author | haftmann |
Tue, 06 Sep 2005 08:30:43 +0200 | |
changeset 17271 | 2756a73f63a5 |
parent 17257 | 0ab67cb765da |
child 17795 | 5b18c3343028 |
permissions | -rw-r--r-- |
4078 | 1 |
(* Title: Provers/blast.ML |
2894 | 2 |
ID: $Id$ |
3 |
Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
|
3083 | 4 |
Copyright 1997 University of Cambridge |
2894 | 5 |
|
6 |
Generic tableau prover with proof reconstruction |
|
7 |
||
2854 | 8 |
SKOLEMIZES ReplaceI WRONGLY: allow new vars in prems, or forbid such rules?? |
2894 | 9 |
Needs explicit instantiation of assumptions? |
10 |
||
11 |
||
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
12 |
Blast_tac is often more powerful than fast_tac, but has some limitations. |
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
13 |
Blast_tac... |
4651 | 14 |
* ignores wrappers (addss, addbefore, addafter, addWrapper, ...); |
15 |
this restriction is intrinsic |
|
2894 | 16 |
* ignores elimination rules that don't have the correct format |
17 |
(conclusion must be a formula variable) |
|
18 |
* ignores types, which can make HOL proofs fail |
|
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
19 |
* rules must not require higher-order unification, e.g. apply_type in ZF |
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
20 |
+ message "Function Var's argument not a bound variable" relates to this |
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
21 |
* its proof strategy is more general but can actually be slower |
2894 | 22 |
|
23 |
Known problems: |
|
3092 | 24 |
"Recursive" chains of rules can sometimes exclude other unsafe formulae |
3021
39806db47be9
Loop detection: before expanding a haz formula, see whether it is a duplicate
paulson
parents:
2999
diff
changeset
|
25 |
from expansion. This happens because newly-created formulae always |
3092 | 26 |
have priority over existing ones. But obviously recursive rules |
15661
9ef583b08647
reverted renaming of Some/None in comments and strings;
wenzelm
parents:
15574
diff
changeset
|
27 |
such as transitivity are treated specially to prevent this. Sometimes |
5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset
|
28 |
the formulae get into the wrong order (see WRONG below). |
3021
39806db47be9
Loop detection: before expanding a haz formula, see whether it is a duplicate
paulson
parents:
2999
diff
changeset
|
29 |
|
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
30 |
With substition for equalities (hyp_subst_tac): |
3092 | 31 |
When substitution affects a haz formula or literal, it is moved |
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
32 |
back to the list of safe formulae. |
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
33 |
But there's no way of putting it in the right place. A "moved" or |
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
34 |
"no DETERM" flag would prevent proofs failing here. |
2854 | 35 |
*) |
36 |
||
37 |
(*Should be a type abbreviation?*) |
|
38 |
type netpair = (int*(bool*thm)) Net.net * (int*(bool*thm)) Net.net; |
|
39 |
||
40 |
||
41 |
(*Assumptions about constants: |
|
42 |
--The negation symbol is "Not" |
|
43 |
--The equality symbol is "op =" |
|
44 |
--The is-true judgement symbol is "Trueprop" |
|
45 |
--There are no constants named "*Goal* or "*False*" |
|
46 |
*) |
|
47 |
signature BLAST_DATA = |
|
48 |
sig |
|
49 |
type claset |
|
50 |
val notE : thm (* [| ~P; P |] ==> R *) |
|
16774
515b6020cf5d
experimental code to reduce the amount of type information in blast
paulson
parents:
15786
diff
changeset
|
51 |
val is_hol : bool (*Is this HOL or FOL/ZF?*) |
2854 | 52 |
val ccontr : thm |
53 |
val contr_tac : int -> tactic |
|
54 |
val dup_intr : thm -> thm |
|
4466
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset
|
55 |
val hyp_subst_tac : bool ref -> int -> tactic |
4078 | 56 |
val claset : unit -> claset |
4653 | 57 |
val rep_cs : (* dependent on classical.ML *) |
2854 | 58 |
claset -> {safeIs: thm list, safeEs: thm list, |
59 |
hazIs: thm list, hazEs: thm list, |
|
4651 | 60 |
swrappers: (string * wrapper) list, |
61 |
uwrappers: (string * wrapper) list, |
|
2854 | 62 |
safe0_netpair: netpair, safep_netpair: netpair, |
12403 | 63 |
haz_netpair: netpair, dup_netpair: netpair, xtra_netpair: ContextRules.netpair} |
7272 | 64 |
val cla_modifiers: (Args.T list -> (Method.modifier * Args.T list)) list |
7559 | 65 |
val cla_meth': (claset -> int -> tactic) -> thm list -> Proof.context -> Proof.method |
2854 | 66 |
end; |
67 |
||
68 |
||
69 |
signature BLAST = |
|
70 |
sig |
|
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
71 |
type claset |
4233
85d004a96b98
Rationalized error handling: if low-level tactic (depth_tac) cannot accept the
paulson
parents:
4196
diff
changeset
|
72 |
exception TRANS of string (*reports translation errors*) |
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
73 |
datatype term = |
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
74 |
Const of string |
4065 | 75 |
| TConst of string * term |
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
76 |
| Skolem of string * term option ref list |
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
77 |
| Free of string |
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
78 |
| Var of term option ref |
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
79 |
| Bound of int |
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
80 |
| Abs of string*term |
15786
81e9f17823ea
Added op in front of constructor for better parsing.
gagern
parents:
15661
diff
changeset
|
81 |
| op $ of term*term; |
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
82 |
type branch |
2883 | 83 |
val depth_tac : claset -> int -> int -> tactic |
15162
670ab8497818
depth limit (previously hard-coded with a value of 20) made a reference
webertj
parents:
14984
diff
changeset
|
84 |
val depth_limit : int ref |
2883 | 85 |
val blast_tac : claset -> int -> tactic |
86 |
val Blast_tac : int -> tactic |
|
5926 | 87 |
val setup : (theory -> theory) list |
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
88 |
(*debugging tools*) |
4323
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset
|
89 |
val stats : bool ref |
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
90 |
val trace : bool ref |
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
91 |
val fullTrace : branch list list ref |
4065 | 92 |
val fromType : (indexname * term) list ref -> Term.typ -> term |
93 |
val fromTerm : Term.term -> term |
|
94 |
val fromSubgoal : Term.term -> term |
|
95 |
val instVars : term -> (unit -> unit) |
|
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
96 |
val toTerm : int -> term -> Term.term |
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
97 |
val readGoal : Sign.sg -> string -> term |
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
98 |
val tryInThy : theory -> int -> string -> |
3083 | 99 |
(int->tactic) list * branch list list * (int*int*exn) list |
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
100 |
val trygl : claset -> int -> int -> |
3083 | 101 |
(int->tactic) list * branch list list * (int*int*exn) list |
102 |
val Trygl : int -> int -> |
|
103 |
(int->tactic) list * branch list list * (int*int*exn) list |
|
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
104 |
val normBr : branch -> branch |
2854 | 105 |
end; |
106 |
||
107 |
||
3092 | 108 |
functor BlastFun(Data: BLAST_DATA) : BLAST = |
2854 | 109 |
struct |
110 |
||
111 |
type claset = Data.claset; |
|
112 |
||
4323
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset
|
113 |
val trace = ref false |
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset
|
114 |
and stats = ref false; (*for runtime and search statistics*) |
2854 | 115 |
|
116 |
datatype term = |
|
5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset
|
117 |
Const of string |
4065 | 118 |
| TConst of string * term (*type of overloaded constant--as a term!*) |
2854 | 119 |
| Skolem of string * term option ref list |
5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset
|
120 |
| Free of string |
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset
|
121 |
| Var of term option ref |
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset
|
122 |
| Bound of int |
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset
|
123 |
| Abs of string*term |
5613 | 124 |
| op $ of term*term; |
2854 | 125 |
|
126 |
||
127 |
(** Basic syntactic operations **) |
|
128 |
||
129 |
fun is_Var (Var _) = true |
|
130 |
| is_Var _ = false; |
|
131 |
||
132 |
fun dest_Var (Var x) = x; |
|
133 |
||
134 |
fun rand (f$x) = x; |
|
135 |
||
136 |
(* maps (f, [t1,...,tn]) to f(t1,...,tn) *) |
|
15570 | 137 |
val list_comb : term * term list -> term = Library.foldl (op $); |
2854 | 138 |
|
139 |
(* maps f(t1,...,tn) to (f, [t1,...,tn]) ; naturally tail-recursive*) |
|
140 |
fun strip_comb u : term * term list = |
|
141 |
let fun stripc (f$t, ts) = stripc (f, t::ts) |
|
142 |
| stripc x = x |
|
143 |
in stripc(u,[]) end; |
|
144 |
||
145 |
(* maps f(t1,...,tn) to f , which is never a combination *) |
|
146 |
fun head_of (f$t) = head_of f |
|
147 |
| head_of u = u; |
|
148 |
||
149 |
||
150 |
(** Particular constants **) |
|
151 |
||
152 |
fun negate P = Const"Not" $ P; |
|
153 |
||
154 |
fun mkGoal P = Const"*Goal*" $ P; |
|
155 |
||
156 |
fun isGoal (Const"*Goal*" $ _) = true |
|
157 |
| isGoal _ = false; |
|
158 |
||
16774
515b6020cf5d
experimental code to reduce the amount of type information in blast
paulson
parents:
15786
diff
changeset
|
159 |
val boolT = if Data.is_hol then "bool" else "o"; |
515b6020cf5d
experimental code to reduce the amount of type information in blast
paulson
parents:
15786
diff
changeset
|
160 |
val Trueprop = Term.Const("Trueprop", Type(boolT,[])-->propT); |
2854 | 161 |
fun mk_tprop P = Term.$ (Trueprop, P); |
162 |
||
163 |
fun isTrueprop (Term.Const("Trueprop",_)) = true |
|
164 |
| isTrueprop _ = false; |
|
165 |
||
166 |
||
4065 | 167 |
(*** Dealing with overloaded constants ***) |
2854 | 168 |
|
4065 | 169 |
(*alist is a map from TVar names to Vars. We need to unify the TVars |
170 |
faithfully in order to track overloading*) |
|
16774
515b6020cf5d
experimental code to reduce the amount of type information in blast
paulson
parents:
15786
diff
changeset
|
171 |
fun fromType alist (Term.Type(a,Ts)) = list_comb (Const a, map (fromType alist) Ts) |
4065 | 172 |
| fromType alist (Term.TFree(a,_)) = Free a |
173 |
| fromType alist (Term.TVar (ixn,_)) = |
|
17271 | 174 |
(case (AList.lookup (op =) (!alist) ixn) of |
15531 | 175 |
NONE => let val t' = Var(ref NONE) |
4065 | 176 |
in alist := (ixn, t') :: !alist; t' |
177 |
end |
|
15531 | 178 |
| SOME v => v) |
2854 | 179 |
|
16774
515b6020cf5d
experimental code to reduce the amount of type information in blast
paulson
parents:
15786
diff
changeset
|
180 |
(*Definitions of the theory in which blast is initialized.*) |
515b6020cf5d
experimental code to reduce the amount of type information in blast
paulson
parents:
15786
diff
changeset
|
181 |
val curr_defs = ref Defs.empty; |
2854 | 182 |
|
13550 | 183 |
(*Convert a Term.Const to a Blast.Const or Blast.TConst, |
184 |
converting its type to a Blast.term in the latter case. |
|
16774
515b6020cf5d
experimental code to reduce the amount of type information in blast
paulson
parents:
15786
diff
changeset
|
185 |
For efficiency, Const is used for FOL and for the logical constants. |
515b6020cf5d
experimental code to reduce the amount of type information in blast
paulson
parents:
15786
diff
changeset
|
186 |
We can't use it for all non-overloaded operators because some preservation |
515b6020cf5d
experimental code to reduce the amount of type information in blast
paulson
parents:
15786
diff
changeset
|
187 |
of type information is necessary to prevent PROOF FAILED elsewhere.*) |
13550 | 188 |
fun fromConst alist (a,T) = |
16976 | 189 |
if not Data.is_hol orelse a mem_string ["All","Ex","all"] orelse |
190 |
Defs.monomorphic (!curr_defs) a then Const a |
|
191 |
else TConst(a, fromType alist T); |
|
2854 | 192 |
|
193 |
||
194 |
(*Tests whether 2 terms are alpha-convertible; chases instantiations*) |
|
195 |
fun (Const a) aconv (Const b) = a=b |
|
4065 | 196 |
| (TConst (a,ta)) aconv (TConst (b,tb)) = a=b andalso ta aconv tb |
2854 | 197 |
| (Skolem (a,_)) aconv (Skolem (b,_)) = a=b (*arglists must then be equal*) |
198 |
| (Free a) aconv (Free b) = a=b |
|
15531 | 199 |
| (Var(ref(SOME t))) aconv u = t aconv u |
200 |
| t aconv (Var(ref(SOME u))) = t aconv u |
|
2854 | 201 |
| (Var v) aconv (Var w) = v=w (*both Vars are un-assigned*) |
202 |
| (Bound i) aconv (Bound j) = i=j |
|
203 |
| (Abs(_,t)) aconv (Abs(_,u)) = t aconv u |
|
204 |
| (f$t) aconv (g$u) = (f aconv g) andalso (t aconv u) |
|
205 |
| _ aconv _ = false; |
|
206 |
||
207 |
||
208 |
fun mem_term (_, []) = false |
|
209 |
| mem_term (t, t'::ts) = t aconv t' orelse mem_term(t,ts); |
|
210 |
||
211 |
fun ins_term(t,ts) = if mem_term(t,ts) then ts else t :: ts; |
|
212 |
||
213 |
fun mem_var (v: term option ref, []) = false |
|
214 |
| mem_var (v, v'::vs) = v=v' orelse mem_var(v,vs); |
|
215 |
||
216 |
fun ins_var(v,vs) = if mem_var(v,vs) then vs else v :: vs; |
|
217 |
||
218 |
||
219 |
(** Vars **) |
|
220 |
||
221 |
(*Accumulates the Vars in the term, suppressing duplicates*) |
|
222 |
fun add_term_vars (Skolem(a,args), vars) = add_vars_vars(args,vars) |
|
15531 | 223 |
| add_term_vars (Var (v as ref NONE), vars) = ins_var (v, vars) |
224 |
| add_term_vars (Var (ref (SOME u)), vars) = add_term_vars(u,vars) |
|
4065 | 225 |
| add_term_vars (TConst (_,t), vars) = add_term_vars(t,vars) |
2854 | 226 |
| add_term_vars (Abs (_,body), vars) = add_term_vars(body,vars) |
227 |
| add_term_vars (f$t, vars) = add_term_vars (f, add_term_vars(t, vars)) |
|
228 |
| add_term_vars (_, vars) = vars |
|
229 |
(*Term list version. [The fold functionals are slow]*) |
|
230 |
and add_terms_vars ([], vars) = vars |
|
231 |
| add_terms_vars (t::ts, vars) = add_terms_vars (ts, add_term_vars(t,vars)) |
|
232 |
(*Var list version.*) |
|
233 |
and add_vars_vars ([], vars) = vars |
|
15531 | 234 |
| add_vars_vars (ref (SOME u) :: vs, vars) = |
2854 | 235 |
add_vars_vars (vs, add_term_vars(u,vars)) |
15531 | 236 |
| add_vars_vars (v::vs, vars) = (*v must be a ref NONE*) |
2854 | 237 |
add_vars_vars (vs, ins_var (v, vars)); |
238 |
||
239 |
||
240 |
(*Chase assignments in "vars"; return a list of unassigned variables*) |
|
241 |
fun vars_in_vars vars = add_vars_vars(vars,[]); |
|
242 |
||
243 |
||
244 |
||
245 |
(*increment a term's non-local bound variables |
|
246 |
inc is increment for bound variables |
|
247 |
lev is level at which a bound variable is considered 'loose'*) |
|
248 |
fun incr_bv (inc, lev, u as Bound i) = if i>=lev then Bound(i+inc) else u |
|
249 |
| incr_bv (inc, lev, Abs(a,body)) = Abs(a, incr_bv(inc,lev+1,body)) |
|
250 |
| incr_bv (inc, lev, f$t) = incr_bv(inc,lev,f) $ incr_bv(inc,lev,t) |
|
251 |
| incr_bv (inc, lev, u) = u; |
|
252 |
||
253 |
fun incr_boundvars 0 t = t |
|
254 |
| incr_boundvars inc t = incr_bv(inc,0,t); |
|
255 |
||
256 |
||
257 |
(*Accumulate all 'loose' bound vars referring to level 'lev' or beyond. |
|
258 |
(Bound 0) is loose at level 0 *) |
|
259 |
fun add_loose_bnos (Bound i, lev, js) = if i<lev then js |
|
260 |
else (i-lev) ins_int js |
|
261 |
| add_loose_bnos (Abs (_,t), lev, js) = add_loose_bnos (t, lev+1, js) |
|
262 |
| add_loose_bnos (f$t, lev, js) = |
|
263 |
add_loose_bnos (f, lev, add_loose_bnos (t, lev, js)) |
|
264 |
| add_loose_bnos (_, _, js) = js; |
|
265 |
||
266 |
fun loose_bnos t = add_loose_bnos (t, 0, []); |
|
267 |
||
268 |
fun subst_bound (arg, t) : term = |
|
269 |
let fun subst (t as Bound i, lev) = |
|
270 |
if i<lev then t (*var is locally bound*) |
|
271 |
else if i=lev then incr_boundvars lev arg |
|
272 |
else Bound(i-1) (*loose: change it*) |
|
273 |
| subst (Abs(a,body), lev) = Abs(a, subst(body,lev+1)) |
|
274 |
| subst (f$t, lev) = subst(f,lev) $ subst(t,lev) |
|
275 |
| subst (t,lev) = t |
|
276 |
in subst (t,0) end; |
|
277 |
||
278 |
||
3101
e8a92f497295
Again "norm" DOES NOT normalize bodies of abstractions
paulson
parents:
3092
diff
changeset
|
279 |
(*Normalize...but not the bodies of ABSTRACTIONS*) |
2854 | 280 |
fun norm t = case t of |
2952 | 281 |
Skolem (a,args) => Skolem(a, vars_in_vars args) |
4065 | 282 |
| TConst(a,aT) => TConst(a, norm aT) |
15531 | 283 |
| (Var (ref NONE)) => t |
284 |
| (Var (ref (SOME u))) => norm u |
|
2854 | 285 |
| (f $ u) => (case norm f of |
3101
e8a92f497295
Again "norm" DOES NOT normalize bodies of abstractions
paulson
parents:
3092
diff
changeset
|
286 |
Abs(_,body) => norm (subst_bound (u, body)) |
e8a92f497295
Again "norm" DOES NOT normalize bodies of abstractions
paulson
parents:
3092
diff
changeset
|
287 |
| nf => nf $ norm u) |
2854 | 288 |
| _ => t; |
289 |
||
290 |
||
291 |
(*Weak (one-level) normalize for use in unification*) |
|
292 |
fun wkNormAux t = case t of |
|
293 |
(Var v) => (case !v of |
|
15531 | 294 |
SOME u => wkNorm u |
295 |
| NONE => t) |
|
2854 | 296 |
| (f $ u) => (case wkNormAux f of |
297 |
Abs(_,body) => wkNorm (subst_bound (u, body)) |
|
298 |
| nf => nf $ u) |
|
2952 | 299 |
| Abs (a,body) => (*eta-contract if possible*) |
300 |
(case wkNormAux body of |
|
301 |
nb as (f $ t) => |
|
302 |
if (0 mem_int loose_bnos f) orelse wkNorm t <> Bound 0 |
|
303 |
then Abs(a,nb) |
|
304 |
else wkNorm (incr_boundvars ~1 f) |
|
3092 | 305 |
| nb => Abs (a,nb)) |
2854 | 306 |
| _ => t |
307 |
and wkNorm t = case head_of t of |
|
308 |
Const _ => t |
|
4065 | 309 |
| TConst _ => t |
2854 | 310 |
| Skolem(a,args) => t |
311 |
| Free _ => t |
|
312 |
| _ => wkNormAux t; |
|
313 |
||
314 |
||
5734
bebd10cb7a8d
occurs check now handles Bound variables (for soundness)
paulson
parents:
5613
diff
changeset
|
315 |
(*Does variable v occur in u? For unification. |
bebd10cb7a8d
occurs check now handles Bound variables (for soundness)
paulson
parents:
5613
diff
changeset
|
316 |
Dangling bound vars are also forbidden.*) |
2854 | 317 |
fun varOccur v = |
5734
bebd10cb7a8d
occurs check now handles Bound variables (for soundness)
paulson
parents:
5613
diff
changeset
|
318 |
let fun occL lev [] = false (*same as (exists occ), but faster*) |
bebd10cb7a8d
occurs check now handles Bound variables (for soundness)
paulson
parents:
5613
diff
changeset
|
319 |
| occL lev (u::us) = occ lev u orelse occL lev us |
bebd10cb7a8d
occurs check now handles Bound variables (for soundness)
paulson
parents:
5613
diff
changeset
|
320 |
and occ lev (Var w) = |
2854 | 321 |
v=w orelse |
15531 | 322 |
(case !w of NONE => false |
323 |
| SOME u => occ lev u) |
|
5734
bebd10cb7a8d
occurs check now handles Bound variables (for soundness)
paulson
parents:
5613
diff
changeset
|
324 |
| occ lev (Skolem(_,args)) = occL lev (map Var args) |
bebd10cb7a8d
occurs check now handles Bound variables (for soundness)
paulson
parents:
5613
diff
changeset
|
325 |
(*ignore TConst, since term variables can't occur in types (?) *) |
bebd10cb7a8d
occurs check now handles Bound variables (for soundness)
paulson
parents:
5613
diff
changeset
|
326 |
| occ lev (Bound i) = lev <= i |
bebd10cb7a8d
occurs check now handles Bound variables (for soundness)
paulson
parents:
5613
diff
changeset
|
327 |
| occ lev (Abs(_,u)) = occ (lev+1) u |
bebd10cb7a8d
occurs check now handles Bound variables (for soundness)
paulson
parents:
5613
diff
changeset
|
328 |
| occ lev (f$u) = occ lev u orelse occ lev f |
bebd10cb7a8d
occurs check now handles Bound variables (for soundness)
paulson
parents:
5613
diff
changeset
|
329 |
| occ lev _ = false; |
bebd10cb7a8d
occurs check now handles Bound variables (for soundness)
paulson
parents:
5613
diff
changeset
|
330 |
in occ 0 end; |
2854 | 331 |
|
332 |
exception UNIFY; |
|
333 |
||
334 |
val trail = ref [] : term option ref list ref; |
|
335 |
val ntrail = ref 0; |
|
336 |
||
337 |
||
338 |
(*Restore the trail to some previous state: for backtracking*) |
|
339 |
fun clearTo n = |
|
3083 | 340 |
while !ntrail<>n do |
15531 | 341 |
(hd(!trail) := NONE; |
2854 | 342 |
trail := tl (!trail); |
343 |
ntrail := !ntrail - 1); |
|
344 |
||
345 |
||
346 |
(*First-order unification with bound variables. |
|
347 |
"vars" is a list of variables local to the rule and NOT to be put |
|
348 |
on the trail (no point in doing so) |
|
349 |
*) |
|
4065 | 350 |
fun unify(vars,t,u) = |
2854 | 351 |
let val n = !ntrail |
352 |
fun update (t as Var v, u) = |
|
353 |
if t aconv u then () |
|
354 |
else if varOccur v u then raise UNIFY |
|
15531 | 355 |
else if mem_var(v, vars) then v := SOME u |
2854 | 356 |
else (*avoid updating Vars in the branch if possible!*) |
357 |
if is_Var u andalso mem_var(dest_Var u, vars) |
|
15531 | 358 |
then dest_Var u := SOME t |
359 |
else (v := SOME u; |
|
2854 | 360 |
trail := v :: !trail; ntrail := !ntrail + 1) |
361 |
fun unifyAux (t,u) = |
|
362 |
case (wkNorm t, wkNorm u) of |
|
363 |
(nt as Var v, nu) => update(nt,nu) |
|
364 |
| (nu, nt as Var v) => update(nt,nu) |
|
4065 | 365 |
| (TConst(a,at), TConst(b,bt)) => if a=b then unifyAux(at,bt) |
366 |
else raise UNIFY |
|
2854 | 367 |
| (Abs(_,t'), Abs(_,u')) => unifyAux(t',u') |
368 |
(*NB: can yield unifiers having dangling Bound vars!*) |
|
369 |
| (f$t', g$u') => (unifyAux(f,g); unifyAux(t',u')) |
|
370 |
| (nt, nu) => if nt aconv nu then () else raise UNIFY |
|
3083 | 371 |
in (unifyAux(t,u); true) handle UNIFY => (clearTo n; false) |
2854 | 372 |
end; |
373 |
||
374 |
||
16774
515b6020cf5d
experimental code to reduce the amount of type information in blast
paulson
parents:
15786
diff
changeset
|
375 |
(*Convert from "real" terms to prototerms; eta-contract. |
515b6020cf5d
experimental code to reduce the amount of type information in blast
paulson
parents:
15786
diff
changeset
|
376 |
Code is similar to fromSubgoal.*) |
4065 | 377 |
fun fromTerm t = |
378 |
let val alistVar = ref [] |
|
379 |
and alistTVar = ref [] |
|
380 |
fun from (Term.Const aT) = fromConst alistTVar aT |
|
2854 | 381 |
| from (Term.Free (a,_)) = Free a |
382 |
| from (Term.Bound i) = Bound i |
|
383 |
| from (Term.Var (ixn,T)) = |
|
17271 | 384 |
(case (AList.lookup (op =) (!alistVar) ixn) of |
15531 | 385 |
NONE => let val t' = Var(ref NONE) |
4065 | 386 |
in alistVar := (ixn, t') :: !alistVar; t' |
2854 | 387 |
end |
15531 | 388 |
| SOME v => v) |
2854 | 389 |
| from (Term.Abs (a,_,u)) = |
390 |
(case from u of |
|
391 |
u' as (f $ Bound 0) => |
|
392 |
if (0 mem_int loose_bnos f) then Abs(a,u') |
|
393 |
else incr_boundvars ~1 f |
|
394 |
| u' => Abs(a,u')) |
|
395 |
| from (Term.$ (f,u)) = from f $ from u |
|
396 |
in from t end; |
|
397 |
||
4065 | 398 |
(*A debugging function: replaces all Vars by dummy Frees for visual inspection |
399 |
of whether they are distinct. Function revert undoes the assignments.*) |
|
400 |
fun instVars t = |
|
12902 | 401 |
let val name = ref "a" |
4065 | 402 |
val updated = ref [] |
403 |
fun inst (TConst(a,t)) = inst t |
|
15531 | 404 |
| inst (Var(v as ref NONE)) = (updated := v :: (!updated); |
405 |
v := SOME (Free ("?" ^ !name)); |
|
12902 | 406 |
name := Symbol.bump_string (!name)) |
4065 | 407 |
| inst (Abs(a,t)) = inst t |
408 |
| inst (f $ u) = (inst f; inst u) |
|
409 |
| inst _ = () |
|
15570 | 410 |
fun revert() = List.app (fn v => v:=NONE) (!updated) |
4065 | 411 |
in inst t; revert end; |
412 |
||
413 |
||
2854 | 414 |
(* A1==>...An==>B goes to [A1,...,An], where B is not an implication *) |
415 |
fun strip_imp_prems (Const"==>" $ (Const"Trueprop" $ A) $ B) = |
|
416 |
A :: strip_imp_prems B |
|
417 |
| strip_imp_prems (Const"==>" $ A $ B) = A :: strip_imp_prems B |
|
418 |
| strip_imp_prems _ = []; |
|
419 |
||
420 |
(* A1==>...An==>B goes to B, where B is not an implication *) |
|
421 |
fun strip_imp_concl (Const"==>" $ A $ B) = strip_imp_concl B |
|
422 |
| strip_imp_concl (Const"Trueprop" $ A) = A |
|
423 |
| strip_imp_concl A = A : term; |
|
424 |
||
425 |
||
426 |
(*** Conversion of Elimination Rules to Tableau Operations ***) |
|
427 |
||
9170 | 428 |
exception ElimBadConcl and ElimBadPrem; |
429 |
||
430 |
(*The conclusion becomes the goal/negated assumption *False*: delete it! |
|
431 |
If we don't find it then the premise is ill-formed and could cause |
|
432 |
PROOF FAILED*) |
|
433 |
fun delete_concl [] = raise ElimBadPrem |
|
15531 | 434 |
| delete_concl (Const "*Goal*" $ (Var (ref (SOME (Const"*False*")))) :: Ps) = |
9170 | 435 |
Ps |
15531 | 436 |
| delete_concl (Const "Not" $ (Var (ref (SOME (Const"*False*")))) :: Ps) = |
9170 | 437 |
Ps |
438 |
| delete_concl (P::Ps) = P :: delete_concl Ps; |
|
2854 | 439 |
|
440 |
fun skoPrem vars (Const "all" $ Abs (_, P)) = |
|
441 |
skoPrem vars (subst_bound (Skolem (gensym "S_", vars), P)) |
|
442 |
| skoPrem vars P = P; |
|
443 |
||
444 |
fun convertPrem t = |
|
9170 | 445 |
delete_concl (mkGoal (strip_imp_concl t) :: strip_imp_prems t); |
2854 | 446 |
|
447 |
(*Expects elimination rules to have a formula variable as conclusion*) |
|
448 |
fun convertRule vars t = |
|
449 |
let val (P::Ps) = strip_imp_prems t |
|
450 |
val Var v = strip_imp_concl t |
|
15531 | 451 |
in v := SOME (Const"*False*"); |
2854 | 452 |
(P, map (convertPrem o skoPrem vars) Ps) |
9170 | 453 |
end |
454 |
handle Bind => raise ElimBadConcl; |
|
2854 | 455 |
|
456 |
||
457 |
(*Like dup_elim, but puts the duplicated major premise FIRST*) |
|
17257
0ab67cb765da
introduced binding priority 1 for linear combinators etc.
haftmann
parents:
16976
diff
changeset
|
458 |
fun rev_dup_elim th = (th RSN (2, revcut_rl)) |> assumption 2 |> Seq.hd; |
2854 | 459 |
|
460 |
||
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
461 |
(*Rotate the assumptions in all new subgoals for the LIFO discipline*) |
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
462 |
local |
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
463 |
(*Count new hyps so that they can be rotated*) |
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
464 |
fun nNewHyps [] = 0 |
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
465 |
| nNewHyps (Const "*Goal*" $ _ :: Ps) = nNewHyps Ps |
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
466 |
| nNewHyps (P::Ps) = 1 + nNewHyps Ps; |
2854 | 467 |
|
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
468 |
fun rot_tac [] i st = Seq.single st |
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
469 |
| rot_tac (0::ks) i st = rot_tac ks (i+1) st |
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
470 |
| rot_tac (k::ks) i st = rot_tac ks (i+1) (rotate_rule (~k) i st); |
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
471 |
in |
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
472 |
fun rot_subgoals_tac (rot, rl) = |
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
473 |
rot_tac (if rot then map nNewHyps rl else []) |
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
474 |
end; |
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
475 |
|
2854 | 476 |
|
2999
fad7cc426242
Penalty for branching instantiations reduced from log3 to log4.
paulson
parents:
2952
diff
changeset
|
477 |
fun TRACE rl tac st i = if !trace then (prth rl; tac st i) else tac st i; |
2854 | 478 |
|
5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset
|
479 |
(*Resolution/matching tactics: if upd then the proof state may be updated. |
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset
|
480 |
Matching makes the tactics more deterministic in the presence of Vars.*) |
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset
|
481 |
fun emtac upd rl = TRACE rl (if upd then etac rl else ematch_tac [rl]); |
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset
|
482 |
fun rmtac upd rl = TRACE rl (if upd then rtac rl else match_tac [rl]); |
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset
|
483 |
|
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset
|
484 |
(*Tableau rule from elimination rule. |
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset
|
485 |
Flag "upd" says that the inference updated the branch. |
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset
|
486 |
Flag "dup" requests duplication of the affected formula.*) |
2854 | 487 |
fun fromRule vars rl = |
4065 | 488 |
let val trl = rl |> rep_thm |> #prop |> fromTerm |> convertRule vars |
5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset
|
489 |
fun tac (upd, dup,rot) i = |
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset
|
490 |
emtac upd (if dup then rev_dup_elim rl else rl) i |
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
491 |
THEN |
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
492 |
rot_subgoals_tac (rot, #2 trl) i |
3244
71b760618f30
Basis library version of type "option" now resides in its own structure Option
paulson
parents:
3101
diff
changeset
|
493 |
in Option.SOME (trl, tac) end |
9170 | 494 |
handle ElimBadPrem => (*reject: prems don't preserve conclusion*) |
495 |
(warning("Ignoring weak elimination rule\n" ^ string_of_thm rl); |
|
496 |
Option.NONE) |
|
497 |
| ElimBadConcl => (*ignore: conclusion is not just a variable*) |
|
498 |
(if !trace then (warning("Ignoring ill-formed elimination rule:\n" ^ |
|
499 |
"conclusion should be a variable\n" ^ string_of_thm rl)) |
|
500 |
else (); |
|
501 |
Option.NONE); |
|
2854 | 502 |
|
503 |
||
3101
e8a92f497295
Again "norm" DOES NOT normalize bodies of abstractions
paulson
parents:
3092
diff
changeset
|
504 |
(*** Conversion of Introduction Rules ***) |
2854 | 505 |
|
506 |
fun convertIntrPrem t = mkGoal (strip_imp_concl t) :: strip_imp_prems t; |
|
507 |
||
508 |
fun convertIntrRule vars t = |
|
509 |
let val Ps = strip_imp_prems t |
|
510 |
val P = strip_imp_concl t |
|
511 |
in (mkGoal P, map (convertIntrPrem o skoPrem vars) Ps) |
|
512 |
end; |
|
513 |
||
5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset
|
514 |
(*Tableau rule from introduction rule. |
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset
|
515 |
Flag "upd" says that the inference updated the branch. |
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset
|
516 |
Flag "dup" requests duplication of the affected formula. |
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset
|
517 |
Since haz rules are now delayed, "dup" is always FALSE for |
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset
|
518 |
introduction rules.*) |
2854 | 519 |
fun fromIntrRule vars rl = |
4065 | 520 |
let val trl = rl |> rep_thm |> #prop |> fromTerm |> convertIntrRule vars |
5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset
|
521 |
fun tac (upd,dup,rot) i = |
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset
|
522 |
rmtac upd (if dup then Data.dup_intr rl else rl) i |
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
523 |
THEN |
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
524 |
rot_subgoals_tac (rot, #2 trl) i |
2854 | 525 |
in (trl, tac) end; |
526 |
||
527 |
||
3030 | 528 |
val dummyVar = Term.Var (("etc",0), dummyT); |
2854 | 529 |
|
530 |
(*Convert from prototerms to ordinary terms with dummy types |
|
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
531 |
Ignore abstractions; identify all Vars; STOP at given depth*) |
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
532 |
fun toTerm 0 _ = dummyVar |
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
533 |
| toTerm d (Const a) = Term.Const (a,dummyT) |
4065 | 534 |
| toTerm d (TConst(a,_)) = Term.Const (a,dummyT) (*no need to convert type*) |
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
535 |
| toTerm d (Skolem(a,_)) = Term.Const (a,dummyT) |
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
536 |
| toTerm d (Free a) = Term.Free (a,dummyT) |
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
537 |
| toTerm d (Bound i) = Term.Bound i |
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
538 |
| toTerm d (Var _) = dummyVar |
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
539 |
| toTerm d (Abs(a,_)) = dummyVar |
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
540 |
| toTerm d (f $ u) = Term.$ (toTerm d f, toTerm (d-1) u); |
2854 | 541 |
|
542 |
||
543 |
fun netMkRules P vars (nps: netpair list) = |
|
544 |
case P of |
|
545 |
(Const "*Goal*" $ G) => |
|
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
546 |
let val pG = mk_tprop (toTerm 2 G) |
2854 | 547 |
val intrs = List.concat |
548 |
(map (fn (inet,_) => Net.unify_term inet pG) |
|
549 |
nps) |
|
11783 | 550 |
in map (fromIntrRule vars o #2) (Tactic.orderlist intrs) end |
2854 | 551 |
| _ => |
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
552 |
let val pP = mk_tprop (toTerm 3 P) |
2854 | 553 |
val elims = List.concat |
554 |
(map (fn (_,enet) => Net.unify_term enet pP) |
|
555 |
nps) |
|
11783 | 556 |
in List.mapPartial (fromRule vars o #2) (Tactic.orderlist elims) end; |
2854 | 557 |
|
3092 | 558 |
|
559 |
(*Pending formulae carry md (may duplicate) flags*) |
|
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
560 |
type branch = |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
561 |
{pairs: ((term*bool) list * (*safe formulae on this level*) |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
562 |
(term*bool) list) list, (*haz formulae on this level*) |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
563 |
lits: term list, (*literals: irreducible formulae*) |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
564 |
vars: term option ref list, (*variables occurring in branch*) |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
565 |
lim: int}; (*resource limit*) |
3092 | 566 |
|
567 |
val fullTrace = ref[] : branch list list ref; |
|
568 |
||
569 |
(*Normalize a branch--for tracing*) |
|
570 |
fun norm2 (G,md) = (norm G, md); |
|
571 |
||
572 |
fun normLev (Gs,Hs) = (map norm2 Gs, map norm2 Hs); |
|
573 |
||
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
574 |
fun normBr {pairs, lits, vars, lim} = |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
575 |
{pairs = map normLev pairs, |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
576 |
lits = map norm lits, |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
577 |
vars = vars, |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
578 |
lim = lim}; |
3092 | 579 |
|
580 |
||
4065 | 581 |
val dummyTVar = Term.TVar(("a",0), []); |
3092 | 582 |
val dummyVar2 = Term.Var(("var",0), dummyT); |
583 |
||
4065 | 584 |
(*convert Blast_tac's type representation to real types for tracing*) |
585 |
fun showType (Free a) = Term.TFree (a,[]) |
|
586 |
| showType (Var _) = dummyTVar |
|
587 |
| showType t = |
|
588 |
(case strip_comb t of |
|
589 |
(Const a, us) => Term.Type(a, map showType us) |
|
590 |
| _ => dummyT); |
|
591 |
||
592 |
(*Display top-level overloading if any*) |
|
15531 | 593 |
fun topType (TConst(a,t)) = SOME (showType t) |
4065 | 594 |
| topType (Abs(a,t)) = topType t |
16774
515b6020cf5d
experimental code to reduce the amount of type information in blast
paulson
parents:
15786
diff
changeset
|
595 |
| topType (f $ u) = (case topType f of NONE => topType u | some => some) |
15531 | 596 |
| topType _ = NONE; |
4065 | 597 |
|
598 |
||
3092 | 599 |
(*Convert from prototerms to ordinary terms with dummy types for tracing*) |
600 |
fun showTerm d (Const a) = Term.Const (a,dummyT) |
|
4065 | 601 |
| showTerm d (TConst(a,_)) = Term.Const (a,dummyT) |
3092 | 602 |
| showTerm d (Skolem(a,_)) = Term.Const (a,dummyT) |
603 |
| showTerm d (Free a) = Term.Free (a,dummyT) |
|
604 |
| showTerm d (Bound i) = Term.Bound i |
|
15531 | 605 |
| showTerm d (Var(ref(SOME u))) = showTerm d u |
606 |
| showTerm d (Var(ref NONE)) = dummyVar2 |
|
3092 | 607 |
| showTerm d (Abs(a,t)) = if d=0 then dummyVar |
608 |
else Term.Abs(a, dummyT, showTerm (d-1) t) |
|
609 |
| showTerm d (f $ u) = if d=0 then dummyVar |
|
610 |
else Term.$ (showTerm d f, showTerm (d-1) u); |
|
611 |
||
4065 | 612 |
fun string_of sign d t = Sign.string_of_term sign (showTerm d t); |
3092 | 613 |
|
4065 | 614 |
fun traceTerm sign t = |
615 |
let val t' = norm t |
|
616 |
val stm = string_of sign 8 t' |
|
617 |
in |
|
618 |
case topType t' of |
|
15531 | 619 |
NONE => stm (*no type to attach*) |
620 |
| SOME T => stm ^ "\t:: " ^ Sign.string_of_typ sign T |
|
4065 | 621 |
end; |
3092 | 622 |
|
623 |
||
624 |
(*Print tracing information at each iteration of prover*) |
|
625 |
fun tracing sign brs = |
|
14984 | 626 |
let fun printPairs (((G,_)::_,_)::_) = immediate_output(traceTerm sign G) |
627 |
| printPairs (([],(H,_)::_)::_) = immediate_output(traceTerm sign H ^ "\t (Unsafe)") |
|
3092 | 628 |
| printPairs _ = () |
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
629 |
fun printBrs (brs0 as {pairs, lits, lim, ...} :: brs) = |
3092 | 630 |
(fullTrace := brs0 :: !fullTrace; |
15570 | 631 |
List.app (fn _ => immediate_output "+") brs; |
14984 | 632 |
immediate_output (" [" ^ Int.toString lim ^ "] "); |
3092 | 633 |
printPairs pairs; |
634 |
writeln"") |
|
635 |
in if !trace then printBrs (map normBr brs) else () |
|
636 |
end; |
|
637 |
||
5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset
|
638 |
fun traceMsg s = if !trace then writeln s else (); |
4065 | 639 |
|
3092 | 640 |
(*Tracing: variables updated in the last branch operation?*) |
4065 | 641 |
fun traceVars sign ntrl = |
642 |
if !trace then |
|
643 |
(case !ntrail-ntrl of |
|
644 |
0 => () |
|
14984 | 645 |
| 1 => immediate_output"\t1 variable UPDATED:" |
646 |
| n => immediate_output("\t" ^ Int.toString n ^ " variables UPDATED:"); |
|
4065 | 647 |
(*display the instantiations themselves, though no variable names*) |
15570 | 648 |
List.app (fn v => immediate_output(" " ^ string_of sign 4 (valOf (!v)))) |
4065 | 649 |
(List.take(!trail, !ntrail-ntrl)); |
650 |
writeln"") |
|
3092 | 651 |
else (); |
652 |
||
653 |
(*Tracing: how many new branches are created?*) |
|
654 |
fun traceNew prems = |
|
655 |
if !trace then |
|
656 |
case length prems of |
|
14984 | 657 |
0 => immediate_output"branch closed by rule" |
658 |
| 1 => immediate_output"branch extended (1 new subgoal)" |
|
659 |
| n => immediate_output("branch split: "^ Int.toString n ^ " new subgoals") |
|
3092 | 660 |
else (); |
661 |
||
662 |
||
663 |
||
2854 | 664 |
(*** Code for handling equality: naive substitution, like hyp_subst_tac ***) |
665 |
||
666 |
(*Replace the ATOMIC term "old" by "new" in t*) |
|
667 |
fun subst_atomic (old,new) t = |
|
15531 | 668 |
let fun subst (Var(ref(SOME u))) = subst u |
2854 | 669 |
| subst (Abs(a,body)) = Abs(a, subst body) |
670 |
| subst (f$t) = subst f $ subst t |
|
671 |
| subst t = if t aconv old then new else t |
|
672 |
in subst t end; |
|
673 |
||
674 |
(*Eta-contract a term from outside: just enough to reduce it to an atom*) |
|
675 |
fun eta_contract_atom (t0 as Abs(a, body)) = |
|
676 |
(case eta_contract2 body of |
|
677 |
f $ Bound 0 => if (0 mem_int loose_bnos f) then t0 |
|
678 |
else eta_contract_atom (incr_boundvars ~1 f) |
|
679 |
| _ => t0) |
|
680 |
| eta_contract_atom t = t |
|
681 |
and eta_contract2 (f$t) = f $ eta_contract_atom t |
|
682 |
| eta_contract2 t = eta_contract_atom t; |
|
683 |
||
684 |
||
685 |
(*When can we safely delete the equality? |
|
686 |
Not if it equates two constants; consider 0=1. |
|
687 |
Not if it resembles x=t[x], since substitution does not eliminate x. |
|
688 |
Not if it resembles ?x=0; another goal could instantiate ?x to Suc(i) |
|
689 |
Prefer to eliminate Bound variables if possible. |
|
690 |
Result: true = use as is, false = reorient first *) |
|
691 |
||
4354
7f4da01bdf0e
Fixed the treatment of substitution for equations, restricting occurrences of
paulson
parents:
4323
diff
changeset
|
692 |
(*Can t occur in u? For substitution. |
7f4da01bdf0e
Fixed the treatment of substitution for equations, restricting occurrences of
paulson
parents:
4323
diff
changeset
|
693 |
Does NOT examine the args of Skolem terms: substitution does not affect them. |
4196
9953c0995b79
Now applies "map negOfGoal" to lits when expanding haz rules.
paulson
parents:
4149
diff
changeset
|
694 |
REFLEXIVE because hyp_subst_tac fails on x=x.*) |
2854 | 695 |
fun substOccur t = |
4354
7f4da01bdf0e
Fixed the treatment of substitution for equations, restricting occurrences of
paulson
parents:
4323
diff
changeset
|
696 |
let (*NO vars are permitted in u except the arguments of t, if it is |
7f4da01bdf0e
Fixed the treatment of substitution for equations, restricting occurrences of
paulson
parents:
4323
diff
changeset
|
697 |
a Skolem term. This ensures that no equations are deleted that could |
7f4da01bdf0e
Fixed the treatment of substitution for equations, restricting occurrences of
paulson
parents:
4323
diff
changeset
|
698 |
be instantiated to a cycle. For example, x=?a is rejected because ?a |
7f4da01bdf0e
Fixed the treatment of substitution for equations, restricting occurrences of
paulson
parents:
4323
diff
changeset
|
699 |
could be instantiated to Suc(x).*) |
7f4da01bdf0e
Fixed the treatment of substitution for equations, restricting occurrences of
paulson
parents:
4323
diff
changeset
|
700 |
val vars = case t of |
7f4da01bdf0e
Fixed the treatment of substitution for equations, restricting occurrences of
paulson
parents:
4323
diff
changeset
|
701 |
Skolem(_,vars) => vars |
7f4da01bdf0e
Fixed the treatment of substitution for equations, restricting occurrences of
paulson
parents:
4323
diff
changeset
|
702 |
| _ => [] |
7f4da01bdf0e
Fixed the treatment of substitution for equations, restricting occurrences of
paulson
parents:
4323
diff
changeset
|
703 |
fun occEq u = (t aconv u) orelse occ u |
15531 | 704 |
and occ (Var(ref(SOME u))) = occEq u |
4354
7f4da01bdf0e
Fixed the treatment of substitution for equations, restricting occurrences of
paulson
parents:
4323
diff
changeset
|
705 |
| occ (Var v) = not (mem_var (v, vars)) |
7f4da01bdf0e
Fixed the treatment of substitution for equations, restricting occurrences of
paulson
parents:
4323
diff
changeset
|
706 |
| occ (Abs(_,u)) = occEq u |
2854 | 707 |
| occ (f$u) = occEq u orelse occEq f |
708 |
| occ (_) = false; |
|
709 |
in occEq end; |
|
710 |
||
3092 | 711 |
exception DEST_EQ; |
712 |
||
713 |
(*Take apart an equality (plain or overloaded). NO constant Trueprop*) |
|
714 |
fun dest_eq (Const "op =" $ t $ u) = |
|
715 |
(eta_contract_atom t, eta_contract_atom u) |
|
4065 | 716 |
| dest_eq (TConst("op =",_) $ t $ u) = |
3092 | 717 |
(eta_contract_atom t, eta_contract_atom u) |
718 |
| dest_eq _ = raise DEST_EQ; |
|
719 |
||
4196
9953c0995b79
Now applies "map negOfGoal" to lits when expanding haz rules.
paulson
parents:
4149
diff
changeset
|
720 |
(*Reject the equality if u occurs in (or equals!) t*) |
2854 | 721 |
fun check (t,u,v) = if substOccur t u then raise DEST_EQ else v; |
722 |
||
723 |
(*IF the goal is an equality with a substitutable variable |
|
724 |
THEN orient that equality ELSE raise exception DEST_EQ*) |
|
3092 | 725 |
fun orientGoal (t,u) = case (t,u) of |
2854 | 726 |
(Skolem _, _) => check(t,u,(t,u)) (*eliminates t*) |
727 |
| (_, Skolem _) => check(u,t,(u,t)) (*eliminates u*) |
|
728 |
| (Free _, _) => check(t,u,(t,u)) (*eliminates t*) |
|
729 |
| (_, Free _) => check(u,t,(u,t)) (*eliminates u*) |
|
730 |
| _ => raise DEST_EQ; |
|
731 |
||
2894 | 732 |
(*Substitute through the branch if an equality goal (else raise DEST_EQ). |
733 |
Moves affected literals back into the branch, but it is not clear where |
|
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
734 |
they should go: this could make proofs fail.*) |
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
735 |
fun equalSubst sign (G, {pairs, lits, vars, lim}) = |
3092 | 736 |
let val (t,u) = orientGoal(dest_eq G) |
737 |
val subst = subst_atomic (t,u) |
|
2854 | 738 |
fun subst2(G,md) = (subst G, md) |
4466
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset
|
739 |
(*substitute throughout list; extract affected formulae*) |
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset
|
740 |
fun subForm ((G,md), (changed, pairs)) = |
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset
|
741 |
let val nG = subst G |
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset
|
742 |
in if nG aconv G then (changed, (G,md)::pairs) |
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset
|
743 |
else ((nG,md)::changed, pairs) |
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
744 |
end |
4466
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset
|
745 |
(*substitute throughout "stack frame"; extract affected formulae*) |
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset
|
746 |
fun subFrame ((Gs,Hs), (changed, frames)) = |
15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15570
diff
changeset
|
747 |
let val (changed', Gs') = foldr subForm (changed, []) Gs |
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15570
diff
changeset
|
748 |
val (changed'', Hs') = foldr subForm (changed', []) Hs |
4466
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset
|
749 |
in (changed'', (Gs',Hs')::frames) end |
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset
|
750 |
(*substitute throughout literals; extract affected ones*) |
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset
|
751 |
fun subLit (lit, (changed, nlits)) = |
2854 | 752 |
let val nlit = subst lit |
4466
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset
|
753 |
in if nlit aconv lit then (changed, nlit::nlits) |
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset
|
754 |
else ((nlit,true)::changed, nlits) |
2854 | 755 |
end |
15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15570
diff
changeset
|
756 |
val (changed, lits') = foldr subLit ([], []) lits |
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15570
diff
changeset
|
757 |
val (changed', pairs') = foldr subFrame (changed, []) pairs |
3092 | 758 |
in if !trace then writeln ("Substituting " ^ traceTerm sign u ^ |
759 |
" for " ^ traceTerm sign t ^ " in branch" ) |
|
760 |
else (); |
|
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
761 |
{pairs = (changed',[])::pairs', (*affected formulas, and others*) |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
762 |
lits = lits', (*unaffected literals*) |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
763 |
vars = vars, |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
764 |
lim = lim} |
2854 | 765 |
end; |
766 |
||
767 |
||
768 |
exception NEWBRANCHES and CLOSEF; |
|
769 |
||
770 |
exception PROVE; |
|
771 |
||
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
772 |
(*Trying eq_contr_tac first INCREASES the effort, slowing reconstruction*) |
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
773 |
val contr_tac = ematch_tac [Data.notE] THEN' |
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
774 |
(eq_assume_tac ORELSE' assume_tac); |
2854 | 775 |
|
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
776 |
val eContr_tac = TRACE Data.notE contr_tac; |
2854 | 777 |
val eAssume_tac = TRACE asm_rl (eq_assume_tac ORELSE' assume_tac); |
778 |
||
779 |
(*Try to unify complementary literals and return the corresponding tactic. *) |
|
3083 | 780 |
fun tryClose (Const"*Goal*" $ G, L) = |
15531 | 781 |
if unify([],G,L) then SOME eAssume_tac else NONE |
3083 | 782 |
| tryClose (G, Const"*Goal*" $ L) = |
15531 | 783 |
if unify([],G,L) then SOME eAssume_tac else NONE |
3083 | 784 |
| tryClose (Const"Not" $ G, L) = |
15531 | 785 |
if unify([],G,L) then SOME eContr_tac else NONE |
3083 | 786 |
| tryClose (G, Const"Not" $ L) = |
15531 | 787 |
if unify([],G,L) then SOME eContr_tac else NONE |
788 |
| tryClose _ = NONE; |
|
2854 | 789 |
|
790 |
||
791 |
(*Were there Skolem terms in the premise? Must NOT chase Vars*) |
|
792 |
fun hasSkolem (Skolem _) = true |
|
793 |
| hasSkolem (Abs (_,body)) = hasSkolem body |
|
794 |
| hasSkolem (f$t) = hasSkolem f orelse hasSkolem t |
|
795 |
| hasSkolem _ = false; |
|
796 |
||
797 |
(*Attach the right "may duplicate" flag to new formulae: if they contain |
|
798 |
Skolem terms then allow duplication.*) |
|
799 |
fun joinMd md [] = [] |
|
800 |
| joinMd md (G::Gs) = (G, hasSkolem G orelse md) :: joinMd md Gs; |
|
801 |
||
2894 | 802 |
(*Convert a Goal to an ordinary Not. Used also in dup_intr, where a goal like |
803 |
Ex(P) is duplicated as the assumption ~Ex(P). *) |
|
804 |
fun negOfGoal (Const"*Goal*" $ G) = negate G |
|
805 |
| negOfGoal G = G; |
|
806 |
||
807 |
fun negOfGoal2 (G,md) = (negOfGoal G, md); |
|
808 |
||
809 |
(*Converts all Goals to Nots in the safe parts of a branch. They could |
|
810 |
have been moved there from the literals list after substitution (equalSubst). |
|
811 |
There can be at most one--this function could be made more efficient.*) |
|
812 |
fun negOfGoals pairs = map (fn (Gs,haz) => (map negOfGoal2 Gs, haz)) pairs; |
|
813 |
||
814 |
(*Tactic. Convert *Goal* to negated assumption in FIRST position*) |
|
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
815 |
fun negOfGoal_tac i = TRACE Data.ccontr (rtac Data.ccontr) i THEN |
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
816 |
rotate_tac ~1 i; |
2894 | 817 |
|
2854 | 818 |
|
819 |
(** Backtracking and Pruning **) |
|
820 |
||
821 |
(*clashVar vars (n,trail) determines whether any of the last n elements |
|
822 |
of "trail" occur in "vars" OR in their instantiations*) |
|
823 |
fun clashVar [] = (fn _ => false) |
|
824 |
| clashVar vars = |
|
825 |
let fun clash (0, _) = false |
|
826 |
| clash (_, []) = false |
|
827 |
| clash (n, v::vs) = exists (varOccur v) vars orelse clash(n-1,vs) |
|
828 |
in clash end; |
|
829 |
||
830 |
||
831 |
(*nbrs = # of branches just prior to closing this one. Delete choice points |
|
832 |
for goals proved by the latest inference, provided NO variables in the |
|
833 |
next branch have been updated.*) |
|
834 |
fun prune (1, nxtVars, choices) = choices (*DON'T prune at very end: allow |
|
835 |
backtracking over bad proofs*) |
|
836 |
| prune (nbrs, nxtVars, choices) = |
|
837 |
let fun traceIt last = |
|
838 |
let val ll = length last |
|
839 |
and lc = length choices |
|
840 |
in if !trace andalso ll<lc then |
|
3083 | 841 |
(writeln("Pruning " ^ Int.toString(lc-ll) ^ " levels"); |
2854 | 842 |
last) |
843 |
else last |
|
844 |
end |
|
845 |
fun pruneAux (last, _, _, []) = last |
|
3083 | 846 |
| pruneAux (last, ntrl, trl, (ntrl',nbrs',exn) :: choices) = |
2854 | 847 |
if nbrs' < nbrs |
848 |
then last (*don't backtrack beyond first solution of goal*) |
|
849 |
else if nbrs' > nbrs then pruneAux (last, ntrl, trl, choices) |
|
850 |
else (* nbrs'=nbrs *) |
|
851 |
if clashVar nxtVars (ntrl-ntrl', trl) then last |
|
852 |
else (*no clashes: can go back at least this far!*) |
|
853 |
pruneAux(choices, ntrl', List.drop(trl, ntrl-ntrl'), |
|
854 |
choices) |
|
855 |
in traceIt (pruneAux (choices, !ntrail, !trail, choices)) end; |
|
856 |
||
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
857 |
fun nextVars ({pairs, lits, vars, lim} :: _) = map Var vars |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
858 |
| nextVars [] = []; |
2854 | 859 |
|
3083 | 860 |
fun backtrack (choices as (ntrl, nbrs, exn)::_) = |
861 |
(if !trace then (writeln ("Backtracking; now there are " ^ |
|
862 |
Int.toString nbrs ^ " branches")) |
|
863 |
else (); |
|
864 |
raise exn) |
|
865 |
| backtrack _ = raise PROVE; |
|
2854 | 866 |
|
2894 | 867 |
(*Add the literal G, handling *Goal* and detecting duplicates.*) |
868 |
fun addLit (Const "*Goal*" $ G, lits) = |
|
869 |
(*New literal is a *Goal*, so change all other Goals to Nots*) |
|
2854 | 870 |
let fun bad (Const"*Goal*" $ _) = true |
871 |
| bad (Const"Not" $ G') = G aconv G' |
|
872 |
| bad _ = false; |
|
873 |
fun change [] = [] |
|
874 |
| change (Const"*Goal*" $ G' :: lits) = |
|
875 |
if G aconv G' then change lits |
|
876 |
else Const"Not" $ G' :: change lits |
|
877 |
| change (Const"Not" $ G' :: lits) = |
|
878 |
if G aconv G' then change lits |
|
879 |
else Const"Not" $ G' :: change lits |
|
880 |
| change (lit::lits) = lit :: change lits |
|
881 |
in |
|
882 |
Const "*Goal*" $ G :: (if exists bad lits then change lits else lits) |
|
883 |
end |
|
884 |
| addLit (G,lits) = ins_term(G, lits) |
|
885 |
||
886 |
||
2952 | 887 |
(*For calculating the "penalty" to assess on a branching factor of n |
888 |
log2 seems a little too severe*) |
|
3083 | 889 |
fun log n = if n<4 then 0 else 1 + log(n div 4); |
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
890 |
|
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
891 |
|
3021
39806db47be9
Loop detection: before expanding a haz formula, see whether it is a duplicate
paulson
parents:
2999
diff
changeset
|
892 |
(*match(t,u) says whether the term u might be an instance of the pattern t |
39806db47be9
Loop detection: before expanding a haz formula, see whether it is a duplicate
paulson
parents:
2999
diff
changeset
|
893 |
Used to detect "recursive" rules such as transitivity*) |
39806db47be9
Loop detection: before expanding a haz formula, see whether it is a duplicate
paulson
parents:
2999
diff
changeset
|
894 |
fun match (Var _) u = true |
4065 | 895 |
| match (Const"*Goal*") (Const"Not") = true |
896 |
| match (Const"Not") (Const"*Goal*") = true |
|
897 |
| match (Const a) (Const b) = (a=b) |
|
898 |
| match (TConst (a,ta)) (TConst (b,tb)) = a=b andalso match ta tb |
|
899 |
| match (Free a) (Free b) = (a=b) |
|
900 |
| match (Bound i) (Bound j) = (i=j) |
|
901 |
| match (Abs(_,t)) (Abs(_,u)) = match t u |
|
902 |
| match (f$t) (g$u) = match f g andalso match t u |
|
903 |
| match t u = false; |
|
3021
39806db47be9
Loop detection: before expanding a haz formula, see whether it is a duplicate
paulson
parents:
2999
diff
changeset
|
904 |
|
39806db47be9
Loop detection: before expanding a haz formula, see whether it is a duplicate
paulson
parents:
2999
diff
changeset
|
905 |
|
4300 | 906 |
(*Branches closed: number of branches closed during the search |
907 |
Branches tried: number of branches created by splitting (counting from 1)*) |
|
908 |
val nclosed = ref 0 |
|
909 |
and ntried = ref 1; |
|
910 |
||
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
911 |
fun printStats (b, start, tacs) = |
4323
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset
|
912 |
if b then |
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset
|
913 |
writeln (endTiming start ^ " for search. Closed: " |
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset
|
914 |
^ Int.toString (!nclosed) ^ |
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
915 |
" tried: " ^ Int.toString (!ntried) ^ |
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
916 |
" tactics: " ^ Int.toString (length tacs)) |
4323
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset
|
917 |
else (); |
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset
|
918 |
|
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset
|
919 |
|
2854 | 920 |
(*Tableau prover based on leanTaP. Argument is a list of branches. Each |
921 |
branch contains a list of unexpanded formulae, a list of literals, and a |
|
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
922 |
bound on unsafe expansions. |
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
923 |
"start" is CPU time at start, for printing search time |
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
924 |
*) |
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
925 |
fun prove (sign, start, cs, brs, cont) = |
4653 | 926 |
let val {safe0_netpair, safep_netpair, haz_netpair, ...} = Data.rep_cs cs |
2854 | 927 |
val safeList = [safe0_netpair, safep_netpair] |
928 |
and hazList = [haz_netpair] |
|
4065 | 929 |
fun prv (tacs, trs, choices, []) = |
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
930 |
(printStats (!trace orelse !stats, start, tacs); |
4323
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset
|
931 |
cont (tacs, trs, choices)) (*all branches closed!*) |
2854 | 932 |
| prv (tacs, trs, choices, |
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
933 |
brs0 as {pairs = ((G,md)::br, haz)::pairs, |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
934 |
lits, vars, lim} :: brs) = |
3917 | 935 |
(*apply a safe rule only (possibly allowing instantiation); |
936 |
defer any haz formulae*) |
|
2854 | 937 |
let exception PRV (*backtrack to precisely this recursion!*) |
938 |
val ntrl = !ntrail |
|
939 |
val nbrs = length brs0 |
|
940 |
val nxtVars = nextVars brs |
|
941 |
val G = norm G |
|
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
942 |
val rules = netMkRules G vars safeList |
2854 | 943 |
(*Make a new branch, decrementing "lim" if instantiations occur*) |
2894 | 944 |
fun newBr (vars',lim') prems = |
945 |
map (fn prem => |
|
946 |
if (exists isGoal prem) |
|
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
947 |
then {pairs = ((joinMd md prem, []) :: |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
948 |
negOfGoals ((br, haz)::pairs)), |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
949 |
lits = map negOfGoal lits, |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
950 |
vars = vars', |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
951 |
lim = lim'} |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
952 |
else {pairs = ((joinMd md prem, []) :: |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
953 |
(br, haz) :: pairs), |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
954 |
lits = lits, |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
955 |
vars = vars', |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
956 |
lim = lim'}) |
2854 | 957 |
prems @ |
958 |
brs |
|
959 |
(*Seek a matching rule. If unifiable then add new premises |
|
960 |
to branch.*) |
|
961 |
fun deeper [] = raise NEWBRANCHES |
|
962 |
| deeper (((P,prems),tac)::grls) = |
|
4065 | 963 |
if unify(add_term_vars(P,[]), P, G) |
3083 | 964 |
then (*P comes from the rule; G comes from the branch.*) |
5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset
|
965 |
let val updated = ntrl < !ntrail (*branch updated*) |
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset
|
966 |
val lim' = if updated |
3083 | 967 |
then lim - (1+log(length rules)) |
968 |
else lim (*discourage branching updates*) |
|
969 |
val vars = vars_in_vars vars |
|
15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15570
diff
changeset
|
970 |
val vars' = foldr add_terms_vars vars prems |
3083 | 971 |
val choices' = (ntrl, nbrs, PRV) :: choices |
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
972 |
val tacs' = (tac(updated,false,true)) |
5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset
|
973 |
:: tacs (*no duplication; rotate*) |
3083 | 974 |
in |
4065 | 975 |
traceNew prems; traceVars sign ntrl; |
3083 | 976 |
(if null prems then (*closed the branch: prune!*) |
4300 | 977 |
(nclosed := !nclosed + 1; |
978 |
prv(tacs', brs0::trs, |
|
979 |
prune (nbrs, nxtVars, choices'), |
|
980 |
brs)) |
|
981 |
else (*prems non-null*) |
|
3083 | 982 |
if lim'<0 (*faster to kill ALL the alternatives*) |
5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset
|
983 |
then (traceMsg"Excessive branching: KILLED"; |
4065 | 984 |
clearTo ntrl; raise NEWBRANCHES) |
3083 | 985 |
else |
4300 | 986 |
(ntried := !ntried + length prems - 1; |
987 |
prv(tacs', brs0::trs, choices', |
|
988 |
newBr (vars',lim') prems))) |
|
3083 | 989 |
handle PRV => |
5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset
|
990 |
if updated then |
3083 | 991 |
(*Backtrack at this level. |
992 |
Reset Vars and try another rule*) |
|
993 |
(clearTo ntrl; deeper grls) |
|
994 |
else (*backtrack to previous level*) |
|
995 |
backtrack choices |
|
996 |
end |
|
997 |
else deeper grls |
|
2854 | 998 |
(*Try to close branch by unifying with head goal*) |
999 |
fun closeF [] = raise CLOSEF |
|
1000 |
| closeF (L::Ls) = |
|
3083 | 1001 |
case tryClose(G,L) of |
15531 | 1002 |
NONE => closeF Ls |
1003 |
| SOME tac => |
|
3083 | 1004 |
let val choices' = |
14984 | 1005 |
(if !trace then (immediate_output"branch closed"; |
4065 | 1006 |
traceVars sign ntrl) |
3083 | 1007 |
else (); |
1008 |
prune (nbrs, nxtVars, |
|
1009 |
(ntrl, nbrs, PRV) :: choices)) |
|
4300 | 1010 |
in nclosed := !nclosed + 1; |
1011 |
prv (tac::tacs, brs0::trs, choices', brs) |
|
3083 | 1012 |
handle PRV => |
1013 |
(*reset Vars and try another literal |
|
1014 |
[this handler is pruned if possible!]*) |
|
1015 |
(clearTo ntrl; closeF Ls) |
|
1016 |
end |
|
11152
32d002362005
Blast bug fix: now always duplicates when applying a haz rule,
paulson
parents:
11119
diff
changeset
|
1017 |
(*Try to unify a queued formula (safe or haz) with head goal*) |
2894 | 1018 |
fun closeFl [] = raise CLOSEF |
1019 |
| closeFl ((br, haz)::pairs) = |
|
1020 |
closeF (map fst br) |
|
1021 |
handle CLOSEF => closeF (map fst haz) |
|
1022 |
handle CLOSEF => closeFl pairs |
|
3083 | 1023 |
in tracing sign brs0; |
4065 | 1024 |
if lim<0 then (traceMsg "Limit reached. "; backtrack choices) |
2854 | 1025 |
else |
4466
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset
|
1026 |
prv (Data.hyp_subst_tac trace :: tacs, |
2854 | 1027 |
brs0::trs, choices, |
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1028 |
equalSubst sign |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1029 |
(G, {pairs = (br,haz)::pairs, |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1030 |
lits = lits, vars = vars, lim = lim}) |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1031 |
:: brs) |
4065 | 1032 |
handle DEST_EQ => closeF lits |
1033 |
handle CLOSEF => closeFl ((br,haz)::pairs) |
|
1034 |
handle CLOSEF => deeper rules |
|
2894 | 1035 |
handle NEWBRANCHES => |
1036 |
(case netMkRules G vars hazList of |
|
4466
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset
|
1037 |
[] => (*there are no plausible haz rules*) |
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1038 |
(traceMsg "moving formula to literals"; |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1039 |
prv (tacs, brs0::trs, choices, |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1040 |
{pairs = (br,haz)::pairs, |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1041 |
lits = addLit(G,lits), |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1042 |
vars = vars, |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1043 |
lim = lim} :: brs)) |
2894 | 1044 |
| _ => (*G admits some haz rules: try later*) |
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1045 |
(traceMsg "moving formula to haz list"; |
4466
305390f23734
Better equality handling in Blast_tac, usingd a new variant of hyp_subst_tac
paulson
parents:
4391
diff
changeset
|
1046 |
prv (if isGoal G then negOfGoal_tac :: tacs |
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1047 |
else tacs, |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1048 |
brs0::trs, |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1049 |
choices, |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1050 |
{pairs = (br, haz@[(negOfGoal G, md)])::pairs, |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1051 |
lits = lits, |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1052 |
vars = vars, |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1053 |
lim = lim} :: brs))) |
2854 | 1054 |
end |
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
1055 |
| prv (tacs, trs, choices, |
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1056 |
{pairs = ([],haz)::(Gs,haz')::pairs, lits, vars, lim} :: brs) = |
2894 | 1057 |
(*no more "safe" formulae: transfer haz down a level*) |
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
1058 |
prv (tacs, trs, choices, |
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1059 |
{pairs = (Gs,haz@haz')::pairs, |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1060 |
lits = lits, |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1061 |
vars = vars, |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1062 |
lim = lim} :: brs) |
2854 | 1063 |
| prv (tacs, trs, choices, |
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1064 |
brs0 as {pairs = [([], (H,md)::Hs)], |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1065 |
lits, vars, lim} :: brs) = |
2894 | 1066 |
(*no safe steps possible at any level: apply a haz rule*) |
2854 | 1067 |
let exception PRV (*backtrack to precisely this recursion!*) |
2894 | 1068 |
val H = norm H |
2854 | 1069 |
val ntrl = !ntrail |
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
1070 |
val rules = netMkRules H vars hazList |
3021
39806db47be9
Loop detection: before expanding a haz formula, see whether it is a duplicate
paulson
parents:
2999
diff
changeset
|
1071 |
(*new premises of haz rules may NOT be duplicated*) |
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
1072 |
fun newPrem (vars,P,dup,lim') prem = |
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
1073 |
let val Gs' = map (fn Q => (Q,false)) prem |
3021
39806db47be9
Loop detection: before expanding a haz formula, see whether it is a duplicate
paulson
parents:
2999
diff
changeset
|
1074 |
and Hs' = if dup then Hs @ [(negOfGoal H, md)] else Hs |
4196
9953c0995b79
Now applies "map negOfGoal" to lits when expanding haz rules.
paulson
parents:
4149
diff
changeset
|
1075 |
and lits' = if (exists isGoal prem) |
9953c0995b79
Now applies "map negOfGoal" to lits when expanding haz rules.
paulson
parents:
4149
diff
changeset
|
1076 |
then map negOfGoal lits |
9953c0995b79
Now applies "map negOfGoal" to lits when expanding haz rules.
paulson
parents:
4149
diff
changeset
|
1077 |
else lits |
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1078 |
in {pairs = if exists (match P) prem then [(Gs',Hs')] |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1079 |
(*Recursive in this premise. Don't make new |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1080 |
"stack frame". New haz premises will end up |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1081 |
at the BACK of the queue, preventing |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1082 |
exclusion of others*) |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1083 |
else [(Gs',[]), ([],Hs')], |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1084 |
lits = lits', |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1085 |
vars = vars, |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1086 |
lim = lim'} |
3021
39806db47be9
Loop detection: before expanding a haz formula, see whether it is a duplicate
paulson
parents:
2999
diff
changeset
|
1087 |
end |
2854 | 1088 |
fun newBr x prems = map (newPrem x) prems @ brs |
1089 |
(*Seek a matching rule. If unifiable then add new premises |
|
1090 |
to branch.*) |
|
1091 |
fun deeper [] = raise NEWBRANCHES |
|
1092 |
| deeper (((P,prems),tac)::grls) = |
|
4065 | 1093 |
if unify(add_term_vars(P,[]), P, H) |
3083 | 1094 |
then |
5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset
|
1095 |
let val updated = ntrl < !ntrail (*branch updated*) |
3083 | 1096 |
val vars = vars_in_vars vars |
15574
b1d1b5bfc464
Removed practically all references to Library.foldr.
skalberg
parents:
15570
diff
changeset
|
1097 |
val vars' = foldr add_terms_vars vars prems |
11152
32d002362005
Blast bug fix: now always duplicates when applying a haz rule,
paulson
parents:
11119
diff
changeset
|
1098 |
(*duplicate H if md permits*) |
32d002362005
Blast bug fix: now always duplicates when applying a haz rule,
paulson
parents:
11119
diff
changeset
|
1099 |
val dup = md (*earlier had "andalso vars' <> vars": |
32d002362005
Blast bug fix: now always duplicates when applying a haz rule,
paulson
parents:
11119
diff
changeset
|
1100 |
duplicate only if the subgoal has new vars*) |
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1101 |
(*any instances of P in the subgoals? |
11152
32d002362005
Blast bug fix: now always duplicates when applying a haz rule,
paulson
parents:
11119
diff
changeset
|
1102 |
NB: boolean "recur" affects tracing only!*) |
3083 | 1103 |
and recur = exists (exists (match P)) prems |
1104 |
val lim' = (*Decrement "lim" extra if updates occur*) |
|
5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset
|
1105 |
if updated then lim - (1+log(length rules)) |
3083 | 1106 |
else lim-1 |
1107 |
(*It is tempting to leave "lim" UNCHANGED if |
|
1108 |
both dup and recur are false. Proofs are |
|
1109 |
found at shallower depths, but looping |
|
1110 |
occurs too often...*) |
|
3917 | 1111 |
val mayUndo = |
1112 |
(*Allowing backtracking from a rule application |
|
1113 |
if other matching rules exist, if the rule |
|
1114 |
updated variables, or if the rule did not |
|
1115 |
introduce new variables. This latter condition |
|
1116 |
means it is not a standard "gamma-rule" but |
|
1117 |
some other form of unsafe rule. Aim is to |
|
1118 |
emulate Fast_tac, which allows all unsafe steps |
|
1119 |
to be undone.*) |
|
1120 |
not(null grls) (*other rules to try?*) |
|
5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset
|
1121 |
orelse updated |
3917 | 1122 |
orelse vars=vars' (*no new Vars?*) |
5481
c41956742c2e
Less deterministic reconstruction: now more robust but perhaps slower
paulson
parents:
5463
diff
changeset
|
1123 |
val tac' = tac(updated, dup, true) |
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1124 |
(*if recur then perhaps shouldn't call rotate_tac: new |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1125 |
formulae should be last, but that's WRONG if the new |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1126 |
formulae are Goals, since they remain in the first |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1127 |
position*) |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1128 |
|
3083 | 1129 |
in |
1130 |
if lim'<0 andalso not (null prems) |
|
1131 |
then (*it's faster to kill ALL the alternatives*) |
|
5343
871b77df79a0
new version, more resistant to PROOF FAILED. Now it distinguishes between
paulson
parents:
4653
diff
changeset
|
1132 |
(traceMsg"Excessive branching: KILLED"; |
4065 | 1133 |
clearTo ntrl; raise NEWBRANCHES) |
3083 | 1134 |
else |
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
1135 |
traceNew prems; |
14984 | 1136 |
if !trace andalso dup then immediate_output" (duplicating)" |
11152
32d002362005
Blast bug fix: now always duplicates when applying a haz rule,
paulson
parents:
11119
diff
changeset
|
1137 |
else (); |
14984 | 1138 |
if !trace andalso recur then immediate_output" (recursive)" |
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
1139 |
else (); |
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
1140 |
traceVars sign ntrl; |
4300 | 1141 |
if null prems then nclosed := !nclosed + 1 |
1142 |
else ntried := !ntried + length prems - 1; |
|
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
1143 |
prv(tac' :: tacs, |
3083 | 1144 |
brs0::trs, |
1145 |
(ntrl, length brs0, PRV) :: choices, |
|
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
1146 |
newBr (vars', P, dup, lim') prems) |
3083 | 1147 |
handle PRV => |
1148 |
if mayUndo |
|
1149 |
then (*reset Vars and try another rule*) |
|
1150 |
(clearTo ntrl; deeper grls) |
|
1151 |
else (*backtrack to previous level*) |
|
1152 |
backtrack choices |
|
1153 |
end |
|
1154 |
else deeper grls |
|
1155 |
in tracing sign brs0; |
|
4065 | 1156 |
if lim<1 then (traceMsg "Limit reached. "; backtrack choices) |
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
1157 |
else deeper rules |
2854 | 1158 |
handle NEWBRANCHES => |
2894 | 1159 |
(*cannot close branch: move H to literals*) |
2854 | 1160 |
prv (tacs, brs0::trs, choices, |
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1161 |
{pairs = [([], Hs)], |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1162 |
lits = H::lits, |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1163 |
vars = vars, |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1164 |
lim = lim} :: brs) |
2854 | 1165 |
end |
1166 |
| prv (tacs, trs, choices, _ :: brs) = backtrack choices |
|
12346 | 1167 |
in prv ([], [], [(!ntrail, length brs, PROVE)], brs) end; |
2854 | 1168 |
|
1169 |
||
2883 | 1170 |
(*Construct an initial branch.*) |
2854 | 1171 |
fun initBranch (ts,lim) = |
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1172 |
{pairs = [(map (fn t => (t,true)) ts, [])], |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1173 |
lits = [], |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1174 |
vars = add_terms_vars (ts,[]), |
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1175 |
lim = lim}; |
2854 | 1176 |
|
1177 |
||
1178 |
(*** Conversion & Skolemization of the Isabelle proof state ***) |
|
1179 |
||
1180 |
(*Make a list of all the parameters in a subgoal, even if nested*) |
|
1181 |
local open Term |
|
1182 |
in |
|
1183 |
fun discard_foralls (Const("all",_)$Abs(a,T,t)) = discard_foralls t |
|
1184 |
| discard_foralls t = t; |
|
1185 |
end; |
|
1186 |
||
1187 |
||
1188 |
(*List of variables not appearing as arguments to the given parameter*) |
|
1189 |
fun getVars [] i = [] |
|
1190 |
| getVars ((_,(v,is))::alist) i = |
|
1191 |
if i mem is then getVars alist i |
|
1192 |
else v :: getVars alist i; |
|
1193 |
||
4233
85d004a96b98
Rationalized error handling: if low-level tactic (depth_tac) cannot accept the
paulson
parents:
4196
diff
changeset
|
1194 |
exception TRANS of string; |
2854 | 1195 |
|
4233
85d004a96b98
Rationalized error handling: if low-level tactic (depth_tac) cannot accept the
paulson
parents:
4196
diff
changeset
|
1196 |
(*Translation of a subgoal: Skolemize all parameters*) |
4065 | 1197 |
fun fromSubgoal t = |
1198 |
let val alistVar = ref [] |
|
1199 |
and alistTVar = ref [] |
|
2854 | 1200 |
fun hdvar ((ix,(v,is))::_) = v |
1201 |
fun from lev t = |
|
1202 |
let val (ht,ts) = Term.strip_comb t |
|
1203 |
fun apply u = list_comb (u, map (from lev) ts) |
|
1204 |
fun bounds [] = [] |
|
1205 |
| bounds (Term.Bound i::ts) = |
|
4233
85d004a96b98
Rationalized error handling: if low-level tactic (depth_tac) cannot accept the
paulson
parents:
4196
diff
changeset
|
1206 |
if i<lev then raise TRANS |
85d004a96b98
Rationalized error handling: if low-level tactic (depth_tac) cannot accept the
paulson
parents:
4196
diff
changeset
|
1207 |
"Function unknown's argument not a parameter" |
2854 | 1208 |
else i-lev :: bounds ts |
4233
85d004a96b98
Rationalized error handling: if low-level tactic (depth_tac) cannot accept the
paulson
parents:
4196
diff
changeset
|
1209 |
| bounds ts = raise TRANS |
85d004a96b98
Rationalized error handling: if low-level tactic (depth_tac) cannot accept the
paulson
parents:
4196
diff
changeset
|
1210 |
"Function unknown's argument not a bound variable" |
2854 | 1211 |
in |
1212 |
case ht of |
|
4065 | 1213 |
Term.Const aT => apply (fromConst alistTVar aT) |
2854 | 1214 |
| Term.Free (a,_) => apply (Free a) |
1215 |
| Term.Bound i => apply (Bound i) |
|
1216 |
| Term.Var (ix,_) => |
|
17271 | 1217 |
(case (AList.lookup (op =) (!alistVar) ix) of |
15531 | 1218 |
NONE => (alistVar := (ix, (ref NONE, bounds ts)) |
4065 | 1219 |
:: !alistVar; |
1220 |
Var (hdvar(!alistVar))) |
|
15531 | 1221 |
| SOME(v,is) => if is=bounds ts then Var v |
4233
85d004a96b98
Rationalized error handling: if low-level tactic (depth_tac) cannot accept the
paulson
parents:
4196
diff
changeset
|
1222 |
else raise TRANS |
5411 | 1223 |
("Discrepancy among occurrences of " |
4233
85d004a96b98
Rationalized error handling: if low-level tactic (depth_tac) cannot accept the
paulson
parents:
4196
diff
changeset
|
1224 |
^ Syntax.string_of_vname ix)) |
2854 | 1225 |
| Term.Abs (a,_,body) => |
1226 |
if null ts then Abs(a, from (lev+1) body) |
|
4233
85d004a96b98
Rationalized error handling: if low-level tactic (depth_tac) cannot accept the
paulson
parents:
4196
diff
changeset
|
1227 |
else raise TRANS "argument not in normal form" |
2854 | 1228 |
end |
1229 |
||
1230 |
val npars = length (Logic.strip_params t) |
|
1231 |
||
1232 |
(*Skolemize a subgoal from a proof state*) |
|
1233 |
fun skoSubgoal i t = |
|
1234 |
if i<npars then |
|
1235 |
skoSubgoal (i+1) |
|
4065 | 1236 |
(subst_bound (Skolem (gensym "T_", getVars (!alistVar) i), |
2854 | 1237 |
t)) |
1238 |
else t |
|
1239 |
||
1240 |
in skoSubgoal 0 (from 0 (discard_foralls t)) end; |
|
1241 |
||
1242 |
||
16774
515b6020cf5d
experimental code to reduce the amount of type information in blast
paulson
parents:
15786
diff
changeset
|
1243 |
fun initialize thy = |
4300 | 1244 |
(fullTrace:=[]; trail := []; ntrail := 0; |
16774
515b6020cf5d
experimental code to reduce the amount of type information in blast
paulson
parents:
15786
diff
changeset
|
1245 |
nclosed := 0; ntried := 1; curr_defs := Theory.defs_of thy); |
4300 | 1246 |
|
1247 |
||
2854 | 1248 |
(*Tactic using tableau engine and proof reconstruction. |
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
1249 |
"start" is CPU time at start, for printing SEARCH time |
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
1250 |
(also prints reconstruction time) |
2854 | 1251 |
"lim" is depth limit.*) |
9486
2df511ebb956
handle actual object-logic rules by atomizing the goal;
wenzelm
parents:
9170
diff
changeset
|
1252 |
fun timing_depth_tac start cs lim i st0 = |
16774
515b6020cf5d
experimental code to reduce the amount of type information in blast
paulson
parents:
15786
diff
changeset
|
1253 |
let val st = (initialize (theory_of_thm st0); ObjectLogic.atomize_goal i st0); |
9486
2df511ebb956
handle actual object-logic rules by atomizing the goal;
wenzelm
parents:
9170
diff
changeset
|
1254 |
val {sign,...} = rep_thm st |
4323
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset
|
1255 |
val skoprem = fromSubgoal (List.nth(prems_of st, i-1)) |
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset
|
1256 |
val hyps = strip_imp_prems skoprem |
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset
|
1257 |
and concl = strip_imp_concl skoprem |
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset
|
1258 |
fun cont (tacs,_,choices) = |
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset
|
1259 |
let val start = startTiming() |
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset
|
1260 |
in |
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset
|
1261 |
case Seq.pull(EVERY' (rev tacs) i st) of |
15531 | 1262 |
NONE => (writeln ("PROOF FAILED for depth " ^ |
4323
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset
|
1263 |
Int.toString lim); |
16774
515b6020cf5d
experimental code to reduce the amount of type information in blast
paulson
parents:
15786
diff
changeset
|
1264 |
if !trace then error "************************\n" |
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1265 |
else (); |
4323
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset
|
1266 |
backtrack choices) |
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset
|
1267 |
| cell => (if (!trace orelse !stats) |
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset
|
1268 |
then writeln (endTiming start ^ " for reconstruction") |
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset
|
1269 |
else (); |
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset
|
1270 |
Seq.make(fn()=> cell)) |
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset
|
1271 |
end |
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
1272 |
in prove (sign, start, cs, [initBranch (mkGoal concl :: hyps, lim)], cont) |
4323
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset
|
1273 |
end |
16774
515b6020cf5d
experimental code to reduce the amount of type information in blast
paulson
parents:
15786
diff
changeset
|
1274 |
handle PROVE => Seq.empty; |
2854 | 1275 |
|
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
1276 |
(*Public version with fixed depth*) |
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
1277 |
fun depth_tac cs lim i st = timing_depth_tac (startTiming()) cs lim i st; |
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
1278 |
|
15162
670ab8497818
depth limit (previously hard-coded with a value of 20) made a reference
webertj
parents:
14984
diff
changeset
|
1279 |
val depth_limit = ref 20; |
670ab8497818
depth limit (previously hard-coded with a value of 20) made a reference
webertj
parents:
14984
diff
changeset
|
1280 |
|
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
1281 |
fun blast_tac cs i st = |
15162
670ab8497818
depth limit (previously hard-coded with a value of 20) made a reference
webertj
parents:
14984
diff
changeset
|
1282 |
((DEEPEN (1, !depth_limit) (timing_depth_tac (startTiming()) cs) 0) i |
5463
a5479f5cd482
Allows more backtracking in proof reconstruction, making it slower but more
paulson
parents:
5411
diff
changeset
|
1283 |
THEN flexflex_tac) st |
14466 | 1284 |
handle TRANS s => |
1285 |
((if !trace then warning ("blast: " ^ s) else ()); |
|
1286 |
Seq.empty); |
|
2854 | 1287 |
|
4078 | 1288 |
fun Blast_tac i = blast_tac (Data.claset()) i; |
2854 | 1289 |
|
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
1290 |
|
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
1291 |
(*** For debugging: these apply the prover to a subgoal and return |
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
1292 |
the resulting tactics, trace, etc. ***) |
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
1293 |
|
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
1294 |
(*Translate subgoal i from a proof state*) |
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
1295 |
fun trygl cs lim i = |
16774
515b6020cf5d
experimental code to reduce the amount of type information in blast
paulson
parents:
15786
diff
changeset
|
1296 |
let val st = topthm() |
515b6020cf5d
experimental code to reduce the amount of type information in blast
paulson
parents:
15786
diff
changeset
|
1297 |
val {sign,...} = rep_thm st |
515b6020cf5d
experimental code to reduce the amount of type information in blast
paulson
parents:
15786
diff
changeset
|
1298 |
val skoprem = (initialize (theory_of_thm st); |
515b6020cf5d
experimental code to reduce the amount of type information in blast
paulson
parents:
15786
diff
changeset
|
1299 |
fromSubgoal (List.nth(prems_of st, i-1))) |
515b6020cf5d
experimental code to reduce the amount of type information in blast
paulson
parents:
15786
diff
changeset
|
1300 |
val hyps = strip_imp_prems skoprem |
515b6020cf5d
experimental code to reduce the amount of type information in blast
paulson
parents:
15786
diff
changeset
|
1301 |
and concl = strip_imp_concl skoprem |
515b6020cf5d
experimental code to reduce the amount of type information in blast
paulson
parents:
15786
diff
changeset
|
1302 |
in timeap prove (sign, startTiming(), cs, |
515b6020cf5d
experimental code to reduce the amount of type information in blast
paulson
parents:
15786
diff
changeset
|
1303 |
[initBranch (mkGoal concl :: hyps, lim)], I) |
515b6020cf5d
experimental code to reduce the amount of type information in blast
paulson
parents:
15786
diff
changeset
|
1304 |
end |
515b6020cf5d
experimental code to reduce the amount of type information in blast
paulson
parents:
15786
diff
changeset
|
1305 |
handle Subscript => error("There is no subgoal " ^ Int.toString i); |
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
1306 |
|
4078 | 1307 |
fun Trygl lim i = trygl (Data.claset()) lim i; |
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
1308 |
|
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
1309 |
(*Read a string to make an initial, singleton branch*) |
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
1310 |
fun readGoal sign s = read_cterm sign (s,propT) |> |
4065 | 1311 |
term_of |> fromTerm |> rand |> mkGoal; |
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
1312 |
|
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
1313 |
fun tryInThy thy lim s = |
16774
515b6020cf5d
experimental code to reduce the amount of type information in blast
paulson
parents:
15786
diff
changeset
|
1314 |
(initialize thy; |
6391 | 1315 |
timeap prove (Theory.sign_of thy, |
4391
cc3e8453d7f0
More deterministic and therefore faster (sometimes) proof reconstruction
paulson
parents:
4354
diff
changeset
|
1316 |
startTiming(), |
4323
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset
|
1317 |
Data.claset(), |
6391 | 1318 |
[initBranch ([readGoal (Theory.sign_of thy) s], lim)], |
4323
561242f8606b
Printing of statistics including time for search & reconstruction
paulson
parents:
4300
diff
changeset
|
1319 |
I)); |
2924
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
1320 |
|
af506c35b4ed
Control over excessive branching by applying a log2 penalty
paulson
parents:
2894
diff
changeset
|
1321 |
|
5926 | 1322 |
(** method setup **) |
1323 |
||
7559 | 1324 |
fun blast_args m = |
11152
32d002362005
Blast bug fix: now always duplicates when applying a haz rule,
paulson
parents:
11119
diff
changeset
|
1325 |
Method.bang_sectioned_args' |
32d002362005
Blast bug fix: now always duplicates when applying a haz rule,
paulson
parents:
11119
diff
changeset
|
1326 |
Data.cla_modifiers (Scan.lift (Scan.option Args.nat)) m; |
7155 | 1327 |
|
15531 | 1328 |
fun blast_meth NONE = Data.cla_meth' blast_tac |
1329 |
| blast_meth (SOME lim) = Data.cla_meth' (fn cs => depth_tac cs lim); |
|
7155 | 1330 |
|
11152
32d002362005
Blast bug fix: now always duplicates when applying a haz rule,
paulson
parents:
11119
diff
changeset
|
1331 |
val setup = [Method.add_methods [("blast", blast_args blast_meth, |
32d002362005
Blast bug fix: now always duplicates when applying a haz rule,
paulson
parents:
11119
diff
changeset
|
1332 |
"tableau prover")]]; |
5926 | 1333 |
|
1334 |
||
2854 | 1335 |
end; |