src/Sequents/prover.ML
 author wenzelm Thu Dec 07 00:42:04 2006 +0100 (2006-12-07) changeset 21687 f689f729afab parent 21428 f84cf8e9cad8 child 22360 26ead7ed4f4b permissions -rw-r--r--
reorganized structure Goal vs. Tactic;
```     1 (*  Title:      Sequents/prover
```
```     2     ID:         \$Id\$
```
```     3     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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```     4     Copyright   1992  University of Cambridge
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```     5
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```     6 Simple classical reasoner for the sequent calculus, based on "theorem packs"
```
```     7 *)
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```     8
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```     9
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```    10 (*Higher precedence than := facilitates use of references*)
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```    11 infix 4 add_safes add_unsafes;
```
```    12
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```    13 structure Cla =
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```    14
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```    15 struct
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```    16
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```    17 datatype pack = Pack of thm list * thm list;
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```    18
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```    19 val trace = ref false;
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```    20
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```    21 (*A theorem pack has the form  (safe rules, unsafe rules)
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```    22   An unsafe rule is incomplete or introduces variables in subgoals,
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```    23   and is tried only when the safe rules are not applicable.  *)
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```    24
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```    25 fun less (rl1,rl2) = (nprems_of rl1) < (nprems_of rl2);
```
```    26
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```    27 val empty_pack = Pack([],[]);
```
```    28
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```    29 fun warn_duplicates [] = []
```
```    30   | warn_duplicates dups =
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```    31       (warning (cat_lines ("Ignoring duplicate theorems:" :: map string_of_thm dups));
```
```    32        dups);
```
```    33
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```    34 fun (Pack(safes,unsafes)) add_safes ths   =
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```    35     let val dups = warn_duplicates (gen_inter Drule.eq_thm_prop (ths,safes))
```
```    36 	val ths' = subtract Drule.eq_thm_prop dups ths
```
```    37     in
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```    38         Pack(sort (make_ord less) (ths'@safes), unsafes)
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```    39     end;
```
```    40
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```    41 fun (Pack(safes,unsafes)) add_unsafes ths =
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```    42     let val dups = warn_duplicates (gen_inter Drule.eq_thm_prop (ths,unsafes))
```
```    43 	val ths' = subtract Drule.eq_thm_prop dups ths
```
```    44     in
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```    45 	Pack(safes, sort (make_ord less) (ths'@unsafes))
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```    46     end;
```
```    47
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```    48 fun merge_pack (Pack(safes,unsafes), Pack(safes',unsafes')) =
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```    49         Pack(sort (make_ord less) (safes@safes'),
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```    50 	     sort (make_ord less) (unsafes@unsafes'));
```
```    51
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```    52
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```    53 fun print_pack (Pack(safes,unsafes)) =
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```    54     (writeln "Safe rules:";  print_thms safes;
```
```    55      writeln "Unsafe rules:"; print_thms unsafes);
```
```    56
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```    57 (*Returns the list of all formulas in the sequent*)
```
```    58 fun forms_of_seq (Const("SeqO'",_) \$ P \$ u) = P :: forms_of_seq u
```
```    59   | forms_of_seq (H \$ u) = forms_of_seq u
```
```    60   | forms_of_seq _ = [];
```
```    61
```
```    62 (*Tests whether two sequences (left or right sides) could be resolved.
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```    63   seqp is a premise (subgoal), seqc is a conclusion of an object-rule.
```
```    64   Assumes each formula in seqc is surrounded by sequence variables
```
```    65   -- checks that each concl formula looks like some subgoal formula.
```
```    66   It SHOULD check order as well, using recursion rather than forall/exists*)
```
```    67 fun could_res (seqp,seqc) =
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```    68       forall (fn Qc => exists (fn Qp => could_unify (Qp,Qc))
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```    69                               (forms_of_seq seqp))
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```    70              (forms_of_seq seqc);
```
```    71
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```    72
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```    73 (*Tests whether two sequents or pairs of sequents could be resolved*)
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```    74 fun could_resolve_seq (prem,conc) =
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```    75   case (prem,conc) of
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```    76       (_ \$ Abs(_,_,leftp) \$ Abs(_,_,rightp),
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```    77        _ \$ Abs(_,_,leftc) \$ Abs(_,_,rightc)) =>
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```    78 	  could_res (leftp,leftc) andalso could_res (rightp,rightc)
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```    79     | (_ \$ Abs(_,_,leftp) \$ rightp,
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```    80        _ \$ Abs(_,_,leftc) \$ rightc) =>
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```    81 	  could_res (leftp,leftc)  andalso  could_unify (rightp,rightc)
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```    82     | _ => false;
```
```    83
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```    84
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```    85 (*Like filt_resolve_tac, using could_resolve_seq
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```    86   Much faster than resolve_tac when there are many rules.
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```    87   Resolve subgoal i using the rules, unless more than maxr are compatible. *)
```
```    88 fun filseq_resolve_tac rules maxr = SUBGOAL(fn (prem,i) =>
```
```    89   let val rls = filter_thms could_resolve_seq (maxr+1, prem, rules)
```
```    90   in  if length rls > maxr  then  no_tac
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```    91 	  else (*((rtac derelict 1 THEN rtac impl 1
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```    92 		 THEN (rtac identity 2 ORELSE rtac ll_mp 2)
```
```    93 		 THEN rtac context1 1)
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```    94 		 ORELSE *) resolve_tac rls i
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```    95   end);
```
```    96
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```    97
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```    98 (*Predicate: does the rule have n premises? *)
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```    99 fun has_prems n rule =  (nprems_of rule = n);
```
```   100
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```   101 (*Continuation-style tactical for resolution.
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```   102   The list of rules is partitioned into 0, 1, 2 premises.
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```   103   The resulting tactic, gtac, tries to resolve with rules.
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```   104   If successful, it recursively applies nextac to the new subgoals only.
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```   105   Else fails.  (Treatment of goals due to Ph. de Groote)
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```   106   Bind (RESOLVE_THEN rules) to a variable: it preprocesses the rules. *)
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```   107
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```   108 (*Takes rule lists separated in to 0, 1, 2, >2 premises.
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```   109   The abstraction over state prevents needless divergence in recursion.
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```   110   The 9999 should be a parameter, to delay treatment of flexible goals. *)
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```   111
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```   112 fun RESOLVE_THEN rules =
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```   113   let val [rls0,rls1,rls2] = partition_list has_prems 0 2 rules;
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```   114       fun tac nextac i state = state |>
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```   115 	     (filseq_resolve_tac rls0 9999 i
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```   116 	      ORELSE
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```   117 	      (DETERM(filseq_resolve_tac rls1 9999 i) THEN  TRY(nextac i))
```
```   118 	      ORELSE
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```   119 	      (DETERM(filseq_resolve_tac rls2 9999 i) THEN  TRY(nextac(i+1))
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```   120 					    THEN  TRY(nextac i)))
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```   121   in  tac  end;
```
```   122
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```   123
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```   124
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```   125 (*repeated resolution applied to the designated goal*)
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```   126 fun reresolve_tac rules =
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```   127   let val restac = RESOLVE_THEN rules;  (*preprocessing done now*)
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```   128       fun gtac i = restac gtac i
```
```   129   in  gtac  end;
```
```   130
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```   131 (*tries the safe rules repeatedly before the unsafe rules. *)
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```   132 fun repeat_goal_tac (Pack(safes,unsafes)) =
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```   133   let val restac  =    RESOLVE_THEN safes
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```   134       and lastrestac = RESOLVE_THEN unsafes;
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```   135       fun gtac i = restac gtac i
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```   136 	           ORELSE  (if !trace then
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```   137 				(print_tac "" THEN lastrestac gtac i)
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```   138 			    else lastrestac gtac i)
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```   139   in  gtac  end;
```
```   140
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```   141
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```   142 (*Tries safe rules only*)
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```   143 fun safe_tac (Pack(safes,unsafes)) = reresolve_tac safes;
```
```   144
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```   145 val safe_goal_tac = safe_tac;   (*backwards compatibility*)
```
```   146
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```   147 (*Tries a safe rule or else a unsafe rule.  Single-step for tracing. *)
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```   148 fun step_tac (pack as Pack(safes,unsafes)) =
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```   149     safe_tac pack  ORELSE'
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```   150     filseq_resolve_tac unsafes 9999;
```
```   151
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```   152
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```   153 (* Tactic for reducing a goal, using Predicate Calculus rules.
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```   154    A decision procedure for Propositional Calculus, it is incomplete
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```   155    for Predicate-Calculus because of allL_thin and exR_thin.
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```   156    Fails if it can do nothing.      *)
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```   157 fun pc_tac pack = SELECT_GOAL (DEPTH_SOLVE (repeat_goal_tac pack 1));
```
```   158
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```   159
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```   160 (*The following two tactics are analogous to those provided by
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```   161   Provers/classical.  In fact, pc_tac is usually FASTER than fast_tac!*)
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```   162 fun fast_tac pack =
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```   163   SELECT_GOAL (DEPTH_SOLVE (step_tac pack 1));
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```   164
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```   165 fun best_tac pack  =
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```   166   SELECT_GOAL (BEST_FIRST (has_fewer_prems 1, size_of_thm)
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```   167 	       (step_tac pack 1));
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```   168
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```   169 end;
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```   170
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```   171
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```   172 open Cla;
```