src/HOL/Tools/Sledgehammer/sledgehammer_isar.ML
author blanchet
Mon Jun 02 17:34:26 2014 +0200 (2014-06-02 ago)
changeset 57158 f028d93798e6
parent 57154 f0eff6393a32
child 57245 f6bf6d5341ee
permissions -rw-r--r--
simplified counterexample handling
     1 (*  Title:      HOL/Tools/Sledgehammer/sledgehammer_isar.ML
     2     Author:     Jasmin Blanchette, TU Muenchen
     3     Author:     Steffen Juilf Smolka, TU Muenchen
     4 
     5 Isar proof reconstruction from ATP proofs.
     6 *)
     7 
     8 signature SLEDGEHAMMER_ISAR =
     9 sig
    10   type atp_step_name = ATP_Proof.atp_step_name
    11   type ('a, 'b) atp_step = ('a, 'b) ATP_Proof.atp_step
    12   type 'a atp_proof = 'a ATP_Proof.atp_proof
    13   type stature = ATP_Problem_Generate.stature
    14   type one_line_params = Sledgehammer_Proof_Methods.one_line_params
    15 
    16   val trace : bool Config.T
    17 
    18   type isar_params =
    19     bool * (string option * string option) * Time.time * real * bool * bool
    20     * (term, string) atp_step list * thm
    21 
    22   val proof_text : Proof.context -> bool -> bool option -> bool option -> (unit -> isar_params) ->
    23     int -> one_line_params -> string
    24 end;
    25 
    26 structure Sledgehammer_Isar : SLEDGEHAMMER_ISAR =
    27 struct
    28 
    29 open ATP_Util
    30 open ATP_Problem
    31 open ATP_Proof
    32 open ATP_Proof_Reconstruct
    33 open Sledgehammer_Util
    34 open Sledgehammer_Proof_Methods
    35 open Sledgehammer_Isar_Proof
    36 open Sledgehammer_Isar_Preplay
    37 open Sledgehammer_Isar_Compress
    38 open Sledgehammer_Isar_Minimize
    39 
    40 structure String_Redirect = ATP_Proof_Redirect(
    41   type key = atp_step_name
    42   val ord = fn ((s, _ : string list), (s', _)) => fast_string_ord (s, s')
    43   val string_of = fst)
    44 
    45 open String_Redirect
    46 
    47 val trace = Attrib.setup_config_bool @{binding sledgehammer_isar_trace} (K false)
    48 
    49 val e_skolemize_rules = ["skolemize", "shift_quantors"]
    50 val spass_pirate_datatype_rule = "DT"
    51 val vampire_skolemisation_rule = "skolemisation"
    52 (* TODO: Use "Z3_Proof.string_of_rule" once it is moved to Isabelle *)
    53 val z3_skolemize_rule = "sk"
    54 val z3_th_lemma_rule = "th-lemma"
    55 
    56 val skolemize_rules =
    57   e_skolemize_rules @ [spass_skolemize_rule, vampire_skolemisation_rule, z3_skolemize_rule]
    58 
    59 val is_skolemize_rule = member (op =) skolemize_rules
    60 val is_arith_rule = String.isPrefix z3_th_lemma_rule
    61 val is_datatype_rule = String.isPrefix spass_pirate_datatype_rule
    62 
    63 fun raw_label_of_num num = (num, 0)
    64 
    65 fun label_of_clause [(num, _)] = raw_label_of_num num
    66   | label_of_clause c = (space_implode "___" (map (fst o raw_label_of_num o fst) c), 0)
    67 
    68 fun add_fact_of_dependencies [(_, ss as _ :: _)] = apsnd (union (op =) ss)
    69   | add_fact_of_dependencies names = apfst (insert (op =) (label_of_clause names))
    70 
    71 fun is_True_prop t = t aconv @{prop True}
    72 
    73 fun add_line_pass1 (line as (name, role, t, rule, [])) lines =
    74     (* No dependencies: lemma (for Z3), fact, conjecture, or (for Vampire) internal facts or
    75        definitions. *)
    76     if role = Conjecture orelse role = Negated_Conjecture then line :: lines
    77     else if is_True_prop t then map (replace_dependencies_in_line (name, [])) lines
    78     else if role = Lemma orelse role = Hypothesis orelse is_arith_rule rule then line :: lines
    79     else if role = Axiom then lines (* axioms (facts) need no proof lines *)
    80     else map (replace_dependencies_in_line (name, [])) lines
    81   | add_line_pass1 line lines = line :: lines
    82 
    83 fun add_lines_pass2 res _ [] = rev res
    84   | add_lines_pass2 res prev_t ((line as (name, role, t, rule, deps)) :: lines) =
    85     let
    86       val is_last_line = null lines
    87 
    88       fun looks_interesting () =
    89         not (is_True_prop t) andalso not (t aconv prev_t) andalso null (Term.add_tvars t []) andalso
    90         length deps >= 2 andalso not (can the_single lines)
    91 
    92       fun is_skolemizing_line (_, _, _, rule', deps') =
    93         is_skolemize_rule rule' andalso member (op =) deps' name
    94       fun is_before_skolemize_rule () = exists is_skolemizing_line lines
    95     in
    96       if role <> Plain orelse is_skolemize_rule rule orelse is_arith_rule rule orelse
    97          is_datatype_rule rule orelse is_last_line orelse looks_interesting () orelse
    98          is_before_skolemize_rule () then
    99         add_lines_pass2 (line :: res) t lines
   100       else
   101         add_lines_pass2 res t (map (replace_dependencies_in_line (name, deps)) lines)
   102     end
   103 
   104 type isar_params =
   105   bool * (string option * string option) * Time.time * real * bool * bool
   106   * (term, string) atp_step list * thm
   107 
   108 val basic_systematic_methods = [Metis_Method (NONE, NONE), Meson_Method, Blast_Method, SATx_Method]
   109 val simp_based_methods = [Auto_Method, Simp_Method, Fastforce_Method, Force_Method]
   110 val basic_arith_methods = [Linarith_Method, Presburger_Method, Algebra_Method]
   111 
   112 val arith_methods = basic_arith_methods @ simp_based_methods @ basic_systematic_methods
   113 val datatype_methods = [Simp_Method, Simp_Size_Method]
   114 val systematic_methods0 = basic_systematic_methods @ basic_arith_methods @ simp_based_methods @
   115   [Metis_Method (SOME no_typesN, NONE)]
   116 val rewrite_methods = simp_based_methods @ basic_systematic_methods @ basic_arith_methods
   117 val skolem_methods = basic_systematic_methods
   118 
   119 fun isar_proof_text ctxt debug isar_proofs smt_proofs isar_params
   120     (one_line_params as (_, _, _, _, subgoal, subgoal_count)) =
   121   let
   122     val _ = if debug then Output.urgent_message "Constructing Isar proof..." else ()
   123 
   124     fun isar_proof_of () =
   125       let
   126         val (verbose, alt_metis_args, preplay_timeout, compress_isar, try0_isar, minimize,
   127           atp_proof, goal) = isar_params ()
   128 
   129         val systematic_methods = insert (op =) (Metis_Method alt_metis_args) systematic_methods0
   130 
   131         fun massage_methods (meths as meth :: _) =
   132           if not try0_isar then [meth]
   133           else if smt_proofs = SOME true then SMT2_Method :: meths
   134           else meths
   135 
   136         val (params, _, concl_t) = strip_subgoal goal subgoal ctxt
   137         val fixes = map (fn (s, T) => (Binding.name s, SOME T, NoSyn)) params
   138         val ctxt = ctxt |> Variable.set_body false |> Proof_Context.add_fixes fixes |> snd
   139 
   140         val do_preplay = preplay_timeout <> Time.zeroTime
   141         val compress_isar = if isar_proofs = NONE andalso do_preplay then 1000.0 else compress_isar
   142 
   143         val is_fixed = Variable.is_declared ctxt orf Name.is_skolem
   144         fun skolems_of t = Term.add_frees t [] |> filter_out (is_fixed o fst) |> rev
   145 
   146         fun get_role keep_role ((num, _), role, t, rule, _) =
   147           if keep_role role then SOME ((raw_label_of_num num, t), rule) else NONE
   148 
   149         val atp_proof =
   150           atp_proof
   151           |> rpair [] |-> fold_rev add_line_pass1
   152           |> add_lines_pass2 [] Term.dummy
   153 
   154         val conjs =
   155           map_filter (fn (name, role, _, _, _) =>
   156               if member (op =) [Conjecture, Negated_Conjecture] role then SOME name else NONE)
   157             atp_proof
   158         val assms = map_filter (Option.map fst o get_role (curry (op =) Hypothesis)) atp_proof
   159         val lems =
   160           map_filter (get_role (curry (op =) Lemma)) atp_proof
   161           |> map (fn ((l, t), rule) =>
   162             let
   163               val (skos, meths) =
   164                 (if is_skolemize_rule rule then (skolems_of t, skolem_methods)
   165                  else if is_arith_rule rule then ([], arith_methods)
   166                  else ([], rewrite_methods))
   167                 ||> massage_methods
   168             in
   169               Prove ([], skos, l, t, [], ([], []), meths, "")
   170             end)
   171 
   172         val bot = atp_proof |> List.last |> #1
   173 
   174         val refute_graph =
   175           atp_proof
   176           |> map (fn (name, _, _, _, from) => (from, name))
   177           |> make_refute_graph bot
   178           |> fold (Atom_Graph.default_node o rpair ()) conjs
   179 
   180         val axioms = axioms_of_refute_graph refute_graph conjs
   181 
   182         val tainted = tainted_atoms_of_refute_graph refute_graph conjs
   183         val is_clause_tainted = exists (member (op =) tainted)
   184         val steps =
   185           Symtab.empty
   186           |> fold (fn (name as (s, _), role, t, rule, _) =>
   187               Symtab.update_new (s, (rule, t
   188                 |> (if is_clause_tainted [name] then
   189                       HOLogic.dest_Trueprop
   190                       #> role <> Conjecture ? s_not
   191                       #> fold exists_of (map Var (Term.add_vars t []))
   192                       #> HOLogic.mk_Trueprop
   193                     else
   194                       I))))
   195             atp_proof
   196 
   197         val rule_of_clause_id = fst o the o Symtab.lookup steps o fst
   198 
   199         fun prop_of_clause [(num, _)] = Symtab.lookup steps num |> the |> snd |> close_form
   200           | prop_of_clause names =
   201             let
   202               val lits = map (HOLogic.dest_Trueprop o snd)
   203                 (map_filter (Symtab.lookup steps o fst) names)
   204             in
   205               (case List.partition (can HOLogic.dest_not) lits of
   206                 (negs as _ :: _, pos as _ :: _) =>
   207                 s_imp (Library.foldr1 s_conj (map HOLogic.dest_not negs), Library.foldr1 s_disj pos)
   208               | _ => fold (curry s_disj) lits @{term False})
   209             end
   210             |> HOLogic.mk_Trueprop |> close_form
   211 
   212         fun maybe_show outer c = (outer andalso eq_set (op =) (c, conjs)) ? cons Show
   213 
   214         fun isar_steps outer predecessor accum [] =
   215             accum
   216             |> (if tainted = [] then
   217                   cons (Prove (if outer then [Show] else [], [], no_label, concl_t, [],
   218                     (the_list predecessor, []), massage_methods systematic_methods, ""))
   219                 else
   220                   I)
   221             |> rev
   222           | isar_steps outer _ accum (Have (id, (gamma, c)) :: infs) =
   223             let
   224               val l = label_of_clause c
   225               val t = prop_of_clause c
   226               val rule = rule_of_clause_id id
   227               val skolem = is_skolemize_rule rule
   228 
   229               val deps = fold add_fact_of_dependencies gamma ([], [])
   230               val meths =
   231                 (if skolem then skolem_methods
   232                  else if is_arith_rule rule then arith_methods
   233                  else if is_datatype_rule rule then datatype_methods
   234                  else systematic_methods)
   235                 |> massage_methods
   236 
   237               fun prove sub facts = Prove (maybe_show outer c [], [], l, t, sub, facts, meths, "")
   238               fun steps_of_rest step = isar_steps outer (SOME l) (step :: accum) infs
   239             in
   240               if is_clause_tainted c then
   241                 (case gamma of
   242                   [g] =>
   243                   if skolem andalso is_clause_tainted g then
   244                     let val subproof = Proof (skolems_of (prop_of_clause g), [], rev accum) in
   245                       isar_steps outer (SOME l) [prove [subproof] ([], [])] infs
   246                     end
   247                   else
   248                     steps_of_rest (prove [] deps)
   249                 | _ => steps_of_rest (prove [] deps))
   250               else
   251                 steps_of_rest (if skolem then Prove ([], skolems_of t, l, t, [], deps, meths, "")
   252                   else prove [] deps)
   253             end
   254           | isar_steps outer predecessor accum (Cases cases :: infs) =
   255             let
   256               fun isar_case (c, subinfs) =
   257                 isar_proof false [] [(label_of_clause c, prop_of_clause c)] [] subinfs
   258               val c = succedent_of_cases cases
   259               val l = label_of_clause c
   260               val t = prop_of_clause c
   261               val step =
   262                 Prove (maybe_show outer c [], [], l, t,
   263                   map isar_case (filter_out (null o snd) cases),
   264                   (the_list predecessor, []), massage_methods systematic_methods, "")
   265             in
   266               isar_steps outer (SOME l) (step :: accum) infs
   267             end
   268         and isar_proof outer fix assms lems infs =
   269           Proof (fix, assms, lems @ isar_steps outer NONE [] infs)
   270 
   271         val trace = Config.get ctxt trace
   272 
   273         val canonical_isar_proof =
   274           refute_graph
   275           |> trace ? tap (tracing o prefix "Refute graph: " o string_of_refute_graph)
   276           |> redirect_graph axioms tainted bot
   277           |> trace ? tap (tracing o prefix "Direct proof: " o string_of_direct_proof)
   278           |> isar_proof true params assms lems
   279           |> postprocess_isar_proof_remove_unreferenced_steps I
   280           |> relabel_isar_proof_canonically
   281 
   282         val ctxt = ctxt |> enrich_context_with_local_facts canonical_isar_proof
   283 
   284         val preplay_data = Unsynchronized.ref Canonical_Label_Tab.empty
   285 
   286         val _ = fold_isar_steps (fn meth =>
   287             K (set_preplay_outcomes_of_isar_step ctxt preplay_timeout preplay_data meth []))
   288           (steps_of_isar_proof canonical_isar_proof) ()
   289 
   290         fun str_of_preplay_outcome outcome =
   291           if Lazy.is_finished outcome then string_of_play_outcome (Lazy.force outcome) else "?"
   292         fun str_of_meth l meth =
   293           string_of_proof_method ctxt [] meth ^ " " ^
   294           str_of_preplay_outcome (preplay_outcome_of_isar_step_for_method (!preplay_data) l meth)
   295         fun comment_of l = map (str_of_meth l) #> commas
   296 
   297         fun trace_isar_proof label proof =
   298           if trace then
   299             tracing (timestamp () ^ "\n" ^ label ^ ":\n\n" ^
   300               string_of_isar_proof ctxt subgoal subgoal_count
   301                 (comment_isar_proof comment_of proof) ^ "\n")
   302           else
   303             ()
   304 
   305         fun comment_of l (meth :: _) =
   306           (case (verbose,
   307               Lazy.force (preplay_outcome_of_isar_step_for_method (!preplay_data) l meth)) of
   308             (false, Played _) => ""
   309           | (_, outcome) => string_of_play_outcome outcome)
   310 
   311         val (play_outcome, isar_proof) =
   312           canonical_isar_proof
   313           |> tap (trace_isar_proof "Original")
   314           |> compress_isar_proof ctxt compress_isar preplay_timeout preplay_data
   315           |> tap (trace_isar_proof "Compressed")
   316           |> postprocess_isar_proof_remove_unreferenced_steps
   317                (keep_fastest_method_of_isar_step (!preplay_data)
   318                 #> minimize ? minimize_isar_step_dependencies ctxt preplay_data)
   319           |> tap (trace_isar_proof "Minimized")
   320           (* It's not clear whether this is worth the trouble (and if so, "isar_compress" has an
   321              unnatural semantics): *)
   322 (*
   323           |> minimize
   324                ? (compress_isar_proof ctxt compress_isar preplay_timeout preplay_data
   325                   #> tap (trace_isar_proof "Compressed again"))
   326 *)
   327           |> `(preplay_outcome_of_isar_proof (!preplay_data))
   328           ||> (comment_isar_proof comment_of
   329                #> chain_isar_proof
   330                #> kill_useless_labels_in_isar_proof
   331                #> relabel_isar_proof_nicely)
   332       in
   333         (case string_of_isar_proof ctxt subgoal subgoal_count isar_proof of
   334           "" =>
   335           if isar_proofs = SOME true then "\nNo structured proof available (proof too simple)."
   336           else ""
   337         | isar_text =>
   338           let
   339             val msg =
   340               (if verbose then
   341                  let val num_steps = add_isar_steps (steps_of_isar_proof isar_proof) 0 in
   342                    [string_of_int num_steps ^ " step" ^ plural_s num_steps]
   343                  end
   344                else
   345                  []) @
   346               (if do_preplay then [string_of_play_outcome play_outcome] else [])
   347           in
   348             "\n\nStructured proof" ^ (commas msg |> not (null msg) ? enclose " (" ")") ^ ":\n" ^
   349             Active.sendback_markup [Markup.padding_command] isar_text
   350           end)
   351       end
   352 
   353     val one_line_proof = one_line_proof_text ctxt 0 one_line_params
   354     val isar_proof =
   355       if debug then
   356         isar_proof_of ()
   357       else
   358         (case try isar_proof_of () of
   359           SOME s => s
   360         | NONE =>
   361           if isar_proofs = SOME true then "\nWarning: Isar proof construction failed." else "")
   362   in
   363     one_line_proof ^ isar_proof
   364   end
   365 
   366 fun isar_proof_would_be_a_good_idea smt_proofs (meth, play) =
   367   (case play of
   368     Played _ => meth = SMT2_Method andalso smt_proofs <> SOME true
   369   | Play_Timed_Out time => Time.> (time, Time.zeroTime)
   370   | Play_Failed => true)
   371 
   372 fun proof_text ctxt debug isar_proofs smt_proofs isar_params num_chained
   373     (one_line_params as (preplay, _, _, _, _, _)) =
   374   (if isar_proofs = SOME true orelse
   375       (isar_proofs = NONE andalso isar_proof_would_be_a_good_idea smt_proofs preplay) then
   376      isar_proof_text ctxt debug isar_proofs smt_proofs isar_params
   377    else
   378      one_line_proof_text ctxt num_chained) one_line_params
   379 
   380 end;