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
     5 
     6 For HOL.thy
     7 Derived rules from Appendix of Mike Gordons HOL Report, Cambridge TR 68 
     8 *)
     9 
    10 open HOL;
    11 
    12 
    13 (** Equality **)
    14 section "=";
    15 
    16 qed_goal "sym" HOL.thy "s=t ==> t=s"
    17  (fn prems => [cut_facts_tac prems 1, etac subst 1, rtac refl 1]);
    18 
    19 (*calling "standard" reduces maxidx to 0*)
    20 bind_thm ("ssubst", (sym RS subst));
    21 
    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]);
    25 
    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)) ]);
    37 
    38 
    39 (** Congruence rules for meta-application **)
    40 section "Congruence";
    41 
    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]);
    45 
    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]);
    49 
    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]);
    54 
    55 
    56 (** Equality of booleans -- iff **)
    57 section "iff";
    58 
    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)) ]);
    62 
    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]);
    66 
    67 val iffD1 = sym RS iffD2;
    68 
    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)]);
    72 
    73 
    74 (** True **)
    75 section "True";
    76 
    77 qed_goalw "TrueI" HOL.thy [True_def] "True"
    78   (fn _ => [rtac refl 1]);
    79 
    80 qed_goal "eqTrueI " HOL.thy "P ==> P=True" 
    81  (fn prems => [REPEAT(resolve_tac ([iffI,TrueI]@prems) 1)]);
    82 
    83 qed_goal "eqTrueE" HOL.thy "P=True ==> P" 
    84  (fn prems => [REPEAT(resolve_tac (prems@[TrueI,iffD2]) 1)]);
    85 
    86 
    87 (** Universal quantifier **)
    88 section "!";
    89 
    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]);
    92 
    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]);
    95 
    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)) ]);
    99 
   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)) ]);
   104 
   105 
   106 (** False ** Depends upon spec; it is impossible to do propositional logic
   107              before quantifiers! **)
   108 section "False";
   109 
   110 qed_goalw "FalseE" HOL.thy [False_def] "False ==> P"
   111  (fn [major] => [rtac (major RS spec) 1]);
   112 
   113 qed_goal "False_neq_True" HOL.thy "False=True ==> P"
   114  (fn [prem] => [rtac (prem RS eqTrueE RS FalseE) 1]);
   115 
   116 
   117 (** Negation **)
   118 section "~";
   119 
   120 qed_goalw "notI" HOL.thy [not_def] "(P ==> False) ==> ~P"
   121  (fn prems=> [rtac impI 1, eresolve_tac prems 1]);
   122 
   123 qed_goalw "notE" HOL.thy [not_def] "[| ~P;  P |] ==> R"
   124  (fn prems => [rtac (prems MRS mp RS FalseE) 1]);
   125 
   126 
   127 (** Implication **)
   128 section "-->";
   129 
   130 qed_goal "impE" HOL.thy "[| P-->Q;  P;  Q ==> R |] ==> R"
   131  (fn prems=> [ (REPEAT (resolve_tac (prems@[mp]) 1)) ]);
   132 
   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)) ]);
   136 
   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) ]);
   141 
   142 qed_goal "rev_contrapos" HOL.thy "[| P==>Q; ~Q |] ==> ~P"
   143  (fn [major,minor]=> 
   144   [ (rtac (minor RS contrapos) 1), (etac major 1) ]);
   145 
   146 (* ~(?t = ?s) ==> ~(?s = ?t) *)
   147 bind_thm("not_sym", sym COMP rev_contrapos);
   148 
   149 
   150 (** Existential quantifier **)
   151 section "?";
   152 
   153 qed_goalw "exI" HOL.thy [Ex_def] "P(x) ==> ? x::'a.P(x)"
   154  (fn prems => [rtac selectI 1, resolve_tac prems 1]);
   155 
   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)]);
   159 
   160 
   161 (** Conjunction **)
   162 section "&";
   163 
   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)]);
   167 
   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)]);
   171 
   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)]);
   175 
   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]);
   180 
   181 
   182 (** Disjunction *)
   183 section "|";
   184 
   185 qed_goalw "disjI1" HOL.thy [or_def] "P ==> P|Q"
   186  (fn [prem] => [REPEAT(ares_tac [allI,impI, prem RSN (2,mp)] 1)]);
   187 
   188 qed_goalw "disjI2" HOL.thy [or_def] "Q ==> P|Q"
   189  (fn [prem] => [REPEAT(ares_tac [allI,impI, prem RSN (2,mp)] 1)]);
   190 
   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]);
   195 
   196 
   197 (** CCONTR -- classical logic **)
   198 section "classical logic";
   199 
   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]);
   205 
   206 val ccontr = FalseE RS classical;
   207 
   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) ]);
   212 
   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]);
   218 
   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]);
   224 
   225 (** Unique existence **)
   226 section "?!";
   227 
   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)]);
   232 
   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)]);
   237 
   238 
   239 (** Select: Hilbert's Epsilon-operator **)
   240 section "@";
   241 
   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 ]);
   248 
   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) ]);
   253 
   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]);
   259 
   260 
   261 (** Classical intro rules for disjunction and existential quantifiers *)
   262 section "classical intro rules";
   263 
   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)) ]);
   269 
   270 qed_goal "excluded_middle" HOL.thy "~P | P"
   271  (fn _ => [ (REPEAT (ares_tac [disjCI] 1)) ]);
   272 
   273 (*For disjunctive case analysis*)
   274 fun excluded_middle_tac sP =
   275     res_inst_tac [("Q",sP)] (excluded_middle RS disjE);
   276 
   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))]);
   282 
   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))) ]);
   290 
   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))  ]);
   295 
   296 
   297 (* case distinction *)
   298 
   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]);
   302 
   303 fun case_tac a = res_inst_tac [("P",a)] case_split_thm;
   304 
   305 
   306 (** Standard abbreviations **)
   307 
   308 fun stac th = rtac(th RS ssubst);
   309 fun strip_tac i = REPEAT(resolve_tac [impI,allI] i); 
   310 
   311 (** strip proved goal while preserving !-bound var names **)
   312 
   313 local
   314 
   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;
   320 
   321 in
   322 
   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]));
   329 
   330 fun RSmp th =
   331   (case concl_of th of
   332      _ $ (Const("op -->",_)$_$_) => th RS mp
   333   | _ => raise THM("RSmp",0,[th]));
   334 
   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;
   339 
   340 fun qed_spec_mp name =
   341   let val thm = normalize_thm [RSspec,RSmp] (result())
   342   in bind_thm(name, thm) end;
   343 
   344 end;
   345 
   346 
   347 
   348 (*** Load simpdata.ML to be able to initialize HOL's simpset ***)
   349 
   350 
   351 (** Applying HypsubstFun to generate hyp_subst_tac **)
   352 section "Classical Reasoner";
   353 
   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;
   365 
   366 structure Hypsubst = HypsubstFun(Hypsubst_Data);
   367 open Hypsubst;
   368 
   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;
   378 
   379 structure Classical = ClassicalFun(Classical_Data);
   380 open Classical;
   381 
   382 (*Propositional rules*)
   383 val prop_cs = empty_cs addSIs [refl,TrueI,conjI,disjCI,impI,notI,iffI]
   384                        addSEs [conjE,disjE,impCE,FalseE,iffE];
   385 
   386 (*Quantifier rules*)
   387 val HOL_cs = prop_cs addSIs [allI] addIs [exI,ex1I]
   388                      addSEs [exE,ex1E] addEs [allE];
   389 
   390 
   391 section "Simplifier";
   392 
   393 use     "simpdata.ML";
   394 simpset := HOL_ss;
   395 
   396 
   397 (** Install simpsets and datatypes in theory structure **)
   398 exception SS_DATA of simpset;
   399 
   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;
   403 
   404     fun put (SS_DATA ss) = simpset := ss;
   405 
   406     fun get () = SS_DATA (!simpset);
   407 in add_thydata "HOL"
   408      ("simpset", ThyMethods {merge = merge, put = put, get = get})
   409 end;
   410 
   411 
   412 type dtype_info = {case_const:term, case_rewrites:thm list,
   413                    constructors:term list, nchotomy:thm, case_cong:thm};
   414 
   415 exception DT_DATA of (string * dtype_info) list;
   416 val datatypes = ref [] : (string * dtype_info) list ref;
   417 
   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;
   422 
   423     fun put (DT_DATA ds) = datatypes := ds;
   424 
   425     fun get () = DT_DATA (!datatypes);
   426 in add_thydata "HOL"
   427      ("datatypes", ThyMethods {merge = merge, put = put, get = get})
   428 end;
   429 
   430 
   431 add_thy_reader_file "thy_data.ML";