src/HOL/HOL.ML
 author clasohm Fri Apr 19 11:33:24 1996 +0200 (1996-04-19) changeset 1668 8ead1fe65aad parent 1660 8cb42cd97579 child 1672 2c109cd2fdd0 permissions -rw-r--r--
added Konrad's code for the datatype package
1 (*  Title:      HOL/HOL.ML
2     ID:         \$Id\$
3     Author:     Tobias Nipkow
4     Copyright   1991  University of Cambridge
6 For HOL.thy
7 Derived rules from Appendix of Mike Gordons HOL Report, Cambridge TR 68
8 *)
10 open HOL;
13 (** Equality **)
14 section "=";
16 qed_goal "sym" HOL.thy "s=t ==> t=s"
17  (fn prems => [cut_facts_tac prems 1, etac subst 1, rtac refl 1]);
19 (*calling "standard" reduces maxidx to 0*)
20 bind_thm ("ssubst", (sym RS subst));
22 qed_goal "trans" HOL.thy "[| r=s; s=t |] ==> r=t"
23  (fn prems =>
24         [rtac subst 1, resolve_tac prems 1, resolve_tac prems 1]);
26 (*Useful with eresolve_tac for proving equalties from known equalities.
27         a = b
28         |   |
29         c = d   *)
30 qed_goal "box_equals" HOL.thy
31     "[| a=b;  a=c;  b=d |] ==> c=d"
32  (fn prems=>
33   [ (rtac trans 1),
34     (rtac trans 1),
35     (rtac sym 1),
36     (REPEAT (resolve_tac prems 1)) ]);
39 (** Congruence rules for meta-application **)
40 section "Congruence";
42 (*similar to AP_THM in Gordon's HOL*)
43 qed_goal "fun_cong" HOL.thy "(f::'a=>'b) = g ==> f(x)=g(x)"
44   (fn [prem] => [rtac (prem RS subst) 1, rtac refl 1]);
46 (*similar to AP_TERM in Gordon's HOL and FOL's subst_context*)
47 qed_goal "arg_cong" HOL.thy "x=y ==> f(x)=f(y)"
48  (fn [prem] => [rtac (prem RS subst) 1, rtac refl 1]);
50 qed_goal "cong" HOL.thy
51    "[| f = g; (x::'a) = y |] ==> f(x) = g(y)"
52  (fn [prem1,prem2] =>
53    [rtac (prem1 RS subst) 1, rtac (prem2 RS subst) 1, rtac refl 1]);
56 (** Equality of booleans -- iff **)
57 section "iff";
59 qed_goal "iffI" HOL.thy
60    "[| P ==> Q;  Q ==> P |] ==> P=Q"
61  (fn prems=> [ (REPEAT (ares_tac (prems@[impI, iff RS mp RS mp]) 1)) ]);
63 qed_goal "iffD2" HOL.thy "[| P=Q; Q |] ==> P"
64  (fn prems =>
65         [rtac ssubst 1, resolve_tac prems 1, resolve_tac prems 1]);
67 val iffD1 = sym RS iffD2;
69 qed_goal "iffE" HOL.thy
70     "[| P=Q; [| P --> Q; Q --> P |] ==> R |] ==> R"
71  (fn [p1,p2] => [REPEAT(ares_tac([p1 RS iffD2, p1 RS iffD1, p2, impI])1)]);
74 (** True **)
75 section "True";
77 qed_goalw "TrueI" HOL.thy [True_def] "True"
78   (fn _ => [rtac refl 1]);
80 qed_goal "eqTrueI " HOL.thy "P ==> P=True"
81  (fn prems => [REPEAT(resolve_tac ([iffI,TrueI]@prems) 1)]);
83 qed_goal "eqTrueE" HOL.thy "P=True ==> P"
84  (fn prems => [REPEAT(resolve_tac (prems@[TrueI,iffD2]) 1)]);
87 (** Universal quantifier **)
88 section "!";
90 qed_goalw "allI" HOL.thy [All_def] "(!!x::'a. P(x)) ==> !x. P(x)"
91  (fn prems => [resolve_tac (prems RL [eqTrueI RS ext]) 1]);
93 qed_goalw "spec" HOL.thy [All_def] "! x::'a.P(x) ==> P(x)"
94  (fn prems => [rtac eqTrueE 1, resolve_tac (prems RL [fun_cong]) 1]);
96 qed_goal "allE" HOL.thy "[| !x.P(x);  P(x) ==> R |] ==> R"
97  (fn major::prems=>
98   [ (REPEAT (resolve_tac (prems @ [major RS spec]) 1)) ]);
100 qed_goal "all_dupE" HOL.thy
101     "[| ! x.P(x);  [| P(x); ! x.P(x) |] ==> R |] ==> R"
102  (fn prems =>
103   [ (REPEAT (resolve_tac (prems @ (prems RL [spec])) 1)) ]);
106 (** False ** Depends upon spec; it is impossible to do propositional logic
107              before quantifiers! **)
108 section "False";
110 qed_goalw "FalseE" HOL.thy [False_def] "False ==> P"
111  (fn [major] => [rtac (major RS spec) 1]);
113 qed_goal "False_neq_True" HOL.thy "False=True ==> P"
114  (fn [prem] => [rtac (prem RS eqTrueE RS FalseE) 1]);
117 (** Negation **)
118 section "~";
120 qed_goalw "notI" HOL.thy [not_def] "(P ==> False) ==> ~P"
121  (fn prems=> [rtac impI 1, eresolve_tac prems 1]);
123 qed_goalw "notE" HOL.thy [not_def] "[| ~P;  P |] ==> R"
124  (fn prems => [rtac (prems MRS mp RS FalseE) 1]);
127 (** Implication **)
128 section "-->";
130 qed_goal "impE" HOL.thy "[| P-->Q;  P;  Q ==> R |] ==> R"
131  (fn prems=> [ (REPEAT (resolve_tac (prems@[mp]) 1)) ]);
133 (* Reduces Q to P-->Q, allowing substitution in P. *)
134 qed_goal "rev_mp" HOL.thy "[| P;  P --> Q |] ==> Q"
135  (fn prems=>  [ (REPEAT (resolve_tac (prems@[mp]) 1)) ]);
137 qed_goal "contrapos" HOL.thy "[| ~Q;  P==>Q |] ==> ~P"
138  (fn [major,minor]=>
139   [ (rtac (major RS notE RS notI) 1),
140     (etac minor 1) ]);
142 qed_goal "rev_contrapos" HOL.thy "[| P==>Q; ~Q |] ==> ~P"
143  (fn [major,minor]=>
144   [ (rtac (minor RS contrapos) 1), (etac major 1) ]);
146 (* ~(?t = ?s) ==> ~(?s = ?t) *)
147 bind_thm("not_sym", sym COMP rev_contrapos);
150 (** Existential quantifier **)
151 section "?";
153 qed_goalw "exI" HOL.thy [Ex_def] "P(x) ==> ? x::'a.P(x)"
154  (fn prems => [rtac selectI 1, resolve_tac prems 1]);
156 qed_goalw "exE" HOL.thy [Ex_def]
157   "[| ? x::'a.P(x); !!x. P(x) ==> Q |] ==> Q"
158   (fn prems => [REPEAT(resolve_tac prems 1)]);
161 (** Conjunction **)
162 section "&";
164 qed_goalw "conjI" HOL.thy [and_def] "[| P; Q |] ==> P&Q"
165  (fn prems =>
166   [REPEAT (resolve_tac (prems@[allI,impI]) 1 ORELSE etac (mp RS mp) 1)]);
168 qed_goalw "conjunct1" HOL.thy [and_def] "[| P & Q |] ==> P"
169  (fn prems =>
170    [resolve_tac (prems RL [spec] RL [mp]) 1, REPEAT(ares_tac [impI] 1)]);
172 qed_goalw "conjunct2" HOL.thy [and_def] "[| P & Q |] ==> Q"
173  (fn prems =>
174    [resolve_tac (prems RL [spec] RL [mp]) 1, REPEAT(ares_tac [impI] 1)]);
176 qed_goal "conjE" HOL.thy "[| P&Q;  [| P; Q |] ==> R |] ==> R"
177  (fn prems =>
178          [cut_facts_tac prems 1, resolve_tac prems 1,
179           etac conjunct1 1, etac conjunct2 1]);
182 (** Disjunction *)
183 section "|";
185 qed_goalw "disjI1" HOL.thy [or_def] "P ==> P|Q"
186  (fn [prem] => [REPEAT(ares_tac [allI,impI, prem RSN (2,mp)] 1)]);
188 qed_goalw "disjI2" HOL.thy [or_def] "Q ==> P|Q"
189  (fn [prem] => [REPEAT(ares_tac [allI,impI, prem RSN (2,mp)] 1)]);
191 qed_goalw "disjE" HOL.thy [or_def] "[| P | Q; P ==> R; Q ==> R |] ==> R"
192  (fn [a1,a2,a3] =>
193         [rtac (mp RS mp) 1, rtac spec 1, rtac a1 1,
194          rtac (a2 RS impI) 1, assume_tac 1, rtac (a3 RS impI) 1, assume_tac 1]);
197 (** CCONTR -- classical logic **)
198 section "classical logic";
200 qed_goalw "classical" HOL.thy [not_def]  "(~P ==> P) ==> P"
201  (fn [prem] =>
202    [rtac (True_or_False RS (disjE RS eqTrueE)) 1,  assume_tac 1,
203     rtac (impI RS prem RS eqTrueI) 1,
204     etac subst 1,  assume_tac 1]);
206 val ccontr = FalseE RS classical;
208 (*Double negation law*)
209 qed_goal "notnotD" HOL.thy "~~P ==> P"
210  (fn [major]=>
211   [ (rtac classical 1), (eresolve_tac [major RS notE] 1) ]);
213 qed_goal "contrapos2" HOL.thy "[| Q; ~ P ==> ~ Q |] ==> P" (fn [p1,p2] => [
214 	rtac classical 1,
215 	dtac p2 1,
216 	etac notE 1,
217 	rtac p1 1]);
219 qed_goal "swap2" HOL.thy "[| P;  Q ==> ~ P |] ==> ~ Q" (fn [p1,p2] => [
220 	rtac notI 1,
221 	dtac p2 1,
222 	etac notE 1,
223 	rtac p1 1]);
225 (** Unique existence **)
226 section "?!";
228 qed_goalw "ex1I" HOL.thy [Ex1_def]
229 	    "[| P(a);  !!x. P(x) ==> x=a |] ==> ?! x. P(x)"
230  (fn prems =>
231   [REPEAT (ares_tac (prems@[exI,conjI,allI,impI]) 1)]);
233 qed_goalw "ex1E" HOL.thy [Ex1_def]
234     "[| ?! x.P(x);  !!x. [| P(x);  ! y. P(y) --> y=x |] ==> R |] ==> R"
235  (fn major::prems =>
236   [rtac (major RS exE) 1, REPEAT (etac conjE 1 ORELSE ares_tac prems 1)]);
239 (** Select: Hilbert's Epsilon-operator **)
240 section "@";
242 (*Easier to apply than selectI: conclusion has only one occurrence of P*)
243 qed_goal "selectI2" HOL.thy
244     "[| P(a);  !!x. P(x) ==> Q(x) |] ==> Q(@x.P(x))"
245  (fn prems => [ resolve_tac prems 1,
246                 rtac selectI 1,
247                 resolve_tac prems 1 ]);
249 qed_goal "select_equality" HOL.thy
250     "[| P(a);  !!x. P(x) ==> x=a |] ==> (@x.P(x)) = a"
251  (fn prems => [ rtac selectI2 1,
252                 REPEAT (ares_tac prems 1) ]);
254 qed_goal "select_eq_Ex" HOL.thy "P (@ x. P x) =  (? x. P x)" (fn prems => [
255         rtac iffI 1,
256         etac exI 1,
257         etac exE 1,
258         etac selectI 1]);
261 (** Classical intro rules for disjunction and existential quantifiers *)
262 section "classical intro rules";
264 qed_goal "disjCI" HOL.thy "(~Q ==> P) ==> P|Q"
265  (fn prems=>
266   [ (rtac classical 1),
267     (REPEAT (ares_tac (prems@[disjI1,notI]) 1)),
268     (REPEAT (ares_tac (prems@[disjI2,notE]) 1)) ]);
270 qed_goal "excluded_middle" HOL.thy "~P | P"
271  (fn _ => [ (REPEAT (ares_tac [disjCI] 1)) ]);
273 (*For disjunctive case analysis*)
274 fun excluded_middle_tac sP =
275     res_inst_tac [("Q",sP)] (excluded_middle RS disjE);
277 (*Classical implies (-->) elimination. *)
278 qed_goal "impCE" HOL.thy "[| P-->Q; ~P ==> R; Q ==> R |] ==> R"
279  (fn major::prems=>
280   [ rtac (excluded_middle RS disjE) 1,
281     REPEAT (DEPTH_SOLVE_1 (ares_tac (prems @ [major RS mp]) 1))]);
283 (*Classical <-> elimination. *)
284 qed_goal "iffCE" HOL.thy
285     "[| P=Q;  [| P; Q |] ==> R;  [| ~P; ~Q |] ==> R |] ==> R"
286  (fn major::prems =>
287   [ (rtac (major RS iffE) 1),
288     (REPEAT (DEPTH_SOLVE_1
289         (eresolve_tac ([asm_rl,impCE,notE]@prems) 1))) ]);
291 qed_goal "exCI" HOL.thy "(! x. ~P(x) ==> P(a)) ==> ? x.P(x)"
292  (fn prems=>
293   [ (rtac ccontr 1),
294     (REPEAT (ares_tac (prems@[exI,allI,notI,notE]) 1))  ]);
297 (* case distinction *)
299 qed_goal "case_split_thm" HOL.thy "[| P ==> Q; ~P ==> Q |] ==> Q"
300   (fn [p1,p2] => [cut_facts_tac [excluded_middle] 1, etac disjE 1,
301                   etac p2 1, etac p1 1]);
303 fun case_tac a = res_inst_tac [("P",a)] case_split_thm;
306 (** Standard abbreviations **)
308 fun stac th = rtac(th RS ssubst);
309 fun strip_tac i = REPEAT(resolve_tac [impI,allI] i);
311 (** strip proved goal while preserving !-bound var names **)
313 local
315 (* Use XXX to avoid forall_intr failing because of duplicate variable name *)
316 val myspec = read_instantiate [("P","?XXX")] spec;
317 val _ \$ (_ \$ (vx as Var(_,vxT))) = concl_of myspec;
318 val cvx = cterm_of (#sign(rep_thm myspec)) vx;
319 val aspec = forall_intr cvx myspec;
321 in
323 fun RSspec th =
324   (case concl_of th of
325      _ \$ (Const("All",_) \$ Abs(a,_,_)) =>
326          let val ca = cterm_of (#sign(rep_thm th)) (Var((a,0),vxT))
327          in th RS forall_elim ca aspec end
328   | _ => raise THM("RSspec",0,[th]));
330 fun RSmp th =
331   (case concl_of th of
332      _ \$ (Const("op -->",_)\$_\$_) => th RS mp
333   | _ => raise THM("RSmp",0,[th]));
335 fun normalize_thm funs =
336 let fun trans [] th = th
337       | trans (f::fs) th = (trans funs (f th)) handle THM _ => trans fs th
338 in trans funs end;
340 fun qed_spec_mp name =
341   let val thm = normalize_thm [RSspec,RSmp] (result())
342   in bind_thm(name, thm) end;
344 end;
348 (*** Load simpdata.ML to be able to initialize HOL's simpset ***)
351 (** Applying HypsubstFun to generate hyp_subst_tac **)
352 section "Classical Reasoner";
354 structure Hypsubst_Data =
355   struct
356   structure Simplifier = Simplifier
357   (*Take apart an equality judgement; otherwise raise Match!*)
358   fun dest_eq (Const("Trueprop",_) \$ (Const("op =",_)  \$ t \$ u)) = (t,u);
359   val eq_reflection = eq_reflection
360   val imp_intr = impI
361   val rev_mp = rev_mp
362   val subst = subst
363   val sym = sym
364   end;
366 structure Hypsubst = HypsubstFun(Hypsubst_Data);
367 open Hypsubst;
369 (*** Applying ClassicalFun to create a classical prover ***)
370 structure Classical_Data =
371   struct
372   val sizef     = size_of_thm
373   val mp        = mp
374   val not_elim  = notE
375   val classical = classical
376   val hyp_subst_tacs=[hyp_subst_tac]
377   end;
379 structure Classical = ClassicalFun(Classical_Data);
380 open Classical;
382 (*Propositional rules*)
383 val prop_cs = empty_cs addSIs [refl,TrueI,conjI,disjCI,impI,notI,iffI]
386 (*Quantifier rules*)
387 val HOL_cs = prop_cs addSIs [allI] addIs [exI,ex1I]
391 section "Simplifier";
393 use     "simpdata.ML";
394 simpset := HOL_ss;
397 (** Install simpsets and datatypes in theory structure **)
398 exception SS_DATA of simpset;
400 let fun merge [] = SS_DATA empty_ss
401       | merge ss = let val ss = map (fn SS_DATA x => x) ss;
402                    in SS_DATA (foldl merge_ss (hd ss, tl ss)) end;
404     fun put (SS_DATA ss) = simpset := ss;
406     fun get () = SS_DATA (!simpset);
407 in add_thydata "HOL"
408      ("simpset", ThyMethods {merge = merge, put = put, get = get})
409 end;
412 type dtype_info = {case_const:term, case_rewrites:thm list,
413                    constructors:term list, nchotomy:thm, case_cong:thm};
415 exception DT_DATA of (string * dtype_info) list;
416 val datatypes = ref [] : (string * dtype_info) list ref;
418 let fun merge [] = DT_DATA []
419       | merge ds =
420           let val ds = map (fn DT_DATA x => x) ds;
421           in DT_DATA (foldl (gen_union eq_fst) (hd ds, tl ds)) end;
423     fun put (DT_DATA ds) = datatypes := ds;
425     fun get () = DT_DATA (!datatypes);
426 in add_thydata "HOL"
427      ("datatypes", ThyMethods {merge = merge, put = put, get = get})
428 end;