 |
||
330 |
(*Compute the type of the term, checking that combinations are well-typed |
|
331 |
Ts = [T0,T1,...] holds types of bound variables 0, 1, ...*) |
|
332 |
fun type_of1 (Ts, Const (_,T)) = T |
|
333 |
| type_of1 (Ts, Free (_,T)) = T |
|
15570 | 334 |
| type_of1 (Ts, Bound i) = (List.nth (Ts,i) |
335 |
handle Subscript => raise TYPE("type_of: bound variable", [], [Bound i])) |
|
0 | 336 |
| type_of1 (Ts, Var (_,T)) = T |
337 |
| type_of1 (Ts, Abs (_,T,body)) = T --> type_of1(T::Ts, body) |
|
13000 | 338 |
| type_of1 (Ts, f$u) = |
0 | 339 |
let val U = type_of1(Ts,u) |
340 |
and T = type_of1(Ts,f) |
|
341 |
in case T of |
|
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
342 |
Type("fun",[T1,T2]) => |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
343 |
if T1=U then T2 else raise TYPE |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
344 |
("type_of: type mismatch in application", [T1,U], [f$u]) |
13000 | 345 |
| _ => raise TYPE |
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
346 |
("type_of: function type is expected in application", |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
347 |
[T,U], [f$u]) |
0 | 348 |
end; |
349 |
||
350 |
fun type_of t : typ = type_of1 ([],t); |
|
351 |
||
352 |
(*Determines the type of a term, with minimal checking*) |
|
13000 | 353 |
fun fastype_of1 (Ts, f$u) = |
61 | 354 |
(case fastype_of1 (Ts,f) of |
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
355 |
Type("fun",[_,T]) => T |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
356 |
| _ => raise TERM("fastype_of: expected function type", [f$u])) |
61 | 357 |
| fastype_of1 (_, Const (_,T)) = T |
358 |
| fastype_of1 (_, Free (_,T)) = T |
|
15570 | 359 |
| fastype_of1 (Ts, Bound i) = (List.nth(Ts,i) |
360 |
handle Subscript => raise TERM("fastype_of: Bound", [Bound i])) |
|
13000 | 361 |
| fastype_of1 (_, Var (_,T)) = T |
61 | 362 |
| fastype_of1 (Ts, Abs (_,T,u)) = T --> fastype_of1 (T::Ts, u); |
363 |
||
364 |
fun fastype_of t : typ = fastype_of1 ([],t); |
|
0 | 365 |
|
16678 | 366 |
(*Determine the argument type of a function*) |
367 |
fun argument_type_of tm = |
|
368 |
let |
|
369 |
fun argT i (Type ("fun", [T, U])) = if i = 0 then T else argT (i - 1) U |
|
370 |
| argT _ T = raise TYPE ("argument_type_of", [T], []); |
|
371 |
||
372 |
fun arg 0 _ (Abs (_, T, _)) = T |
|
373 |
| arg i Ts (Abs (_, T, t)) = arg (i - 1) (T :: Ts) t |
|
374 |
| arg i Ts (t $ _) = arg (i + 1) Ts t |
|
375 |
| arg i Ts a = argT i (fastype_of1 (Ts, a)); |
|
376 |
in arg 0 [] tm end; |
|
377 |
||
0 | 378 |
|
19473 | 379 |
val list_abs = uncurry (fold_rev (fn (x, T) => fn t => Abs (x, T, t))); |
10806 | 380 |
|
18927 | 381 |
fun strip_abs (Abs (a, T, t)) = |
382 |
let val (a', t') = strip_abs t |
|
383 |
in ((a, T) :: a', t') end |
|
384 |
| strip_abs t = ([], t); |
|
385 |
||
0 | 386 |
(* maps (x1,...,xn)t to t *) |
13000 | 387 |
fun strip_abs_body (Abs(_,_,t)) = strip_abs_body t |
0 | 388 |
| strip_abs_body u = u; |
389 |
||
390 |
(* maps (x1,...,xn)t to [x1, ..., xn] *) |
|
13000 | 391 |
fun strip_abs_vars (Abs(a,T,t)) = (a,T) :: strip_abs_vars t |
0 | 392 |
| strip_abs_vars u = [] : (string*typ) list; |
393 |
||
394 |
||
395 |
fun strip_qnt_body qnt = |
|
396 |
let fun strip(tm as Const(c,_)$Abs(_,_,t)) = if c=qnt then strip t else tm |
|
397 |
| strip t = t |
|
398 |
in strip end; |
|
399 |
||
400 |
fun strip_qnt_vars qnt = |
|
401 |
let fun strip(Const(c,_)$Abs(a,T,t)) = if c=qnt then (a,T)::strip t else [] |
|
402 |
| strip t = [] : (string*typ) list |
|
403 |
in strip end; |
|
404 |
||
405 |
||
406 |
(* maps (f, [t1,...,tn]) to f(t1,...,tn) *) |
|
15570 | 407 |
val list_comb : term * term list -> term = Library.foldl (op $); |
0 | 408 |
|
409 |
||
410 |
(* maps f(t1,...,tn) to (f, [t1,...,tn]) ; naturally tail-recursive*) |
|
13000 | 411 |
fun strip_comb u : term * term list = |
0 | 412 |
let fun stripc (f$t, ts) = stripc (f, t::ts) |
13000 | 413 |
| stripc x = x |
0 | 414 |
in stripc(u,[]) end; |
415 |
||
416 |
||
417 |
(* maps f(t1,...,tn) to f , which is never a combination *) |
|
418 |
fun head_of (f$t) = head_of f |
|
419 |
| head_of u = u; |
|
420 |
||
421 |
||
16599 | 422 |
(*number of atoms and abstractions in a term*) |
423 |
fun size_of_term tm = |
|
424 |
let |
|
16678 | 425 |
fun add_size (t $ u, n) = add_size (t, add_size (u, n)) |
426 |
| add_size (Abs (_ ,_, t), n) = add_size (t, n + 1) |
|
427 |
| add_size (_, n) = n + 1; |
|
428 |
in add_size (tm, 0) end; |
|
0 | 429 |
|
18847 | 430 |
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
|
431 |
| map_atyps f T = f T; |
18847 | 432 |
|
433 |
fun map_aterms f (t $ u) = map_aterms f t $ map_aterms f u |
|
434 |
| map_aterms f (Abs (a, T, t)) = Abs (a, T, map_aterms f t) |
|
435 |
| map_aterms f t = f t; |
|
436 |
||
18981 | 437 |
fun map_type_tvar f = map_atyps (fn TVar x => f x | T => T); |
438 |
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
|
439 |
|
0 | 440 |
fun map_term_types f = |
16678 | 441 |
let |
442 |
fun map_aux (Const (a, T)) = Const (a, f T) |
|
443 |
| map_aux (Free (a, T)) = Free (a, f T) |
|
444 |
| map_aux (Var (v, T)) = Var (v, f T) |
|
445 |
| map_aux (t as Bound _) = t |
|
446 |
| map_aux (Abs (a, T, t)) = Abs (a, f T, map_aux t) |
|
447 |
| map_aux (t $ u) = map_aux t $ map_aux u; |
|
448 |
in map_aux end; |
|
0 | 449 |
|
450 |
(* iterate a function over all types in a term *) |
|
451 |
fun it_term_types f = |
|
452 |
let fun iter(Const(_,T), a) = f(T,a) |
|
453 |
| iter(Free(_,T), a) = f(T,a) |
|
454 |
| iter(Var(_,T), a) = f(T,a) |
|
455 |
| iter(Abs(_,T,t), a) = iter(t,f(T,a)) |
|
456 |
| iter(f$u, a) = iter(f, iter(u, a)) |
|
457 |
| iter(Bound _, a) = a |
|
458 |
in iter end |
|
459 |
||
460 |
||
16943 | 461 |
(* fold types and terms *) |
462 |
||
463 |
(*fold atoms of type*) |
|
464 |
fun fold_atyps f (Type (_, Ts)) = fold (fold_atyps f) Ts |
|
465 |
| fold_atyps f T = f T; |
|
466 |
||
467 |
(*fold atoms of term*) |
|
468 |
fun fold_aterms f (t $ u) = fold_aterms f t #> fold_aterms f u |
|
469 |
| fold_aterms f (Abs (_, _, t)) = fold_aterms f t |
|
470 |
| fold_aterms f a = f a; |
|
471 |
||
472 |
(*fold types of term*) |
|
473 |
fun fold_term_types f (t as Const (_, T)) = f t T |
|
474 |
| fold_term_types f (t as Free (_, T)) = f t T |
|
475 |
| fold_term_types f (t as Var (_, T)) = f t T |
|
476 |
| fold_term_types f (Bound _) = I |
|
477 |
| fold_term_types f (t as Abs (_, T, b)) = f t T #> fold_term_types f b |
|
478 |
| fold_term_types f (t $ u) = fold_term_types f t #> fold_term_types f u; |
|
479 |
||
480 |
fun fold_types f = fold_term_types (K f); |
|
481 |
||
482 |
(*collect variables*) |
|
483 |
val add_tvarsT = fold_atyps (fn TVar v => insert (op =) v | _ => I); |
|
484 |
val add_tvars = fold_types add_tvarsT; |
|
485 |
val add_vars = fold_aterms (fn Var v => insert (op =) v | _ => I); |
|
20199 | 486 |
val add_varnames = fold_aterms (fn Var (xi, _) => insert (op =) xi | _ => I); |
16943 | 487 |
val add_tfreesT = fold_atyps (fn TFree v => insert (op =) v | _ => I); |
488 |
val add_tfrees = fold_types add_tfreesT; |
|
489 |
val add_frees = fold_aterms (fn Free v => insert (op =) v | _ => I); |
|
490 |
||
491 |
||
16678 | 492 |
(** Comparing terms, types, sorts etc. **) |
16537 | 493 |
|
16678 | 494 |
(* fast syntactic comparison *) |
495 |
||
496 |
fun fast_indexname_ord ((x, i), (y, j)) = |
|
497 |
(case int_ord (i, j) of EQUAL => fast_string_ord (x, y) | ord => ord); |
|
16537 | 498 |
|
16599 | 499 |
fun sort_ord SS = |
500 |
if pointer_eq SS then EQUAL |
|
16990 | 501 |
else dict_ord fast_string_ord SS; |
16678 | 502 |
|
503 |
local |
|
16537 | 504 |
|
16678 | 505 |
fun cons_nr (TVar _) = 0 |
506 |
| cons_nr (TFree _) = 1 |
|
507 |
| cons_nr (Type _) = 2; |
|
16537 | 508 |
|
16678 | 509 |
in |
16537 | 510 |
|
511 |
fun typ_ord TU = |
|
512 |
if pointer_eq TU then EQUAL |
|
513 |
else |
|
514 |
(case TU of |
|
16678 | 515 |
(Type (a, Ts), Type (b, Us)) => |
16990 | 516 |
(case fast_string_ord (a, b) of EQUAL => dict_ord typ_ord (Ts, Us) | ord => ord) |
16678 | 517 |
| (TFree (a, S), TFree (b, S')) => |
518 |
(case fast_string_ord (a, b) of EQUAL => sort_ord (S, S') | ord => ord) |
|
519 |
| (TVar (xi, S), TVar (yj, S')) => |
|
520 |
(case fast_indexname_ord (xi, yj) of EQUAL => sort_ord (S, S') | ord => ord) |
|
521 |
| (T, U) => int_ord (cons_nr T, cons_nr U)); |
|
522 |
||
523 |
end; |
|
524 |
||
525 |
local |
|
526 |
||
527 |
fun cons_nr (Const _) = 0 |
|
528 |
| cons_nr (Free _) = 1 |
|
529 |
| cons_nr (Var _) = 2 |
|
530 |
| cons_nr (Bound _) = 3 |
|
531 |
| cons_nr (Abs _) = 4 |
|
532 |
| cons_nr (_ $ _) = 5; |
|
533 |
||
534 |
fun struct_ord (Abs (_, _, t), Abs (_, _, u)) = struct_ord (t, u) |
|
535 |
| struct_ord (t1 $ t2, u1 $ u2) = |
|
536 |
(case struct_ord (t1, u1) of EQUAL => struct_ord (t2, u2) | ord => ord) |
|
537 |
| struct_ord (t, u) = int_ord (cons_nr t, cons_nr u); |
|
538 |
||
539 |
fun atoms_ord (Abs (_, _, t), Abs (_, _, u)) = atoms_ord (t, u) |
|
540 |
| atoms_ord (t1 $ t2, u1 $ u2) = |
|
541 |
(case atoms_ord (t1, u1) of EQUAL => atoms_ord (t2, u2) | ord => ord) |
|
542 |
| atoms_ord (Const (a, _), Const (b, _)) = fast_string_ord (a, b) |
|
543 |
| atoms_ord (Free (x, _), Free (y, _)) = fast_string_ord (x, y) |
|
544 |
| atoms_ord (Var (xi, _), Var (yj, _)) = fast_indexname_ord (xi, yj) |
|
545 |
| atoms_ord (Bound i, Bound j) = int_ord (i, j) |
|
546 |
| atoms_ord _ = sys_error "atoms_ord"; |
|
547 |
||
548 |
fun types_ord (Abs (_, T, t), Abs (_, U, u)) = |
|
549 |
(case typ_ord (T, U) of EQUAL => types_ord (t, u) | ord => ord) |
|
550 |
| types_ord (t1 $ t2, u1 $ u2) = |
|
551 |
(case types_ord (t1, u1) of EQUAL => types_ord (t2, u2) | ord => ord) |
|
552 |
| types_ord (Const (_, T), Const (_, U)) = typ_ord (T, U) |
|
553 |
| types_ord (Free (_, T), Free (_, U)) = typ_ord (T, U) |
|
554 |
| types_ord (Var (_, T), Var (_, U)) = typ_ord (T, U) |
|
555 |
| types_ord (Bound _, Bound _) = EQUAL |
|
556 |
| types_ord _ = sys_error "types_ord"; |
|
557 |
||
558 |
in |
|
559 |
||
560 |
fun fast_term_ord tu = |
|
561 |
if pointer_eq tu then EQUAL |
|
562 |
else |
|
563 |
(case struct_ord tu of |
|
564 |
EQUAL => (case atoms_ord tu of EQUAL => types_ord tu | ord => ord) |
|
565 |
| ord => ord); |
|
566 |
||
567 |
fun op aconv tu = (fast_term_ord tu = EQUAL); |
|
568 |
fun aconvs ts_us = (list_ord fast_term_ord ts_us = EQUAL); |
|
569 |
||
570 |
structure Vartab = TableFun(type key = indexname val ord = fast_indexname_ord); |
|
571 |
structure Typtab = TableFun(type key = typ val ord = typ_ord); |
|
572 |
structure Termtab = TableFun(type key = term val ord = fast_term_ord); |
|
573 |
||
574 |
end; |
|
16537 | 575 |
|
576 |
||
577 |
(* term_ord *) |
|
578 |
||
579 |
(*a linear well-founded AC-compatible ordering for terms: |
|
580 |
s < t <=> 1. size(s) < size(t) or |
|
581 |
2. size(s) = size(t) and s=f(...) and t=g(...) and f<g or |
|
582 |
3. size(s) = size(t) and s=f(s1..sn) and t=f(t1..tn) and |
|
583 |
(s1..sn) < (t1..tn) (lexicographically)*) |
|
16678 | 584 |
|
585 |
fun indexname_ord ((x, i), (y, j)) = |
|
586 |
(case int_ord (i, j) of EQUAL => string_ord (x, y) | ord => ord); |
|
587 |
||
16667 | 588 |
local |
589 |
||
590 |
fun hd_depth (t $ _, n) = hd_depth (t, n + 1) |
|
591 |
| hd_depth p = p; |
|
16537 | 592 |
|
593 |
fun dest_hd (Const (a, T)) = (((a, 0), T), 0) |
|
594 |
| dest_hd (Free (a, T)) = (((a, 0), T), 1) |
|
595 |
| dest_hd (Var v) = (v, 2) |
|
596 |
| dest_hd (Bound i) = ((("", i), dummyT), 3) |
|
597 |
| dest_hd (Abs (_, T, _)) = ((("", 0), T), 4); |
|
598 |
||
16667 | 599 |
in |
600 |
||
16537 | 601 |
fun term_ord tu = |
602 |
if pointer_eq tu then EQUAL |
|
603 |
else |
|
604 |
(case tu of |
|
605 |
(Abs (_, T, t), Abs(_, U, u)) => |
|
606 |
(case term_ord (t, u) of EQUAL => typ_ord (T, U) | ord => ord) |
|
16667 | 607 |
| (t, u) => |
16537 | 608 |
(case int_ord (size_of_term t, size_of_term u) of |
609 |
EQUAL => |
|
16943 | 610 |
(case prod_ord hd_ord int_ord (hd_depth (t, 0), hd_depth (u, 0)) of |
611 |
EQUAL => args_ord (t, u) | ord => ord) |
|
16537 | 612 |
| ord => ord)) |
613 |
and hd_ord (f, g) = |
|
614 |
prod_ord (prod_ord indexname_ord typ_ord) int_ord (dest_hd f, dest_hd g) |
|
16667 | 615 |
and args_ord (f $ t, g $ u) = |
616 |
(case args_ord (f, g) of EQUAL => term_ord (t, u) | ord => ord) |
|
617 |
| args_ord _ = EQUAL; |
|
16537 | 618 |
|
619 |
fun termless tu = (term_ord tu = LESS); |
|
620 |
||
16667 | 621 |
end; |
622 |
||
623 |
||
624 |
(** Lexicographic path order on terms **) |
|
625 |
||
626 |
(* |
|
16570 | 627 |
See Baader & Nipkow, Term rewriting, CUP 1998. |
628 |
Without variables. Const, Var, Bound, Free and Abs are treated all as |
|
629 |
constants. |
|
630 |
||
20129
95e84d2c9f2c
Term.term_lpo takes order on terms rather than strings as argument.
ballarin
parents:
20122
diff
changeset
|
631 |
f_ord maps terms to integers and serves two purposes: |
16570 | 632 |
- Predicate on constant symbols. Those that are not recognised by f_ord |
633 |
must be mapped to ~1. |
|
634 |
- Order on the recognised symbols. These must be mapped to distinct |
|
635 |
integers >= 0. |
|
20129
95e84d2c9f2c
Term.term_lpo takes order on terms rather than strings as argument.
ballarin
parents:
20122
diff
changeset
|
636 |
The argument of f_ord is never an application. |
16667 | 637 |
*) |
16570 | 638 |
|
639 |
local |
|
20129
95e84d2c9f2c
Term.term_lpo takes order on terms rather than strings as argument.
ballarin
parents:
20122
diff
changeset
|
640 |
|
95e84d2c9f2c
Term.term_lpo takes order on terms rather than strings as argument.
ballarin
parents:
20122
diff
changeset
|
641 |
fun unrecognized (Const (a, T)) = ((1, ((a, 0), T)), 0) |
95e84d2c9f2c
Term.term_lpo takes order on terms rather than strings as argument.
ballarin
parents:
20122
diff
changeset
|
642 |
| unrecognized (Free (a, T)) = ((1, ((a, 0), T)), 0) |
95e84d2c9f2c
Term.term_lpo takes order on terms rather than strings as argument.
ballarin
parents:
20122
diff
changeset
|
643 |
| unrecognized (Var v) = ((1, v), 1) |
95e84d2c9f2c
Term.term_lpo takes order on terms rather than strings as argument.
ballarin
parents:
20122
diff
changeset
|
644 |
| unrecognized (Bound i) = ((1, (("", i), dummyT)), 2) |
95e84d2c9f2c
Term.term_lpo takes order on terms rather than strings as argument.
ballarin
parents:
20122
diff
changeset
|
645 |
| unrecognized (Abs (_, T, _)) = ((1, (("", 0), T)), 3); |
95e84d2c9f2c
Term.term_lpo takes order on terms rather than strings as argument.
ballarin
parents:
20122
diff
changeset
|
646 |
|
95e84d2c9f2c
Term.term_lpo takes order on terms rather than strings as argument.
ballarin
parents:
20122
diff
changeset
|
647 |
fun dest_hd f_ord t = |
95e84d2c9f2c
Term.term_lpo takes order on terms rather than strings as argument.
ballarin
parents:
20122
diff
changeset
|
648 |
let val ord = f_ord t in |
95e84d2c9f2c
Term.term_lpo takes order on terms rather than strings as argument.
ballarin
parents:
20122
diff
changeset
|
649 |
if ord = ~1 then unrecognized t else ((0, (("", ord), fastype_of t)), 0) |
16570 | 650 |
end |
651 |
||
652 |
fun term_lpo f_ord (s, t) = |
|
653 |
let val (f, ss) = strip_comb s and (g, ts) = strip_comb t in |
|
654 |
if forall (fn si => term_lpo f_ord (si, t) = LESS) ss |
|
655 |
then case hd_ord f_ord (f, g) of |
|
16667 | 656 |
GREATER => |
657 |
if forall (fn ti => term_lpo f_ord (s, ti) = GREATER) ts |
|
658 |
then GREATER else LESS |
|
16570 | 659 |
| EQUAL => |
16667 | 660 |
if forall (fn ti => term_lpo f_ord (s, ti) = GREATER) ts |
661 |
then list_ord (term_lpo f_ord) (ss, ts) |
|
662 |
else LESS |
|
16570 | 663 |
| LESS => LESS |
664 |
else GREATER |
|
665 |
end |
|
666 |
and hd_ord f_ord (f, g) = case (f, g) of |
|
667 |
(Abs (_, T, t), Abs (_, U, u)) => |
|
668 |
(case term_lpo f_ord (t, u) of EQUAL => typ_ord (T, U) | ord => ord) |
|
669 |
| (_, _) => prod_ord (prod_ord int_ord |
|
670 |
(prod_ord indexname_ord typ_ord)) int_ord |
|
671 |
(dest_hd f_ord f, dest_hd f_ord g) |
|
672 |
in |
|
673 |
val term_lpo = term_lpo |
|
674 |
end; |
|
675 |
||
16537 | 676 |
|
0 | 677 |
(** Connectives of higher order logic **) |
678 |
||
19394 | 679 |
fun aT S = TFree ("'a", S); |
680 |
||
375 | 681 |
fun itselfT ty = Type ("itself", [ty]); |
14854 | 682 |
val a_itselfT = itselfT (TFree ("'a", [])); |
375 | 683 |
|
0 | 684 |
val propT : typ = Type("prop",[]); |
685 |
||
686 |
val implies = Const("==>", propT-->propT-->propT); |
|
687 |
||
688 |
fun all T = Const("all", (T-->propT)-->propT); |
|
689 |
||
690 |
fun equals T = Const("==", T-->T-->propT); |
|
691 |
||
692 |
(* maps !!x1...xn. t to t *) |
|
13000 | 693 |
fun strip_all_body (Const("all",_)$Abs(_,_,t)) = strip_all_body t |
0 | 694 |
| strip_all_body t = t; |
695 |
||
696 |
(* maps !!x1...xn. t to [x1, ..., xn] *) |
|
697 |
fun strip_all_vars (Const("all",_)$Abs(a,T,t)) = |
|
13000 | 698 |
(a,T) :: strip_all_vars t |
0 | 699 |
| strip_all_vars t = [] : (string*typ) list; |
700 |
||
701 |
(*increments a term's non-local bound variables |
|
702 |
required when moving a term within abstractions |
|
703 |
inc is increment for bound variables |
|
704 |
lev is level at which a bound variable is considered 'loose'*) |
|
13000 | 705 |
fun incr_bv (inc, lev, u as Bound i) = if i>=lev then Bound(i+inc) else u |
0 | 706 |
| incr_bv (inc, lev, Abs(a,T,body)) = |
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
707 |
Abs(a, T, incr_bv(inc,lev+1,body)) |
13000 | 708 |
| incr_bv (inc, lev, f$t) = |
0 | 709 |
incr_bv(inc,lev,f) $ incr_bv(inc,lev,t) |
710 |
| incr_bv (inc, lev, u) = u; |
|
711 |
||
712 |
fun incr_boundvars 0 t = t |
|
713 |
| incr_boundvars inc t = incr_bv(inc,0,t); |
|
714 |
||
12981 | 715 |
(*Scan a pair of terms; while they are similar, |
716 |
accumulate corresponding bound vars in "al"*) |
|
717 |
fun match_bvs(Abs(x,_,s),Abs(y,_,t), al) = |
|
718 |
match_bvs(s, t, if x="" orelse y="" then al |
|
719 |
else (x,y)::al) |
|
720 |
| match_bvs(f$s, g$t, al) = match_bvs(f,g,match_bvs(s,t,al)) |
|
721 |
| match_bvs(_,_,al) = al; |
|
722 |
||
723 |
(* strip abstractions created by parameters *) |
|
724 |
fun match_bvars((s,t),al) = match_bvs(strip_abs_body s, strip_abs_body t, al); |
|
725 |
||
726 |
fun rename_abs pat obj t = |
|
727 |
let |
|
728 |
val ren = match_bvs (pat, obj, []); |
|
729 |
fun ren_abs (Abs (x, T, b)) = |
|
18942 | 730 |
Abs (the_default x (AList.lookup (op =) ren x), T, ren_abs b) |
12981 | 731 |
| ren_abs (f $ t) = ren_abs f $ ren_abs t |
732 |
| ren_abs t = t |
|
15531 | 733 |
in if null ren then NONE else SOME (ren_abs t) end; |
0 | 734 |
|
735 |
(*Accumulate all 'loose' bound vars referring to level 'lev' or beyond. |
|
736 |
(Bound 0) is loose at level 0 *) |
|
13000 | 737 |
fun add_loose_bnos (Bound i, lev, js) = |
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
738 |
if i<lev then js else (i-lev) ins_int js |
0 | 739 |
| add_loose_bnos (Abs (_,_,t), lev, js) = add_loose_bnos (t, lev+1, js) |
740 |
| add_loose_bnos (f$t, lev, js) = |
|
13000 | 741 |
add_loose_bnos (f, lev, add_loose_bnos (t, lev, js)) |
0 | 742 |
| add_loose_bnos (_, _, js) = js; |
743 |
||
744 |
fun loose_bnos t = add_loose_bnos (t, 0, []); |
|
745 |
||
746 |
(* loose_bvar(t,k) iff t contains a 'loose' bound variable referring to |
|
747 |
level k or beyond. *) |
|
748 |
fun loose_bvar(Bound i,k) = i >= k |
|
749 |
| loose_bvar(f$t, k) = loose_bvar(f,k) orelse loose_bvar(t,k) |
|
750 |
| loose_bvar(Abs(_,_,t),k) = loose_bvar(t,k+1) |
|
751 |
| loose_bvar _ = false; |
|
752 |
||
2792 | 753 |
fun loose_bvar1(Bound i,k) = i = k |
754 |
| loose_bvar1(f$t, k) = loose_bvar1(f,k) orelse loose_bvar1(t,k) |
|
755 |
| loose_bvar1(Abs(_,_,t),k) = loose_bvar1(t,k+1) |
|
756 |
| loose_bvar1 _ = false; |
|
0 | 757 |
|
758 |
(*Substitute arguments for loose bound variables. |
|
759 |
Beta-reduction of arg(n-1)...arg0 into t replacing (Bound i) with (argi). |
|
4626 | 760 |
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
|
761 |
and the appropriate call is subst_bounds([b,a], c) . |
0 | 762 |
Loose bound variables >=n are reduced by "n" to |
763 |
compensate for the disappearance of lambdas. |
|
764 |
*) |
|
13000 | 765 |
fun subst_bounds (args: term list, t) : term = |
19065 | 766 |
let |
767 |
exception SAME; |
|
768 |
val n = length args; |
|
769 |
fun subst (t as Bound i, lev) = |
|
770 |
(if i < lev then raise SAME (*var is locally bound*) |
|
771 |
else incr_boundvars lev (List.nth (args, i - lev)) |
|
772 |
handle Subscript => Bound (i - n)) (*loose: change it*) |
|
773 |
| subst (Abs (a, T, body), lev) = Abs (a, T, subst (body, lev + 1)) |
|
774 |
| subst (f $ t, lev) = |
|
775 |
(subst (f, lev) $ (subst (t, lev) handle SAME => t) handle SAME => f $ subst (t, lev)) |
|
776 |
| subst _ = raise SAME; |
|
777 |
in case args of [] => t | _ => (subst (t, 0) handle SAME => t) end; |
|
0 | 778 |
|
2192
3bf092b5310b
Optimizations: removal of polymorphic equality; one-argument case
paulson
parents:
2182
diff
changeset
|
779 |
(*Special case: one argument*) |
13000 | 780 |
fun subst_bound (arg, t) : term = |
19065 | 781 |
let |
782 |
exception SAME; |
|
783 |
fun subst (Bound i, lev) = |
|
784 |
if i < lev then raise SAME (*var is locally bound*) |
|
785 |
else if i = lev then incr_boundvars lev arg |
|
786 |
else Bound (i - 1) (*loose: change it*) |
|
787 |
| subst (Abs (a, T, body), lev) = Abs (a, T, subst (body, lev + 1)) |
|
788 |
| subst (f $ t, lev) = |
|
789 |
(subst (f, lev) $ (subst (t, lev) handle SAME => t) handle SAME => f $ subst (t, lev)) |
|
790 |
| subst _ = raise SAME; |
|
791 |
in subst (t, 0) handle SAME => t end; |
|
2192
3bf092b5310b
Optimizations: removal of polymorphic equality; one-argument case
paulson
parents:
2182
diff
changeset
|
792 |
|
0 | 793 |
(*beta-reduce if possible, else form application*) |
2192
3bf092b5310b
Optimizations: removal of polymorphic equality; one-argument case
paulson
parents:
2182
diff
changeset
|
794 |
fun betapply (Abs(_,_,t), u) = subst_bound (u,t) |
0 | 795 |
| betapply (f,u) = f$u; |
796 |
||
18183 | 797 |
val betapplys = Library.foldl betapply; |
798 |
||
14786
24a7bc97a27a
moved some sort ops to sorts.ML; added string_of_vname (from Syntax module);
wenzelm
parents:
14695
diff
changeset
|
799 |
|
20109 | 800 |
(*unfolding abstractions with substitution |
801 |
of bound variables and implicit eta-expansion*) |
|
802 |
fun strip_abs_eta k t = |
|
803 |
let |
|
20122 | 804 |
val used = fold_aterms (fn Free (v, _) => Name.declare v | _ => I) t Name.context; |
20109 | 805 |
fun strip_abs t (0, used) = (([], t), (0, used)) |
806 |
| strip_abs (Abs (v, T, t)) (k, used) = |
|
807 |
let |
|
20122 | 808 |
val ([v'], used') = Name.variants [v] used; |
20109 | 809 |
val t' = subst_bound (Free (v, T), t); |
20122 | 810 |
val ((vs, t''), (k', used'')) = strip_abs t' (k - 1, used'); |
811 |
in (((v', T) :: vs, t''), (k', used'')) end |
|
20109 | 812 |
| strip_abs t (k, used) = (([], t), (k, used)); |
813 |
fun expand_eta [] t _ = ([], t) |
|
814 |
| expand_eta (T::Ts) t used = |
|
815 |
let |
|
20122 | 816 |
val ([v], used') = Name.variants [""] used; |
817 |
val (vs, t') = expand_eta Ts (t $ Free (v, T)) used'; |
|
20109 | 818 |
in ((v, T) :: vs, t') end; |
819 |
val ((vs1, t'), (k', used')) = strip_abs t (k, used); |
|
820 |
val Ts = (fst o chop k' o fst o strip_type o fastype_of) t'; |
|
821 |
val (vs2, t'') = expand_eta Ts t' used'; |
|
822 |
in (vs1 @ vs2, t'') end; |
|
823 |
||
824 |
||
20199 | 825 |
(* comparing variables *) |
16882 | 826 |
|
16724 | 827 |
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
|
828 |
|
16943 | 829 |
fun eq_tvar ((xi, S: sort), (xi', S')) = eq_ix (xi, xi') andalso S = S'; |
830 |
fun eq_var ((xi, T: typ), (xi', T')) = eq_ix (xi, xi') andalso T = T'; |
|
831 |
||
832 |
val tvar_ord = prod_ord indexname_ord sort_ord; |
|
833 |
val var_ord = prod_ord indexname_ord typ_ord; |
|
16882 | 834 |
|
835 |
||
13000 | 836 |
(*A fast unification filter: true unless the two terms cannot be unified. |
0 | 837 |
Terms must be NORMAL. Treats all Vars as distinct. *) |
838 |
fun could_unify (t,u) = |
|
839 |
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
|
840 |
| matchrands _ = true |
0 | 841 |
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
|
842 |
(_, Var _) => true |
0 | 843 |
| (Var _, _) => true |
844 |
| (Const(a,_), Const(b,_)) => a=b andalso matchrands(t,u) |
|
845 |
| (Free(a,_), Free(b,_)) => a=b andalso matchrands(t,u) |
|
846 |
| (Bound i, Bound j) => i=j andalso matchrands(t,u) |
|
847 |
| (Abs _, _) => true (*because of possible eta equality*) |
|
848 |
| (_, Abs _) => true |
|
849 |
| _ => false |
|
850 |
end; |
|
851 |
||
852 |
(*Substitute new for free occurrences of old in a term*) |
|
853 |
fun subst_free [] = (fn t=>t) |
|
854 |
| subst_free pairs = |
|
13000 | 855 |
let fun substf u = |
17314 | 856 |
case AList.lookup (op aconv) pairs u of |
15531 | 857 |
SOME u' => u' |
858 |
| 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
|
859 |
| t$u' => substf t $ substf u' |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
860 |
| _ => u) |
0 | 861 |
in substf end; |
862 |
||
13000 | 863 |
(*Abstraction of the term "body" over its occurrences of v, |
0 | 864 |
which must contain no loose bound variables. |
865 |
The resulting term is ready to become the body of an Abs.*) |
|
16882 | 866 |
fun abstract_over (v, body) = |
867 |
let |
|
16990 | 868 |
exception SAME; |
869 |
fun abs lev tm = |
|
870 |
if v aconv tm then Bound lev |
|
16882 | 871 |
else |
16990 | 872 |
(case tm of |
873 |
Abs (a, T, t) => Abs (a, T, abs (lev + 1) t) |
|
874 |
| t $ u => (abs lev t $ (abs lev u handle SAME => u) handle SAME => t $ abs lev u) |
|
875 |
| _ => raise SAME); |
|
876 |
in abs 0 body handle SAME => body end; |
|
0 | 877 |
|
18975 | 878 |
fun lambda (v as Const (x, T)) t = Abs (NameSpace.base x, T, abstract_over (v, t)) |
18942 | 879 |
| lambda (v as Free (x, T)) t = Abs (x, T, abstract_over (v, t)) |
13665 | 880 |
| lambda (v as Var ((x, _), T)) t = Abs (x, T, abstract_over (v, t)) |
881 |
| lambda v t = raise TERM ("lambda", [v, t]); |
|
0 | 882 |
|
883 |
(*Form an abstraction over a free variable.*) |
|
884 |
fun absfree (a,T,body) = Abs(a, T, abstract_over (Free(a,T), body)); |
|
17786 | 885 |
fun absdummy (T, body) = Abs ("uu", T, body); |
0 | 886 |
|
887 |
(*Abstraction over a list of free variables*) |
|
888 |
fun list_abs_free ([ ] , t) = t |
|
13000 | 889 |
| list_abs_free ((a,T)::vars, t) = |
0 | 890 |
absfree(a, T, list_abs_free(vars,t)); |
891 |
||
892 |
(*Quantification over a list of free variables*) |
|
893 |
fun list_all_free ([], t: term) = t |
|
13000 | 894 |
| list_all_free ((a,T)::vars, t) = |
0 | 895 |
(all T) $ (absfree(a, T, list_all_free(vars,t))); |
896 |
||
897 |
(*Quantification over a list of variables (already bound in body) *) |
|
898 |
fun list_all ([], t) = t |
|
13000 | 899 |
| list_all ((a,T)::vars, t) = |
0 | 900 |
(all T) $ (Abs(a, T, list_all(vars,t))); |
901 |
||
16678 | 902 |
(*Replace the ATOMIC term ti by ui; inst = [(t1,u1), ..., (tn,un)]. |
0 | 903 |
A simultaneous substitution: [ (a,b), (b,a) ] swaps a and b. *) |
16678 | 904 |
fun subst_atomic [] tm = tm |
905 |
| subst_atomic inst tm = |
|
906 |
let |
|
907 |
fun subst (Abs (a, T, body)) = Abs (a, T, subst body) |
|
908 |
| subst (t $ u) = subst t $ subst u |
|
18942 | 909 |
| subst t = the_default t (AList.lookup (op aconv) inst t); |
16678 | 910 |
in subst tm end; |
0 | 911 |
|
16678 | 912 |
(*Replace the ATOMIC type Ti by Ui; inst = [(T1,U1), ..., (Tn,Un)].*) |
913 |
fun typ_subst_atomic [] ty = ty |
|
914 |
| typ_subst_atomic inst ty = |
|
915 |
let |
|
916 |
fun subst (Type (a, Ts)) = Type (a, map subst Ts) |
|
18942 | 917 |
| subst T = the_default T (AList.lookup (op = : typ * typ -> bool) inst T); |
16678 | 918 |
in subst ty end; |
15797 | 919 |
|
16678 | 920 |
fun subst_atomic_types [] tm = tm |
921 |
| subst_atomic_types inst tm = map_term_types (typ_subst_atomic inst) tm; |
|
922 |
||
923 |
fun typ_subst_TVars [] ty = ty |
|
924 |
| typ_subst_TVars inst ty = |
|
925 |
let |
|
926 |
fun subst (Type (a, Ts)) = Type (a, map subst Ts) |
|
18942 | 927 |
| subst (T as TVar (xi, _)) = the_default T (AList.lookup (op =) inst xi) |
16678 | 928 |
| subst T = T; |
929 |
in subst ty end; |
|
0 | 930 |
|
16678 | 931 |
fun subst_TVars [] tm = tm |
932 |
| subst_TVars inst tm = map_term_types (typ_subst_TVars inst) tm; |
|
0 | 933 |
|
16678 | 934 |
fun subst_Vars [] tm = tm |
935 |
| subst_Vars inst tm = |
|
936 |
let |
|
18942 | 937 |
fun subst (t as Var (xi, _)) = the_default t (AList.lookup (op =) inst xi) |
16678 | 938 |
| subst (Abs (a, T, t)) = Abs (a, T, subst t) |
939 |
| subst (t $ u) = subst t $ subst u |
|
940 |
| subst t = t; |
|
941 |
in subst tm end; |
|
0 | 942 |
|
16678 | 943 |
fun subst_vars ([], []) tm = tm |
944 |
| subst_vars ([], inst) tm = subst_Vars inst tm |
|
945 |
| subst_vars (instT, inst) tm = |
|
946 |
let |
|
947 |
fun subst (Const (a, T)) = Const (a, typ_subst_TVars instT T) |
|
948 |
| subst (Free (a, T)) = Free (a, typ_subst_TVars instT T) |
|
949 |
| subst (t as Var (xi, T)) = |
|
17271 | 950 |
(case AList.lookup (op =) inst xi of |
16678 | 951 |
NONE => Var (xi, typ_subst_TVars instT T) |
952 |
| SOME t => t) |
|
953 |
| subst (t as Bound _) = t |
|
954 |
| subst (Abs (a, T, t)) = Abs (a, typ_subst_TVars instT T, subst t) |
|
955 |
| subst (t $ u) = subst t $ subst u; |
|
956 |
in subst tm end; |
|
0 | 957 |
|
958 |
||
19909 | 959 |
(* generalization of fixed variables *) |
960 |
||
961 |
local exception SAME in |
|
962 |
||
963 |
fun generalizeT_same [] _ _ = raise SAME |
|
964 |
| generalizeT_same tfrees idx ty = |
|
965 |
let |
|
966 |
fun gen_typ (Type (a, Ts)) = Type (a, gen_typs Ts) |
|
967 |
| gen_typ (TFree (a, S)) = |
|
968 |
if member (op =) tfrees a then TVar ((a, idx), S) |
|
969 |
else raise SAME |
|
970 |
| gen_typ _ = raise SAME |
|
971 |
and gen_typs (T :: Ts) = |
|
972 |
(gen_typ T :: (gen_typs Ts handle SAME => Ts) |
|
973 |
handle SAME => T :: gen_typs Ts) |
|
974 |
| gen_typs [] = raise SAME; |
|
975 |
in gen_typ ty end; |
|
976 |
||
20001 | 977 |
fun generalize_same ([], []) _ _ = raise SAME |
978 |
| generalize_same (tfrees, frees) idx tm = |
|
19909 | 979 |
let |
980 |
val genT = generalizeT_same tfrees idx; |
|
981 |
fun gen (Free (x, T)) = |
|
20082
b0f5981b9267
removed obsolete ins_ix, mem_ix, ins_term, mem_term;
wenzelm
parents:
20001
diff
changeset
|
982 |
if member (op =) frees x then |
b0f5981b9267
removed obsolete ins_ix, mem_ix, ins_term, mem_term;
wenzelm
parents:
20001
diff
changeset
|
983 |
Var (Name.clean_index (x, idx), genT T handle SAME => T) |
19909 | 984 |
else Free (x, genT T) |
985 |
| gen (Var (xi, T)) = Var (xi, genT T) |
|
986 |
| gen (Const (c, T)) = Const (c, genT T) |
|
987 |
| gen (Bound _) = raise SAME |
|
988 |
| gen (Abs (x, T, t)) = |
|
989 |
(Abs (x, genT T, gen t handle SAME => t) |
|
990 |
handle SAME => Abs (x, T, gen t)) |
|
991 |
| gen (t $ u) = (gen t $ (gen u handle SAME => u) handle SAME => t $ gen u); |
|
20001 | 992 |
in gen tm end; |
19909 | 993 |
|
20001 | 994 |
fun generalize names i tm = generalize_same names i tm handle SAME => tm; |
995 |
fun generalizeT names i ty = generalizeT_same names i ty handle SAME => ty; |
|
996 |
||
997 |
fun generalize_option names i tm = SOME (generalize_same names i tm) handle SAME => NONE; |
|
998 |
fun generalizeT_option names i ty = SOME (generalizeT_same names i ty) handle SAME => NONE; |
|
19909 | 999 |
|
1000 |
end; |
|
1001 |
||
1002 |
||
16943 | 1003 |
(* instantiation of schematic variables (types before terms) *) |
16882 | 1004 |
|
1005 |
local exception SAME in |
|
1006 |
||
16943 | 1007 |
fun instantiateT_same [] _ = raise SAME |
1008 |
| instantiateT_same instT ty = |
|
16882 | 1009 |
let |
1010 |
fun subst_typ (Type (a, Ts)) = Type (a, subst_typs Ts) |
|
1011 |
| subst_typ (TVar v) = |
|
17314 | 1012 |
(case AList.lookup eq_tvar instT v of |
16882 | 1013 |
SOME T => T |
1014 |
| NONE => raise SAME) |
|
1015 |
| subst_typ _ = raise SAME |
|
1016 |
and subst_typs (T :: Ts) = |
|
1017 |
(subst_typ T :: (subst_typs Ts handle SAME => Ts) |
|
1018 |
handle SAME => T :: subst_typs Ts) |
|
1019 |
| subst_typs [] = raise SAME; |
|
1020 |
in subst_typ ty end; |
|
1021 |
||
20001 | 1022 |
fun instantiate_same ([], []) _ = raise SAME |
1023 |
| instantiate_same (instT, inst) tm = |
|
16882 | 1024 |
let |
16943 | 1025 |
val substT = instantiateT_same instT; |
1026 |
fun subst (Const (c, T)) = Const (c, substT T) |
|
1027 |
| subst (Free (x, T)) = Free (x, substT T) |
|
16882 | 1028 |
| subst (Var (xi, T)) = |
16943 | 1029 |
let val (T', same) = (substT T, false) handle SAME => (T, true) in |
17314 | 1030 |
(case AList.lookup eq_var inst (xi, T') of |
16882 | 1031 |
SOME t => t |
1032 |
| NONE => if same then raise SAME else Var (xi, T')) |
|
1033 |
end |
|
1034 |
| subst (Bound _) = raise SAME |
|
1035 |
| subst (Abs (x, T, t)) = |
|
16943 | 1036 |
(Abs (x, substT T, subst t handle SAME => t) |
16882 | 1037 |
handle SAME => Abs (x, T, subst t)) |
1038 |
| subst (t $ u) = (subst t $ (subst u handle SAME => u) handle SAME => t $ subst u); |
|
20001 | 1039 |
in subst tm end; |
16882 | 1040 |
|
20001 | 1041 |
fun instantiate insts tm = instantiate_same insts tm handle SAME => tm; |
1042 |
fun instantiateT insts ty = instantiateT_same insts ty handle SAME => ty; |
|
1043 |
||
1044 |
fun instantiate_option insts tm = SOME (instantiate_same insts tm) handle SAME => NONE; |
|
1045 |
fun instantiateT_option insts ty = SOME (instantiateT_same insts ty) handle SAME => NONE; |
|
16882 | 1046 |
|
1047 |
end; |
|
1048 |
||
1049 |
||
15573 | 1050 |
(** Identifying first-order terms **) |
1051 |
||
20199 | 1052 |
(*Differs from proofterm/is_fun in its treatment of TVar*) |
1053 |
fun is_funtype (Type("fun",[_,_])) = true |
|
1054 |
| is_funtype _ = false; |
|
1055 |
||
15573 | 1056 |
(*Argument Ts is a reverse list of binder types, needed if term t contains Bound vars*) |
1057 |
fun has_not_funtype Ts t = not (is_funtype (fastype_of1 (Ts,t))); |
|
1058 |
||
16537 | 1059 |
(*First order means in all terms of the form f(t1,...,tn) no argument has a |
16589 | 1060 |
function type. The supplied quantifiers are excluded: their argument always |
1061 |
has a function type through a recursive call into its body.*) |
|
16667 | 1062 |
fun is_first_order quants = |
16589 | 1063 |
let fun first_order1 Ts (Abs (_,T,body)) = first_order1 (T::Ts) body |
16667 | 1064 |
| first_order1 Ts (Const(q,_) $ Abs(a,T,body)) = |
1065 |
q mem_string quants andalso (*it is a known quantifier*) |
|
16589 | 1066 |
not (is_funtype T) andalso first_order1 (T::Ts) body |
16667 | 1067 |
| first_order1 Ts t = |
1068 |
case strip_comb t of |
|
1069 |
(Var _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts |
|
1070 |
| (Free _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts |
|
1071 |
| (Const _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts |
|
1072 |
| (Bound _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts |
|
1073 |
| (Abs _, ts) => false (*not in beta-normal form*) |
|
1074 |
| _ => error "first_order: unexpected case" |
|
16589 | 1075 |
in first_order1 [] end; |
15573 | 1076 |
|
16710 | 1077 |
|
16990 | 1078 |
(* maximum index of typs and terms *) |
0 | 1079 |
|
16710 | 1080 |
fun maxidx_typ (TVar ((_, j), _)) i = Int.max (i, j) |
1081 |
| maxidx_typ (Type (_, Ts)) i = maxidx_typs Ts i |
|
1082 |
| maxidx_typ (TFree _) i = i |
|
1083 |
and maxidx_typs [] i = i |
|
1084 |
| maxidx_typs (T :: Ts) i = maxidx_typs Ts (maxidx_typ T i); |
|
0 | 1085 |
|
16710 | 1086 |
fun maxidx_term (Var ((_, j), T)) i = maxidx_typ T (Int.max (i, j)) |
1087 |
| maxidx_term (Const (_, T)) i = maxidx_typ T i |
|
1088 |
| maxidx_term (Free (_, T)) i = maxidx_typ T i |
|
1089 |
| maxidx_term (Bound _) i = i |
|
1090 |
| maxidx_term (Abs (_, T, t)) i = maxidx_term t (maxidx_typ T i) |
|
1091 |
| maxidx_term (t $ u) i = maxidx_term u (maxidx_term t i); |
|
0 | 1092 |
|
16710 | 1093 |
fun maxidx_of_typ T = maxidx_typ T ~1; |
1094 |
fun maxidx_of_typs Ts = maxidx_typs Ts ~1; |
|
1095 |
fun maxidx_of_term t = maxidx_term t ~1; |
|
13665 | 1096 |
|
0 | 1097 |
|
1098 |
||
1099 |
(**** Syntax-related declarations ****) |
|
1100 |
||
19909 | 1101 |
(* substructure *) |
4017
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset
|
1102 |
|
19909 | 1103 |
fun exists_subtype P = |
1104 |
let |
|
1105 |
fun ex ty = P ty orelse |
|
1106 |
(case ty of Type (_, Ts) => exists ex Ts | _ => false); |
|
1107 |
in ex end; |
|
13646 | 1108 |
|
16943 | 1109 |
fun exists_subterm P = |
1110 |
let |
|
1111 |
fun ex tm = P tm orelse |
|
1112 |
(case tm of |
|
1113 |
t $ u => ex t orelse ex u |
|
1114 |
| Abs (_, _, t) => ex t |
|
1115 |
| _ => false); |
|
1116 |
in ex end; |
|
16108
cf468b93a02e
Implement cycle-free overloading, so that definitions cannot harm consistency any more (except of course via interaction with axioms).
obua
parents:
16035
diff
changeset
|
1117 |
|
19909 | 1118 |
|
1119 |
(** Consts etc. **) |
|
1120 |
||
1121 |
fun add_term_consts (Const (c, _), cs) = insert (op =) c cs |
|
1122 |
| add_term_consts (t $ u, cs) = add_term_consts (t, add_term_consts (u, cs)) |
|
1123 |
| add_term_consts (Abs (_, _, t), cs) = add_term_consts (t, cs) |
|
1124 |
| add_term_consts (_, cs) = cs; |
|
1125 |
||
1126 |
fun term_consts t = add_term_consts(t,[]); |
|
1127 |
||
16943 | 1128 |
fun exists_Const P = exists_subterm (fn Const c => P c | _ => false); |
4631 | 1129 |
|
4017
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset
|
1130 |
|
0 | 1131 |
(** TFrees and TVars **) |
1132 |
||
12802
c69bd9754473
added add_term_free_names (more precise/efficient than add_term_names);
wenzelm
parents:
12499
diff
changeset
|
1133 |
(*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
|
1134 |
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
|
1135 |
| add_term_free_names (f$u, bs) = add_term_free_names (f, add_term_free_names(u, bs)) |
c69bd9754473
added add_term_free_names (more precise/efficient than add_term_names);
wenzelm
parents:
12499
diff
changeset
|
1136 |
| add_term_free_names (Abs(_,_,t), bs) = add_term_free_names(t,bs) |
c69bd9754473
added add_term_free_names (more precise/efficient than add_term_names);
wenzelm
parents:
12499
diff
changeset
|
1137 |
| add_term_free_names (_, bs) = bs; |
c69bd9754473
added add_term_free_names (more precise/efficient than add_term_names);
wenzelm
parents:
12499
diff
changeset
|
1138 |
|
0 | 1139 |
(*Accumulates the names in the term, suppressing duplicates. |
1140 |
Includes Frees and Consts. For choosing unambiguous bound var names.*) |
|
10666 | 1141 |
fun add_term_names (Const(a,_), bs) = NameSpace.base a ins_string bs |
2176 | 1142 |
| add_term_names (Free(a,_), bs) = a ins_string bs |
0 | 1143 |
| add_term_names (f$u, bs) = add_term_names (f, add_term_names(u, bs)) |
1144 |
| add_term_names (Abs(_,_,t), bs) = add_term_names(t,bs) |
|
1145 |
| add_term_names (_, bs) = bs; |
|
1146 |
||
1147 |
(*Accumulates the TVars in a type, suppressing duplicates. *) |
|
15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15573
diff
changeset
|
1148 |
fun add_typ_tvars(Type(_,Ts),vs) = foldr add_typ_tvars vs Ts |
0 | 1149 |
| add_typ_tvars(TFree(_),vs) = vs |
16294 | 1150 |
| add_typ_tvars(TVar(v),vs) = insert (op =) v vs; |
0 | 1151 |
|
1152 |
(*Accumulates the TFrees in a type, suppressing duplicates. *) |
|
15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15573
diff
changeset
|
1153 |
fun add_typ_tfree_names(Type(_,Ts),fs) = foldr add_typ_tfree_names fs Ts |
2176 | 1154 |
| add_typ_tfree_names(TFree(f,_),fs) = f ins_string fs |
0 | 1155 |
| add_typ_tfree_names(TVar(_),fs) = fs; |
1156 |
||
15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15573
diff
changeset
|
1157 |
fun add_typ_tfrees(Type(_,Ts),fs) = foldr add_typ_tfrees fs Ts |
16294 | 1158 |
| add_typ_tfrees(TFree(f),fs) = insert (op =) f fs |
0 | 1159 |
| add_typ_tfrees(TVar(_),fs) = fs; |
1160 |
||
15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15573
diff
changeset
|
1161 |
fun add_typ_varnames(Type(_,Ts),nms) = foldr add_typ_varnames nms Ts |
2176 | 1162 |
| add_typ_varnames(TFree(nm,_),nms) = nm ins_string nms |
1163 |
| 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
|
1164 |
|
0 | 1165 |
(*Accumulates the TVars in a term, suppressing duplicates. *) |
1166 |
val add_term_tvars = it_term_types add_typ_tvars; |
|
1167 |
||
1168 |
(*Accumulates the TFrees in a term, suppressing duplicates. *) |
|
1169 |
val add_term_tfrees = it_term_types add_typ_tfrees; |
|
1170 |
val add_term_tfree_names = it_term_types add_typ_tfree_names; |
|
1171 |
||
949
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
1172 |
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
|
1173 |
|
0 | 1174 |
(*Non-list versions*) |
1175 |
fun typ_tfrees T = add_typ_tfrees(T,[]); |
|
1176 |
fun typ_tvars T = add_typ_tvars(T,[]); |
|
1177 |
fun term_tfrees t = add_term_tfrees(t,[]); |
|
1178 |
fun term_tvars t = add_term_tvars(t,[]); |
|
1179 |
||
949
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
1180 |
(*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
|
1181 |
|
15570 | 1182 |
fun add_typ_ixns(ixns,Type(_,Ts)) = Library.foldl add_typ_ixns (ixns,Ts) |
20082
b0f5981b9267
removed obsolete ins_ix, mem_ix, ins_term, mem_term;
wenzelm
parents:
20001
diff
changeset
|
1183 |
| add_typ_ixns(ixns,TVar(ixn,_)) = if member (op =) ixns ixn then ixns |
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
1184 |
else ixns@[ixn] |
949
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
1185 |
| add_typ_ixns(ixns,TFree(_)) = ixns; |
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
1186 |
|
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
1187 |
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
|
1188 |
| 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
|
1189 |
| 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
|
1190 |
| add_term_tvar_ixns(Bound _,ixns) = ixns |
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
1191 |
| add_term_tvar_ixns(Abs(_,T,t),ixns) = |
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
1192 |
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
|
1193 |
| add_term_tvar_ixns(f$t,ixns) = |
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
1194 |
add_term_tvar_ixns(t,add_term_tvar_ixns(f,ixns)); |
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
1195 |
|
16537 | 1196 |
|
0 | 1197 |
(** Frees and Vars **) |
1198 |
||
1199 |
(*Accumulates the Vars in the term, suppressing duplicates*) |
|
1200 |
fun add_term_vars (t, vars: term list) = case t of |
|
16990 | 1201 |
Var _ => OrdList.insert term_ord t vars |
0 | 1202 |
| Abs (_,_,body) => add_term_vars(body,vars) |
1203 |
| f$t => add_term_vars (f, add_term_vars(t, vars)) |
|
1204 |
| _ => vars; |
|
1205 |
||
1206 |
fun term_vars t = add_term_vars(t,[]); |
|
1207 |
||
1208 |
(*Accumulates the Frees in the term, suppressing duplicates*) |
|
1209 |
fun add_term_frees (t, frees: term list) = case t of |
|
16990 | 1210 |
Free _ => OrdList.insert term_ord t frees |
0 | 1211 |
| Abs (_,_,body) => add_term_frees(body,frees) |
1212 |
| f$t => add_term_frees (f, add_term_frees(t, frees)) |
|
1213 |
| _ => frees; |
|
1214 |
||
1215 |
fun term_frees t = add_term_frees(t,[]); |
|
1216 |
||
20199 | 1217 |
|
1218 |
(* dest abstraction *) |
|
0 | 1219 |
|
16678 | 1220 |
fun dest_abs (x, T, body) = |
1221 |
let |
|
1222 |
fun name_clash (Free (y, _)) = (x = y) |
|
1223 |
| name_clash (t $ u) = name_clash t orelse name_clash u |
|
1224 |
| name_clash (Abs (_, _, t)) = name_clash t |
|
1225 |
| name_clash _ = false; |
|
1226 |
in |
|
1227 |
if name_clash body then |
|
20082
b0f5981b9267
removed obsolete ins_ix, mem_ix, ins_term, mem_term;
wenzelm
parents:
20001
diff
changeset
|
1228 |
dest_abs (Name.variant [x] x, T, body) (*potentially slow, but rarely happens*) |
16678 | 1229 |
else (x, subst_bound (Free (x, T), body)) |
1230 |
end; |
|
1231 |
||
20160 | 1232 |
|
1233 |
(* renaming variables *) |
|
0 | 1234 |
|
20239 | 1235 |
fun declare_term_names tm = |
1236 |
fold_aterms |
|
1237 |
(fn Const (a, _) => Name.declare (NameSpace.base a) |
|
1238 |
| Free (a, _) => Name.declare a |
|
1239 |
| _ => I) tm #> |
|
1240 |
fold_types (fold_atyps (fn TFree (a, _) => Name.declare a | _ => I)) tm; |
|
1241 |
||
20160 | 1242 |
fun variant_frees t frees = |
1243 |
fst (Name.variants (map fst frees) (declare_term_names t Name.context)) ~~ map snd frees; |
|
1244 |
||
1245 |
fun rename_wrt_term t frees = rev (variant_frees t frees); (*reversed result!*) |
|
1364
8ea1a962ad72
files now define a structure to allow SML/NJ to optimize the code
clasohm
parents:
1029
diff
changeset
|
1246 |
|
1417 | 1247 |
|
16943 | 1248 |
(* zero var indexes *) |
4286
a09e3e6da2de
added foldl_atyps: ('a * typ -> 'a) -> 'a * typ -> 'a;
wenzelm
parents:
4188
diff
changeset
|
1249 |
|
16943 | 1250 |
fun zero_var_inst vars = |
20239 | 1251 |
fold (fn v as ((x, i), X) => fn (inst, used) => |
16943 | 1252 |
let |
20100 | 1253 |
val ([x'], used') = Name.variants [if Name.is_bound x then "u" else x] used; |
20239 | 1254 |
in if x = x' andalso i = 0 then (inst, used') else ((v, ((x', 0), X)) :: inst, used') end) |
1255 |
vars ([], Name.context) |> #1; |
|
16790 | 1256 |
|
16943 | 1257 |
fun zero_var_indexes_inst tm = |
1258 |
let |
|
20239 | 1259 |
val instT = zero_var_inst (sort tvar_ord (add_tvars tm [])) |> map (apsnd TVar); |
1260 |
val inst = zero_var_inst (sort var_ord (map (apsnd (instantiateT instT)) (add_vars tm []))) |
|
1261 |
|> map (apsnd Var); |
|
16943 | 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 |
|
20100 | 1301 |
(* display variables *) |
1302 |
||
15986 | 1303 |
val show_question_marks = ref true; |
15472 | 1304 |
|
14786
24a7bc97a27a
moved some sort ops to sorts.ML; added string_of_vname (from Syntax module);
wenzelm
parents:
14695
diff
changeset
|
1305 |
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
|
1306 |
let |
15986 | 1307 |
val question_mark = if ! show_question_marks then "?" else ""; |
1308 |
val idx = string_of_int i; |
|
1309 |
val dot = |
|
1310 |
(case rev (Symbol.explode x) of |
|
1311 |
_ :: "\\<^isub>" :: _ => false |
|
1312 |
| _ :: "\\<^isup>" :: _ => false |
|
1313 |
| c :: _ => Symbol.is_digit c |
|
1314 |
| _ => true); |
|
14786
24a7bc97a27a
moved some sort ops to sorts.ML; added string_of_vname (from Syntax module);
wenzelm
parents:
14695
diff
changeset
|
1315 |
in |
15986 | 1316 |
if dot then question_mark ^ x ^ "." ^ idx |
1317 |
else if i <> 0 then question_mark ^ x ^ idx |
|
1318 |
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
|
1319 |
end; |
24a7bc97a27a
moved some sort ops to sorts.ML; added string_of_vname (from Syntax module);
wenzelm
parents:
14695
diff
changeset
|
1320 |
|
24a7bc97a27a
moved some sort ops to sorts.ML; added string_of_vname (from Syntax module);
wenzelm
parents:
14695
diff
changeset
|
1321 |
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
|
1322 |
| 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
|
1323 |
|
1364
8ea1a962ad72
files now define a structure to allow SML/NJ to optimize the code
clasohm
parents:
1029
diff
changeset
|
1324 |
end; |
8ea1a962ad72
files now define a structure to allow SML/NJ to optimize the code
clasohm
parents:
1029
diff
changeset
|
1325 |
|
4444 | 1326 |
structure BasicTerm: BASIC_TERM = Term; |
1327 |
open BasicTerm; |