src/Provers/classical.ML
author lcp
Tue, 12 Jul 1994 18:30:53 +0200
changeset 469 b571d997178d
parent 54 3dea30013b58
child 681 9b02474744ca
permissions -rw-r--r--
chain_tac: deleted; just use etac mp
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
     1
(*  Title: 	Provers/classical
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
     2
    ID:         $Id$
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
     3
    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
     4
    Copyright   1992  University of Cambridge
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
     5
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
     6
Theorem prover for classical reasoning, including predicate calculus, set
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
     7
theory, etc.
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
     8
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
     9
Rules must be classified as intr, elim, safe, hazardous.
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    10
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    11
A rule is unsafe unless it can be applied blindly without harmful results.
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    12
For a rule to be safe, its premises and conclusion should be logically
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    13
equivalent.  There should be no variables in the premises that are not in
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    14
the conclusion.
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    15
*)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    16
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    17
signature CLASSICAL_DATA =
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    18
  sig
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    19
  val mp: thm    		(* [| P-->Q;  P |] ==> Q *)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    20
  val not_elim: thm		(* [| ~P;  P |] ==> R *)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    21
  val swap: thm			(* ~P ==> (~Q ==> P) ==> Q *)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    22
  val sizef : thm -> int	(* size function for BEST_FIRST *)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    23
  val hyp_subst_tacs: (int -> tactic) list
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    24
  end;
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    25
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    26
(*Higher precedence than := facilitates use of references*)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    27
infix 4 addSIs addSEs addSDs addIs addEs addDs;
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    28
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    29
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    30
signature CLASSICAL =
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    31
  sig
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    32
  type claset
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    33
  val empty_cs: claset
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    34
  val addDs : claset * thm list -> claset
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    35
  val addEs : claset * thm list -> claset
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    36
  val addIs : claset * thm list -> claset
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    37
  val addSDs: claset * thm list -> claset
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    38
  val addSEs: claset * thm list -> claset
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    39
  val addSIs: claset * thm list -> claset
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    40
  val print_cs: claset -> unit
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    41
  val rep_claset: claset -> 
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    42
      {safeIs: thm list, safeEs: thm list, hazIs: thm list, hazEs: thm list}
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    43
  val best_tac : claset -> int -> tactic
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    44
  val contr_tac : int -> tactic
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    45
  val eq_mp_tac: int -> tactic
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    46
  val fast_tac : claset -> int -> tactic
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    47
  val joinrules : thm list * thm list -> (bool * thm) list
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    48
  val mp_tac: int -> tactic
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    49
  val safe_tac : claset -> tactic
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    50
  val safe_step_tac : claset -> int -> tactic
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    51
  val slow_step_tac : claset -> int -> tactic
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    52
  val slow_best_tac : claset -> int -> tactic
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    53
  val slow_tac : claset -> int -> tactic
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    54
  val step_tac : claset -> int -> tactic
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    55
  val swapify : thm list -> thm list
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    56
  val swap_res_tac : thm list -> int -> tactic
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    57
  val inst_step_tac : claset -> int -> tactic
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    58
  end;
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    59
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    60
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    61
functor ClassicalFun(Data: CLASSICAL_DATA): CLASSICAL = 
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    62
struct
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    63
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    64
local open Data in
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    65
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    66
(** Useful tactics for classical reasoning **)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    67
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    68
val imp_elim = make_elim mp;
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    69
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    70
(*Solve goal that assumes both P and ~P. *)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    71
val contr_tac = eresolve_tac [not_elim]  THEN'  assume_tac;
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    72
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    73
(*Finds P-->Q and P in the assumptions, replaces implication by Q *)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    74
fun mp_tac i = eresolve_tac ([not_elim,imp_elim]) i  THEN  assume_tac i;
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    75
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    76
(*Like mp_tac but instantiates no variables*)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    77
fun eq_mp_tac i = ematch_tac ([not_elim,imp_elim]) i  THEN  eq_assume_tac i;
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    78
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    79
(*Creates rules to eliminate ~A, from rules to introduce A*)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    80
fun swapify intrs = intrs RLN (2, [swap]);
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    81
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    82
(*Uses introduction rules in the normal way, or on negated assumptions,
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    83
  trying rules in order. *)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    84
fun swap_res_tac rls = 
54
3dea30013b58 classical/swap_res_tac: recoded to allow backtracking
lcp
parents: 0
diff changeset
    85
    let fun addrl (rl,brls) = (false, rl) :: (true, rl RSN (2,swap)) :: brls
3dea30013b58 classical/swap_res_tac: recoded to allow backtracking
lcp
parents: 0
diff changeset
    86
    in  assume_tac 	ORELSE' 
3dea30013b58 classical/swap_res_tac: recoded to allow backtracking
lcp
parents: 0
diff changeset
    87
	contr_tac 	ORELSE' 
3dea30013b58 classical/swap_res_tac: recoded to allow backtracking
lcp
parents: 0
diff changeset
    88
        biresolve_tac (foldr addrl (rls,[]))
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    89
    end;
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    90
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    91
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    92
(*** Classical rule sets ***)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    93
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    94
type netpair = (int*(bool*thm)) Net.net * (int*(bool*thm)) Net.net;
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    95
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    96
datatype claset =
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    97
  CS of {safeIs		: thm list,
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    98
	 safeEs		: thm list,
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
    99
	 hazIs		: thm list,
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   100
	 hazEs		: thm list,
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   101
	 safe0_netpair	: netpair,
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   102
	 safep_netpair	: netpair,
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   103
	 haz_netpair  	: netpair};
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   104
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   105
fun rep_claset (CS{safeIs,safeEs,hazIs,hazEs,...}) = 
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   106
    {safeIs=safeIs, safeEs=safeEs, hazIs=hazIs, hazEs=hazEs};
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   107
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   108
(*For use with biresolve_tac.  Combines intrs with swap to catch negated
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   109
  assumptions; pairs elims with true; sorts. *)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   110
fun joinrules (intrs,elims) =  
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   111
  sort lessb 
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   112
    (map (pair true) (elims @ swapify intrs)  @
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   113
     map (pair false) intrs);
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   114
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   115
(*Make a claset from the four kinds of rules*)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   116
fun make_cs {safeIs,safeEs,hazIs,hazEs} =
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   117
  let val (safe0_brls, safep_brls) = (*0 subgoals vs 1 or more*)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   118
          take_prefix (fn brl => subgoals_of_brl brl=0)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   119
             (joinrules(safeIs, safeEs))
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   120
  in CS{safeIs = safeIs, 
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   121
        safeEs = safeEs,
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   122
	hazIs = hazIs,
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   123
	hazEs = hazEs,
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   124
	safe0_netpair = build_netpair safe0_brls,
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   125
	safep_netpair = build_netpair safep_brls,
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   126
	haz_netpair = build_netpair (joinrules(hazIs, hazEs))}
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   127
  end;
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   128
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   129
(*** Manipulation of clasets ***)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   130
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   131
val empty_cs = make_cs{safeIs=[], safeEs=[], hazIs=[], hazEs=[]};
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   132
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   133
fun print_cs (CS{safeIs,safeEs,hazIs,hazEs,...}) =
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   134
 (writeln"Introduction rules";  prths hazIs;
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   135
  writeln"Safe introduction rules";  prths safeIs;
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   136
  writeln"Elimination rules";  prths hazEs;
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   137
  writeln"Safe elimination rules";  prths safeEs;
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   138
  ());
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   139
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   140
fun (CS{safeIs,safeEs,hazIs,hazEs,...}) addSIs ths =
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   141
  make_cs {safeIs=ths@safeIs, safeEs=safeEs, hazIs=hazIs, hazEs=hazEs};
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   142
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   143
fun (CS{safeIs,safeEs,hazIs,hazEs,...}) addSEs ths =
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   144
  make_cs {safeIs=safeIs, safeEs=ths@safeEs, hazIs=hazIs, hazEs=hazEs};
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   145
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   146
fun cs addSDs ths = cs addSEs (map make_elim ths);
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   147
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   148
fun (CS{safeIs,safeEs,hazIs,hazEs,...}) addIs ths =
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   149
  make_cs {safeIs=safeIs, safeEs=safeEs, hazIs=ths@hazIs, hazEs=hazEs};
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   150
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   151
fun (CS{safeIs,safeEs,hazIs,hazEs,...}) addEs ths =
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   152
  make_cs {safeIs=safeIs, safeEs=safeEs, hazIs=hazIs, hazEs=ths@hazEs};
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   153
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   154
fun cs addDs ths = cs addEs (map make_elim ths);
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   155
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   156
(*** Simple tactics for theorem proving ***)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   157
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   158
(*Attack subgoals using safe inferences -- matching, not resolution*)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   159
fun safe_step_tac (CS{safe0_netpair,safep_netpair,...}) = 
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   160
  FIRST' [eq_assume_tac,
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   161
	  eq_mp_tac,
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   162
	  bimatch_from_nets_tac safe0_netpair,
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   163
	  FIRST' hyp_subst_tacs,
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   164
	  bimatch_from_nets_tac safep_netpair] ;
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   165
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   166
(*Repeatedly attack subgoals using safe inferences -- it's deterministic!*)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   167
fun safe_tac cs = DETERM (REPEAT_FIRST (safe_step_tac cs));
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   168
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   169
(*These steps could instantiate variables and are therefore unsafe.*)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   170
fun inst_step_tac (CS{safe0_netpair,safep_netpair,...}) =
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   171
  assume_tac 			  APPEND' 
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   172
  contr_tac 			  APPEND' 
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   173
  biresolve_from_nets_tac safe0_netpair APPEND' 
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   174
  biresolve_from_nets_tac safep_netpair;
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   175
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   176
(*Single step for the prover.  FAILS unless it makes progress. *)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   177
fun step_tac (cs as (CS{haz_netpair,...})) i = 
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   178
  FIRST [safe_tac cs,
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   179
         inst_step_tac cs i,
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   180
         biresolve_from_nets_tac haz_netpair i];
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   181
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   182
(*Using a "safe" rule to instantiate variables is unsafe.  This tactic
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   183
  allows backtracking from "safe" rules to "unsafe" rules here.*)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   184
fun slow_step_tac (cs as (CS{haz_netpair,...})) i = 
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   185
    safe_tac cs ORELSE 
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   186
    (inst_step_tac cs i APPEND biresolve_from_nets_tac haz_netpair i);
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   187
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   188
(*** The following tactics all fail unless they solve one goal ***)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   189
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   190
(*Dumb but fast*)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   191
fun fast_tac cs = SELECT_GOAL (DEPTH_SOLVE (step_tac cs 1));
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   192
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   193
(*Slower but smarter than fast_tac*)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   194
fun best_tac cs = 
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   195
  SELECT_GOAL (BEST_FIRST (has_fewer_prems 1, sizef) (step_tac cs 1));
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   196
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   197
fun slow_tac cs = SELECT_GOAL (DEPTH_SOLVE (slow_step_tac cs 1));
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   198
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   199
fun slow_best_tac cs = 
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   200
  SELECT_GOAL (BEST_FIRST (has_fewer_prems 1, sizef) (slow_step_tac cs 1));
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   201
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   202
end; 
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   203
end;