src/Sequents/prover.ML
author bulwahn
Tue Aug 31 08:00:53 2010 +0200 (2010-08-31)
changeset 38950 62578950e748
parent 38500 d5477ee35820
child 55228 901a6696cdd8
permissions -rw-r--r--
storing options for prolog code generation in the theory
     1 (*  Title:      Sequents/prover.ML
     2     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     3     Copyright   1992  University of Cambridge
     4 
     5 Simple classical reasoner for the sequent calculus, based on "theorem packs".
     6 *)
     7 
     8 
     9 (*Higher precedence than := facilitates use of references*)
    10 infix 4 add_safes add_unsafes;
    11 
    12 structure Cla =
    13 struct
    14 
    15 datatype pack = Pack of thm list * thm list;
    16 
    17 val trace = Unsynchronized.ref false;
    18 
    19 (*A theorem pack has the form  (safe rules, unsafe rules)
    20   An unsafe rule is incomplete or introduces variables in subgoals,
    21   and is tried only when the safe rules are not applicable.  *)
    22 
    23 fun less (rl1,rl2) = (nprems_of rl1) < (nprems_of rl2);
    24 
    25 val empty_pack = Pack([],[]);
    26 
    27 fun warn_duplicates [] = []
    28   | warn_duplicates dups =
    29       (warning (cat_lines ("Ignoring duplicate theorems:" ::
    30           map Display.string_of_thm_without_context dups));
    31        dups);
    32 
    33 fun (Pack(safes,unsafes)) add_safes ths   = 
    34     let val dups = warn_duplicates (inter Thm.eq_thm_prop ths safes)
    35         val ths' = subtract Thm.eq_thm_prop dups ths
    36     in
    37         Pack(sort (make_ord less) (ths'@safes), unsafes)
    38     end;
    39 
    40 fun (Pack(safes,unsafes)) add_unsafes ths = 
    41     let val dups = warn_duplicates (inter Thm.eq_thm_prop unsafes ths)
    42         val ths' = subtract Thm.eq_thm_prop dups ths
    43     in
    44         Pack(safes, sort (make_ord less) (ths'@unsafes))
    45     end;
    46 
    47 fun merge_pack (Pack(safes,unsafes), Pack(safes',unsafes')) =
    48         Pack(sort (make_ord less) (safes@safes'), 
    49              sort (make_ord less) (unsafes@unsafes'));
    50 
    51 
    52 fun print_pack (Pack(safes,unsafes)) =
    53   writeln (cat_lines
    54    (["Safe rules:"] @ map Display.string_of_thm_without_context safes @
    55     ["Unsafe rules:"] @ map Display.string_of_thm_without_context unsafes));
    56 
    57 (*Returns the list of all formulas in the sequent*)
    58 fun forms_of_seq (Const(@{const_name "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.
    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) =
    68       forall (fn Qc => exists (fn Qp => Term.could_unify (Qp,Qc)) 
    69                               (forms_of_seq seqp))
    70              (forms_of_seq seqc);
    71 
    72 
    73 (*Tests whether two sequents or pairs of sequents could be resolved*)
    74 fun could_resolve_seq (prem,conc) =
    75   case (prem,conc) of
    76       (_ $ Abs(_,_,leftp) $ Abs(_,_,rightp),
    77        _ $ Abs(_,_,leftc) $ Abs(_,_,rightc)) =>
    78           could_res (leftp,leftc) andalso could_res (rightp,rightc)
    79     | (_ $ Abs(_,_,leftp) $ rightp,
    80        _ $ Abs(_,_,leftc) $ rightc) =>
    81           could_res (leftp,leftc)  andalso  Term.could_unify (rightp,rightc)
    82     | _ => false;
    83 
    84 
    85 (*Like filt_resolve_tac, using could_resolve_seq
    86   Much faster than resolve_tac when there are many rules.
    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
    91           else (*((rtac derelict 1 THEN rtac impl 1
    92                  THEN (rtac identity 2 ORELSE rtac ll_mp 2)
    93                  THEN rtac context1 1)
    94                  ORELSE *) resolve_tac rls i
    95   end);
    96 
    97 
    98 (*Predicate: does the rule have n premises? *)
    99 fun has_prems n rule =  (nprems_of rule = n);
   100 
   101 (*Continuation-style tactical for resolution.
   102   The list of rules is partitioned into 0, 1, 2 premises.
   103   The resulting tactic, gtac, tries to resolve with rules.
   104   If successful, it recursively applies nextac to the new subgoals only.
   105   Else fails.  (Treatment of goals due to Ph. de Groote) 
   106   Bind (RESOLVE_THEN rules) to a variable: it preprocesses the rules. *)
   107 
   108 (*Takes rule lists separated in to 0, 1, 2, >2 premises.
   109   The abstraction over state prevents needless divergence in recursion.
   110   The 9999 should be a parameter, to delay treatment of flexible goals. *)
   111 
   112 fun RESOLVE_THEN rules =
   113   let val [rls0,rls1,rls2] = partition_list has_prems 0 2 rules;
   114       fun tac nextac i state = state |>
   115              (filseq_resolve_tac rls0 9999 i 
   116               ORELSE
   117               (DETERM(filseq_resolve_tac rls1 9999 i) THEN  TRY(nextac i))
   118               ORELSE
   119               (DETERM(filseq_resolve_tac rls2 9999 i) THEN  TRY(nextac(i+1))
   120                                             THEN  TRY(nextac i)))
   121   in  tac  end;
   122 
   123 
   124 
   125 (*repeated resolution applied to the designated goal*)
   126 fun reresolve_tac rules = 
   127   let val restac = RESOLVE_THEN rules;  (*preprocessing done now*)
   128       fun gtac i = restac gtac i
   129   in  gtac  end; 
   130 
   131 (*tries the safe rules repeatedly before the unsafe rules. *)
   132 fun repeat_goal_tac (Pack(safes,unsafes)) = 
   133   let val restac  =    RESOLVE_THEN safes
   134       and lastrestac = RESOLVE_THEN unsafes;
   135       fun gtac i = restac gtac i  
   136                    ORELSE  (if !trace then
   137                                 (print_tac "" THEN lastrestac gtac i)
   138                             else lastrestac gtac i)
   139   in  gtac  end; 
   140 
   141 
   142 (*Tries safe rules only*)
   143 fun safe_tac (Pack(safes,unsafes)) = reresolve_tac safes;
   144 
   145 val safe_goal_tac = safe_tac;   (*backwards compatibility*)
   146 
   147 (*Tries a safe rule or else a unsafe rule.  Single-step for tracing. *)
   148 fun step_tac (pack as Pack(safes,unsafes)) =
   149     safe_tac pack  ORELSE'
   150     filseq_resolve_tac unsafes 9999;
   151 
   152 
   153 (* Tactic for reducing a goal, using Predicate Calculus rules.
   154    A decision procedure for Propositional Calculus, it is incomplete
   155    for Predicate-Calculus because of allL_thin and exR_thin.  
   156    Fails if it can do nothing.      *)
   157 fun pc_tac pack = SELECT_GOAL (DEPTH_SOLVE (repeat_goal_tac pack 1));
   158 
   159 
   160 (*The following two tactics are analogous to those provided by 
   161   Provers/classical.  In fact, pc_tac is usually FASTER than fast_tac!*)
   162 fun fast_tac pack =
   163   SELECT_GOAL (DEPTH_SOLVE (step_tac pack 1));
   164 
   165 fun best_tac pack  = 
   166   SELECT_GOAL (BEST_FIRST (has_fewer_prems 1, size_of_thm) 
   167                (step_tac pack 1));
   168 
   169 end;
   170 
   171 
   172 open Cla;