author | paulson |
Tue, 28 Jun 2005 15:28:30 +0200 | |
changeset 16589 | 24c32abc8b84 |
parent 16570 | 861b9fa2c98c |
child 16599 | 34f99c3221bb |
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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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 | |
|
30 |
op $ of term * term |
|
31 |
exception TYPE of string * typ list * term list |
|
32 |
exception TERM of string * term list |
|
4444 | 33 |
val --> : typ * typ -> typ |
34 |
val ---> : typ list * typ -> typ |
|
35 |
val is_TVar: typ -> bool |
|
15573 | 36 |
val is_funtype: typ -> bool |
4444 | 37 |
val domain_type: typ -> typ |
4480 | 38 |
val range_type: typ -> typ |
4444 | 39 |
val binder_types: typ -> typ list |
40 |
val body_type: typ -> typ |
|
41 |
val strip_type: typ -> typ list * typ |
|
7318 | 42 |
val is_Bound: term -> bool |
4444 | 43 |
val is_Const: term -> bool |
44 |
val is_Free: term -> bool |
|
45 |
val is_Var: term -> bool |
|
16589 | 46 |
val is_first_order: string list -> term -> bool |
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47 |
val dest_Type: typ -> string * typ list |
15914 | 48 |
val dest_TVar: typ -> indexname * sort |
49 |
val dest_TFree: typ -> string * sort |
|
4444 | 50 |
val dest_Const: term -> string * typ |
51 |
val dest_Free: term -> string * typ |
|
52 |
val dest_Var: term -> indexname * typ |
|
53 |
val type_of: term -> typ |
|
54 |
val type_of1: typ list * term -> typ |
|
55 |
val fastype_of: term -> typ |
|
56 |
val fastype_of1: typ list * term -> typ |
|
10806 | 57 |
val list_abs: (string * typ) list * term -> term |
4444 | 58 |
val strip_abs_body: term -> term |
59 |
val strip_abs_vars: term -> (string * typ) list |
|
60 |
val strip_qnt_body: string -> term -> term |
|
61 |
val strip_qnt_vars: string -> term -> (string * typ) list |
|
62 |
val list_comb: term * term list -> term |
|
63 |
val strip_comb: term -> term * term list |
|
64 |
val head_of: term -> term |
|
65 |
val size_of_term: term -> int |
|
66 |
val map_type_tvar: (indexname * sort -> typ) -> typ -> typ |
|
67 |
val map_type_tfree: (string * sort -> typ) -> typ -> typ |
|
68 |
val map_term_types: (typ -> typ) -> term -> term |
|
69 |
val it_term_types: (typ * 'a -> 'a) -> term * 'a -> 'a |
|
16537 | 70 |
structure Vartab: TABLE |
71 |
structure Typtab: TABLE |
|
72 |
structure Termtab: TABLE |
|
73 |
val aconv: term * term -> bool |
|
74 |
val aconvs: term list * term list -> bool |
|
4444 | 75 |
val foldl_atyps: ('a * typ -> 'a) -> 'a * typ -> 'a |
8609 | 76 |
val foldl_term_types: (term -> 'a * typ -> 'a) -> 'a * term -> 'a |
4444 | 77 |
val foldl_types: ('a * typ -> 'a) -> 'a * term -> 'a |
78 |
val foldl_aterms: ('a * term -> 'a) -> 'a * term -> 'a |
|
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val foldl_map_aterms: ('a * term -> 'a * term) -> 'a * term -> 'a * term;
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79 |
val foldl_map_aterms: ('a * term -> 'a * term) -> 'a * term -> 'a * term |
15025 | 80 |
val add_term_varnames: indexname list * term -> indexname list |
81 |
val term_varnames: term -> indexname list |
|
4444 | 82 |
val dummyT: typ |
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 subst_TVars: (indexname * typ) list -> term -> term |
|
100 |
val betapply: term * term -> term |
|
101 |
val eq_ix: indexname * indexname -> bool |
|
102 |
val ins_ix: indexname * indexname list -> indexname list |
|
103 |
val mem_ix: indexname * indexname list -> bool |
|
104 |
val mem_term: term * term list -> bool |
|
105 |
val subset_term: term list * term list -> bool |
|
106 |
val eq_set_term: term list * term list -> bool |
|
107 |
val ins_term: term * term list -> term list |
|
108 |
val union_term: term list * term list -> term list |
|
5585 | 109 |
val inter_term: term list * term list -> term list |
4444 | 110 |
val could_unify: term * term -> bool |
111 |
val subst_free: (term * term) list -> term -> term |
|
112 |
val subst_atomic: (term * term) list -> term -> term |
|
15797 | 113 |
val typ_subst_atomic: (typ * typ) list -> typ -> typ |
4444 | 114 |
val subst_vars: (indexname * typ) list * (indexname * term) list -> term -> term |
115 |
val typ_subst_TVars: (indexname * typ) list -> typ -> typ |
|
116 |
val subst_Vars: (indexname * term) list -> term -> term |
|
117 |
val incr_tvar: int -> typ -> typ |
|
118 |
val xless: (string * int) * indexname -> bool |
|
119 |
val atless: term * term -> bool |
|
120 |
val insert_aterm: term * term list -> term list |
|
121 |
val abstract_over: term * term -> term |
|
11922 | 122 |
val lambda: term -> term -> term |
4444 | 123 |
val absfree: string * typ * term -> term |
124 |
val list_abs_free: (string * typ) list * term -> term |
|
125 |
val list_all_free: (string * typ) list * term -> term |
|
126 |
val list_all: (string * typ) list * term -> term |
|
127 |
val maxidx_of_typ: typ -> int |
|
128 |
val maxidx_of_typs: typ list -> int |
|
129 |
val maxidx_of_term: term -> int |
|
13665 | 130 |
val maxidx_of_terms: term list -> int |
4444 | 131 |
val variant: string list -> string -> string |
132 |
val variantlist: string list * string list -> string list |
|
16537 | 133 |
(*note reversed order of args wrt. variant!*) |
4444 | 134 |
val variant_abs: string * typ * term -> string * term |
135 |
val rename_wrt_term: term -> (string * typ) list -> (string * typ) list |
|
136 |
val add_new_id: string list * string -> string list |
|
137 |
val add_typ_classes: typ * class list -> class list |
|
138 |
val add_typ_ixns: indexname list * typ -> indexname list |
|
139 |
val add_typ_tfree_names: typ * string list -> string list |
|
140 |
val add_typ_tfrees: typ * (string * sort) list -> (string * sort) list |
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141 |
val typ_tfrees: typ -> (string * sort) list |
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142 |
val add_typ_tvars: typ * (indexname * sort) list -> (indexname * sort) list |
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143 |
val typ_tvars: typ -> (indexname * sort) list |
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144 |
val add_typ_tycons: typ * string list -> string list |
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145 |
val add_typ_varnames: typ * string list -> string list |
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146 |
val add_term_classes: term * class list -> class list |
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147 |
val add_term_consts: term * string list -> string list |
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13646 | 148 |
val term_consts: term -> string list |
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149 |
val term_constsT: term -> (string * typ) list |
4444 | 150 |
val add_term_frees: term * term list -> term list |
151 |
val term_frees: term -> term list |
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152 |
val add_term_free_names: term * string list -> string list |
4444 | 153 |
val add_term_names: term * string list -> string list |
154 |
val add_term_tfree_names: term * string list -> string list |
|
155 |
val add_term_tfrees: term * (string * sort) list -> (string * sort) list |
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156 |
val term_tfrees: term -> (string * sort) list |
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157 |
val add_term_tvar_ixns: term * indexname list -> indexname list |
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158 |
val add_term_tvarnames: term * string list -> string list |
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159 |
val add_term_tvars: term * (indexname * sort) list -> (indexname * sort) list |
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160 |
val term_tvars: term -> (indexname * sort) list |
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161 |
val add_term_tycons: term * string list -> string list |
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162 |
val add_term_vars: term * term list -> term list |
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163 |
val term_vars: term -> term list |
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164 |
val exists_Const: (string * typ -> bool) -> term -> bool |
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4631 | 165 |
val exists_subterm: (term -> bool) -> term -> bool |
4444 | 166 |
val compress_type: typ -> typ |
167 |
val compress_term: term -> term |
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15986 | 168 |
val show_question_marks: bool ref |
4444 | 169 |
end; |
0 | 170 |
|
4444 | 171 |
signature TERM = |
172 |
sig |
|
173 |
include BASIC_TERM |
|
16537 | 174 |
val indexname_ord: indexname * indexname -> order |
175 |
val sort_ord: sort * sort -> order |
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176 |
val typ_ord: typ * typ -> order |
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177 |
val typs_ord: typ list * typ list -> order |
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178 |
val term_ord: term * term -> order |
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179 |
val terms_ord: term list * term list -> order |
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180 |
val hd_ord: term * term -> order |
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181 |
val termless: term * term -> bool |
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16570 | 182 |
val term_lpo: (string -> int) -> term * term -> order |
12981 | 183 |
val match_bvars: (term * term) * (string * string) list -> (string * string) list |
184 |
val rename_abs: term -> term -> term -> term option |
|
12499 | 185 |
val invent_names: string list -> string -> int -> string list |
16338 | 186 |
val map_typ: (string -> string) -> (string -> string) -> typ -> typ |
187 |
val map_term: (string -> string) -> (string -> string) -> (string -> string) -> term -> term |
|
12499 | 188 |
val add_tvarsT: (indexname * sort) list * typ -> (indexname * sort) list |
189 |
val add_tvars: (indexname * sort) list * term -> (indexname * sort) list |
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190 |
val add_vars: (indexname * typ) list * term -> (indexname * typ) list |
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191 |
val add_frees: (string * typ) list * term -> (string * typ) list |
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val no_dummyT: typ -> typ |
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193 |
val dummy_patternN: string |
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194 |
val no_dummy_patterns: term -> term |
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195 |
val replace_dummy_patterns: int * term -> int * term |
10552 | 196 |
val is_replaced_dummy_pattern: indexname -> bool |
16035 | 197 |
val show_dummy_patterns: term -> term |
13484 | 198 |
val adhoc_freeze_vars: term -> term * string list |
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199 |
val string_of_vname: indexname -> string |
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200 |
val string_of_vname': indexname -> string |
15612 | 201 |
val string_of_term: term -> string |
4444 | 202 |
end; |
203 |
||
204 |
structure Term: TERM = |
|
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205 |
struct |
0 | 206 |
|
207 |
(*Indexnames can be quickly renamed by adding an offset to the integer part, |
|
208 |
for resolution.*) |
|
16537 | 209 |
type indexname = string * int; |
0 | 210 |
|
4626 | 211 |
(* Types are classified by sorts. *) |
0 | 212 |
type class = string; |
213 |
type sort = class list; |
|
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214 |
type arity = string * sort list * sort; |
0 | 215 |
|
216 |
(* The sorts attached to TFrees and TVars specify the sort of that variable *) |
|
217 |
datatype typ = Type of string * typ list |
|
218 |
| TFree of string * sort |
|
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| TVar of indexname * sort; |
0 | 220 |
|
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221 |
(*Terms. Bound variables are indicated by depth number. |
0 | 222 |
Free variables, (scheme) variables and constants have names. |
4626 | 223 |
An term is "closed" if every bound variable of level "lev" |
13000 | 224 |
is enclosed by at least "lev" abstractions. |
0 | 225 |
|
226 |
It is possible to create meaningless terms containing loose bound vars |
|
227 |
or type mismatches. But such terms are not allowed in rules. *) |
|
228 |
||
13000 | 229 |
datatype term = |
0 | 230 |
Const of string * typ |
13000 | 231 |
| Free of string * typ |
0 | 232 |
| Var of indexname * typ |
233 |
| Bound of int |
|
234 |
| Abs of string*typ*term |
|
3965 | 235 |
| op $ of term*term; |
0 | 236 |
|
16537 | 237 |
(*Errors involving type mismatches*) |
0 | 238 |
exception TYPE of string * typ list * term list; |
239 |
||
16537 | 240 |
(*Errors errors involving terms*) |
0 | 241 |
exception TERM of string * term list; |
242 |
||
243 |
(*Note variable naming conventions! |
|
244 |
a,b,c: string |
|
245 |
f,g,h: functions (including terms of function type) |
|
246 |
i,j,m,n: int |
|
247 |
t,u: term |
|
248 |
v,w: indexnames |
|
249 |
x,y: any |
|
250 |
A,B,C: term (denoting formulae) |
|
251 |
T,U: typ |
|
252 |
*) |
|
253 |
||
254 |
||
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255 |
(** Types **) |
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256 |
|
16537 | 257 |
(*dummy type for parsing and printing etc.*) |
258 |
val dummyT = Type ("dummy", []); |
|
259 |
||
260 |
fun no_dummyT typ = |
|
261 |
let |
|
262 |
fun check (T as Type ("dummy", _)) = |
|
263 |
raise TYPE ("Illegal occurrence of '_' dummy type", [T], []) |
|
264 |
| check (Type (_, Ts)) = List.app check Ts |
|
265 |
| check _ = (); |
|
266 |
in check typ; typ end; |
|
267 |
||
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268 |
fun S --> T = Type("fun",[S,T]); |
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269 |
|
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270 |
(*handy for multiple args: [T1,...,Tn]--->T gives T1-->(T2--> ... -->T)*) |
15570 | 271 |
val op ---> = Library.foldr (op -->); |
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272 |
|
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273 |
fun dest_Type (Type x) = x |
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274 |
| dest_Type T = raise TYPE ("dest_Type", [T], []); |
15914 | 275 |
fun dest_TVar (TVar x) = x |
276 |
| dest_TVar T = raise TYPE ("dest_TVar", [T], []); |
|
277 |
fun dest_TFree (TFree x) = x |
|
278 |
| dest_TFree T = raise TYPE ("dest_TFree", [T], []); |
|
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279 |
|
16537 | 280 |
|
0 | 281 |
(** Discriminators **) |
282 |
||
7318 | 283 |
fun is_Bound (Bound _) = true |
284 |
| is_Bound _ = false; |
|
285 |
||
0 | 286 |
fun is_Const (Const _) = true |
287 |
| is_Const _ = false; |
|
288 |
||
289 |
fun is_Free (Free _) = true |
|
290 |
| is_Free _ = false; |
|
291 |
||
292 |
fun is_Var (Var _) = true |
|
293 |
| is_Var _ = false; |
|
294 |
||
295 |
fun is_TVar (TVar _) = true |
|
296 |
| is_TVar _ = false; |
|
297 |
||
15573 | 298 |
(*Differs from proofterm/is_fun in its treatment of TVar*) |
299 |
fun is_funtype (Type("fun",[_,_])) = true |
|
300 |
| is_funtype _ = false; |
|
301 |
||
16537 | 302 |
|
0 | 303 |
(** Destructors **) |
304 |
||
305 |
fun dest_Const (Const x) = x |
|
306 |
| dest_Const t = raise TERM("dest_Const", [t]); |
|
307 |
||
308 |
fun dest_Free (Free x) = x |
|
309 |
| dest_Free t = raise TERM("dest_Free", [t]); |
|
310 |
||
311 |
fun dest_Var (Var x) = x |
|
312 |
| dest_Var t = raise TERM("dest_Var", [t]); |
|
313 |
||
314 |
||
4464 | 315 |
fun domain_type (Type("fun", [T,_])) = T |
316 |
and range_type (Type("fun", [_,T])) = T; |
|
4064 | 317 |
|
0 | 318 |
(* maps [T1,...,Tn]--->T to the list [T1,T2,...,Tn]*) |
319 |
fun binder_types (Type("fun",[S,T])) = S :: binder_types T |
|
320 |
| binder_types _ = []; |
|
321 |
||
322 |
(* maps [T1,...,Tn]--->T to T*) |
|
323 |
fun body_type (Type("fun",[S,T])) = body_type T |
|
324 |
| body_type T = T; |
|
325 |
||
326 |
(* maps [T1,...,Tn]--->T to ([T1,T2,...,Tn], T) *) |
|
327 |
fun strip_type T : typ list * typ = |
|
328 |
(binder_types T, body_type T); |
|
329 |
||
330 |
||
331 |
(*Compute the type of the term, checking that combinations are well-typed |
|
332 |
Ts = [T0,T1,...] holds types of bound variables 0, 1, ...*) |
|
333 |
fun type_of1 (Ts, Const (_,T)) = T |
|
334 |
| type_of1 (Ts, Free (_,T)) = T |
|
15570 | 335 |
| type_of1 (Ts, Bound i) = (List.nth (Ts,i) |
336 |
handle Subscript => raise TYPE("type_of: bound variable", [], [Bound i])) |
|
0 | 337 |
| type_of1 (Ts, Var (_,T)) = T |
338 |
| type_of1 (Ts, Abs (_,T,body)) = T --> type_of1(T::Ts, body) |
|
13000 | 339 |
| type_of1 (Ts, f$u) = |
0 | 340 |
let val U = type_of1(Ts,u) |
341 |
and T = type_of1(Ts,f) |
|
342 |
in case T of |
|
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
343 |
Type("fun",[T1,T2]) => |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
344 |
if T1=U then T2 else raise TYPE |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
345 |
("type_of: type mismatch in application", [T1,U], [f$u]) |
13000 | 346 |
| _ => raise TYPE |
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
347 |
("type_of: function type is expected in application", |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
348 |
[T,U], [f$u]) |
0 | 349 |
end; |
350 |
||
351 |
fun type_of t : typ = type_of1 ([],t); |
|
352 |
||
353 |
(*Determines the type of a term, with minimal checking*) |
|
13000 | 354 |
fun fastype_of1 (Ts, f$u) = |
61 | 355 |
(case fastype_of1 (Ts,f) of |
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
356 |
Type("fun",[_,T]) => T |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
357 |
| _ => raise TERM("fastype_of: expected function type", [f$u])) |
61 | 358 |
| fastype_of1 (_, Const (_,T)) = T |
359 |
| fastype_of1 (_, Free (_,T)) = T |
|
15570 | 360 |
| fastype_of1 (Ts, Bound i) = (List.nth(Ts,i) |
361 |
handle Subscript => raise TERM("fastype_of: Bound", [Bound i])) |
|
13000 | 362 |
| fastype_of1 (_, Var (_,T)) = T |
61 | 363 |
| fastype_of1 (Ts, Abs (_,T,u)) = T --> fastype_of1 (T::Ts, u); |
364 |
||
365 |
fun fastype_of t : typ = fastype_of1 ([],t); |
|
0 | 366 |
|
367 |
||
15570 | 368 |
val list_abs = Library.foldr (fn ((x, T), t) => Abs (x, T, t)); |
10806 | 369 |
|
0 | 370 |
(* maps (x1,...,xn)t to t *) |
13000 | 371 |
fun strip_abs_body (Abs(_,_,t)) = strip_abs_body t |
0 | 372 |
| strip_abs_body u = u; |
373 |
||
374 |
(* maps (x1,...,xn)t to [x1, ..., xn] *) |
|
13000 | 375 |
fun strip_abs_vars (Abs(a,T,t)) = (a,T) :: strip_abs_vars t |
0 | 376 |
| strip_abs_vars u = [] : (string*typ) list; |
377 |
||
378 |
||
379 |
fun strip_qnt_body qnt = |
|
380 |
let fun strip(tm as Const(c,_)$Abs(_,_,t)) = if c=qnt then strip t else tm |
|
381 |
| strip t = t |
|
382 |
in strip end; |
|
383 |
||
384 |
fun strip_qnt_vars qnt = |
|
385 |
let fun strip(Const(c,_)$Abs(a,T,t)) = if c=qnt then (a,T)::strip t else [] |
|
386 |
| strip t = [] : (string*typ) list |
|
387 |
in strip end; |
|
388 |
||
389 |
||
390 |
(* maps (f, [t1,...,tn]) to f(t1,...,tn) *) |
|
15570 | 391 |
val list_comb : term * term list -> term = Library.foldl (op $); |
0 | 392 |
|
393 |
||
394 |
(* maps f(t1,...,tn) to (f, [t1,...,tn]) ; naturally tail-recursive*) |
|
13000 | 395 |
fun strip_comb u : term * term list = |
0 | 396 |
let fun stripc (f$t, ts) = stripc (f, t::ts) |
13000 | 397 |
| stripc x = x |
0 | 398 |
in stripc(u,[]) end; |
399 |
||
400 |
||
401 |
(* maps f(t1,...,tn) to f , which is never a combination *) |
|
402 |
fun head_of (f$t) = head_of f |
|
403 |
| head_of u = u; |
|
404 |
||
405 |
||
406 |
(*Number of atoms and abstractions in a term*) |
|
407 |
fun size_of_term (Abs (_,_,body)) = 1 + size_of_term body |
|
408 |
| size_of_term (f$t) = size_of_term f + size_of_term t |
|
409 |
| size_of_term _ = 1; |
|
410 |
||
949
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
411 |
fun map_type_tvar f (Type(a,Ts)) = Type(a, map (map_type_tvar f) Ts) |
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
412 |
| map_type_tvar f (T as TFree _) = T |
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
413 |
| map_type_tvar f (TVar x) = f x; |
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
414 |
|
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
415 |
fun map_type_tfree f (Type(a,Ts)) = Type(a, map (map_type_tfree f) Ts) |
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
416 |
| map_type_tfree f (TFree x) = f x |
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
417 |
| map_type_tfree f (T as TVar _) = T; |
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
418 |
|
0 | 419 |
(* apply a function to all types in a term *) |
420 |
fun map_term_types f = |
|
421 |
let fun map(Const(a,T)) = Const(a, f T) |
|
422 |
| map(Free(a,T)) = Free(a, f T) |
|
423 |
| map(Var(v,T)) = Var(v, f T) |
|
424 |
| map(t as Bound _) = t |
|
425 |
| map(Abs(a,T,t)) = Abs(a, f T, map t) |
|
426 |
| map(f$t) = map f $ map t; |
|
427 |
in map end; |
|
428 |
||
429 |
(* iterate a function over all types in a term *) |
|
430 |
fun it_term_types f = |
|
431 |
let fun iter(Const(_,T), a) = f(T,a) |
|
432 |
| iter(Free(_,T), a) = f(T,a) |
|
433 |
| iter(Var(_,T), a) = f(T,a) |
|
434 |
| iter(Abs(_,T,t), a) = iter(t,f(T,a)) |
|
435 |
| iter(f$u, a) = iter(f, iter(u, a)) |
|
436 |
| iter(Bound _, a) = a |
|
437 |
in iter end |
|
438 |
||
439 |
||
16537 | 440 |
(** Comparing terms, types etc. **) |
441 |
||
442 |
fun indexname_ord ((x, i), (y, j)) = |
|
443 |
(case int_ord (i, j) of EQUAL => string_ord (x, y) | ord => ord); |
|
444 |
||
445 |
val sort_ord = list_ord string_ord; |
|
446 |
||
447 |
||
448 |
(* typ_ord *) |
|
449 |
||
450 |
fun typ_ord TU = |
|
451 |
if pointer_eq TU then EQUAL |
|
452 |
else |
|
453 |
(case TU of |
|
454 |
(Type x, Type y) => prod_ord string_ord typs_ord (x, y) |
|
455 |
| (Type _, _) => GREATER |
|
456 |
| (TFree _, Type _) => LESS |
|
457 |
| (TFree x, TFree y) => prod_ord string_ord sort_ord (x, y) |
|
458 |
| (TFree _, TVar _) => GREATER |
|
459 |
| (TVar _, Type _) => LESS |
|
460 |
| (TVar _, TFree _) => LESS |
|
461 |
| (TVar x, TVar y) => prod_ord indexname_ord sort_ord (x, y)) |
|
462 |
and typs_ord Ts_Us = list_ord typ_ord Ts_Us; |
|
463 |
||
464 |
||
465 |
(* term_ord *) |
|
466 |
||
467 |
(*a linear well-founded AC-compatible ordering for terms: |
|
468 |
s < t <=> 1. size(s) < size(t) or |
|
469 |
2. size(s) = size(t) and s=f(...) and t=g(...) and f<g or |
|
470 |
3. size(s) = size(t) and s=f(s1..sn) and t=f(t1..tn) and |
|
471 |
(s1..sn) < (t1..tn) (lexicographically)*) |
|
472 |
||
473 |
fun dest_hd (Const (a, T)) = (((a, 0), T), 0) |
|
474 |
| dest_hd (Free (a, T)) = (((a, 0), T), 1) |
|
475 |
| dest_hd (Var v) = (v, 2) |
|
476 |
| dest_hd (Bound i) = ((("", i), dummyT), 3) |
|
477 |
| dest_hd (Abs (_, T, _)) = ((("", 0), T), 4); |
|
478 |
||
479 |
fun term_ord tu = |
|
480 |
if pointer_eq tu then EQUAL |
|
481 |
else |
|
482 |
(case tu of |
|
483 |
(Abs (_, T, t), Abs(_, U, u)) => |
|
484 |
(case term_ord (t, u) of EQUAL => typ_ord (T, U) | ord => ord) |
|
485 |
| (t, u) => |
|
486 |
(case int_ord (size_of_term t, size_of_term u) of |
|
487 |
EQUAL => |
|
488 |
let |
|
489 |
val (f, ts) = strip_comb t |
|
490 |
and (g, us) = strip_comb u |
|
491 |
in case hd_ord (f, g) of EQUAL => terms_ord (ts, us) | ord => ord end |
|
492 |
| ord => ord)) |
|
493 |
and hd_ord (f, g) = |
|
494 |
prod_ord (prod_ord indexname_ord typ_ord) int_ord (dest_hd f, dest_hd g) |
|
495 |
and terms_ord (ts, us) = list_ord term_ord (ts, us); |
|
496 |
||
497 |
fun op aconv tu = (term_ord tu = EQUAL); |
|
498 |
fun aconvs ts_us = (list_ord term_ord ts_us = EQUAL); |
|
499 |
fun termless tu = (term_ord tu = LESS); |
|
500 |
||
16570 | 501 |
(*** Lexicographic path order on terms. |
502 |
||
503 |
See Baader & Nipkow, Term rewriting, CUP 1998. |
|
504 |
Without variables. Const, Var, Bound, Free and Abs are treated all as |
|
505 |
constants. |
|
506 |
||
507 |
f_ord maps strings to integers and serves two purposes: |
|
508 |
- Predicate on constant symbols. Those that are not recognised by f_ord |
|
509 |
must be mapped to ~1. |
|
510 |
- Order on the recognised symbols. These must be mapped to distinct |
|
511 |
integers >= 0. |
|
512 |
||
513 |
***) |
|
514 |
||
515 |
local |
|
516 |
fun dest_hd f_ord (Const (a, T)) = |
|
517 |
let val ord = f_ord a in |
|
518 |
if ord = ~1 then ((1, ((a, 0), T)), 0) else ((0, (("", ord), T)), 0) |
|
519 |
end |
|
520 |
| dest_hd _ (Free (a, T)) = ((1, ((a, 0), T)), 0) |
|
521 |
| dest_hd _ (Var v) = ((1, v), 1) |
|
522 |
| dest_hd _ (Bound i) = ((1, (("", i), dummyT)), 2) |
|
523 |
| dest_hd _ (Abs (_, T, _)) = ((1, (("", 0), T)), 3); |
|
524 |
||
525 |
fun term_lpo f_ord (s, t) = |
|
526 |
let val (f, ss) = strip_comb s and (g, ts) = strip_comb t in |
|
527 |
if forall (fn si => term_lpo f_ord (si, t) = LESS) ss |
|
528 |
then case hd_ord f_ord (f, g) of |
|
529 |
GREATER => |
|
530 |
if forall (fn ti => term_lpo f_ord (s, ti) = GREATER) ts |
|
531 |
then GREATER else LESS |
|
532 |
| EQUAL => |
|
533 |
if forall (fn ti => term_lpo f_ord (s, ti) = GREATER) ts |
|
534 |
then list_ord (term_lpo f_ord) (ss, ts) |
|
535 |
else LESS |
|
536 |
| LESS => LESS |
|
537 |
else GREATER |
|
538 |
end |
|
539 |
and hd_ord f_ord (f, g) = case (f, g) of |
|
540 |
(Abs (_, T, t), Abs (_, U, u)) => |
|
541 |
(case term_lpo f_ord (t, u) of EQUAL => typ_ord (T, U) | ord => ord) |
|
542 |
| (_, _) => prod_ord (prod_ord int_ord |
|
543 |
(prod_ord indexname_ord typ_ord)) int_ord |
|
544 |
(dest_hd f_ord f, dest_hd f_ord g) |
|
545 |
in |
|
546 |
val term_lpo = term_lpo |
|
547 |
end; |
|
548 |
||
16537 | 549 |
structure Vartab = TableFun(type key = indexname val ord = indexname_ord); |
550 |
structure Typtab = TableFun(type key = typ val ord = typ_ord); |
|
551 |
structure Termtab = TableFun(type key = term val ord = term_ord); |
|
552 |
||
553 |
||
0 | 554 |
(** Connectives of higher order logic **) |
555 |
||
375 | 556 |
fun itselfT ty = Type ("itself", [ty]); |
14854 | 557 |
val a_itselfT = itselfT (TFree ("'a", [])); |
375 | 558 |
|
0 | 559 |
val propT : typ = Type("prop",[]); |
560 |
||
561 |
val implies = Const("==>", propT-->propT-->propT); |
|
562 |
||
563 |
fun all T = Const("all", (T-->propT)-->propT); |
|
564 |
||
565 |
fun equals T = Const("==", T-->T-->propT); |
|
566 |
||
567 |
(* maps !!x1...xn. t to t *) |
|
13000 | 568 |
fun strip_all_body (Const("all",_)$Abs(_,_,t)) = strip_all_body t |
0 | 569 |
| strip_all_body t = t; |
570 |
||
571 |
(* maps !!x1...xn. t to [x1, ..., xn] *) |
|
572 |
fun strip_all_vars (Const("all",_)$Abs(a,T,t)) = |
|
13000 | 573 |
(a,T) :: strip_all_vars t |
0 | 574 |
| strip_all_vars t = [] : (string*typ) list; |
575 |
||
576 |
(*increments a term's non-local bound variables |
|
577 |
required when moving a term within abstractions |
|
578 |
inc is increment for bound variables |
|
579 |
lev is level at which a bound variable is considered 'loose'*) |
|
13000 | 580 |
fun incr_bv (inc, lev, u as Bound i) = if i>=lev then Bound(i+inc) else u |
0 | 581 |
| incr_bv (inc, lev, Abs(a,T,body)) = |
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
582 |
Abs(a, T, incr_bv(inc,lev+1,body)) |
13000 | 583 |
| incr_bv (inc, lev, f$t) = |
0 | 584 |
incr_bv(inc,lev,f) $ incr_bv(inc,lev,t) |
585 |
| incr_bv (inc, lev, u) = u; |
|
586 |
||
587 |
fun incr_boundvars 0 t = t |
|
588 |
| incr_boundvars inc t = incr_bv(inc,0,t); |
|
589 |
||
12981 | 590 |
(*Scan a pair of terms; while they are similar, |
591 |
accumulate corresponding bound vars in "al"*) |
|
592 |
fun match_bvs(Abs(x,_,s),Abs(y,_,t), al) = |
|
593 |
match_bvs(s, t, if x="" orelse y="" then al |
|
594 |
else (x,y)::al) |
|
595 |
| match_bvs(f$s, g$t, al) = match_bvs(f,g,match_bvs(s,t,al)) |
|
596 |
| match_bvs(_,_,al) = al; |
|
597 |
||
598 |
(* strip abstractions created by parameters *) |
|
599 |
fun match_bvars((s,t),al) = match_bvs(strip_abs_body s, strip_abs_body t, al); |
|
600 |
||
601 |
fun rename_abs pat obj t = |
|
602 |
let |
|
603 |
val ren = match_bvs (pat, obj, []); |
|
604 |
fun ren_abs (Abs (x, T, b)) = |
|
15570 | 605 |
Abs (getOpt (assoc_string (ren, x), x), T, ren_abs b) |
12981 | 606 |
| ren_abs (f $ t) = ren_abs f $ ren_abs t |
607 |
| ren_abs t = t |
|
15531 | 608 |
in if null ren then NONE else SOME (ren_abs t) end; |
0 | 609 |
|
610 |
(*Accumulate all 'loose' bound vars referring to level 'lev' or beyond. |
|
611 |
(Bound 0) is loose at level 0 *) |
|
13000 | 612 |
fun add_loose_bnos (Bound i, lev, js) = |
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
613 |
if i<lev then js else (i-lev) ins_int js |
0 | 614 |
| add_loose_bnos (Abs (_,_,t), lev, js) = add_loose_bnos (t, lev+1, js) |
615 |
| add_loose_bnos (f$t, lev, js) = |
|
13000 | 616 |
add_loose_bnos (f, lev, add_loose_bnos (t, lev, js)) |
0 | 617 |
| add_loose_bnos (_, _, js) = js; |
618 |
||
619 |
fun loose_bnos t = add_loose_bnos (t, 0, []); |
|
620 |
||
621 |
(* loose_bvar(t,k) iff t contains a 'loose' bound variable referring to |
|
622 |
level k or beyond. *) |
|
623 |
fun loose_bvar(Bound i,k) = i >= k |
|
624 |
| loose_bvar(f$t, k) = loose_bvar(f,k) orelse loose_bvar(t,k) |
|
625 |
| loose_bvar(Abs(_,_,t),k) = loose_bvar(t,k+1) |
|
626 |
| loose_bvar _ = false; |
|
627 |
||
2792 | 628 |
fun loose_bvar1(Bound i,k) = i = k |
629 |
| loose_bvar1(f$t, k) = loose_bvar1(f,k) orelse loose_bvar1(t,k) |
|
630 |
| loose_bvar1(Abs(_,_,t),k) = loose_bvar1(t,k+1) |
|
631 |
| loose_bvar1 _ = false; |
|
0 | 632 |
|
633 |
(*Substitute arguments for loose bound variables. |
|
634 |
Beta-reduction of arg(n-1)...arg0 into t replacing (Bound i) with (argi). |
|
4626 | 635 |
Note that for ((%x y. c) a b), the bound vars in c are x=1 and y=0 |
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
636 |
and the appropriate call is subst_bounds([b,a], c) . |
0 | 637 |
Loose bound variables >=n are reduced by "n" to |
638 |
compensate for the disappearance of lambdas. |
|
639 |
*) |
|
13000 | 640 |
fun subst_bounds (args: term list, t) : term = |
0 | 641 |
let val n = length args; |
642 |
fun subst (t as Bound i, lev) = |
|
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
643 |
(if i<lev then t (*var is locally bound*) |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
644 |
else incr_boundvars lev (List.nth(args, i-lev)) |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
645 |
handle Subscript => Bound(i-n) (*loose: change it*)) |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
646 |
| subst (Abs(a,T,body), lev) = Abs(a, T, subst(body,lev+1)) |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
647 |
| subst (f$t, lev) = subst(f,lev) $ subst(t,lev) |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
648 |
| subst (t,lev) = t |
0 | 649 |
in case args of [] => t | _ => subst (t,0) end; |
650 |
||
2192
3bf092b5310b
Optimizations: removal of polymorphic equality; one-argument case
paulson
parents:
2182
diff
changeset
|
651 |
(*Special case: one argument*) |
13000 | 652 |
fun subst_bound (arg, t) : term = |
2192
3bf092b5310b
Optimizations: removal of polymorphic equality; one-argument case
paulson
parents:
2182
diff
changeset
|
653 |
let fun subst (t as Bound i, lev) = |
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
654 |
if i<lev then t (*var is locally bound*) |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
655 |
else if i=lev then incr_boundvars lev arg |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
656 |
else Bound(i-1) (*loose: change it*) |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
657 |
| 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
|
658 |
| 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
|
659 |
| subst (t,lev) = t |
2192
3bf092b5310b
Optimizations: removal of polymorphic equality; one-argument case
paulson
parents:
2182
diff
changeset
|
660 |
in subst (t,0) end; |
3bf092b5310b
Optimizations: removal of polymorphic equality; one-argument case
paulson
parents:
2182
diff
changeset
|
661 |
|
0 | 662 |
(*beta-reduce if possible, else form application*) |
2192
3bf092b5310b
Optimizations: removal of polymorphic equality; one-argument case
paulson
parents:
2182
diff
changeset
|
663 |
fun betapply (Abs(_,_,t), u) = subst_bound (u,t) |
0 | 664 |
| betapply (f,u) = f$u; |
665 |
||
14786
24a7bc97a27a
moved some sort ops to sorts.ML; added string_of_vname (from Syntax module);
wenzelm
parents:
14695
diff
changeset
|
666 |
|
2192
3bf092b5310b
Optimizations: removal of polymorphic equality; one-argument case
paulson
parents:
2182
diff
changeset
|
667 |
(** Equality, membership and insertion of indexnames (string*ints) **) |
3bf092b5310b
Optimizations: removal of polymorphic equality; one-argument case
paulson
parents:
2182
diff
changeset
|
668 |
|
3bf092b5310b
Optimizations: removal of polymorphic equality; one-argument case
paulson
parents:
2182
diff
changeset
|
669 |
(*optimized equality test for indexnames. Yields a huge gain under Poly/ML*) |
2959 | 670 |
fun eq_ix ((a, i):indexname, (a',i'):indexname) = (a=a') andalso i=i'; |
2192
3bf092b5310b
Optimizations: removal of polymorphic equality; one-argument case
paulson
parents:
2182
diff
changeset
|
671 |
|
3bf092b5310b
Optimizations: removal of polymorphic equality; one-argument case
paulson
parents:
2182
diff
changeset
|
672 |
(*membership in a list, optimized version for indexnames*) |
2959 | 673 |
fun mem_ix (_, []) = false |
2192
3bf092b5310b
Optimizations: removal of polymorphic equality; one-argument case
paulson
parents:
2182
diff
changeset
|
674 |
| mem_ix (x, y :: ys) = eq_ix(x,y) orelse mem_ix (x, ys); |
3bf092b5310b
Optimizations: removal of polymorphic equality; one-argument case
paulson
parents:
2182
diff
changeset
|
675 |
|
3bf092b5310b
Optimizations: removal of polymorphic equality; one-argument case
paulson
parents:
2182
diff
changeset
|
676 |
(*insertion into list, optimized version for indexnames*) |
3bf092b5310b
Optimizations: removal of polymorphic equality; one-argument case
paulson
parents:
2182
diff
changeset
|
677 |
fun ins_ix (x,xs) = if mem_ix (x, xs) then xs else x :: xs; |
3bf092b5310b
Optimizations: removal of polymorphic equality; one-argument case
paulson
parents:
2182
diff
changeset
|
678 |
|
0 | 679 |
|
2176 | 680 |
(** Membership, insertion, union for terms **) |
681 |
||
682 |
fun mem_term (_, []) = false |
|
683 |
| mem_term (t, t'::ts) = t aconv t' orelse mem_term(t,ts); |
|
684 |
||
2182
29e56f003599
Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
parents:
2176
diff
changeset
|
685 |
fun subset_term ([], ys) = true |
29e56f003599
Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
parents:
2176
diff
changeset
|
686 |
| 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
|
687 |
|
29e56f003599
Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
parents:
2176
diff
changeset
|
688 |
fun eq_set_term (xs, ys) = |
29e56f003599
Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
parents:
2176
diff
changeset
|
689 |
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
|
690 |
|
2176 | 691 |
fun ins_term(t,ts) = if mem_term(t,ts) then ts else t :: ts; |
692 |
||
693 |
fun union_term (xs, []) = xs |
|
694 |
| union_term ([], ys) = ys |
|
695 |
| union_term ((x :: xs), ys) = union_term (xs, ins_term (x, ys)); |
|
696 |
||
5585 | 697 |
fun inter_term ([], ys) = [] |
698 |
| inter_term (x::xs, ys) = |
|
699 |
if mem_term (x,ys) then x :: inter_term(xs,ys) else inter_term(xs,ys); |
|
700 |
||
13000 | 701 |
(*A fast unification filter: true unless the two terms cannot be unified. |
0 | 702 |
Terms must be NORMAL. Treats all Vars as distinct. *) |
703 |
fun could_unify (t,u) = |
|
704 |
let fun matchrands (f$t, g$u) = could_unify(t,u) andalso matchrands(f,g) |
|
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
705 |
| matchrands _ = true |
0 | 706 |
in case (head_of t , head_of u) of |
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
707 |
(_, Var _) => true |
0 | 708 |
| (Var _, _) => true |
709 |
| (Const(a,_), Const(b,_)) => a=b andalso matchrands(t,u) |
|
710 |
| (Free(a,_), Free(b,_)) => a=b andalso matchrands(t,u) |
|
711 |
| (Bound i, Bound j) => i=j andalso matchrands(t,u) |
|
712 |
| (Abs _, _) => true (*because of possible eta equality*) |
|
713 |
| (_, Abs _) => true |
|
714 |
| _ => false |
|
715 |
end; |
|
716 |
||
717 |
(*Substitute new for free occurrences of old in a term*) |
|
718 |
fun subst_free [] = (fn t=>t) |
|
719 |
| subst_free pairs = |
|
13000 | 720 |
let fun substf u = |
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
721 |
case gen_assoc (op aconv) (pairs, u) of |
15531 | 722 |
SOME u' => u' |
723 |
| NONE => (case u of Abs(a,T,t) => Abs(a, T, substf t) |
|
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
724 |
| t$u' => substf t $ substf u' |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
725 |
| _ => u) |
0 | 726 |
in substf end; |
727 |
||
728 |
(*a total, irreflexive ordering on index names*) |
|
729 |
fun xless ((a,i), (b,j): indexname) = i<j orelse (i=j andalso a<b); |
|
730 |
||
731 |
||
13000 | 732 |
(*Abstraction of the term "body" over its occurrences of v, |
0 | 733 |
which must contain no loose bound variables. |
734 |
The resulting term is ready to become the body of an Abs.*) |
|
735 |
fun abstract_over (v,body) = |
|
736 |
let fun abst (lev,u) = if (v aconv u) then (Bound lev) else |
|
737 |
(case u of |
|
738 |
Abs(a,T,t) => Abs(a, T, abst(lev+1, t)) |
|
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
739 |
| f$rand => abst(lev,f) $ abst(lev,rand) |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
740 |
| _ => u) |
0 | 741 |
in abst(0,body) end; |
742 |
||
13665 | 743 |
fun lambda (v as Free (x, T)) t = Abs (x, T, abstract_over (v, t)) |
744 |
| lambda (v as Var ((x, _), T)) t = Abs (x, T, abstract_over (v, t)) |
|
745 |
| lambda v t = raise TERM ("lambda", [v, t]); |
|
0 | 746 |
|
747 |
(*Form an abstraction over a free variable.*) |
|
748 |
fun absfree (a,T,body) = Abs(a, T, abstract_over (Free(a,T), body)); |
|
749 |
||
750 |
(*Abstraction over a list of free variables*) |
|
751 |
fun list_abs_free ([ ] , t) = t |
|
13000 | 752 |
| list_abs_free ((a,T)::vars, t) = |
0 | 753 |
absfree(a, T, list_abs_free(vars,t)); |
754 |
||
755 |
(*Quantification over a list of free variables*) |
|
756 |
fun list_all_free ([], t: term) = t |
|
13000 | 757 |
| list_all_free ((a,T)::vars, t) = |
0 | 758 |
(all T) $ (absfree(a, T, list_all_free(vars,t))); |
759 |
||
760 |
(*Quantification over a list of variables (already bound in body) *) |
|
761 |
fun list_all ([], t) = t |
|
13000 | 762 |
| list_all ((a,T)::vars, t) = |
0 | 763 |
(all T) $ (Abs(a, T, list_all(vars,t))); |
764 |
||
13000 | 765 |
(*Replace the ATOMIC term ti by ui; instl = [(t1,u1), ..., (tn,un)]. |
0 | 766 |
A simultaneous substitution: [ (a,b), (b,a) ] swaps a and b. *) |
767 |
fun subst_atomic [] t = t : term |
|
768 |
| subst_atomic (instl: (term*term) list) t = |
|
769 |
let fun subst (Abs(a,T,body)) = Abs(a, T, subst body) |
|
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
770 |
| subst (f$t') = subst f $ subst t' |
15570 | 771 |
| subst t = getOpt (assoc(instl,t),t) |
0 | 772 |
in subst t end; |
773 |
||
15797 | 774 |
(*Replace the ATOMIC type Ti by Ui; instl = [(T1,U1), ..., (Tn,Un)].*) |
775 |
fun typ_subst_atomic [] T = T |
|
776 |
| typ_subst_atomic instl (Type (s, Ts)) = |
|
777 |
Type (s, map (typ_subst_atomic instl) Ts) |
|
778 |
| typ_subst_atomic instl T = getOpt (assoc (instl, T), T); |
|
779 |
||
728
9a973c3ba350
Pure/term: commented typ_subst_TVars, subst_TVars, subst_Vars, subst_vars
lcp
parents:
375
diff
changeset
|
780 |
(*Substitute for type Vars in a type*) |
0 | 781 |
fun typ_subst_TVars iTs T = if null iTs then T else |
782 |
let fun subst(Type(a,Ts)) = Type(a, map subst Ts) |
|
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
783 |
| subst(T as TFree _) = T |
15570 | 784 |
| subst(T as TVar(ixn,_)) = getOpt (assoc(iTs,ixn),T) |
0 | 785 |
in subst T end; |
786 |
||
728
9a973c3ba350
Pure/term: commented typ_subst_TVars, subst_TVars, subst_Vars, subst_vars
lcp
parents:
375
diff
changeset
|
787 |
(*Substitute for type Vars in a term*) |
0 | 788 |
val subst_TVars = map_term_types o typ_subst_TVars; |
789 |
||
728
9a973c3ba350
Pure/term: commented typ_subst_TVars, subst_TVars, subst_Vars, subst_vars
lcp
parents:
375
diff
changeset
|
790 |
(*Substitute for Vars in a term; see also envir/norm_term*) |
0 | 791 |
fun subst_Vars itms t = if null itms then t else |
15570 | 792 |
let fun subst(v as Var(ixn,_)) = getOpt (assoc(itms,ixn),v) |
0 | 793 |
| subst(Abs(a,T,t)) = Abs(a,T,subst t) |
794 |
| subst(f$t) = subst f $ subst t |
|
795 |
| subst(t) = t |
|
796 |
in subst t end; |
|
797 |
||
728
9a973c3ba350
Pure/term: commented typ_subst_TVars, subst_TVars, subst_Vars, subst_vars
lcp
parents:
375
diff
changeset
|
798 |
(*Substitute for type/term Vars in a term; see also envir/norm_term*) |
0 | 799 |
fun subst_vars(iTs,itms) = if null iTs then subst_Vars itms else |
800 |
let fun subst(Const(a,T)) = Const(a,typ_subst_TVars iTs T) |
|
801 |
| subst(Free(a,T)) = Free(a,typ_subst_TVars iTs T) |
|
802 |
| subst(v as Var(ixn,T)) = (case assoc(itms,ixn) of |
|
15531 | 803 |
NONE => Var(ixn,typ_subst_TVars iTs T) |
804 |
| SOME t => t) |
|
0 | 805 |
| subst(b as Bound _) = b |
806 |
| subst(Abs(a,T,t)) = Abs(a,typ_subst_TVars iTs T,subst t) |
|
807 |
| subst(f$t) = subst f $ subst t |
|
808 |
in subst end; |
|
809 |
||
810 |
||
15573 | 811 |
(** Identifying first-order terms **) |
812 |
||
813 |
(*Argument Ts is a reverse list of binder types, needed if term t contains Bound vars*) |
|
814 |
fun has_not_funtype Ts t = not (is_funtype (fastype_of1 (Ts,t))); |
|
815 |
||
16537 | 816 |
(*First order means in all terms of the form f(t1,...,tn) no argument has a |
16589 | 817 |
function type. The supplied quantifiers are excluded: their argument always |
818 |
has a function type through a recursive call into its body.*) |
|
819 |
fun is_first_order quants = |
|
820 |
let fun first_order1 Ts (Abs (_,T,body)) = first_order1 (T::Ts) body |
|
821 |
| first_order1 Ts (Const(q,_) $ Abs(a,T,body)) = |
|
822 |
q mem_string quants andalso (*it is a known quantifier*) |
|
823 |
not (is_funtype T) andalso first_order1 (T::Ts) body |
|
824 |
| first_order1 Ts t = |
|
825 |
case strip_comb t of |
|
826 |
(Var _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts |
|
827 |
| (Free _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts |
|
828 |
| (Const _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts |
|
829 |
| (Bound _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts |
|
830 |
| (Abs _, ts) => false (*not in beta-normal form*) |
|
831 |
| _ => error "first_order: unexpected case" |
|
832 |
in first_order1 [] end; |
|
15573 | 833 |
|
0 | 834 |
(*Computing the maximum index of a typ*) |
2146 | 835 |
fun maxidx_of_typ(Type(_,Ts)) = maxidx_of_typs Ts |
0 | 836 |
| maxidx_of_typ(TFree _) = ~1 |
2146 | 837 |
| maxidx_of_typ(TVar((_,i),_)) = i |
838 |
and maxidx_of_typs [] = ~1 |
|
839 |
| maxidx_of_typs (T::Ts) = Int.max(maxidx_of_typ T, maxidx_of_typs Ts); |
|
0 | 840 |
|
841 |
||
842 |
(*Computing the maximum index of a term*) |
|
843 |
fun maxidx_of_term (Const(_,T)) = maxidx_of_typ T |
|
844 |
| maxidx_of_term (Bound _) = ~1 |
|
845 |
| maxidx_of_term (Free(_,T)) = maxidx_of_typ T |
|
2146 | 846 |
| maxidx_of_term (Var ((_,i), T)) = Int.max(i, maxidx_of_typ T) |
847 |
| maxidx_of_term (Abs (_,T,u)) = Int.max(maxidx_of_term u, maxidx_of_typ T) |
|
848 |
| maxidx_of_term (f$t) = Int.max(maxidx_of_term f, maxidx_of_term t); |
|
0 | 849 |
|
15570 | 850 |
fun maxidx_of_terms ts = Library.foldl Int.max (~1, map maxidx_of_term ts); |
13665 | 851 |
|
0 | 852 |
|
853 |
(* Increment the index of all Poly's in T by k *) |
|
949
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
854 |
fun incr_tvar k = map_type_tvar (fn ((a,i),S) => TVar((a,i+k),S)); |
0 | 855 |
|
856 |
||
857 |
(**** Syntax-related declarations ****) |
|
858 |
||
859 |
(*** Printing ***) |
|
860 |
||
14676 | 861 |
(*Makes a variant of a name distinct from the names in bs. |
862 |
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
|
863 |
preserves a suffix of underscores "_". *) |
749a04f0cfb0
variant: preserve suffix of underscores (for skolem/internal names etc.);
wenzelm
parents:
11922
diff
changeset
|
864 |
fun variant bs name = |
749a04f0cfb0
variant: preserve suffix of underscores (for skolem/internal names etc.);
wenzelm
parents:
11922
diff
changeset
|
865 |
let |
749a04f0cfb0
variant: preserve suffix of underscores (for skolem/internal names etc.);
wenzelm
parents:
11922
diff
changeset
|
866 |
val (c, u) = pairself implode (Library.take_suffix (equal "_") (Symbol.explode name)); |
12902 | 867 |
fun vary2 c = if ((c ^ u) mem_string bs) then vary2 (Symbol.bump_string c) else c; |
14676 | 868 |
fun vary1 c = if ((c ^ u) mem_string bs) 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
|
869 |
in vary1 (if c = "" then "u" else c) ^ u end; |
0 | 870 |
|
871 |
(*Create variants of the list of names, with priority to the first ones*) |
|
872 |
fun variantlist ([], used) = [] |
|
13000 | 873 |
| variantlist(b::bs, used) = |
0 | 874 |
let val b' = variant used b |
875 |
in b' :: variantlist (bs, b'::used) end; |
|
876 |
||
14695 | 877 |
(*Invent fresh names*) |
878 |
fun invent_names _ _ 0 = [] |
|
879 |
| invent_names used a n = |
|
880 |
let val b = Symbol.bump_string a in |
|
881 |
if a mem_string used then invent_names used b n |
|
882 |
else a :: invent_names used b (n - 1) |
|
883 |
end; |
|
11353 | 884 |
|
16537 | 885 |
|
4017
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset
|
886 |
(** Consts etc. **) |
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset
|
887 |
|
15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15573
diff
changeset
|
888 |
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
|
889 |
| 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
|
890 |
| 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
|
891 |
|
16294 | 892 |
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
|
893 |
| add_typ_tycons (_, cs) = cs; |
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset
|
894 |
|
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset
|
895 |
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
|
896 |
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
|
897 |
|
9319 | 898 |
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
|
899 |
| 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
|
900 |
| 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
|
901 |
| add_term_consts (_, cs) = cs; |
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset
|
902 |
|
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
|
903 |
fun add_term_constsT (Const c, cs) = c::cs |
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
|
904 |
| add_term_constsT (t $ u, cs) = add_term_constsT (t, add_term_constsT (u, cs)) |
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
|
905 |
| add_term_constsT (Abs (_, _, t), cs) = add_term_constsT (t, cs) |
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
|
906 |
| add_term_constsT (_, cs) = cs; |
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
|
907 |
|
13646 | 908 |
fun term_consts t = add_term_consts(t,[]); |
909 |
||
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
|
910 |
fun term_constsT t = add_term_constsT(t,[]); |
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
|
911 |
|
4185 | 912 |
fun exists_Const P t = let |
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
913 |
fun ex (Const c ) = P c |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
914 |
| ex (t $ u ) = ex t orelse ex u |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
915 |
| ex (Abs (_, _, t)) = ex t |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
916 |
| ex _ = false |
4185 | 917 |
in ex t end; |
4017
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset
|
918 |
|
4631 | 919 |
fun exists_subterm P = |
920 |
let fun ex t = P t orelse |
|
921 |
(case t of |
|
922 |
u $ v => ex u orelse ex v |
|
923 |
| Abs(_, _, u) => ex u |
|
924 |
| _ => false) |
|
925 |
in ex end; |
|
926 |
||
4017
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset
|
927 |
(*map classes, tycons*) |
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset
|
928 |
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
|
929 |
| 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
|
930 |
| 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
|
931 |
|
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset
|
932 |
(*map classes, tycons, consts*) |
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset
|
933 |
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
|
934 |
| 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
|
935 |
| 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
|
936 |
| map_term _ _ _ (t as Bound _) = t |
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset
|
937 |
| 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
|
938 |
| 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
|
939 |
|
63878e2587a7
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents:
3965
diff
changeset
|
940 |
|
0 | 941 |
(** TFrees and TVars **) |
942 |
||
943 |
(*maps (bs,v) to v'::bs this reverses the identifiers bs*) |
|
944 |
fun add_new_id (bs, c) : string list = variant bs c :: bs; |
|
945 |
||
12802
c69bd9754473
added add_term_free_names (more precise/efficient than add_term_names);
wenzelm
parents:
12499
diff
changeset
|
946 |
(*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
|
947 |
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
|
948 |
| add_term_free_names (f$u, bs) = add_term_free_names (f, add_term_free_names(u, bs)) |
c69bd9754473
added add_term_free_names (more precise/efficient than add_term_names);
wenzelm
parents:
12499
diff
changeset
|
949 |
| add_term_free_names (Abs(_,_,t), bs) = add_term_free_names(t,bs) |
c69bd9754473
added add_term_free_names (more precise/efficient than add_term_names);
wenzelm
parents:
12499
diff
changeset
|
950 |
| add_term_free_names (_, bs) = bs; |
c69bd9754473
added add_term_free_names (more precise/efficient than add_term_names);
wenzelm
parents:
12499
diff
changeset
|
951 |
|
0 | 952 |
(*Accumulates the names in the term, suppressing duplicates. |
953 |
Includes Frees and Consts. For choosing unambiguous bound var names.*) |
|
10666 | 954 |
fun add_term_names (Const(a,_), bs) = NameSpace.base a ins_string bs |
2176 | 955 |
| add_term_names (Free(a,_), bs) = a ins_string bs |
0 | 956 |
| add_term_names (f$u, bs) = add_term_names (f, add_term_names(u, bs)) |
957 |
| add_term_names (Abs(_,_,t), bs) = add_term_names(t,bs) |
|
958 |
| add_term_names (_, bs) = bs; |
|
959 |
||
960 |
(*Accumulates the TVars in a type, suppressing duplicates. *) |
|
15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15573
diff
changeset
|
961 |
fun add_typ_tvars(Type(_,Ts),vs) = foldr add_typ_tvars vs Ts |
0 | 962 |
| add_typ_tvars(TFree(_),vs) = vs |
16294 | 963 |
| add_typ_tvars(TVar(v),vs) = insert (op =) v vs; |
0 | 964 |
|
965 |
(*Accumulates the TFrees in a type, suppressing duplicates. *) |
|
15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15573
diff
changeset
|
966 |
fun add_typ_tfree_names(Type(_,Ts),fs) = foldr add_typ_tfree_names fs Ts |
2176 | 967 |
| add_typ_tfree_names(TFree(f,_),fs) = f ins_string fs |
0 | 968 |
| add_typ_tfree_names(TVar(_),fs) = fs; |
969 |
||
15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15573
diff
changeset
|
970 |
fun add_typ_tfrees(Type(_,Ts),fs) = foldr add_typ_tfrees fs Ts |
16294 | 971 |
| add_typ_tfrees(TFree(f),fs) = insert (op =) f fs |
0 | 972 |
| add_typ_tfrees(TVar(_),fs) = fs; |
973 |
||
15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15573
diff
changeset
|
974 |
fun add_typ_varnames(Type(_,Ts),nms) = foldr add_typ_varnames nms Ts |
2176 | 975 |
| add_typ_varnames(TFree(nm,_),nms) = nm ins_string nms |
976 |
| 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
|
977 |
|
0 | 978 |
(*Accumulates the TVars in a term, suppressing duplicates. *) |
979 |
val add_term_tvars = it_term_types add_typ_tvars; |
|
980 |
||
981 |
(*Accumulates the TFrees in a term, suppressing duplicates. *) |
|
982 |
val add_term_tfrees = it_term_types add_typ_tfrees; |
|
983 |
val add_term_tfree_names = it_term_types add_typ_tfree_names; |
|
984 |
||
949
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
985 |
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
|
986 |
|
0 | 987 |
(*Non-list versions*) |
988 |
fun typ_tfrees T = add_typ_tfrees(T,[]); |
|
989 |
fun typ_tvars T = add_typ_tvars(T,[]); |
|
990 |
fun term_tfrees t = add_term_tfrees(t,[]); |
|
991 |
fun term_tvars t = add_term_tvars(t,[]); |
|
992 |
||
949
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
993 |
(*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
|
994 |
|
15570 | 995 |
fun add_typ_ixns(ixns,Type(_,Ts)) = Library.foldl add_typ_ixns (ixns,Ts) |
13000 | 996 |
| 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
|
997 |
else ixns@[ixn] |
949
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
998 |
| add_typ_ixns(ixns,TFree(_)) = ixns; |
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
999 |
|
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
1000 |
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
|
1001 |
| 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
|
1002 |
| 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
|
1003 |
| add_term_tvar_ixns(Bound _,ixns) = ixns |
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
1004 |
| add_term_tvar_ixns(Abs(_,T,t),ixns) = |
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
1005 |
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
|
1006 |
| add_term_tvar_ixns(f$t,ixns) = |
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
1007 |
add_term_tvar_ixns(t,add_term_tvar_ixns(f,ixns)); |
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
1008 |
|
16537 | 1009 |
|
0 | 1010 |
(** Frees and Vars **) |
1011 |
||
1012 |
(*a partial ordering (not reflexive) for atomic terms*) |
|
1013 |
fun atless (Const (a,_), Const (b,_)) = a<b |
|
1014 |
| atless (Free (a,_), Free (b,_)) = a<b |
|
1015 |
| atless (Var(v,_), Var(w,_)) = xless(v,w) |
|
1016 |
| atless (Bound i, Bound j) = i<j |
|
1017 |
| atless _ = false; |
|
1018 |
||
1019 |
(*insert atomic term into partially sorted list, suppressing duplicates (?)*) |
|
1020 |
fun insert_aterm (t,us) = |
|
1021 |
let fun inserta [] = [t] |
|
13000 | 1022 |
| inserta (us as u::us') = |
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
1023 |
if atless(t,u) then t::us |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
1024 |
else if t=u then us (*duplicate*) |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
1025 |
else u :: inserta(us') |
0 | 1026 |
in inserta us end; |
1027 |
||
1028 |
(*Accumulates the Vars in the term, suppressing duplicates*) |
|
1029 |
fun add_term_vars (t, vars: term list) = case t of |
|
1030 |
Var _ => insert_aterm(t,vars) |
|
1031 |
| Abs (_,_,body) => add_term_vars(body,vars) |
|
1032 |
| f$t => add_term_vars (f, add_term_vars(t, vars)) |
|
1033 |
| _ => vars; |
|
1034 |
||
1035 |
fun term_vars t = add_term_vars(t,[]); |
|
1036 |
||
1037 |
(*Accumulates the Frees in the term, suppressing duplicates*) |
|
1038 |
fun add_term_frees (t, frees: term list) = case t of |
|
1039 |
Free _ => insert_aterm(t,frees) |
|
1040 |
| Abs (_,_,body) => add_term_frees(body,frees) |
|
1041 |
| f$t => add_term_frees (f, add_term_frees(t, frees)) |
|
1042 |
| _ => frees; |
|
1043 |
||
1044 |
fun term_frees t = add_term_frees(t,[]); |
|
1045 |
||
1046 |
(*Given an abstraction over P, replaces the bound variable by a Free variable |
|
1047 |
having a unique name. *) |
|
1048 |
fun variant_abs (a,T,P) = |
|
1049 |
let val b = variant (add_term_names(P,[])) a |
|
2192
3bf092b5310b
Optimizations: removal of polymorphic equality; one-argument case
paulson
parents:
2182
diff
changeset
|
1050 |
in (b, subst_bound (Free(b,T), P)) end; |
0 | 1051 |
|
1052 |
(* renames and reverses the strings in vars away from names *) |
|
1053 |
fun rename_aTs names vars : (string*typ)list = |
|
1054 |
let fun rename_aT (vars,(a,T)) = |
|
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
1055 |
(variant (map #1 vars @ names) a, T) :: vars |
15570 | 1056 |
in Library.foldl rename_aT ([],vars) end; |
0 | 1057 |
|
1058 |
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
|
1059 |
|
1417 | 1060 |
|
4286
a09e3e6da2de
added foldl_atyps: ('a * typ -> 'a) -> 'a * typ -> 'a;
wenzelm
parents:
4188
diff
changeset
|
1061 |
(* left-ro-right traversal *) |
a09e3e6da2de
added foldl_atyps: ('a * typ -> 'a) -> 'a * typ -> 'a;
wenzelm
parents:
4188
diff
changeset
|
1062 |
|
a09e3e6da2de
added foldl_atyps: ('a * typ -> 'a) -> 'a * typ -> 'a;
wenzelm
parents:
4188
diff
changeset
|
1063 |
(*foldl atoms of type*) |
15570 | 1064 |
fun foldl_atyps f (x, Type (_, Ts)) = Library.foldl (foldl_atyps f) (x, Ts) |
4286
a09e3e6da2de
added foldl_atyps: ('a * typ -> 'a) -> 'a * typ -> 'a;
wenzelm
parents:
4188
diff
changeset
|
1065 |
| foldl_atyps f x_atom = f x_atom; |
a09e3e6da2de
added foldl_atyps: ('a * typ -> 'a) -> 'a * typ -> 'a;
wenzelm
parents:
4188
diff
changeset
|
1066 |
|
a09e3e6da2de
added foldl_atyps: ('a * typ -> 'a) -> 'a * typ -> 'a;
wenzelm
parents:
4188
diff
changeset
|
1067 |
(*foldl atoms of term*) |
a09e3e6da2de
added foldl_atyps: ('a * typ -> 'a) -> 'a * typ -> 'a;
wenzelm
parents:
4188
diff
changeset
|
1068 |
fun foldl_aterms f (x, t $ u) = foldl_aterms f (foldl_aterms f (x, t), u) |
a09e3e6da2de
added foldl_atyps: ('a * typ -> 'a) -> 'a * typ -> 'a;
wenzelm
parents:
4188
diff
changeset
|
1069 |
| foldl_aterms f (x, Abs (_, _, t)) = foldl_aterms f (x, t) |
a09e3e6da2de
added foldl_atyps: ('a * typ -> 'a) -> 'a * typ -> 'a;
wenzelm
parents:
4188
diff
changeset
|
1070 |
| foldl_aterms f x_atom = f x_atom; |
a09e3e6da2de
added foldl_atyps: ('a * typ -> 'a) -> 'a * typ -> 'a;
wenzelm
parents:
4188
diff
changeset
|
1071 |
|
6548
9b108dd75c25
val foldl_map_aterms: ('a * term -> 'a * term) -> 'a * term -> 'a * term;
wenzelm
parents:
6033
diff
changeset
|
1072 |
fun foldl_map_aterms f (x, t $ u) = |
9b108dd75c25
val foldl_map_aterms: ('a * term -> 'a * term) -> 'a * term -> 'a * term;
wenzelm
parents:
6033
diff
changeset
|
1073 |
let val (x', t') = foldl_map_aterms f (x, t); val (x'', u') = foldl_map_aterms f (x', u); |
9b108dd75c25
val foldl_map_aterms: ('a * term -> 'a * term) -> 'a * term -> 'a * term;
wenzelm
parents:
6033
diff
changeset
|
1074 |
in (x'', t' $ u') end |
9b108dd75c25
val foldl_map_aterms: ('a * term -> 'a * term) -> 'a * term -> 'a * term;
wenzelm
parents:
6033
diff
changeset
|
1075 |
| foldl_map_aterms f (x, Abs (a, T, t)) = |
9b108dd75c25
val foldl_map_aterms: ('a * term -> 'a * term) -> 'a * term -> 'a * term;
wenzelm
parents:
6033
diff
changeset
|
1076 |
let val (x', t') = foldl_map_aterms f (x, t) in (x', Abs (a, T, t')) end |
9b108dd75c25
val foldl_map_aterms: ('a * term -> 'a * term) -> 'a * term -> 'a * term;
wenzelm
parents:
6033
diff
changeset
|
1077 |
| foldl_map_aterms f x_atom = f x_atom; |
9b108dd75c25
val foldl_map_aterms: ('a * term -> 'a * term) -> 'a * term -> 'a * term;
wenzelm
parents:
6033
diff
changeset
|
1078 |
|
4286
a09e3e6da2de
added foldl_atyps: ('a * typ -> 'a) -> 'a * typ -> 'a;
wenzelm
parents:
4188
diff
changeset
|
1079 |
(*foldl types of term*) |
8609 | 1080 |
fun foldl_term_types f (x, t as Const (_, T)) = f t (x, T) |
1081 |
| foldl_term_types f (x, t as Free (_, T)) = f t (x, T) |
|
1082 |
| foldl_term_types f (x, t as Var (_, T)) = f t (x, T) |
|
1083 |
| foldl_term_types f (x, Bound _) = x |
|
1084 |
| foldl_term_types f (x, t as Abs (_, T, b)) = foldl_term_types f (f t (x, T), b) |
|
1085 |
| foldl_term_types f (x, t $ u) = foldl_term_types f (foldl_term_types f (x, t), u); |
|
1086 |
||
1087 |
fun foldl_types f = foldl_term_types (fn _ => f); |
|
4286
a09e3e6da2de
added foldl_atyps: ('a * typ -> 'a) -> 'a * typ -> 'a;
wenzelm
parents:
4188
diff
changeset
|
1088 |
|
12499 | 1089 |
(*collect variables*) |
16294 | 1090 |
val add_tvarsT = foldl_atyps (fn (vs, TVar v) => insert (op =) v vs | (vs, _) => vs); |
12499 | 1091 |
val add_tvars = foldl_types add_tvarsT; |
16294 | 1092 |
val add_vars = foldl_aterms (fn (vs, Var v) => insert (op =) v vs | (vs, _) => vs); |
1093 |
val add_frees = foldl_aterms (fn (vs, Free v) => insert (op =) v vs | (vs, _) => vs); |
|
12499 | 1094 |
|
15025 | 1095 |
(*collect variable names*) |
1096 |
val add_term_varnames = foldl_aterms (fn (xs, Var (x, _)) => ins_ix (x, xs) | (xs, _) => xs); |
|
1097 |
fun term_varnames t = add_term_varnames ([], t); |
|
4286
a09e3e6da2de
added foldl_atyps: ('a * typ -> 'a) -> 'a * typ -> 'a;
wenzelm
parents:
4188
diff
changeset
|
1098 |
|
1417 | 1099 |
|
4444 | 1100 |
|
13000 | 1101 |
(*** Compression of terms and types by sharing common subtrees. |
1102 |
Saves 50-75% on storage requirements. As it is a bit slow, |
|
1103 |
it should be called only for axioms, stored theorems, etc. |
|
1104 |
Recorded term and type fragments are never disposed. ***) |
|
1417 | 1105 |
|
16338 | 1106 |
|
1417 | 1107 |
(** Sharing of types **) |
1108 |
||
13000 | 1109 |
val memo_types = ref (Typtab.empty: typ Typtab.table); |
1417 | 1110 |
|
1111 |
fun compress_type T = |
|
13000 | 1112 |
(case Typtab.lookup (! memo_types, T) of |
15531 | 1113 |
SOME T' => T' |
1114 |
| NONE => |
|
13000 | 1115 |
let val T' = (case T of Type (a, Ts) => Type (a, map compress_type Ts) | _ => T) |
1116 |
in memo_types := Typtab.update ((T', T'), ! memo_types); T' end); |
|
1117 |
||
1417 | 1118 |
|
1119 |
(** Sharing of atomic terms **) |
|
1120 |
||
13000 | 1121 |
val memo_terms = ref (Termtab.empty : term Termtab.table); |
1417 | 1122 |
|
1123 |
fun share_term (t $ u) = share_term t $ share_term u |
|
13000 | 1124 |
| share_term (Abs (a, T, u)) = Abs (a, T, share_term u) |
1417 | 1125 |
| share_term t = |
13000 | 1126 |
(case Termtab.lookup (! memo_terms, t) of |
15531 | 1127 |
SOME t' => t' |
1128 |
| NONE => (memo_terms := Termtab.update ((t, t), ! memo_terms); t)); |
|
1417 | 1129 |
|
1130 |
val compress_term = share_term o map_term_types compress_type; |
|
1131 |
||
4444 | 1132 |
|
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
1133 |
(* dummy patterns *) |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
1134 |
|
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
1135 |
val dummy_patternN = "dummy_pattern"; |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
1136 |
|
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
1137 |
fun is_dummy_pattern (Const ("dummy_pattern", _)) = true |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
1138 |
| is_dummy_pattern _ = false; |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
1139 |
|
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
1140 |
fun no_dummy_patterns tm = |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
1141 |
if not (foldl_aterms (fn (b, t) => b orelse is_dummy_pattern t) (false, tm)) then tm |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
1142 |
else raise TERM ("Illegal occurrence of '_' dummy pattern", [tm]); |
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
1143 |
|
11903 | 1144 |
fun replace_dummy Ts (i, Const ("dummy_pattern", T)) = |
1145 |
(i + 1, list_comb (Var (("_dummy_", i), Ts ---> T), map Bound (0 upto length Ts - 1))) |
|
1146 |
| replace_dummy Ts (i, Abs (x, T, t)) = |
|
1147 |
let val (i', t') = replace_dummy (T :: Ts) (i, t) |
|
1148 |
in (i', Abs (x, T, t')) end |
|
1149 |
| replace_dummy Ts (i, t $ u) = |
|
1150 |
let val (i', t') = replace_dummy Ts (i, t); val (i'', u') = replace_dummy Ts (i', u) |
|
1151 |
in (i'', t' $ u') end |
|
1152 |
| replace_dummy _ (i, a) = (i, a); |
|
1153 |
||
1154 |
val replace_dummy_patterns = replace_dummy []; |
|
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
1155 |
|
10552 | 1156 |
fun is_replaced_dummy_pattern ("_dummy_", _) = true |
1157 |
| is_replaced_dummy_pattern _ = false; |
|
9536
b79b002f32ae
added dummy_patternN, no_dummy_patterns, replace_dummy_patterns;
wenzelm
parents:
9319
diff
changeset
|
1158 |
|
16035 | 1159 |
fun show_dummy_patterns (Var (("_dummy_", _), T)) = Const ("dummy_pattern", T) |
1160 |
| show_dummy_patterns (t $ u) = show_dummy_patterns t $ show_dummy_patterns u |
|
1161 |
| show_dummy_patterns (Abs (x, T, t)) = Abs (x, T, show_dummy_patterns t) |
|
1162 |
| show_dummy_patterns a = a; |
|
1163 |
||
13484 | 1164 |
|
1165 |
(* adhoc freezing *) |
|
1166 |
||
1167 |
fun adhoc_freeze_vars tm = |
|
1168 |
let |
|
1169 |
fun mk_inst (var as Var ((a, i), T)) = |
|
1170 |
let val x = a ^ Library.gensym "_" ^ string_of_int i |
|
1171 |
in ((var, Free(x, T)), x) end; |
|
1172 |
val (insts, xs) = split_list (map mk_inst (term_vars tm)); |
|
1173 |
in (subst_atomic insts tm, xs) end; |
|
1174 |
||
1175 |
||
14786
24a7bc97a27a
moved some sort ops to sorts.ML; added string_of_vname (from Syntax module);
wenzelm
parents:
14695
diff
changeset
|
1176 |
(* string_of_vname *) |
24a7bc97a27a
moved some sort ops to sorts.ML; added string_of_vname (from Syntax module);
wenzelm
parents:
14695
diff
changeset
|
1177 |
|
15986 | 1178 |
val show_question_marks = ref true; |
15472 | 1179 |
|
14786
24a7bc97a27a
moved some sort ops to sorts.ML; added string_of_vname (from Syntax module);
wenzelm
parents:
14695
diff
changeset
|
1180 |
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
|
1181 |
let |
15986 | 1182 |
val question_mark = if ! show_question_marks then "?" else ""; |
1183 |
val idx = string_of_int i; |
|
1184 |
val dot = |
|
1185 |
(case rev (Symbol.explode x) of |
|
1186 |
_ :: "\\<^isub>" :: _ => false |
|
1187 |
| _ :: "\\<^isup>" :: _ => false |
|
1188 |
| c :: _ => Symbol.is_digit c |
|
1189 |
| _ => true); |
|
14786
24a7bc97a27a
moved some sort ops to sorts.ML; added string_of_vname (from Syntax module);
wenzelm
parents:
14695
diff
changeset
|
1190 |
in |
15986 | 1191 |
if dot then question_mark ^ x ^ "." ^ idx |
1192 |
else if i <> 0 then question_mark ^ x ^ idx |
|
1193 |
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
|
1194 |
end; |
24a7bc97a27a
moved some sort ops to sorts.ML; added string_of_vname (from Syntax module);
wenzelm
parents:
14695
diff
changeset
|
1195 |
|
24a7bc97a27a
moved some sort ops to sorts.ML; added string_of_vname (from Syntax module);
wenzelm
parents:
14695
diff
changeset
|
1196 |
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
|
1197 |
| 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
|
1198 |
|
15612 | 1199 |
fun string_of_term (Const(s,_)) = s |
1200 |
| string_of_term (Free(s,_)) = s |
|
1201 |
| string_of_term (Var(ix,_)) = string_of_vname ix |
|
1202 |
| string_of_term (Bound i) = string_of_int i |
|
1203 |
| string_of_term (Abs(x,_,t)) = "%" ^ x ^ ". " ^ string_of_term t |
|
1204 |
| string_of_term (s $ t) = |
|
1205 |
"(" ^ string_of_term s ^ " " ^ string_of_term t ^ ")" |
|
1206 |
||
1364
8ea1a962ad72
files now define a structure to allow SML/NJ to optimize the code
clasohm
parents:
1029
diff
changeset
|
1207 |
end; |
8ea1a962ad72
files now define a structure to allow SML/NJ to optimize the code
clasohm
parents:
1029
diff
changeset
|
1208 |
|
4444 | 1209 |
structure BasicTerm: BASIC_TERM = Term; |
1210 |
open BasicTerm; |