wenzelm@30160
|
1 |
(* Title: Tools/eqsubst.ML
|
wenzelm@29269
|
2 |
Author: Lucas Dixon, University of Edinburgh
|
wenzelm@18598
|
3 |
|
wenzelm@18598
|
4 |
A proof method to perform a substiution using an equation.
|
paulson@15481
|
5 |
*)
|
paulson@15481
|
6 |
|
wenzelm@18591
|
7 |
signature EQSUBST =
|
paulson@15481
|
8 |
sig
|
wenzelm@29269
|
9 |
(* a type abbreviation for match information *)
|
dixon@19871
|
10 |
type match =
|
dixon@19871
|
11 |
((indexname * (sort * typ)) list (* type instantiations *)
|
dixon@19871
|
12 |
* (indexname * (typ * term)) list) (* term instantiations *)
|
dixon@19871
|
13 |
* (string * typ) list (* fake named type abs env *)
|
dixon@19871
|
14 |
* (string * typ) list (* type abs env *)
|
dixon@19871
|
15 |
* term (* outer term *)
|
dixon@19871
|
16 |
|
dixon@19871
|
17 |
type searchinfo =
|
dixon@19871
|
18 |
theory
|
dixon@19871
|
19 |
* int (* maxidx *)
|
dixon@19871
|
20 |
* Zipper.T (* focusterm to search under *)
|
dixon@19871
|
21 |
|
dixon@19871
|
22 |
exception eqsubst_occL_exp of
|
wenzelm@31301
|
23 |
string * int list * thm list * int * thm
|
dixon@19871
|
24 |
|
dixon@19871
|
25 |
(* low level substitution functions *)
|
dixon@19871
|
26 |
val apply_subst_in_asm :
|
dixon@19871
|
27 |
int ->
|
wenzelm@31301
|
28 |
thm ->
|
wenzelm@31301
|
29 |
thm ->
|
wenzelm@31301
|
30 |
(cterm list * int * 'a * thm) * match -> thm Seq.seq
|
dixon@19871
|
31 |
val apply_subst_in_concl :
|
dixon@19871
|
32 |
int ->
|
wenzelm@31301
|
33 |
thm ->
|
wenzelm@31301
|
34 |
cterm list * thm ->
|
wenzelm@31301
|
35 |
thm -> match -> thm Seq.seq
|
dixon@19871
|
36 |
|
dixon@19871
|
37 |
(* matching/unification within zippers *)
|
dixon@19871
|
38 |
val clean_match_z :
|
wenzelm@31301
|
39 |
theory -> term -> Zipper.T -> match option
|
dixon@19871
|
40 |
val clean_unify_z :
|
wenzelm@31301
|
41 |
theory -> int -> term -> Zipper.T -> match Seq.seq
|
dixon@19871
|
42 |
|
dixon@19871
|
43 |
(* skipping things in seq seq's *)
|
dixon@19871
|
44 |
|
dixon@19871
|
45 |
(* skipping non-empty sub-sequences but when we reach the end
|
dixon@19871
|
46 |
of the seq, remembering how much we have left to skip. *)
|
dixon@19871
|
47 |
datatype 'a skipseq = SkipMore of int
|
dixon@19871
|
48 |
| SkipSeq of 'a Seq.seq Seq.seq;
|
dixon@19871
|
49 |
|
dixon@19871
|
50 |
val skip_first_asm_occs_search :
|
dixon@19871
|
51 |
('a -> 'b -> 'c Seq.seq Seq.seq) ->
|
dixon@19871
|
52 |
'a -> int -> 'b -> 'c skipseq
|
dixon@19871
|
53 |
val skip_first_occs_search :
|
dixon@19871
|
54 |
int -> ('a -> 'b -> 'c Seq.seq Seq.seq) -> 'a -> 'b -> 'c Seq.seq
|
dixon@19871
|
55 |
val skipto_skipseq : int -> 'a Seq.seq Seq.seq -> 'a skipseq
|
dixon@19871
|
56 |
|
dixon@19871
|
57 |
(* tactics *)
|
dixon@19871
|
58 |
val eqsubst_asm_tac :
|
dixon@19871
|
59 |
Proof.context ->
|
wenzelm@31301
|
60 |
int list -> thm list -> int -> tactic
|
dixon@19871
|
61 |
val eqsubst_asm_tac' :
|
dixon@19871
|
62 |
Proof.context ->
|
wenzelm@31301
|
63 |
(searchinfo -> int -> term -> match skipseq) ->
|
wenzelm@31301
|
64 |
int -> thm -> int -> tactic
|
dixon@19871
|
65 |
val eqsubst_tac :
|
dixon@19871
|
66 |
Proof.context ->
|
dixon@22727
|
67 |
int list -> (* list of occurences to rewrite, use [0] for any *)
|
wenzelm@31301
|
68 |
thm list -> int -> tactic
|
dixon@19871
|
69 |
val eqsubst_tac' :
|
dixon@22727
|
70 |
Proof.context -> (* proof context *)
|
wenzelm@31301
|
71 |
(searchinfo -> term -> match Seq.seq) (* search function *)
|
wenzelm@31301
|
72 |
-> thm (* equation theorem to rewrite with *)
|
dixon@22727
|
73 |
-> int (* subgoal number in goal theorem *)
|
wenzelm@31301
|
74 |
-> thm (* goal theorem *)
|
wenzelm@31301
|
75 |
-> thm Seq.seq (* rewritten goal theorem *)
|
dixon@19871
|
76 |
|
dixon@19871
|
77 |
|
dixon@19871
|
78 |
val fakefree_badbounds :
|
wenzelm@31301
|
79 |
(string * typ) list ->
|
wenzelm@31301
|
80 |
term ->
|
wenzelm@31301
|
81 |
(string * typ) list * (string * typ) list * term
|
dixon@19871
|
82 |
|
dixon@19871
|
83 |
val mk_foo_match :
|
wenzelm@31301
|
84 |
(term -> term) ->
|
wenzelm@31301
|
85 |
('a * typ) list -> term -> term
|
dixon@19871
|
86 |
|
dixon@19871
|
87 |
(* preparing substitution *)
|
wenzelm@31301
|
88 |
val prep_meta_eq : Proof.context -> thm -> thm list
|
dixon@19871
|
89 |
val prep_concl_subst :
|
wenzelm@31301
|
90 |
int -> thm -> (cterm list * thm) * searchinfo
|
dixon@19871
|
91 |
val prep_subst_in_asm :
|
wenzelm@31301
|
92 |
int -> thm -> int ->
|
wenzelm@31301
|
93 |
(cterm list * int * int * thm) * searchinfo
|
dixon@19871
|
94 |
val prep_subst_in_asms :
|
wenzelm@31301
|
95 |
int -> thm ->
|
wenzelm@31301
|
96 |
((cterm list * int * int * thm) * searchinfo) list
|
dixon@19871
|
97 |
val prep_zipper_match :
|
wenzelm@31301
|
98 |
Zipper.T -> term * ((string * typ) list * (string * typ) list * term)
|
dixon@19871
|
99 |
|
dixon@19871
|
100 |
(* search for substitutions *)
|
dixon@19871
|
101 |
val valid_match_start : Zipper.T -> bool
|
dixon@19871
|
102 |
val search_lr_all : Zipper.T -> Zipper.T Seq.seq
|
dixon@19871
|
103 |
val search_lr_valid : (Zipper.T -> bool) -> Zipper.T -> Zipper.T Seq.seq
|
dixon@19871
|
104 |
val searchf_lr_unify_all :
|
wenzelm@31301
|
105 |
searchinfo -> term -> match Seq.seq Seq.seq
|
dixon@19871
|
106 |
val searchf_lr_unify_valid :
|
wenzelm@31301
|
107 |
searchinfo -> term -> match Seq.seq Seq.seq
|
narboux@23064
|
108 |
val searchf_bt_unify_valid :
|
wenzelm@31301
|
109 |
searchinfo -> term -> match Seq.seq Seq.seq
|
dixon@19871
|
110 |
|
dixon@19871
|
111 |
(* Isar level hooks *)
|
wenzelm@31301
|
112 |
val eqsubst_asm_meth : Proof.context -> int list -> thm list -> Proof.method
|
wenzelm@31301
|
113 |
val eqsubst_meth : Proof.context -> int list -> thm list -> Proof.method
|
dixon@19871
|
114 |
val setup : theory -> theory
|
dixon@19871
|
115 |
|
paulson@15481
|
116 |
end;
|
paulson@15481
|
117 |
|
wenzelm@41417
|
118 |
structure EqSubst: EQSUBST =
|
wenzelm@41417
|
119 |
struct
|
dixon@19835
|
120 |
|
dixon@19835
|
121 |
(* changes object "=" to meta "==" which prepares a given rewrite rule *)
|
wenzelm@18598
|
122 |
fun prep_meta_eq ctxt =
|
wenzelm@32149
|
123 |
Simplifier.mksimps (simpset_of ctxt) #> map Drule.zero_var_indexes;
|
wenzelm@18598
|
124 |
|
paulson@15481
|
125 |
|
dixon@15915
|
126 |
(* a type abriviation for match information *)
|
wenzelm@16978
|
127 |
type match =
|
wenzelm@16978
|
128 |
((indexname * (sort * typ)) list (* type instantiations *)
|
wenzelm@16978
|
129 |
* (indexname * (typ * term)) list) (* term instantiations *)
|
wenzelm@16978
|
130 |
* (string * typ) list (* fake named type abs env *)
|
wenzelm@16978
|
131 |
* (string * typ) list (* type abs env *)
|
wenzelm@16978
|
132 |
* term (* outer term *)
|
dixon@15550
|
133 |
|
wenzelm@16978
|
134 |
type searchinfo =
|
wenzelm@18598
|
135 |
theory
|
dixon@16004
|
136 |
* int (* maxidx *)
|
dixon@19835
|
137 |
* Zipper.T (* focusterm to search under *)
|
dixon@19835
|
138 |
|
dixon@19835
|
139 |
|
dixon@19835
|
140 |
(* skipping non-empty sub-sequences but when we reach the end
|
dixon@19835
|
141 |
of the seq, remembering how much we have left to skip. *)
|
dixon@19835
|
142 |
datatype 'a skipseq = SkipMore of int
|
dixon@19835
|
143 |
| SkipSeq of 'a Seq.seq Seq.seq;
|
dixon@19835
|
144 |
(* given a seqseq, skip the first m non-empty seq's, note deficit *)
|
dixon@19835
|
145 |
fun skipto_skipseq m s =
|
dixon@19835
|
146 |
let
|
dixon@19835
|
147 |
fun skip_occs n sq =
|
dixon@19835
|
148 |
case Seq.pull sq of
|
dixon@19835
|
149 |
NONE => SkipMore n
|
dixon@19835
|
150 |
| SOME (h,t) =>
|
dixon@19835
|
151 |
(case Seq.pull h of NONE => skip_occs n t
|
dixon@19835
|
152 |
| SOME _ => if n <= 1 then SkipSeq (Seq.cons h t)
|
dixon@19835
|
153 |
else skip_occs (n - 1) t)
|
dixon@19835
|
154 |
in (skip_occs m s) end;
|
dixon@19835
|
155 |
|
dixon@19835
|
156 |
(* note: outerterm is the taget with the match replaced by a bound
|
dixon@19835
|
157 |
variable : ie: "P lhs" beocmes "%x. P x"
|
dixon@19835
|
158 |
insts is the types of instantiations of vars in lhs
|
dixon@19835
|
159 |
and typinsts is the type instantiations of types in the lhs
|
dixon@19835
|
160 |
Note: Final rule is the rule lifted into the ontext of the
|
dixon@19835
|
161 |
taget thm. *)
|
dixon@19835
|
162 |
fun mk_foo_match mkuptermfunc Ts t =
|
dixon@19835
|
163 |
let
|
dixon@19835
|
164 |
val ty = Term.type_of t
|
dixon@19835
|
165 |
val bigtype = (rev (map snd Ts)) ---> ty
|
dixon@19835
|
166 |
fun mk_foo 0 t = t
|
dixon@19835
|
167 |
| mk_foo i t = mk_foo (i - 1) (t $ (Bound (i - 1)))
|
dixon@19835
|
168 |
val num_of_bnds = (length Ts)
|
dixon@19835
|
169 |
(* foo_term = "fooabs y0 ... yn" where y's are local bounds *)
|
dixon@19835
|
170 |
val foo_term = mk_foo num_of_bnds (Bound num_of_bnds)
|
dixon@19835
|
171 |
in Abs("fooabs", bigtype, mkuptermfunc foo_term) end;
|
dixon@19835
|
172 |
|
dixon@19835
|
173 |
(* T is outer bound vars, n is number of locally bound vars *)
|
dixon@19835
|
174 |
(* THINK: is order of Ts correct...? or reversed? *)
|
dixon@19835
|
175 |
fun fakefree_badbounds Ts t =
|
dixon@19835
|
176 |
let val (FakeTs,Ts,newnames) =
|
dixon@19835
|
177 |
List.foldr (fn ((n,ty),(FakeTs,Ts,usednames)) =>
|
wenzelm@44206
|
178 |
let val newname = singleton (Name.variant_list usednames) n
|
dixon@19835
|
179 |
in ((RWTools.mk_fake_bound_name newname,ty)::FakeTs,
|
dixon@19835
|
180 |
(newname,ty)::Ts,
|
dixon@19835
|
181 |
newname::usednames) end)
|
dixon@19835
|
182 |
([],[],[])
|
dixon@19835
|
183 |
Ts
|
dixon@19835
|
184 |
in (FakeTs, Ts, Term.subst_bounds (map Free FakeTs, t)) end;
|
dixon@19835
|
185 |
|
dixon@19835
|
186 |
(* before matching we need to fake the bound vars that are missing an
|
dixon@19835
|
187 |
abstraction. In this function we additionally construct the
|
dixon@19835
|
188 |
abstraction environment, and an outer context term (with the focus
|
dixon@19835
|
189 |
abstracted out) for use in rewriting with RWInst.rw *)
|
dixon@19835
|
190 |
fun prep_zipper_match z =
|
dixon@19835
|
191 |
let
|
wenzelm@41417
|
192 |
val t = Zipper.trm z
|
wenzelm@41417
|
193 |
val c = Zipper.ctxt z
|
wenzelm@41417
|
194 |
val Ts = Zipper.C.nty_ctxt c
|
dixon@19835
|
195 |
val (FakeTs', Ts', t') = fakefree_badbounds Ts t
|
wenzelm@41417
|
196 |
val absterm = mk_foo_match (Zipper.C.apply c) Ts' t'
|
dixon@19835
|
197 |
in
|
dixon@19835
|
198 |
(t', (FakeTs', Ts', absterm))
|
dixon@19835
|
199 |
end;
|
dixon@19835
|
200 |
|
dixon@19835
|
201 |
(* Matching and Unification with exception handled *)
|
dixon@19835
|
202 |
fun clean_match thy (a as (pat, t)) =
|
dixon@19835
|
203 |
let val (tyenv, tenv) = Pattern.match thy a (Vartab.empty, Vartab.empty)
|
dixon@19835
|
204 |
in SOME (Vartab.dest tyenv, Vartab.dest tenv)
|
dixon@19835
|
205 |
end handle Pattern.MATCH => NONE;
|
dixon@27033
|
206 |
|
dixon@19835
|
207 |
(* given theory, max var index, pat, tgt; returns Seq of instantiations *)
|
dixon@27033
|
208 |
fun clean_unify thry ix (a as (pat, tgt)) =
|
dixon@19835
|
209 |
let
|
dixon@19835
|
210 |
(* type info will be re-derived, maybe this can be cached
|
dixon@19835
|
211 |
for efficiency? *)
|
dixon@19835
|
212 |
val pat_ty = Term.type_of pat;
|
dixon@19835
|
213 |
val tgt_ty = Term.type_of tgt;
|
dixon@19835
|
214 |
(* is it OK to ignore the type instantiation info?
|
dixon@19835
|
215 |
or should I be using it? *)
|
dixon@19835
|
216 |
val typs_unify =
|
wenzelm@29269
|
217 |
SOME (Sign.typ_unify thry (pat_ty, tgt_ty) (Vartab.empty, ix))
|
dixon@19835
|
218 |
handle Type.TUNIFY => NONE;
|
dixon@19835
|
219 |
in
|
dixon@19835
|
220 |
case typs_unify of
|
dixon@19835
|
221 |
SOME (typinsttab, ix2) =>
|
dixon@19835
|
222 |
let
|
dixon@19835
|
223 |
(* is it right to throw away the flexes?
|
dixon@19835
|
224 |
or should I be using them somehow? *)
|
dixon@19835
|
225 |
fun mk_insts env =
|
dixon@19835
|
226 |
(Vartab.dest (Envir.type_env env),
|
wenzelm@32043
|
227 |
Vartab.dest (Envir.term_env env));
|
wenzelm@32043
|
228 |
val initenv =
|
wenzelm@32043
|
229 |
Envir.Envir {maxidx = ix2, tenv = Vartab.empty, tyenv = typinsttab};
|
dixon@27033
|
230 |
val useq = Unify.smash_unifiers thry [a] initenv
|
wenzelm@40978
|
231 |
handle ListPair.UnequalLengths => Seq.empty
|
wenzelm@32962
|
232 |
| Term.TERM _ => Seq.empty;
|
dixon@19835
|
233 |
fun clean_unify' useq () =
|
dixon@19835
|
234 |
(case (Seq.pull useq) of
|
dixon@19835
|
235 |
NONE => NONE
|
dixon@19835
|
236 |
| SOME (h,t) => SOME (mk_insts h, Seq.make (clean_unify' t)))
|
wenzelm@40978
|
237 |
handle ListPair.UnequalLengths => NONE
|
dixon@27033
|
238 |
| Term.TERM _ => NONE
|
dixon@19835
|
239 |
in
|
dixon@19835
|
240 |
(Seq.make (clean_unify' useq))
|
dixon@19835
|
241 |
end
|
dixon@19835
|
242 |
| NONE => Seq.empty
|
dixon@19835
|
243 |
end;
|
dixon@19835
|
244 |
|
dixon@19835
|
245 |
(* Matching and Unification for zippers *)
|
dixon@19835
|
246 |
(* Note: Ts is a modified version of the original names of the outer
|
dixon@19835
|
247 |
bound variables. New names have been introduced to make sure they are
|
dixon@19835
|
248 |
unique w.r.t all names in the term and each other. usednames' is
|
dixon@19835
|
249 |
oldnames + new names. *)
|
dixon@19835
|
250 |
fun clean_match_z thy pat z =
|
dixon@19835
|
251 |
let val (t, (FakeTs,Ts,absterm)) = prep_zipper_match z in
|
dixon@19835
|
252 |
case clean_match thy (pat, t) of
|
dixon@19835
|
253 |
NONE => NONE
|
dixon@19835
|
254 |
| SOME insts => SOME (insts, FakeTs, Ts, absterm) end;
|
dixon@19835
|
255 |
(* ix = max var index *)
|
dixon@19835
|
256 |
fun clean_unify_z sgn ix pat z =
|
dixon@19835
|
257 |
let val (t, (FakeTs, Ts,absterm)) = prep_zipper_match z in
|
dixon@19835
|
258 |
Seq.map (fn insts => (insts, FakeTs, Ts, absterm))
|
dixon@19835
|
259 |
(clean_unify sgn ix (t, pat)) end;
|
dixon@19835
|
260 |
|
dixon@15550
|
261 |
|
dixon@15538
|
262 |
(* FOR DEBUGGING...
|
dixon@15538
|
263 |
type trace_subst_errT = int (* subgoal *)
|
wenzelm@16978
|
264 |
* thm (* thm with all goals *)
|
wenzelm@33259
|
265 |
* (cterm list (* certified free var placeholders for vars *)
|
wenzelm@16978
|
266 |
* thm) (* trivial thm of goal concl *)
|
dixon@15538
|
267 |
(* possible matches/unifiers *)
|
wenzelm@16978
|
268 |
* thm (* rule *)
|
wenzelm@16978
|
269 |
* (((indexname * typ) list (* type instantiations *)
|
wenzelm@16978
|
270 |
* (indexname * term) list ) (* term instantiations *)
|
wenzelm@16978
|
271 |
* (string * typ) list (* Type abs env *)
|
wenzelm@16978
|
272 |
* term) (* outer term *);
|
dixon@15538
|
273 |
|
wenzelm@32740
|
274 |
val trace_subst_err = (Unsynchronized.ref NONE : trace_subst_errT option Unsynchronized.ref);
|
wenzelm@32740
|
275 |
val trace_subst_search = Unsynchronized.ref false;
|
dixon@15538
|
276 |
exception trace_subst_exp of trace_subst_errT;
|
dixon@19835
|
277 |
*)
|
dixon@19835
|
278 |
|
dixon@19835
|
279 |
|
dixon@19835
|
280 |
fun bot_left_leaf_of (l $ r) = bot_left_leaf_of l
|
dixon@19835
|
281 |
| bot_left_leaf_of (Abs(s,ty,t)) = bot_left_leaf_of t
|
dixon@19835
|
282 |
| bot_left_leaf_of x = x;
|
dixon@19835
|
283 |
|
dixon@19975
|
284 |
(* Avoid considering replacing terms which have a var at the head as
|
dixon@19975
|
285 |
they always succeed trivially, and uninterestingly. *)
|
dixon@19835
|
286 |
fun valid_match_start z =
|
wenzelm@41417
|
287 |
(case bot_left_leaf_of (Zipper.trm z) of
|
dixon@19975
|
288 |
Var _ => false
|
dixon@19975
|
289 |
| _ => true);
|
dixon@19975
|
290 |
|
dixon@19835
|
291 |
(* search from top, left to right, then down *)
|
dixon@19871
|
292 |
val search_lr_all = ZipperSearch.all_bl_ur;
|
dixon@15538
|
293 |
|
dixon@15814
|
294 |
(* search from top, left to right, then down *)
|
dixon@19871
|
295 |
fun search_lr_valid validf =
|
dixon@19835
|
296 |
let
|
dixon@19835
|
297 |
fun sf_valid_td_lr z =
|
wenzelm@41417
|
298 |
let val here = if validf z then [Zipper.Here z] else [] in
|
wenzelm@41417
|
299 |
case Zipper.trm z
|
wenzelm@41417
|
300 |
of _ $ _ => [Zipper.LookIn (Zipper.move_down_left z)]
|
dixon@19871
|
301 |
@ here
|
wenzelm@41417
|
302 |
@ [Zipper.LookIn (Zipper.move_down_right z)]
|
wenzelm@41417
|
303 |
| Abs _ => here @ [Zipper.LookIn (Zipper.move_down_abs z)]
|
dixon@19835
|
304 |
| _ => here
|
dixon@19835
|
305 |
end;
|
wenzelm@41417
|
306 |
in Zipper.lzy_search sf_valid_td_lr end;
|
dixon@15814
|
307 |
|
narboux@23064
|
308 |
(* search from bottom to top, left to right *)
|
narboux@23064
|
309 |
|
narboux@23064
|
310 |
fun search_bt_valid validf =
|
narboux@23064
|
311 |
let
|
narboux@23064
|
312 |
fun sf_valid_td_lr z =
|
wenzelm@41417
|
313 |
let val here = if validf z then [Zipper.Here z] else [] in
|
wenzelm@41417
|
314 |
case Zipper.trm z
|
wenzelm@41417
|
315 |
of _ $ _ => [Zipper.LookIn (Zipper.move_down_left z),
|
wenzelm@41417
|
316 |
Zipper.LookIn (Zipper.move_down_right z)] @ here
|
wenzelm@41417
|
317 |
| Abs _ => [Zipper.LookIn (Zipper.move_down_abs z)] @ here
|
narboux@23064
|
318 |
| _ => here
|
narboux@23064
|
319 |
end;
|
wenzelm@41417
|
320 |
in Zipper.lzy_search sf_valid_td_lr end;
|
narboux@23064
|
321 |
|
narboux@23064
|
322 |
fun searchf_unify_gen f (sgn, maxidx, z) lhs =
|
narboux@23064
|
323 |
Seq.map (clean_unify_z sgn maxidx lhs)
|
wenzelm@41417
|
324 |
(Zipper.limit_apply f z);
|
narboux@23064
|
325 |
|
dixon@15814
|
326 |
(* search all unifications *)
|
narboux@23064
|
327 |
val searchf_lr_unify_all =
|
narboux@23064
|
328 |
searchf_unify_gen search_lr_all;
|
paulson@15481
|
329 |
|
dixon@15814
|
330 |
(* search only for 'valid' unifiers (non abs subterms and non vars) *)
|
narboux@23064
|
331 |
val searchf_lr_unify_valid =
|
narboux@23064
|
332 |
searchf_unify_gen (search_lr_valid valid_match_start);
|
dixon@15929
|
333 |
|
narboux@23064
|
334 |
val searchf_bt_unify_valid =
|
narboux@23064
|
335 |
searchf_unify_gen (search_bt_valid valid_match_start);
|
dixon@15814
|
336 |
|
dixon@15538
|
337 |
(* apply a substitution in the conclusion of the theorem th *)
|
dixon@15538
|
338 |
(* cfvs are certified free var placeholders for goal params *)
|
dixon@15538
|
339 |
(* conclthm is a theorem of for just the conclusion *)
|
dixon@15538
|
340 |
(* m is instantiation/match information *)
|
dixon@15538
|
341 |
(* rule is the equation for substitution *)
|
wenzelm@16978
|
342 |
fun apply_subst_in_concl i th (cfvs, conclthm) rule m =
|
dixon@15538
|
343 |
(RWInst.rw m rule conclthm)
|
dixon@15855
|
344 |
|> IsaND.unfix_frees cfvs
|
dixon@15915
|
345 |
|> RWInst.beta_eta_contract
|
dixon@15538
|
346 |
|> (fn r => Tactic.rtac r i th);
|
paulson@15481
|
347 |
|
paulson@15481
|
348 |
(* substitute within the conclusion of goal i of gth, using a meta
|
dixon@15538
|
349 |
equation rule. Note that we assume rule has var indicies zero'd *)
|
wenzelm@16978
|
350 |
fun prep_concl_subst i gth =
|
wenzelm@16978
|
351 |
let
|
paulson@15481
|
352 |
val th = Thm.incr_indexes 1 gth;
|
paulson@15481
|
353 |
val tgt_term = Thm.prop_of th;
|
paulson@15481
|
354 |
|
wenzelm@22578
|
355 |
val sgn = Thm.theory_of_thm th;
|
paulson@15481
|
356 |
val ctermify = Thm.cterm_of sgn;
|
paulson@15481
|
357 |
val trivify = Thm.trivial o ctermify;
|
paulson@15481
|
358 |
|
paulson@15481
|
359 |
val (fixedbody, fvs) = IsaND.fix_alls_term i tgt_term;
|
paulson@15481
|
360 |
val cfvs = rev (map ctermify fvs);
|
paulson@15481
|
361 |
|
dixon@15538
|
362 |
val conclterm = Logic.strip_imp_concl fixedbody;
|
dixon@15538
|
363 |
val conclthm = trivify conclterm;
|
dixon@27033
|
364 |
val maxidx = Thm.maxidx_of th;
|
wenzelm@41417
|
365 |
val ft = ((Zipper.move_down_right (* ==> *)
|
wenzelm@41417
|
366 |
o Zipper.move_down_left (* Trueprop *)
|
wenzelm@41417
|
367 |
o Zipper.mktop
|
dixon@16004
|
368 |
o Thm.prop_of) conclthm)
|
paulson@15481
|
369 |
in
|
dixon@16004
|
370 |
((cfvs, conclthm), (sgn, maxidx, ft))
|
paulson@15481
|
371 |
end;
|
paulson@15481
|
372 |
|
paulson@15481
|
373 |
(* substitute using an object or meta level equality *)
|
wenzelm@18598
|
374 |
fun eqsubst_tac' ctxt searchf instepthm i th =
|
wenzelm@16978
|
375 |
let
|
dixon@16004
|
376 |
val (cvfsconclthm, searchinfo) = prep_concl_subst i th;
|
wenzelm@18598
|
377 |
val stepthms = Seq.of_list (prep_meta_eq ctxt instepthm);
|
dixon@15538
|
378 |
fun rewrite_with_thm r =
|
dixon@15538
|
379 |
let val (lhs,_) = Logic.dest_equals (Thm.concl_of r);
|
wenzelm@18598
|
380 |
in searchf searchinfo lhs
|
wenzelm@18598
|
381 |
|> Seq.maps (apply_subst_in_concl i th cvfsconclthm r) end;
|
wenzelm@18598
|
382 |
in stepthms |> Seq.maps rewrite_with_thm end;
|
dixon@15538
|
383 |
|
dixon@15538
|
384 |
|
wenzelm@19047
|
385 |
(* distinct subgoals *)
|
wenzelm@19047
|
386 |
fun distinct_subgoals th =
|
wenzelm@19047
|
387 |
the_default th (SINGLE distinct_subgoals_tac th);
|
dixon@15959
|
388 |
|
wenzelm@19047
|
389 |
(* General substitution of multiple occurances using one of
|
dixon@15936
|
390 |
the given theorems*)
|
dixon@19835
|
391 |
|
dixon@19835
|
392 |
|
wenzelm@16978
|
393 |
exception eqsubst_occL_exp of
|
wenzelm@16978
|
394 |
string * (int list) * (thm list) * int * thm;
|
wenzelm@16978
|
395 |
fun skip_first_occs_search occ srchf sinfo lhs =
|
dixon@19835
|
396 |
case (skipto_skipseq occ (srchf sinfo lhs)) of
|
dixon@19835
|
397 |
SkipMore _ => Seq.empty
|
dixon@19835
|
398 |
| SkipSeq ss => Seq.flat ss;
|
dixon@16004
|
399 |
|
dixon@22727
|
400 |
(* The occL is a list of integers indicating which occurence
|
dixon@22727
|
401 |
w.r.t. the search order, to rewrite. Backtracking will also find later
|
dixon@22727
|
402 |
occurences, but all earlier ones are skipped. Thus you can use [0] to
|
dixon@22727
|
403 |
just find all rewrites. *)
|
dixon@22727
|
404 |
|
wenzelm@18598
|
405 |
fun eqsubst_tac ctxt occL thms i th =
|
dixon@15936
|
406 |
let val nprems = Thm.nprems_of th in
|
dixon@15936
|
407 |
if nprems < i then Seq.empty else
|
wenzelm@16978
|
408 |
let val thmseq = (Seq.of_list thms)
|
wenzelm@16978
|
409 |
fun apply_occ occ th =
|
wenzelm@18598
|
410 |
thmseq |> Seq.maps
|
dixon@19835
|
411 |
(fn r => eqsubst_tac'
|
dixon@19835
|
412 |
ctxt
|
dixon@19835
|
413 |
(skip_first_occs_search
|
dixon@19871
|
414 |
occ searchf_lr_unify_valid) r
|
dixon@15936
|
415 |
(i + ((Thm.nprems_of th) - nprems))
|
dixon@15936
|
416 |
th);
|
wenzelm@16978
|
417 |
val sortedoccL =
|
dixon@16004
|
418 |
Library.sort (Library.rev_order o Library.int_ord) occL;
|
dixon@15936
|
419 |
in
|
dixon@16004
|
420 |
Seq.map distinct_subgoals (Seq.EVERY (map apply_occ sortedoccL) th)
|
dixon@15936
|
421 |
end
|
dixon@15959
|
422 |
end
|
dixon@15959
|
423 |
handle THM _ => raise eqsubst_occL_exp ("THM",occL,thms,i,th);
|
dixon@15959
|
424 |
|
paulson@15481
|
425 |
|
paulson@15481
|
426 |
(* inthms are the given arguments in Isar, and treated as eqstep with
|
paulson@15481
|
427 |
the first one, then the second etc *)
|
wenzelm@18598
|
428 |
fun eqsubst_meth ctxt occL inthms =
|
wenzelm@30515
|
429 |
SIMPLE_METHOD' (eqsubst_tac ctxt occL inthms);
|
paulson@15481
|
430 |
|
dixon@16004
|
431 |
(* apply a substitution inside assumption j, keeps asm in the same place *)
|
wenzelm@16978
|
432 |
fun apply_subst_in_asm i th rule ((cfvs, j, ngoalprems, pth),m) =
|
wenzelm@16978
|
433 |
let
|
dixon@16004
|
434 |
val th2 = Thm.rotate_rule (j - 1) i th; (* put premice first *)
|
wenzelm@16978
|
435 |
val preelimrule =
|
dixon@16004
|
436 |
(RWInst.rw m rule pth)
|
wenzelm@21708
|
437 |
|> (Seq.hd o prune_params_tac)
|
dixon@16004
|
438 |
|> Thm.permute_prems 0 ~1 (* put old asm first *)
|
dixon@16004
|
439 |
|> IsaND.unfix_frees cfvs (* unfix any global params *)
|
dixon@16004
|
440 |
|> RWInst.beta_eta_contract; (* normal form *)
|
wenzelm@16978
|
441 |
(* val elimrule =
|
dixon@16004
|
442 |
preelimrule
|
dixon@16004
|
443 |
|> Tactic.make_elim (* make into elim rule *)
|
dixon@16004
|
444 |
|> Thm.lift_rule (th2, i); (* lift into context *)
|
dixon@16007
|
445 |
*)
|
dixon@16004
|
446 |
in
|
dixon@16004
|
447 |
(* ~j because new asm starts at back, thus we subtract 1 *)
|
dixon@16007
|
448 |
Seq.map (Thm.rotate_rule (~j) ((Thm.nprems_of rule) + i))
|
dixon@16007
|
449 |
(Tactic.dtac preelimrule i th2)
|
dixon@16007
|
450 |
|
wenzelm@16978
|
451 |
(* (Thm.bicompose
|
dixon@16004
|
452 |
false (* use unification *)
|
dixon@16004
|
453 |
(true, (* elim resolution *)
|
dixon@16007
|
454 |
elimrule, (2 + (Thm.nprems_of rule)) - ngoalprems)
|
dixon@16007
|
455 |
i th2) *)
|
dixon@16004
|
456 |
end;
|
dixon@15538
|
457 |
|
dixon@15538
|
458 |
|
dixon@15538
|
459 |
(* prepare to substitute within the j'th premise of subgoal i of gth,
|
dixon@15538
|
460 |
using a meta-level equation. Note that we assume rule has var indicies
|
dixon@15538
|
461 |
zero'd. Note that we also assume that premt is the j'th premice of
|
dixon@15538
|
462 |
subgoal i of gth. Note the repetition of work done for each
|
dixon@15538
|
463 |
assumption, i.e. this can be made more efficient for search over
|
dixon@15538
|
464 |
multiple assumptions. *)
|
wenzelm@16978
|
465 |
fun prep_subst_in_asm i gth j =
|
wenzelm@16978
|
466 |
let
|
paulson@15481
|
467 |
val th = Thm.incr_indexes 1 gth;
|
paulson@15481
|
468 |
val tgt_term = Thm.prop_of th;
|
paulson@15481
|
469 |
|
wenzelm@22578
|
470 |
val sgn = Thm.theory_of_thm th;
|
paulson@15481
|
471 |
val ctermify = Thm.cterm_of sgn;
|
paulson@15481
|
472 |
val trivify = Thm.trivial o ctermify;
|
paulson@15481
|
473 |
|
paulson@15481
|
474 |
val (fixedbody, fvs) = IsaND.fix_alls_term i tgt_term;
|
paulson@15481
|
475 |
val cfvs = rev (map ctermify fvs);
|
paulson@15481
|
476 |
|
haftmann@18011
|
477 |
val asmt = nth (Logic.strip_imp_prems fixedbody) (j - 1);
|
dixon@15538
|
478 |
val asm_nprems = length (Logic.strip_imp_prems asmt);
|
dixon@15538
|
479 |
|
dixon@15538
|
480 |
val pth = trivify asmt;
|
dixon@27033
|
481 |
val maxidx = Thm.maxidx_of th;
|
dixon@15538
|
482 |
|
wenzelm@41417
|
483 |
val ft = ((Zipper.move_down_right (* trueprop *)
|
wenzelm@41417
|
484 |
o Zipper.mktop
|
dixon@16004
|
485 |
o Thm.prop_of) pth)
|
dixon@16004
|
486 |
in ((cfvs, j, asm_nprems, pth), (sgn, maxidx, ft)) end;
|
paulson@15481
|
487 |
|
dixon@15538
|
488 |
(* prepare subst in every possible assumption *)
|
wenzelm@16978
|
489 |
fun prep_subst_in_asms i gth =
|
dixon@16004
|
490 |
map (prep_subst_in_asm i gth)
|
dixon@19835
|
491 |
((fn l => Library.upto (1, length l))
|
dixon@16004
|
492 |
(Logic.prems_of_goal (Thm.prop_of gth) i));
|
dixon@15538
|
493 |
|
dixon@15538
|
494 |
|
dixon@15538
|
495 |
(* substitute in an assumption using an object or meta level equality *)
|
wenzelm@18598
|
496 |
fun eqsubst_asm_tac' ctxt searchf skipocc instepthm i th =
|
wenzelm@16978
|
497 |
let
|
dixon@16004
|
498 |
val asmpreps = prep_subst_in_asms i th;
|
wenzelm@18598
|
499 |
val stepthms = Seq.of_list (prep_meta_eq ctxt instepthm);
|
dixon@16004
|
500 |
fun rewrite_with_thm r =
|
dixon@16004
|
501 |
let val (lhs,_) = Logic.dest_equals (Thm.concl_of r)
|
dixon@16004
|
502 |
fun occ_search occ [] = Seq.empty
|
dixon@16004
|
503 |
| occ_search occ ((asminfo, searchinfo)::moreasms) =
|
wenzelm@16978
|
504 |
(case searchf searchinfo occ lhs of
|
dixon@19835
|
505 |
SkipMore i => occ_search i moreasms
|
dixon@19835
|
506 |
| SkipSeq ss =>
|
wenzelm@19861
|
507 |
Seq.append (Seq.map (Library.pair asminfo) (Seq.flat ss))
|
wenzelm@19861
|
508 |
(occ_search 1 moreasms))
|
dixon@16004
|
509 |
(* find later substs also *)
|
wenzelm@16978
|
510 |
in
|
wenzelm@18598
|
511 |
occ_search skipocc asmpreps |> Seq.maps (apply_subst_in_asm i th r)
|
dixon@16004
|
512 |
end;
|
wenzelm@18598
|
513 |
in stepthms |> Seq.maps rewrite_with_thm end;
|
dixon@15538
|
514 |
|
dixon@16004
|
515 |
|
wenzelm@16978
|
516 |
fun skip_first_asm_occs_search searchf sinfo occ lhs =
|
dixon@19835
|
517 |
skipto_skipseq occ (searchf sinfo lhs);
|
dixon@16004
|
518 |
|
wenzelm@18598
|
519 |
fun eqsubst_asm_tac ctxt occL thms i th =
|
wenzelm@16978
|
520 |
let val nprems = Thm.nprems_of th
|
dixon@15538
|
521 |
in
|
dixon@16004
|
522 |
if nprems < i then Seq.empty else
|
wenzelm@16978
|
523 |
let val thmseq = (Seq.of_list thms)
|
wenzelm@16978
|
524 |
fun apply_occ occK th =
|
wenzelm@18598
|
525 |
thmseq |> Seq.maps
|
wenzelm@16978
|
526 |
(fn r =>
|
wenzelm@18598
|
527 |
eqsubst_asm_tac' ctxt (skip_first_asm_occs_search
|
dixon@19871
|
528 |
searchf_lr_unify_valid) occK r
|
dixon@16004
|
529 |
(i + ((Thm.nprems_of th) - nprems))
|
dixon@16004
|
530 |
th);
|
wenzelm@16978
|
531 |
val sortedoccs =
|
dixon@16004
|
532 |
Library.sort (Library.rev_order o Library.int_ord) occL
|
dixon@16004
|
533 |
in
|
dixon@16004
|
534 |
Seq.map distinct_subgoals
|
dixon@16004
|
535 |
(Seq.EVERY (map apply_occ sortedoccs) th)
|
dixon@16004
|
536 |
end
|
dixon@16004
|
537 |
end
|
dixon@16004
|
538 |
handle THM _ => raise eqsubst_occL_exp ("THM",occL,thms,i,th);
|
paulson@15481
|
539 |
|
paulson@15481
|
540 |
(* inthms are the given arguments in Isar, and treated as eqstep with
|
paulson@15481
|
541 |
the first one, then the second etc *)
|
wenzelm@18598
|
542 |
fun eqsubst_asm_meth ctxt occL inthms =
|
wenzelm@30515
|
543 |
SIMPLE_METHOD' (eqsubst_asm_tac ctxt occL inthms);
|
paulson@15481
|
544 |
|
wenzelm@18598
|
545 |
(* combination method that takes a flag (true indicates that subst
|
wenzelm@31301
|
546 |
should be done to an assumption, false = apply to the conclusion of
|
wenzelm@31301
|
547 |
the goal) as well as the theorems to use *)
|
wenzelm@16978
|
548 |
val setup =
|
wenzelm@31301
|
549 |
Method.setup @{binding subst}
|
wenzelm@44966
|
550 |
(Args.mode "asm" -- Scan.lift (Scan.optional (Args.parens (Scan.repeat Parse.nat)) [0]) --
|
wenzelm@44966
|
551 |
Attrib.thms >>
|
wenzelm@44966
|
552 |
(fn ((asm, occL), inthms) => fn ctxt =>
|
wenzelm@44966
|
553 |
(if asm then eqsubst_asm_meth else eqsubst_meth) ctxt occL inthms))
|
wenzelm@31301
|
554 |
"single-step substitution";
|
paulson@15481
|
555 |
|
wenzelm@16978
|
556 |
end;
|