src/Pure/Isar/proof.ML
author wenzelm
Fri May 21 11:38:57 1999 +0200 (1999-05-21)
changeset 6683 b7293047b0f4
parent 6529 0f4c2ebc5018
child 6731 57e761134c85
permissions -rw-r--r--
local_qed: obtain interactive flag;
     1 (*  Title:      Pure/Isar/proof.ML
     2     ID:         $Id$
     3     Author:     Markus Wenzel, TU Muenchen
     4 
     5 Proof states and methods.
     6 
     7 TODO:
     8   - assume: improve schematic Vars handling (!?);
     9   - warn_vars;
    10   - bind: check rhs (extra (T)Vars etc.) (How to handle these anyway?);
    11   - prep_result: avoid duplicate asms;
    12   - prep_result error: use error channel (!);
    13   - check_finished: trace results (!?);
    14   - next_block: fetch_facts (!?);
    15 *)
    16 
    17 signature PROOF =
    18 sig
    19   type context
    20   type state
    21   exception STATE of string * state
    22   val context_of: state -> context
    23   val theory_of: state -> theory
    24   val sign_of: state -> Sign.sg
    25   val the_facts: state -> thm list
    26   val goal_facts: (state -> thm list) -> state -> state
    27   val use_facts: state -> state
    28   val reset_facts: state -> state
    29   val assert_backward: state -> state
    30   val enter_forward: state -> state
    31   val verbose: bool ref
    32   val print_state: state -> unit
    33   type method
    34   val method: (thm list -> thm ->
    35     (thm * (indexname * term) list * (string * thm list) list) Seq.seq) -> method
    36   val refine: (context -> method) -> state -> state Seq.seq
    37   val bind: (indexname * string) list -> state -> state
    38   val bind_i: (indexname * term) list -> state -> state
    39   val match_bind: (string list * string) list -> state -> state
    40   val match_bind_i: (term list * term) list -> state -> state
    41   val have_thmss: string -> context attribute list ->
    42     (thm list * context attribute list) list -> state -> state
    43   val assume: string -> context attribute list -> (string * string list) list -> state -> state
    44   val assume_i: string -> context attribute list -> (term * term list) list -> state -> state
    45   val fix: (string * string option) list -> state -> state
    46   val fix_i: (string * typ) list -> state -> state
    47   val theorem: bstring -> theory attribute list -> string * string list -> theory -> state
    48   val theorem_i: bstring -> theory attribute list -> term * term list -> theory -> state
    49   val lemma: bstring -> theory attribute list -> string * string list -> theory -> state
    50   val lemma_i: bstring -> theory attribute list -> term * term list -> theory -> state
    51   val chain: state -> state
    52   val from_facts: thm list -> state -> state
    53   val show: string -> context attribute list -> string * string list -> state -> state
    54   val show_i: string -> context attribute list -> term * term list -> state -> state
    55   val have: string -> context attribute list -> string * string list -> state -> state
    56   val have_i: string -> context attribute list -> term * term list -> state -> state
    57   val begin_block: state -> state
    58   val next_block: state -> state
    59   val end_block: state -> state
    60   val at_bottom: state -> bool
    61   val local_qed: (state -> state Seq.seq) -> bool -> state -> state Seq.seq
    62   val global_qed: (state -> state Seq.seq) -> bstring option
    63     -> theory attribute list option -> state -> theory * {kind: string, name: string, thm: thm}
    64 end;
    65 
    66 signature PROOF_PRIVATE =
    67 sig
    68   include PROOF
    69   val put_data: Object.kind -> ('a -> Object.T) -> 'a -> state -> state
    70 end;
    71 
    72 structure Proof: PROOF_PRIVATE =
    73 struct
    74 
    75 
    76 (** proof state **)
    77 
    78 type context = ProofContext.context;
    79 
    80 
    81 (* type goal *)
    82 
    83 datatype kind =
    84   Theorem of theory attribute list |    (*top-level theorem*)
    85   Lemma of theory attribute list |      (*top-level lemma*)
    86   Goal of context attribute list |      (*intermediate result, solving subgoal*)
    87   Aux of context attribute list ;       (*intermediate result*)
    88 
    89 val kind_name =
    90   fn Theorem _ => "theorem" | Lemma _ => "lemma" | Goal _ => "show" | Aux _ => "have";
    91 
    92 type goal =
    93  (kind *                (*result kind*)
    94   string *              (*result name*)
    95   cterm list *          (*result assumptions*)
    96   term) *               (*result statement*)
    97  (thm list *            (*use facts*)
    98   thm);                 (*goal: subgoals ==> statement*)
    99 
   100 
   101 (* type mode *)
   102 
   103 datatype mode = Forward | ForwardChain | Backward;
   104 
   105 val mode_name =
   106   fn Forward => "state" | ForwardChain => "chain" | Backward => "prove";
   107 
   108 
   109 (* type node *)
   110 
   111 type node =
   112  {context: context,
   113   facts: thm list option,
   114   mode: mode,
   115   goal: goal option};
   116 
   117 fun make_node (context, facts, mode, goal) =
   118   {context = context, facts = facts, mode = mode, goal = goal}: node;
   119 
   120 
   121 (* datatype state *)
   122 
   123 datatype state =
   124   State of
   125     node *              (*current*)
   126     node list;          (*parents wrt. block structure*)
   127 
   128 exception STATE of string * state;
   129 
   130 fun err_malformed name state =
   131   raise STATE (name ^ ": internal error -- malformed proof state", state);
   132 
   133 
   134 fun map_current f (State ({context, facts, mode, goal}, nodes)) =
   135   State (make_node (f (context, facts, mode, goal)), nodes);
   136 
   137 fun init_state thy =
   138   State (make_node (ProofContext.init thy, None, Forward, None), []);
   139 
   140 
   141 
   142 (** basic proof state operations **)
   143 
   144 (* context *)
   145 
   146 fun context_of (State ({context, ...}, _)) = context;
   147 val theory_of = ProofContext.theory_of o context_of;
   148 val sign_of = ProofContext.sign_of o context_of;
   149 
   150 fun map_context f = map_current (fn (ctxt, facts, mode, goal) => (f ctxt, facts, mode, goal));
   151 
   152 fun map_context_result f (state as State ({context, facts, mode, goal}, nodes)) =
   153   let val (context', result) = f context
   154   in (State (make_node (context', facts, mode, goal), nodes), result) end;
   155 
   156 
   157 fun put_data kind f = map_context o ProofContext.put_data kind f;
   158 val declare_term = map_context o ProofContext.declare_term;
   159 val add_binds = map_context o ProofContext.add_binds_i;
   160 val put_thms = map_context o ProofContext.put_thms;
   161 val put_thmss = map_context o ProofContext.put_thmss;
   162 
   163 
   164 (* bind statements *)
   165 
   166 fun bind_props bs state =
   167   let val mk_bind = map (fn (x, t) => ((Syntax.binding x, 0), t)) o ObjectLogic.dest_statement
   168   in state |> add_binds (flat (map mk_bind bs)) end;
   169 
   170 fun bind_thms (name, thms) state =
   171   let
   172     val props = map (#prop o Thm.rep_thm) thms;
   173     val named_props =
   174       (case props of
   175         [prop] => [(name, prop)]
   176       | props => map2 (fn (i, t) => (name ^ string_of_int i, t)) (1 upto length props, props));
   177   in state |> bind_props named_props end;
   178 
   179 fun let_thms name_thms state =
   180   state
   181   |> put_thms name_thms
   182   |> bind_thms name_thms;
   183 
   184 
   185 (* facts *)
   186 
   187 fun the_facts (State ({facts = Some facts, ...}, _)) = facts
   188   | the_facts state = raise STATE ("No current facts available", state);
   189 
   190 fun put_facts facts state =
   191   state
   192   |> map_current (fn (ctxt, _, mode, goal) => (ctxt, facts, mode, goal))
   193   |> let_thms ("facts", if_none facts []);
   194 
   195 val reset_facts = put_facts None;
   196 
   197 fun have_facts (name, facts) state =
   198   state
   199   |> put_facts (Some facts)
   200   |> let_thms (name, facts);
   201 
   202 fun these_facts (state, ths) = have_facts ths state;
   203 fun fetch_facts (State ({facts, ...}, _)) = put_facts facts;
   204 
   205 
   206 (* goal *)
   207 
   208 fun find_goal i (State ({goal = Some goal, ...}, _)) = (i, goal)
   209   | find_goal i (State ({goal = None, ...}, node :: nodes)) =
   210       find_goal (i + 1) (State (node, nodes))
   211   | find_goal _ (state as State (_, [])) = err_malformed "find_goal" state;
   212 
   213 fun put_goal goal = map_current (fn (ctxt, facts, mode, _) => (ctxt, facts, mode, goal));
   214 
   215 fun map_goal f (State ({context, facts, mode, goal = Some goal}, nodes)) =
   216       State (make_node (context, facts, mode, Some (f goal)), nodes)
   217   | map_goal f (State (nd, node :: nodes)) =
   218       let val State (node', nodes') = map_goal f (State (node, nodes))
   219       in State (nd, node' :: nodes') end
   220   | map_goal _ state = state;
   221 
   222 fun goal_facts get state =
   223   state
   224   |> map_goal (fn (result, (_, thm)) => (result, (get state, thm)));
   225 
   226 fun use_facts state =
   227   state
   228   |> goal_facts the_facts
   229   |> reset_facts;
   230 
   231 
   232 (* mode *)
   233 
   234 fun get_mode (State ({mode, ...}, _)) = mode;
   235 fun put_mode mode = map_current (fn (ctxt, facts, _, goal) => (ctxt, facts, mode, goal));
   236 
   237 val enter_forward = put_mode Forward;
   238 val enter_forward_chain = put_mode ForwardChain;
   239 val enter_backward = put_mode Backward;
   240 
   241 fun assert_mode pred state =
   242   let val mode = get_mode state in
   243     if pred mode then state
   244     else raise STATE ("Illegal application of command in " ^ mode_name mode ^ " mode", state)
   245   end;
   246 
   247 fun is_chain state = get_mode state = ForwardChain;
   248 val assert_forward = assert_mode (equal Forward);
   249 val assert_forward_or_chain = assert_mode (equal Forward orf equal ForwardChain);
   250 val assert_backward = assert_mode (equal Backward);
   251 
   252 
   253 (* blocks *)
   254 
   255 fun open_block (State (node, nodes)) = State (node, node :: nodes);
   256 
   257 fun new_block state =
   258   state
   259   |> open_block
   260   |> put_goal None;
   261 
   262 fun close_block (State (_, node :: nodes)) = State (node, nodes)
   263   | close_block state = raise STATE ("Unbalanced block parentheses", state);
   264 
   265 
   266 
   267 (** print_state **)
   268 
   269 val verbose = ProofContext.verbose;
   270 
   271 fun print_state (state as State ({context, facts, mode, goal = _}, nodes)) =
   272   let
   273     val ref (_, _, begin_goal) = Goals.current_goals_markers;
   274 
   275     fun print_facts None = ()
   276       | print_facts (Some ths) =
   277           Pretty.writeln (Pretty.big_list "Current facts:" (map Display.pretty_thm ths));
   278 
   279     fun levels_up 0 = ""
   280       | levels_up i = " (" ^ string_of_int i ^ " levels up)";
   281 
   282     fun print_goal (i, ((kind, name, _, _), (_, thm))) =
   283       (writeln (kind_name kind ^ " " ^ quote name ^ levels_up (i div 2) ^ ":");
   284         Locale.print_goals_marker begin_goal (! goals_limit) thm);
   285   in
   286     writeln ("Nesting level: " ^ string_of_int (length nodes div 2));
   287     writeln "";
   288     writeln (enclose "`" "'" (mode_name mode) ^ " mode");
   289     writeln "";
   290     if ! verbose orelse mode = Forward then
   291       (ProofContext.print_context context;
   292         writeln "";
   293         print_facts facts;
   294         print_goal (find_goal 0 state))
   295     else if mode = ForwardChain then print_facts facts
   296     else print_goal (find_goal 0 state)
   297   end;
   298 
   299 
   300 
   301 (** proof steps **)
   302 
   303 (* datatype method *)
   304 
   305 datatype method = Method of
   306   thm list ->                           (*use facts*)
   307   thm                                   (*goal: subgoals ==> statement*)
   308     -> (thm *                           (*refined goal*)
   309        (indexname * term) list *        (*new bindings*)
   310        (string * thm list) list)        (*new thms*)
   311          Seq.seq;
   312 
   313 val method = Method;
   314 
   315 
   316 (* refine goal *)
   317 
   318 fun check_sign sg state =
   319   if Sign.subsig (sg, sign_of state) then state
   320   else raise STATE ("Bad signature of result: " ^ Sign.str_of_sg sg, state);
   321 
   322 fun refine meth_fun (state as State ({context, ...}, _)) =
   323       let
   324         val Method meth = meth_fun context;
   325         val (_, (result, (facts, thm))) = find_goal 0 state;
   326 
   327         fun refn (thm', new_binds, new_thms) =
   328           state
   329           |> check_sign (sign_of_thm thm')
   330           |> map_goal (K (result, (facts, thm')))
   331           |> add_binds new_binds
   332           |> put_thmss new_thms;
   333       in Seq.map refn (meth facts thm) end;
   334 
   335 
   336 (* prepare result *)
   337 
   338 fun varify_frees names thm =
   339   let
   340     fun get_free x (None, t as Free (y, _)) = if x = y then Some t else None
   341       | get_free _ (opt, _) = opt;
   342 
   343     fun find_free t x = foldl_aterms (get_free x) (None, t);
   344 
   345     val {sign, maxidx, prop, ...} = Thm.rep_thm thm;
   346     val frees = map (Thm.cterm_of sign) (mapfilter (find_free prop) names);
   347   in
   348     thm
   349     |> Drule.forall_intr_list frees
   350     |> Drule.forall_elim_vars (maxidx + 1)
   351   end;
   352 
   353 fun implies_elim_hyps thm =
   354   foldl (uncurry Thm.implies_elim) (thm, map Thm.assume (Drule.cprems_of thm));
   355 
   356 fun prep_result state asms t raw_thm =
   357   let
   358     val ctxt = context_of state;
   359     fun err msg = raise STATE (msg, state);
   360 
   361     val ngoals = Thm.nprems_of raw_thm;
   362     val _ =
   363       if ngoals = 0 then ()
   364       else (Locale.print_goals ngoals raw_thm; err (string_of_int ngoals ^ " unsolved goal(s)!"));
   365 
   366     val thm =
   367       raw_thm RS Drule.rev_triv_goal
   368       |> implies_elim_hyps
   369       |> Drule.implies_intr_list asms
   370       |> varify_frees (ProofContext.fixed_names ctxt);
   371 
   372     val {hyps, prop, sign, ...} = Thm.rep_thm thm;
   373     val tsig = Sign.tsig_of sign;
   374   in
   375 (* FIXME
   376     if not (Pattern.matches tsig (t, Logic.skip_flexpairs prop)) then
   377       warning ("Proved a different theorem: " ^ Sign.string_of_term sign prop)
   378     else ();
   379 *)
   380     if not (null hyps) then
   381       err ("Additional hypotheses:\n" ^ cat_lines (map (Sign.string_of_term sign) hyps))
   382 (* FIXME    else if not (Pattern.matches tsig (t, Logic.skip_flexpairs prop)) then
   383       err ("Proved a different theorem: " ^ Sign.string_of_term sign prop) *)
   384     else thm
   385   end;
   386 
   387 
   388 (* prepare final result *)
   389 
   390 fun strip_flexflex thm =
   391   Seq.hd (Thm.flexflex_rule thm) handle THM _ => thm;
   392 
   393 fun final_result state pre_thm =
   394   let
   395     val thm =
   396       pre_thm
   397       |> strip_flexflex
   398       |> Thm.strip_shyps
   399       |> Drule.standard;
   400 
   401     val str_of_sort = Sign.str_of_sort (Thm.sign_of_thm thm);
   402     val xshyps = Thm.extra_shyps thm;
   403   in
   404     if not (null xshyps) then
   405       raise STATE ("Extra sort hypotheses: " ^ commas (map str_of_sort xshyps), state)
   406     else thm
   407   end;
   408 
   409 
   410 (* solve goal *)
   411 
   412 fun solve_goal rule state =
   413   let
   414     val (_, (result, (facts, thm))) = find_goal 0 state;
   415     val thms' = FIRSTGOAL (rtac rule THEN_ALL_NEW (TRY o assume_tac)) thm;
   416   in Seq.map (fn thm' => map_goal (K (result, (facts, thm'))) state) thms' end;
   417 
   418 
   419 
   420 (*** structured proof commands ***)
   421 
   422 (** context **)
   423 
   424 (* bind *)
   425 
   426 fun gen_bind f x state =
   427   state
   428   |> assert_forward
   429   |> map_context (f x)
   430   |> reset_facts;
   431 
   432 val bind = gen_bind ProofContext.add_binds;
   433 val bind_i = gen_bind ProofContext.add_binds_i;
   434 
   435 val match_bind = gen_bind ProofContext.match_binds;
   436 val match_bind_i = gen_bind ProofContext.match_binds_i;
   437 
   438 
   439 (* have_thmss *)
   440 
   441 fun have_thmss name atts ths_atts state =
   442   state
   443   |> assert_forward
   444   |> map_context_result (ProofContext.have_thmss (PureThy.default_name name) atts ths_atts)
   445   |> these_facts;
   446 
   447 
   448 (* fix *)
   449 
   450 fun gen_fix f xs state =
   451   state
   452   |> assert_forward
   453   |> map_context (f xs)
   454   |> reset_facts;
   455 
   456 val fix = gen_fix ProofContext.fix;
   457 val fix_i = gen_fix ProofContext.fix_i;
   458 
   459 
   460 (* assume *)
   461 
   462 fun gen_assume f name atts props state =
   463   state
   464   |> assert_forward
   465   |> map_context_result (f (PureThy.default_name name) atts props)
   466   |> these_facts
   467   |> (fn st => let_thms ("prems", ProofContext.assumptions (context_of st)) st);
   468 
   469 val assume = gen_assume ProofContext.assume;
   470 val assume_i = gen_assume ProofContext.assume_i;
   471 
   472 
   473 
   474 (** goals **)
   475 
   476 (* forward chaining *)
   477 
   478 fun chain state =
   479   state
   480   |> assert_forward
   481   |> enter_forward_chain;
   482 
   483 fun from_facts facts state =
   484   state
   485   |> put_facts (Some facts)
   486   |> chain;
   487 
   488 
   489 (* setup goals *)
   490 
   491 fun setup_goal opt_block prepp kind name atts raw_propp state =
   492   let
   493     val (state', concl) =
   494       state
   495       |> assert_forward_or_chain
   496       |> enter_forward
   497       |> opt_block
   498       |> map_context_result (fn c => prepp (c, raw_propp));
   499 
   500     val casms = map (#prop o Thm.crep_thm) (ProofContext.assumptions (context_of state'));
   501     val asms = map Thm.term_of casms;
   502 
   503     val prop = Logic.list_implies (asms, concl);
   504     val cprop = Thm.cterm_of (sign_of state') prop;
   505     val thm = Drule.mk_triv_goal cprop;
   506   in
   507     state'
   508     |> put_goal (Some ((kind atts, (PureThy.default_name name), casms, prop), ([], thm)))
   509     |> bind_props [("thesis", prop)]
   510     |> (if is_chain state then use_facts else reset_facts)
   511     |> new_block
   512     |> enter_backward
   513   end;
   514 
   515 
   516 (*global goals*)
   517 fun global_goal prep kind name atts x thy =
   518   setup_goal I prep kind name atts x (init_state thy);
   519 
   520 val theorem = global_goal ProofContext.bind_propp Theorem;
   521 val theorem_i = global_goal ProofContext.bind_propp_i Theorem;
   522 val lemma = global_goal ProofContext.bind_propp Lemma;
   523 val lemma_i = global_goal ProofContext.bind_propp_i Lemma;
   524 
   525 
   526 (*local goals*)
   527 fun local_goal prep kind name atts x =
   528   setup_goal open_block prep kind name atts x;
   529 
   530 val show   = local_goal ProofContext.bind_propp Goal;
   531 val show_i = local_goal ProofContext.bind_propp_i Goal;
   532 val have   = local_goal ProofContext.bind_propp Aux;
   533 val have_i = local_goal ProofContext.bind_propp_i Aux;
   534 
   535 
   536 
   537 (** blocks **)
   538 
   539 (* begin_block *)
   540 
   541 fun begin_block state =
   542   state
   543   |> assert_forward
   544   |> new_block
   545   |> reset_facts
   546   |> open_block;
   547 
   548 
   549 (* next_block *)
   550 
   551 fun next_block state =
   552   state
   553   |> assert_forward
   554   |> close_block
   555   |> new_block;
   556 
   557 
   558 
   559 (** conclusions **)
   560 
   561 (* current goal *)
   562 
   563 fun current_goal (State ({goal = Some goal, ...}, _)) = goal
   564   | current_goal state = raise STATE ("No current goal!", state);
   565 
   566 fun assert_current_goal true (state as State ({goal = None, ...}, _)) =
   567       raise STATE ("No goal in this block!", state)
   568   | assert_current_goal false (state as State ({goal = Some _, ...}, _)) =
   569       raise STATE ("Goal present in this block!", state)
   570   | assert_current_goal _ state = state;
   571 
   572 fun assert_bottom true (state as State (_, _ :: _)) =
   573       raise STATE ("Not at bottom of proof!", state)
   574   | assert_bottom false (state as State (_, [])) =
   575       raise STATE ("Already at bottom of proof!", state)
   576   | assert_bottom _ state = state;
   577 
   578 val at_bottom = can (assert_bottom true o close_block);
   579 
   580 
   581 (* finish proof *)
   582 
   583 fun check_finished state states =
   584   (case Seq.pull states of
   585     None => raise STATE ("Failed to finish proof", state)
   586   | Some s_sq => Seq.cons s_sq);
   587 
   588 fun finish_proof bot finalize state =
   589   state
   590   |> assert_forward
   591   |> close_block
   592   |> assert_bottom bot
   593   |> assert_current_goal true
   594   |> finalize
   595   |> check_finished state;
   596 
   597 
   598 (* end_block *)
   599 
   600 fun end_block state =
   601   state
   602   |> assert_forward
   603   |> close_block
   604   |> assert_current_goal false
   605   |> close_block
   606   |> fetch_facts state;
   607 
   608 
   609 (* local_qed *)
   610 
   611 fun finish_local state =
   612   let
   613     val ((kind, name, asms, t), (_, raw_thm)) = current_goal state;
   614     val result = prep_result state asms t raw_thm;
   615     val (atts, opt_solve) =
   616       (case kind of
   617         Goal atts => (atts, solve_goal result)
   618       | Aux atts => (atts, Seq.single)
   619       | _ => raise STATE ("No local goal!", state));
   620   in
   621     state
   622     |> close_block
   623     |> have_thmss name atts [Thm.no_attributes [result]]
   624     |> opt_solve
   625   end;
   626 
   627 fun local_qed finalize int state =	(* FIXME handle int *)
   628   state
   629   |> finish_proof false finalize
   630   |> (Seq.flat o Seq.map finish_local);
   631 
   632 
   633 (* global_qed *)
   634 
   635 fun finish_global alt_name alt_atts state =
   636   let
   637     val ((kind, def_name, asms, t), (_, raw_thm)) = current_goal state;
   638     val result = final_result state (prep_result state asms t raw_thm);
   639 
   640     val name = if_none alt_name def_name;
   641     val atts =
   642       (case kind of
   643         Theorem atts => if_none alt_atts atts
   644       | Lemma atts => (if_none alt_atts atts) @ [Drule.tag_lemma]
   645       | _ => raise STATE ("No global goal!", state));
   646 
   647     val (thy', result') = PureThy.store_thm ((name, result), atts) (theory_of state);
   648   in (thy', {kind = kind_name kind, name = name, thm = result'}) end;
   649 
   650 fun global_qed finalize alt_name alt_atts state =
   651   state
   652   |> finish_proof true finalize
   653   |> Seq.hd
   654   |> finish_global alt_name alt_atts;
   655 
   656 
   657 end;