src/Sequents/prover.ML
 author wenzelm Mon Mar 19 21:10:33 2012 +0100 (2012-03-19) changeset 47022 8eac39af4ec0 parent 38500 d5477ee35820 child 55228 901a6696cdd8 permissions -rw-r--r--
moved some legacy stuff;
```     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;
```