src/Pure/goal.ML
author wenzelm
Thu Dec 07 00:42:04 2006 +0100 (2006-12-07)
changeset 21687 f689f729afab
parent 21604 1af327306c8e
child 22902 ac833b4bb7ee
permissions -rw-r--r--
reorganized structure Goal vs. Tactic;
     1 (*  Title:      Pure/goal.ML
     2     ID:         $Id$
     3     Author:     Makarius and Lawrence C Paulson
     4 
     5 Goals in tactical theorem proving.
     6 *)
     7 
     8 signature BASIC_GOAL =
     9 sig
    10   val SELECT_GOAL: tactic -> int -> tactic
    11   val CONJUNCTS: tactic -> int -> tactic
    12   val PRECISE_CONJUNCTS: int -> tactic -> int -> tactic
    13 end;
    14 
    15 signature GOAL =
    16 sig
    17   include BASIC_GOAL
    18   val init: cterm -> thm
    19   val protect: thm -> thm
    20   val conclude: thm -> thm
    21   val finish: thm -> thm
    22   val norm_result: thm -> thm
    23   val close_result: thm -> thm
    24   val prove_raw: cterm list -> cterm -> (thm list -> tactic) -> thm
    25   val prove_multi: Proof.context -> string list -> term list -> term list ->
    26     ({prems: thm list, context: Proof.context} -> tactic) -> thm list
    27   val prove: Proof.context -> string list -> term list -> term ->
    28     ({prems: thm list, context: Proof.context} -> tactic) -> thm
    29   val prove_global: theory -> string list -> term list -> term -> (thm list -> tactic) -> thm
    30   val extract: int -> int -> thm -> thm Seq.seq
    31   val retrofit: int -> int -> thm -> thm -> thm Seq.seq
    32   val conjunction_tac: int -> tactic
    33   val precise_conjunction_tac: int -> int -> tactic
    34   val asm_rewrite_goal_tac: bool * bool * bool -> (simpset -> tactic) -> simpset -> int -> tactic
    35   val rewrite_goal_tac: thm list -> int -> tactic
    36   val norm_hhf_tac: int -> tactic
    37   val compose_hhf: thm -> int -> thm -> thm Seq.seq
    38   val compose_hhf_tac: thm -> int -> tactic
    39   val comp_hhf: thm -> thm -> thm
    40 end;
    41 
    42 structure Goal: GOAL =
    43 struct
    44 
    45 (** goals **)
    46 
    47 (*
    48   -------- (init)
    49   C ==> #C
    50 *)
    51 val init =
    52   let val A = #1 (Drule.dest_implies (Thm.cprop_of Drule.protectI))
    53   in fn C => Thm.instantiate ([], [(A, C)]) Drule.protectI end;
    54 
    55 (*
    56    C
    57   --- (protect)
    58   #C
    59 *)
    60 fun protect th = th COMP_INCR Drule.protectI;
    61 
    62 (*
    63   A ==> ... ==> #C
    64   ---------------- (conclude)
    65   A ==> ... ==> C
    66 *)
    67 fun conclude th =
    68   (case SINGLE (Thm.compose_no_flatten false (th, Thm.nprems_of th) 1)
    69       (Drule.incr_indexes th Drule.protectD) of
    70     SOME th' => th'
    71   | NONE => raise THM ("Failed to conclude goal", 0, [th]));
    72 
    73 (*
    74   #C
    75   --- (finish)
    76    C
    77 *)
    78 fun finish th =
    79   (case Thm.nprems_of th of
    80     0 => conclude th
    81   | n => raise THM ("Proof failed.\n" ^
    82       Pretty.string_of (Pretty.chunks (Display.pretty_goals n th)) ^
    83       ("\n" ^ string_of_int n ^ " unsolved goal(s)!"), 0, [th]));
    84 
    85 
    86 
    87 (** results **)
    88 
    89 (* normal form *)
    90 
    91 val norm_result =
    92   Drule.flexflex_unique
    93   #> MetaSimplifier.norm_hhf_protect
    94   #> Thm.strip_shyps
    95   #> Drule.zero_var_indexes;
    96 
    97 val close_result =
    98   Thm.compress
    99   #> Drule.close_derivation;
   100 
   101 
   102 
   103 (** tactical theorem proving **)
   104 
   105 (* prove_raw -- no checks, no normalization of result! *)
   106 
   107 fun prove_raw casms cprop tac =
   108   (case SINGLE (tac (map Assumption.assume casms)) (init cprop) of
   109     SOME th => Drule.implies_intr_list casms (finish th)
   110   | NONE => error "Tactic failed.");
   111 
   112 
   113 (* prove_multi *)
   114 
   115 fun prove_multi ctxt xs asms props tac =
   116   let
   117     val thy = ProofContext.theory_of ctxt;
   118     val string_of_term = Sign.string_of_term thy;
   119 
   120     fun err msg = cat_error msg
   121       ("The error(s) above occurred for the goal statement:\n" ^
   122         string_of_term (Logic.list_implies (asms, Logic.mk_conjunction_list props)));
   123 
   124     fun cert_safe t = Thm.cterm_of thy (Envir.beta_norm (Term.no_dummy_patterns t))
   125       handle TERM (msg, _) => err msg | TYPE (msg, _, _) => err msg;
   126     val casms = map cert_safe asms;
   127     val cprops = map cert_safe props;
   128 
   129     val (prems, ctxt') = ctxt
   130       |> Variable.add_fixes_direct xs
   131       |> fold Variable.declare_internal (asms @ props)
   132       |> Assumption.add_assumes casms;
   133 
   134     val goal = init (Conjunction.mk_conjunction_list cprops);
   135     val res =
   136       (case SINGLE (tac {prems = prems, context = ctxt'}) goal of
   137         NONE => err "Tactic failed."
   138       | SOME res => res);
   139     val [results] = Conjunction.elim_precise [length props] (finish res)
   140       handle THM (msg, _, _) => err msg;
   141     val _ = Unify.matches_list thy (map Thm.term_of cprops) (map Thm.prop_of results)
   142       orelse err ("Proved a different theorem: " ^ string_of_term (Thm.prop_of res));
   143   in
   144     results
   145     |> map (Assumption.export false ctxt' ctxt)
   146     |> Variable.export ctxt' ctxt
   147     |> map Drule.zero_var_indexes
   148   end;
   149 
   150 
   151 (* prove *)
   152 
   153 fun prove ctxt xs asms prop tac = hd (prove_multi ctxt xs asms [prop] tac);
   154 
   155 fun prove_global thy xs asms prop tac =
   156   Drule.standard (prove (ProofContext.init thy) xs asms prop (fn {prems, ...} => tac prems));
   157 
   158 
   159 
   160 (** goal structure **)
   161 
   162 (* nested goals *)
   163 
   164 fun extract i n st =
   165   (if i < 1 orelse n < 1 orelse i + n - 1 > Thm.nprems_of st then Seq.empty
   166    else if n = 1 then Seq.single (Thm.cprem_of st i)
   167    else Seq.single (foldr1 Conjunction.mk_conjunction (map (Thm.cprem_of st) (i upto i + n - 1))))
   168   |> Seq.map (Thm.adjust_maxidx_cterm ~1 #> init);
   169 
   170 fun retrofit i n st' st =
   171   (if n = 1 then st
   172    else st |> Drule.rotate_prems (i - 1) |> Conjunction.uncurry n |> Drule.rotate_prems (1 - i))
   173   |> Thm.compose_no_flatten false (conclude st', Thm.nprems_of st') i;
   174 
   175 fun SELECT_GOAL tac i st =
   176   if Thm.nprems_of st = 1 andalso i = 1 then tac st
   177   else Seq.lifts (retrofit i 1) (Seq.maps tac (extract i 1 st)) st;
   178 
   179 
   180 (* multiple goals *)
   181 
   182 val conj_tac = SUBGOAL (fn (goal, i) =>
   183   if can Logic.dest_conjunction goal then rtac Conjunction.conjunctionI i
   184   else no_tac);
   185 
   186 val conjunction_tac = TRY o REPEAT_ALL_NEW conj_tac;
   187 
   188 val precise_conjunction_tac =
   189   let
   190     fun tac 0 i = eq_assume_tac i
   191       | tac 1 i = SUBGOAL (K all_tac) i
   192       | tac n i = conj_tac i THEN TRY (fn st => tac (n - 1) (i + 1) st);
   193   in TRY oo tac end;
   194 
   195 fun CONJUNCTS tac =
   196   SELECT_GOAL (conjunction_tac 1
   197     THEN tac
   198     THEN PRIMITIVE (Conjunction.uncurry ~1));
   199 
   200 fun PRECISE_CONJUNCTS n tac =
   201   SELECT_GOAL (precise_conjunction_tac n 1
   202     THEN tac
   203     THEN PRIMITIVE (Conjunction.uncurry ~1));
   204 
   205 
   206 (* rewriting *)
   207 
   208 (*Rewrite subgoal i only.  SELECT_GOAL avoids inefficiencies in goals_conv.*)
   209 fun asm_rewrite_goal_tac mode prover_tac ss =
   210   SELECT_GOAL
   211     (PRIMITIVE (MetaSimplifier.rewrite_goal_rule mode (SINGLE o prover_tac) ss 1));
   212 
   213 fun rewrite_goal_tac rews =
   214   let val ss = MetaSimplifier.empty_ss addsimps rews in
   215     fn i => fn st => asm_rewrite_goal_tac (true, false, false) (K no_tac)
   216       (MetaSimplifier.theory_context (Thm.theory_of_thm st) ss) i st
   217   end;
   218 
   219 
   220 (* hhf normal form *)
   221 
   222 val norm_hhf_tac =
   223   rtac Drule.asm_rl  (*cheap approximation -- thanks to builtin Logic.flatten_params*)
   224   THEN' SUBGOAL (fn (t, i) =>
   225     if Drule.is_norm_hhf t then all_tac
   226     else rewrite_goal_tac [Drule.norm_hhf_eq] i);
   227 
   228 fun compose_hhf tha i thb =
   229   Thm.bicompose false (false, Drule.lift_all (Thm.cprem_of thb i) tha, 0) i thb;
   230 
   231 fun compose_hhf_tac th i = PRIMSEQ (compose_hhf th i);
   232 
   233 fun comp_hhf tha thb =
   234   (case Seq.chop 2 (compose_hhf tha 1 thb) of
   235     ([th], _) => th
   236   | ([], _) => raise THM ("comp_hhf: no unifiers", 1, [tha, thb])
   237   | _  => raise THM ("comp_hhf: multiple unifiers", 1, [tha, thb]));
   238 
   239 end;
   240 
   241 structure BasicGoal: BASIC_GOAL = Goal;
   242 open BasicGoal;