src/Pure/tactic.ML
author lcp
Tue Jan 18 15:57:40 1994 +0100 (1994-01-18)
changeset 230 ec8a2b6aa8a7
parent 214 ed6a3e2b1a33
child 270 d506ea00c825
permissions -rw-r--r--
Many other files modified as follows:

s|Sign.cterm|cterm|g
s|Sign.ctyp|ctyp|g
s|Sign.rep_cterm|rep_cterm|g
s|Sign.rep_ctyp|rep_ctyp|g
s|Sign.pprint_cterm|pprint_cterm|g
s|Sign.pprint_ctyp|pprint_ctyp|g
s|Sign.string_of_cterm|string_of_cterm|g
s|Sign.string_of_ctyp|string_of_ctyp|g
s|Sign.term_of|term_of|g
s|Sign.typ_of|typ_of|g
s|Sign.read_cterm|read_cterm|g
s|Sign.read_insts|read_insts|g
s|Sign.cfun|cterm_fun|g
     1 (*  Title: 	tactic
     2     ID:         $Id$
     3     Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
     4     Copyright   1991  University of Cambridge
     5 
     6 Tactics 
     7 *)
     8 
     9 signature TACTIC =
    10 sig
    11   structure Tactical: TACTICAL and Net: NET
    12   local open Tactical Tactical.Thm Net
    13   in
    14   val ares_tac: thm list -> int -> tactic
    15   val asm_rewrite_goal_tac:
    16         bool*bool -> (meta_simpset -> tactic) -> meta_simpset -> int -> tactic
    17   val assume_tac: int -> tactic
    18   val atac: int ->tactic
    19   val bimatch_from_nets_tac: (int*(bool*thm)) net * (int*(bool*thm)) net -> int -> tactic
    20   val bimatch_tac: (bool*thm)list -> int -> tactic
    21   val biresolve_from_nets_tac: (int*(bool*thm)) net * (int*(bool*thm)) net -> int -> tactic
    22   val biresolve_tac: (bool*thm)list -> int -> tactic
    23   val build_net: thm list -> (int*thm) net
    24   val build_netpair: (bool*thm)list -> (int*(bool*thm)) net * (int*(bool*thm)) net
    25   val compose_inst_tac: (string*string)list -> (bool*thm*int) -> int -> tactic
    26   val compose_tac: (bool * thm * int) -> int -> tactic 
    27   val cut_facts_tac: thm list -> int -> tactic
    28   val dmatch_tac: thm list -> int -> tactic
    29   val dresolve_tac: thm list -> int -> tactic
    30   val dres_inst_tac: (string*string)list -> thm -> int -> tactic   
    31   val dtac: thm -> int ->tactic
    32   val etac: thm -> int ->tactic
    33   val eq_assume_tac: int -> tactic   
    34   val ematch_tac: thm list -> int -> tactic
    35   val eresolve_tac: thm list -> int -> tactic
    36   val eres_inst_tac: (string*string)list -> thm -> int -> tactic   
    37   val filter_thms: (term*term->bool) -> int*term*thm list -> thm list
    38   val filt_resolve_tac: thm list -> int -> int -> tactic
    39   val flexflex_tac: tactic
    40   val fold_goals_tac: thm list -> tactic
    41   val fold_tac: thm list -> tactic
    42   val forward_tac: thm list -> int -> tactic   
    43   val forw_inst_tac: (string*string)list -> thm -> int -> tactic
    44   val is_fact: thm -> bool
    45   val lessb: (bool * thm) * (bool * thm) -> bool
    46   val lift_inst_rule: thm * int * (string*string)list * thm -> thm
    47   val make_elim: thm -> thm
    48   val match_from_net_tac: (int*thm) net -> int -> tactic
    49   val match_tac: thm list -> int -> tactic
    50   val metacut_tac: thm -> int -> tactic   
    51   val net_bimatch_tac: (bool*thm) list -> int -> tactic
    52   val net_biresolve_tac: (bool*thm) list -> int -> tactic
    53   val net_match_tac: thm list -> int -> tactic
    54   val net_resolve_tac: thm list -> int -> tactic
    55   val PRIMITIVE: (thm -> thm) -> tactic  
    56   val PRIMSEQ: (thm -> thm Sequence.seq) -> tactic  
    57   val prune_params_tac: tactic
    58   val rename_tac: string -> int -> tactic
    59   val rename_last_tac: string -> string list -> int -> tactic
    60   val resolve_from_net_tac: (int*thm) net -> int -> tactic
    61   val resolve_tac: thm list -> int -> tactic
    62   val res_inst_tac: (string*string)list -> thm -> int -> tactic   
    63   val rewrite_goals_tac: thm list -> tactic
    64   val rewrite_tac: thm list -> tactic
    65   val rewtac: thm -> tactic
    66   val rtac: thm -> int -> tactic
    67   val rule_by_tactic: tactic -> thm -> thm
    68   val subgoals_of_brl: bool * thm -> int
    69   val subgoal_tac: string -> int -> tactic
    70   val trace_goalno_tac: (int -> tactic) -> int -> tactic
    71   end
    72 end;
    73 
    74 
    75 functor TacticFun (structure Logic: LOGIC and Drule: DRULE and 
    76 		   Tactical: TACTICAL and Net: NET
    77 	  sharing Drule.Thm = Tactical.Thm) : TACTIC = 
    78 struct
    79 structure Tactical = Tactical;
    80 structure Thm = Tactical.Thm;
    81 structure Net = Net;
    82 structure Sequence = Thm.Sequence;
    83 structure Sign = Thm.Sign;
    84 local open Tactical Tactical.Thm Drule
    85 in
    86 
    87 (*Discover what goal is chosen:  SOMEGOAL(trace_goalno_tac tac) *)
    88 fun trace_goalno_tac tf i = Tactic (fn state => 
    89     case Sequence.pull(tapply(tf i, state)) of
    90 	None    => Sequence.null
    91       | seqcell => (prs("Subgoal " ^ string_of_int i ^ " selected\n"); 
    92     			 Sequence.seqof(fn()=> seqcell)));
    93 
    94 fun string_of (a,0) = a
    95   | string_of (a,i) = a ^ "_" ^ string_of_int i;
    96 
    97 (*convert all Vars in a theorem to Frees -- export??*)
    98 fun freeze th =
    99   let val fth = freezeT th
   100       val {prop,sign,...} = rep_thm fth
   101       fun mk_inst (Var(v,T)) = 
   102 	  (cterm_of sign (Var(v,T)),
   103 	   cterm_of sign (Free(string_of v, T)))
   104       val insts = map mk_inst (term_vars prop)
   105   in  instantiate ([],insts) fth  end;
   106 
   107 (*Makes a rule by applying a tactic to an existing rule*)
   108 fun rule_by_tactic (Tactic tf) rl =
   109     case Sequence.pull(tf (freeze (standard rl))) of
   110 	None        => raise THM("rule_by_tactic", 0, [rl])
   111       | Some(rl',_) => standard rl';
   112  
   113 (*** Basic tactics ***)
   114 
   115 (*Makes a tactic whose effect on a state is given by thmfun: thm->thm seq.*)
   116 fun PRIMSEQ thmfun = Tactic (fn state => thmfun state
   117 			                 handle THM _ => Sequence.null);
   118 
   119 (*Makes a tactic whose effect on a state is given by thmfun: thm->thm.*)
   120 fun PRIMITIVE thmfun = PRIMSEQ (Sequence.single o thmfun);
   121 
   122 (*** The following fail if the goal number is out of range:
   123      thus (REPEAT (resolve_tac rules i)) stops once subgoal i disappears. *)
   124 
   125 (*Solve subgoal i by assumption*)
   126 fun assume_tac i = PRIMSEQ (assumption i);
   127 
   128 (*Solve subgoal i by assumption, using no unification*)
   129 fun eq_assume_tac i = PRIMITIVE (eq_assumption i);
   130 
   131 (** Resolution/matching tactics **)
   132 
   133 (*The composition rule/state: no lifting or var renaming.
   134   The arg = (bires_flg, orule, m) ;  see bicompose for explanation.*)
   135 fun compose_tac arg i = PRIMSEQ (bicompose false arg i);
   136 
   137 (*Converts a "destruct" rule like P&Q==>P to an "elimination" rule
   138   like [| P&Q; P==>R |] ==> R *)
   139 fun make_elim rl = zero_var_indexes (rl RS revcut_rl);
   140 
   141 (*Attack subgoal i by resolution, using flags to indicate elimination rules*)
   142 fun biresolve_tac brules i = PRIMSEQ (biresolution false brules i);
   143 
   144 (*Resolution: the simple case, works for introduction rules*)
   145 fun resolve_tac rules = biresolve_tac (map (pair false) rules);
   146 
   147 (*Resolution with elimination rules only*)
   148 fun eresolve_tac rules = biresolve_tac (map (pair true) rules);
   149 
   150 (*Forward reasoning using destruction rules.*)
   151 fun forward_tac rls = resolve_tac (map make_elim rls) THEN' assume_tac;
   152 
   153 (*Like forward_tac, but deletes the assumption after use.*)
   154 fun dresolve_tac rls = eresolve_tac (map make_elim rls);
   155 
   156 (*Shorthand versions: for resolution with a single theorem*)
   157 fun rtac rl = resolve_tac [rl];
   158 fun etac rl = eresolve_tac [rl];
   159 fun dtac rl = dresolve_tac [rl];
   160 val atac = assume_tac;
   161 
   162 (*Use an assumption or some rules ... A popular combination!*)
   163 fun ares_tac rules = assume_tac  ORELSE'  resolve_tac rules;
   164 
   165 (*Matching tactics -- as above, but forbid updating of state*)
   166 fun bimatch_tac brules i = PRIMSEQ (biresolution true brules i);
   167 fun match_tac rules  = bimatch_tac (map (pair false) rules);
   168 fun ematch_tac rules = bimatch_tac (map (pair true) rules);
   169 fun dmatch_tac rls   = ematch_tac (map make_elim rls);
   170 
   171 (*Smash all flex-flex disagreement pairs in the proof state.*)
   172 val flexflex_tac = PRIMSEQ flexflex_rule;
   173 
   174 (*Lift and instantiate a rule wrt the given state and subgoal number *)
   175 fun lift_inst_rule (state, i, sinsts, rule) =
   176 let val {maxidx,sign,...} = rep_thm state
   177     val (_, _, Bi, _) = dest_state(state,i)
   178     val params = Logic.strip_params Bi	        (*params of subgoal i*)
   179     val params = rev(rename_wrt_term Bi params) (*as they are printed*)
   180     val paramTs = map #2 params
   181     and inc = maxidx+1
   182     fun liftvar (Var ((a,j), T)) = Var((a, j+inc), paramTs---> incr_tvar inc T)
   183       | liftvar t = raise TERM("Variable expected", [t]);
   184     fun liftterm t = list_abs_free (params, 
   185 				    Logic.incr_indexes(paramTs,inc) t)
   186     (*Lifts instantiation pair over params*)
   187     fun liftpair (cv,ct) = (cterm_fun liftvar cv, cterm_fun liftterm ct)
   188     fun lifttvar((a,i),ctyp) =
   189 	let val {T,sign} = rep_ctyp ctyp
   190 	in  ((a,i+inc), ctyp_of sign (incr_tvar inc T)) end
   191     val rts = types_sorts rule and (types,sorts) = types_sorts state
   192     fun types'(a,~1) = (case assoc(params,a) of None => types(a,~1) | sm => sm)
   193       | types'(ixn) = types ixn;
   194     val (Tinsts,insts) = read_insts sign rts (types',sorts) sinsts
   195 in instantiate (map lifttvar Tinsts, map liftpair insts)
   196 		(lift_rule (state,i) rule)
   197 end;
   198 
   199 
   200 (*** Resolve after lifting and instantation; may refer to parameters of the
   201      subgoal.  Fails if "i" is out of range.  ***)
   202 
   203 (*compose version: arguments are as for bicompose.*)
   204 fun compose_inst_tac sinsts (bires_flg, rule, nsubgoal) i =
   205   STATE ( fn state => 
   206 	   compose_tac (bires_flg, lift_inst_rule (state, i, sinsts, rule),
   207 			nsubgoal) i
   208 	   handle TERM (msg,_) => (writeln msg;  no_tac)
   209 		| THM  (msg,_,_) => (writeln msg;  no_tac) );
   210 
   211 (*Resolve version*)
   212 fun res_inst_tac sinsts rule i =
   213     compose_inst_tac sinsts (false, rule, nprems_of rule) i;
   214 
   215 (*eresolve (elimination) version*)
   216 fun eres_inst_tac sinsts rule i =
   217     compose_inst_tac sinsts (true, rule, nprems_of rule) i;
   218 
   219 (*For forw_inst_tac and dres_inst_tac: preserve Var indexes of rl.
   220   Fails if rl's major premise contains !! or ==> ; it should not anyway!*)
   221 fun make_elim_preserve rl = 
   222   let val revcut_rl' = lift_rule (rl,1) revcut_rl
   223       val arg = (false, rl, nprems_of rl)
   224       val [th] = Sequence.list_of_s (bicompose false arg 1 revcut_rl')
   225   in  th  end
   226   handle Bind => raise THM("make_elim_preserve", 1, [rl]);
   227 
   228 (*forward version*)
   229 fun forw_inst_tac sinsts rule =
   230     res_inst_tac sinsts (make_elim_preserve rule) THEN' assume_tac;
   231 
   232 (*dresolve version*)
   233 fun dres_inst_tac sinsts rule = eres_inst_tac sinsts (make_elim_preserve rule);
   234 
   235 (*** Applications of cut_rl -- forward reasoning ***)
   236 
   237 (*Used by metacut_tac*)
   238 fun bires_cut_tac arg i =
   239     resolve_tac [cut_rl] i  THEN  biresolve_tac arg (i+1) ;
   240 
   241 (*The conclusion of the rule gets assumed in subgoal i,
   242   while subgoal i+1,... are the premises of the rule.*)
   243 fun metacut_tac rule = bires_cut_tac [(false,rule)];
   244 
   245 (*Recognizes theorems that are not rules, but simple propositions*)
   246 fun is_fact rl =
   247     case prems_of rl of
   248 	[] => true  |  _::_ => false;
   249 
   250 (*"Cut" all facts from theorem list into the goal as assumptions. *)
   251 fun cut_facts_tac ths i =
   252     EVERY (map (fn th => metacut_tac th i) (filter is_fact ths));
   253 
   254 (*Introduce the given proposition as a lemma and subgoal*)
   255 fun subgoal_tac sprop = res_inst_tac [("psi", sprop)] cut_rl;
   256 
   257 
   258 (**** Indexing and filtering of theorems ****)
   259 
   260 (*Returns the list of potentially resolvable theorems for the goal "prem",
   261 	using the predicate  could(subgoal,concl).
   262   Resulting list is no longer than "limit"*)
   263 fun filter_thms could (limit, prem, ths) =
   264   let val pb = Logic.strip_assums_concl prem;   (*delete assumptions*)
   265       fun filtr (limit, []) = []
   266 	| filtr (limit, th::ths) =
   267 	    if limit=0 then  []
   268 	    else if could(pb, concl_of th)  then th :: filtr(limit-1, ths)
   269 	    else filtr(limit,ths)
   270   in  filtr(limit,ths)  end;
   271 
   272 
   273 (*** biresolution and resolution using nets ***)
   274 
   275 (** To preserve the order of the rules, tag them with increasing integers **)
   276 
   277 (*insert tags*)
   278 fun taglist k [] = []
   279   | taglist k (x::xs) = (k,x) :: taglist (k+1) xs;
   280 
   281 (*remove tags and suppress duplicates -- list is assumed sorted!*)
   282 fun untaglist [] = []
   283   | untaglist [(k:int,x)] = [x]
   284   | untaglist ((k,x) :: (rest as (k',x')::_)) =
   285       if k=k' then untaglist rest
   286       else    x :: untaglist rest;
   287 
   288 (*return list elements in original order*)
   289 val orderlist = untaglist o sort (fn(x,y)=> #1 x < #1 y); 
   290 
   291 (*insert one tagged brl into the pair of nets*)
   292 fun insert_kbrl (kbrl as (k,(eres,th)), (inet,enet)) =
   293     if eres then 
   294 	case prems_of th of
   295 	    prem::_ => (inet, Net.insert_term ((prem,kbrl), enet, K false))
   296 	  | [] => error"insert_kbrl: elimination rule with no premises"
   297     else (Net.insert_term ((concl_of th, kbrl), inet, K false), enet);
   298 
   299 (*build a pair of nets for biresolution*)
   300 fun build_netpair brls = 
   301     foldr insert_kbrl (taglist 1 brls, (Net.empty,Net.empty));
   302 
   303 (*biresolution using a pair of nets rather than rules*)
   304 fun biresolution_from_nets_tac match (inet,enet) =
   305   SUBGOAL
   306     (fn (prem,i) =>
   307       let val hyps = Logic.strip_assums_hyp prem
   308           and concl = Logic.strip_assums_concl prem 
   309           val kbrls = Net.unify_term inet concl @
   310                       flat (map (Net.unify_term enet) hyps)
   311       in PRIMSEQ (biresolution match (orderlist kbrls) i) end);
   312 
   313 (*versions taking pre-built nets*)
   314 val biresolve_from_nets_tac = biresolution_from_nets_tac false;
   315 val bimatch_from_nets_tac = biresolution_from_nets_tac true;
   316 
   317 (*fast versions using nets internally*)
   318 val net_biresolve_tac = biresolve_from_nets_tac o build_netpair;
   319 val net_bimatch_tac = bimatch_from_nets_tac o build_netpair;
   320 
   321 (*** Simpler version for resolve_tac -- only one net, and no hyps ***)
   322 
   323 (*insert one tagged rl into the net*)
   324 fun insert_krl (krl as (k,th), net) =
   325     Net.insert_term ((concl_of th, krl), net, K false);
   326 
   327 (*build a net of rules for resolution*)
   328 fun build_net rls = 
   329     foldr insert_krl (taglist 1 rls, Net.empty);
   330 
   331 (*resolution using a net rather than rules; pred supports filt_resolve_tac*)
   332 fun filt_resolution_from_net_tac match pred net =
   333   SUBGOAL
   334     (fn (prem,i) =>
   335       let val krls = Net.unify_term net (Logic.strip_assums_concl prem)
   336       in 
   337 	 if pred krls  
   338          then PRIMSEQ
   339 		(biresolution match (map (pair false) (orderlist krls)) i)
   340          else no_tac
   341       end);
   342 
   343 (*Resolve the subgoal using the rules (making a net) unless too flexible,
   344    which means more than maxr rules are unifiable.      *)
   345 fun filt_resolve_tac rules maxr = 
   346     let fun pred krls = length krls <= maxr
   347     in  filt_resolution_from_net_tac false pred (build_net rules)  end;
   348 
   349 (*versions taking pre-built nets*)
   350 val resolve_from_net_tac = filt_resolution_from_net_tac false (K true);
   351 val match_from_net_tac = filt_resolution_from_net_tac true (K true);
   352 
   353 (*fast versions using nets internally*)
   354 val net_resolve_tac = resolve_from_net_tac o build_net;
   355 val net_match_tac = match_from_net_tac o build_net;
   356 
   357 
   358 (*** For Natural Deduction using (bires_flg, rule) pairs ***)
   359 
   360 (*The number of new subgoals produced by the brule*)
   361 fun subgoals_of_brl (true,rule) = length (prems_of rule) - 1
   362   | subgoals_of_brl (false,rule) = length (prems_of rule);
   363 
   364 (*Less-than test: for sorting to minimize number of new subgoals*)
   365 fun lessb (brl1,brl2) = subgoals_of_brl brl1 < subgoals_of_brl brl2;
   366 
   367 
   368 (*** Meta-Rewriting Tactics ***)
   369 
   370 fun result1 tacf mss thm =
   371   case Sequence.pull(tapply(tacf mss,thm)) of
   372     None => None
   373   | Some(thm,_) => Some(thm);
   374 
   375 (*Rewrite subgoal i only *)
   376 fun asm_rewrite_goal_tac mode prover_tac mss i =
   377       PRIMITIVE(rewrite_goal_rule mode (result1 prover_tac) mss i);
   378 
   379 (*Rewrite throughout proof state. *)
   380 fun rewrite_tac defs = PRIMITIVE(rewrite_rule defs);
   381 
   382 (*Rewrite subgoals only, not main goal. *)
   383 fun rewrite_goals_tac defs = PRIMITIVE (rewrite_goals_rule defs);
   384 
   385 fun rewtac def = rewrite_goals_tac [def];
   386 
   387 
   388 (*** Tactic for folding definitions, handling critical pairs ***)
   389 
   390 (*The depth of nesting in a term*)
   391 fun term_depth (Abs(a,T,t)) = 1 + term_depth t
   392   | term_depth (f$t) = 1 + max [term_depth f, term_depth t]
   393   | term_depth _ = 0;
   394 
   395 val lhs_of_thm = #1 o Logic.dest_equals o #prop o rep_thm;
   396 
   397 (*folding should handle critical pairs!  E.g. K == Inl(0),  S == Inr(Inl(0))
   398   Returns longest lhs first to avoid folding its subexpressions.*)
   399 fun sort_lhs_depths defs =
   400   let val keylist = make_keylist (term_depth o lhs_of_thm) defs
   401       val keys = distinct (sort op> (map #2 keylist))
   402   in  map (keyfilter keylist) keys  end;
   403 
   404 fun fold_tac defs = EVERY 
   405     (map rewrite_tac (sort_lhs_depths (map symmetric defs)));
   406 
   407 fun fold_goals_tac defs = EVERY 
   408     (map rewrite_goals_tac (sort_lhs_depths (map symmetric defs)));
   409 
   410 
   411 (*** Renaming of parameters in a subgoal
   412      Names may contain letters, digits or primes and must be
   413      separated by blanks ***)
   414 
   415 (*Calling this will generate the warning "Same as previous level" since
   416   it affects nothing but the names of bound variables!*)
   417 fun rename_tac str i = 
   418   let val cs = explode str 
   419   in  
   420   if !Logic.auto_rename 
   421   then (writeln"Note: setting Logic.auto_rename := false"; 
   422 	Logic.auto_rename := false)
   423   else ();
   424   case #2 (take_prefix (is_letdig orf is_blank) cs) of
   425       [] => PRIMITIVE (rename_params_rule (scanwords is_letdig cs, i))
   426     | c::_ => error ("Illegal character: " ^ c)
   427   end;
   428 
   429 (*Rename recent parameters using names generated from (a) and the suffixes,
   430   provided the string (a), which represents a term, is an identifier. *)
   431 fun rename_last_tac a sufs i = 
   432   let val names = map (curry op^ a) sufs
   433   in  if Syntax.is_identifier a
   434       then PRIMITIVE (rename_params_rule (names,i))
   435       else all_tac
   436   end;
   437 
   438 (*Prunes all redundant parameters from the proof state by rewriting*)
   439 val prune_params_tac = rewrite_tac [triv_forall_equality];
   440 
   441 end;
   442 end;