(*  Title:      HOL/Tools/Sledgehammer/sledgehammer_isar.ML

     Author:     Jasmin Blanchette, TU Muenchen

     Author:     Steffen Juilf Smolka, TU Muenchen

 Isar proof reconstruction from ATP proofs.

 *)

 signature SLEDGEHAMMER_ISAR =

 sig

   type atp_step_name = ATP_Proof.atp_step_name

   type ('a, 'b) atp_step = ('a, 'b) ATP_Proof.atp_step

   type 'a atp_proof = 'a ATP_Proof.atp_proof

   type stature = ATP_Problem_Generate.stature

   type one_line_params = Sledgehammer_Proof_Methods.one_line_params

   val trace : bool Config.T

   type isar_params =

     bool * (string option * string option) * Time.time * real * bool * bool

     * (term, string) atp_step list * thm

   val proof_text : Proof.context -> bool -> bool option -> bool option -> (unit -> isar_params) ->

     int -> one_line_params -> string

 end;

 structure Sledgehammer_Isar : SLEDGEHAMMER_ISAR =

 struct

 open ATP_Util

 open ATP_Problem

 open ATP_Proof

 open ATP_Proof_Reconstruct

 open Sledgehammer_Util

 open Sledgehammer_Proof_Methods

 open Sledgehammer_Isar_Proof

 open Sledgehammer_Isar_Preplay

 open Sledgehammer_Isar_Compress

 open Sledgehammer_Isar_Minimize

 structure String_Redirect = ATP_Proof_Redirect(

   type key = atp_step_name

   val ord = fn ((s, _ : string list), (s', _)) => fast_string_ord (s, s')

   val string_of = fst)

 open String_Redirect

 val trace = Attrib.setup_config_bool @{binding sledgehammer_isar_trace} (K false)

 val e_skolemize_rules = ["skolemize", "shift_quantors"]

 val spass_pirate_datatype_rule = "DT"

 val vampire_skolemisation_rule = "skolemisation"

 (* TODO: Use "Z3_Proof.string_of_rule" once it is moved to Isabelle *)

 val z3_skolemize_rule = "sk"

 val z3_th_lemma_rule = "th-lemma"

 val skolemize_rules =

   e_skolemize_rules @ [spass_skolemize_rule, vampire_skolemisation_rule, z3_skolemize_rule]

 val is_skolemize_rule = member (op =) skolemize_rules

 val is_arith_rule = String.isPrefix z3_th_lemma_rule

 val is_datatype_rule = String.isPrefix spass_pirate_datatype_rule

 fun raw_label_of_num num = (num, 0)

 fun label_of_clause [(num, _)] = raw_label_of_num num

   | label_of_clause c = (space_implode "___" (map (fst o raw_label_of_num o fst) c), 0)

 fun add_fact_of_dependencies [(_, ss as _ :: _)] = apsnd (union (op =) ss)

   | add_fact_of_dependencies names = apfst (insert (op =) (label_of_clause names))

 (* No "real" literals means only type information (tfree_tcs, clsrel, or clsarity). *)

 fun is_only_type_information t = t aconv @{prop True}

 (* Discard facts; consolidate adjacent lines that prove the same formula, since they differ only in

    type information. *)

 fun add_line_pass1 (line as (name, role, t, rule, [])) lines =

     (* No dependencies: lemma (for Z3), fact, conjecture, or (for Vampire) internal facts or

        definitions. *)

     if role = Lemma orelse role = Conjecture orelse role = Negated_Conjecture orelse

        role = Hypothesis orelse is_arith_rule rule then

       line :: lines

     else if role = Axiom then

       (* Facts are not proof lines. *)

       lines |> is_only_type_information t ? map (replace_dependencies_in_line (name, []))

     else

       map (replace_dependencies_in_line (name, [])) lines

   | add_line_pass1 line lines = line :: lines

 fun add_lines_pass2 res [] = rev res

   | add_lines_pass2 res ((line as (name, role, t, rule, deps)) :: lines) =

     let

       val is_last_line = null lines

       fun looks_interesting () =

         not (is_only_type_information t) andalso null (Term.add_tvars t [])

         andalso length deps >= 2 andalso not (can the_single lines)

       fun is_skolemizing_line (_, _, _, rule', deps') =

         is_skolemize_rule rule' andalso member (op =) deps' name

       fun is_before_skolemize_rule () = exists is_skolemizing_line lines

     in

       if role <> Plain orelse is_skolemize_rule rule orelse is_arith_rule rule orelse

          is_datatype_rule rule orelse is_last_line orelse looks_interesting () orelse

          is_before_skolemize_rule () then

         add_lines_pass2 (line :: res) lines

       else

         add_lines_pass2 res (map (replace_dependencies_in_line (name, deps)) lines)

     end

 type isar_params =

   bool * (string option * string option) * Time.time * real * bool * bool

   * (term, string) atp_step list * thm

 val basic_systematic_methods = [Metis_Method (NONE, NONE), Meson_Method, Blast_Method]

 val simp_based_methods = [Auto_Method, Simp_Method, Fastforce_Method, Force_Method]

 val basic_arith_methods = [Linarith_Method, Presburger_Method, Algebra_Method]

 val arith_methods = basic_arith_methods @ simp_based_methods @ basic_systematic_methods

 val datatype_methods = [Simp_Method, Simp_Size_Method]

 val systematic_methods0 = basic_systematic_methods @ basic_arith_methods @ simp_based_methods @

   [Metis_Method (SOME no_typesN, NONE)]

 val rewrite_methods = simp_based_methods @ basic_systematic_methods @ basic_arith_methods

 val skolem_methods = basic_systematic_methods

 fun isar_proof_text ctxt debug isar_proofs smt_proofs isar_params

     (one_line_params as (_, _, _, _, subgoal, subgoal_count)) =

   let

     val _ = if debug then Output.urgent_message "Constructing Isar proof..." else ()

     fun isar_proof_of () =

       let

         val SOME (verbose, alt_metis_args, preplay_timeout, compress_isar, try0_isar, minimize,

           atp_proof, goal) = try isar_params ()

         val systematic_methods = insert (op =) (Metis_Method alt_metis_args) systematic_methods0

         fun massage_methods (meths as meth :: _) =

           if not try0_isar then [meth]

           else if smt_proofs = SOME true then SMT2_Method :: meths

           else meths

         val (params, _, concl_t) = strip_subgoal goal subgoal ctxt

         val fixes = map (fn (s, T) => (Binding.name s, SOME T, NoSyn)) params

         val ctxt = ctxt |> Variable.set_body false |> Proof_Context.add_fixes fixes |> snd

         val do_preplay = preplay_timeout <> Time.zeroTime

         val compress_isar = if isar_proofs = NONE andalso do_preplay then 1000.0 else compress_isar

         val is_fixed = Variable.is_declared ctxt orf Name.is_skolem

         fun skolems_of t = Term.add_frees t [] |> filter_out (is_fixed o fst) |> rev

         fun get_role keep_role ((num, _), role, t, rule, _) =

           if keep_role role then SOME ((raw_label_of_num num, t), rule) else NONE

         val atp_proof =

           atp_proof

           |> rpair [] |-> fold_rev add_line_pass1

           |> add_lines_pass2 []

         val conjs =

           map_filter (fn (name, role, _, _, _) =>

               if member (op =) [Conjecture, Negated_Conjecture] role then SOME name else NONE)

             atp_proof

         val assms = map_filter (Option.map fst o get_role (curry (op =) Hypothesis)) atp_proof

         val lems =

           map_filter (get_role (curry (op =) Lemma)) atp_proof

           |> map (fn ((l, t), rule) =>

             let

               val (skos, meths) =

                 (if is_skolemize_rule rule then (skolems_of t, skolem_methods)

                  else if is_arith_rule rule then ([], arith_methods)

                  else ([], rewrite_methods))

                 ||> massage_methods

             in

               Prove ([], skos, l, t, [], ([], []), meths, "")

             end)

         val bot = atp_proof |> List.last |> #1

         val refute_graph =

           atp_proof

           |> map (fn (name, _, _, _, from) => (from, name))

           |> make_refute_graph bot

           |> fold (Atom_Graph.default_node o rpair ()) conjs

         val axioms = axioms_of_refute_graph refute_graph conjs

         val tainted = tainted_atoms_of_refute_graph refute_graph conjs

         val is_clause_tainted = exists (member (op =) tainted)

         val steps =

           Symtab.empty

           |> fold (fn (name as (s, _), role, t, rule, _) =>

               Symtab.update_new (s, (rule, t

                 |> (if is_clause_tainted [name] then

                       HOLogic.dest_Trueprop

                       #> role <> Conjecture ? s_not

                       #> fold exists_of (map Var (Term.add_vars t []))

                       #> HOLogic.mk_Trueprop

                     else

                       I))))

             atp_proof

         val rule_of_clause_id = fst o the o Symtab.lookup steps o fst

         fun prop_of_clause [(num, _)] = Symtab.lookup steps num |> the |> snd |> close_form

           | prop_of_clause names =

             let

               val lits = map (HOLogic.dest_Trueprop o snd)

                 (map_filter (Symtab.lookup steps o fst) names)

             in

               (case List.partition (can HOLogic.dest_not) lits of

                 (negs as _ :: _, pos as _ :: _) =>

                 s_imp (Library.foldr1 s_conj (map HOLogic.dest_not negs), Library.foldr1 s_disj pos)

               | _ => fold (curry s_disj) lits @{term False})

             end

             |> HOLogic.mk_Trueprop |> close_form

         fun maybe_show outer c = (outer andalso eq_set (op =) (c, conjs)) ? cons Show

         fun isar_steps outer predecessor accum [] =

             accum

             |> (if tainted = [] then

                   cons (Prove (if outer then [Show] else [], [], no_label, concl_t, [],

                     (the_list predecessor, []), massage_methods systematic_methods, ""))

                 else

                   I)

             |> rev

           | isar_steps outer _ accum (Have (id, (gamma, c)) :: infs) =

             let

               val l = label_of_clause c

               val t = prop_of_clause c

               val rule = rule_of_clause_id id

               val skolem = is_skolemize_rule rule

               val deps = fold add_fact_of_dependencies gamma ([], [])

               val meths =

                 (if skolem then skolem_methods

                  else if is_arith_rule rule then arith_methods

                  else if is_datatype_rule rule then datatype_methods

                  else systematic_methods)

                 |> massage_methods

               fun prove sub facts = Prove (maybe_show outer c [], [], l, t, sub, facts, meths, "")

               fun steps_of_rest step = isar_steps outer (SOME l) (step :: accum) infs

             in

               if is_clause_tainted c then

                 (case gamma of

                   [g] =>

                   if skolem andalso is_clause_tainted g then

                     let val subproof = Proof (skolems_of (prop_of_clause g), [], rev accum) in

                       isar_steps outer (SOME l) [prove [subproof] ([], [])] infs

                     end

                   else

                     steps_of_rest (prove [] deps)

                 | _ => steps_of_rest (prove [] deps))

               else

                 steps_of_rest (if skolem then Prove ([], skolems_of t, l, t, [], deps, meths, "")

                   else prove [] deps)

             end

           | isar_steps outer predecessor accum (Cases cases :: infs) =

             let

               fun isar_case (c, subinfs) =

                 isar_proof false [] [(label_of_clause c, prop_of_clause c)] [] subinfs

               val c = succedent_of_cases cases

               val l = label_of_clause c

               val t = prop_of_clause c

               val step =

                 Prove (maybe_show outer c [], [], l, t,

                   map isar_case (filter_out (null o snd) cases),

                   (the_list predecessor, []), massage_methods systematic_methods, "")

             in

               isar_steps outer (SOME l) (step :: accum) infs

             end

         and isar_proof outer fix assms lems infs =

           Proof (fix, assms, lems @ isar_steps outer NONE [] infs)

         val trace = Config.get ctxt trace

         val canonical_isar_proof =

           refute_graph

           |> trace ? tap (tracing o prefix "Refute graph: " o string_of_refute_graph)

           |> redirect_graph axioms tainted bot

           |> trace ? tap (tracing o prefix "Direct proof: " o string_of_direct_proof)

           |> isar_proof true params assms lems

           |> postprocess_isar_proof_remove_unreferenced_steps I

           |> relabel_isar_proof_canonically

         val ctxt = ctxt |> enrich_context_with_local_facts canonical_isar_proof

         val preplay_data = Unsynchronized.ref Canonical_Label_Tab.empty

         val _ = fold_isar_steps (fn meth =>

             K (set_preplay_outcomes_of_isar_step ctxt debug preplay_timeout preplay_data meth []))

           (steps_of_isar_proof canonical_isar_proof) ()

         fun str_of_preplay_outcome outcome =

           if Lazy.is_finished outcome then string_of_play_outcome (Lazy.force outcome) else "?"

         fun str_of_meth l meth =

           string_of_proof_method meth ^ " " ^

           str_of_preplay_outcome (preplay_outcome_of_isar_step_for_method (!preplay_data) l meth)

         fun comment_of l = map (str_of_meth l) #> commas

         fun trace_isar_proof label proof =

           if trace then

             tracing (timestamp () ^ "\n" ^ label ^ ":\n\n" ^

               string_of_isar_proof ctxt subgoal subgoal_count

                 (comment_isar_proof comment_of proof) ^ "\n")

           else

             ()

         fun comment_of l (meth :: _) =

           (case (verbose,

               Lazy.force (preplay_outcome_of_isar_step_for_method (!preplay_data) l meth)) of

             (false, Played _) => ""

           | (_, outcome) => string_of_play_outcome outcome)

         val (play_outcome, isar_proof) =

           canonical_isar_proof

           |> tap (trace_isar_proof "Original")

           |> compress_isar_proof ctxt debug compress_isar preplay_timeout preplay_data

           |> tap (trace_isar_proof "Compressed")

           |> postprocess_isar_proof_remove_unreferenced_steps

                (keep_fastest_method_of_isar_step (!preplay_data)

                 #> minimize ? minimize_isar_step_dependencies ctxt debug preplay_data)

           |> tap (trace_isar_proof "Minimized")

           (* It's not clear whether this is worth the trouble (and if so, "isar_compress" has an

              unnatural semantics): *)

 (*

           |> minimize

                ? (compress_isar_proof ctxt compress_isar preplay_timeout preplay_data

                   #> tap (trace_isar_proof "Compressed again"))

 *)

           |> `(preplay_outcome_of_isar_proof (!preplay_data))

           ||> (comment_isar_proof comment_of

                #> chain_isar_proof

                #> kill_useless_labels_in_isar_proof

                #> relabel_isar_proof_nicely)

       in

         (case string_of_isar_proof ctxt subgoal subgoal_count isar_proof of

           "" =>

           if isar_proofs = SOME true then "\nNo structured proof available (proof too simple)."

           else ""

         | isar_text =>

           let

             val msg =

               (if verbose then

                  let val num_steps = add_isar_steps (steps_of_isar_proof isar_proof) 0 in

                    [string_of_int num_steps ^ " step" ^ plural_s num_steps]

                  end

                else

                  []) @

               (if do_preplay then [string_of_play_outcome play_outcome] else [])

           in

             "\n\nStructured proof" ^ (commas msg |> not (null msg) ? enclose " (" ")") ^ ":\n" ^

             Active.sendback_markup [Markup.padding_command] isar_text

           end)

       end

     val one_line_proof = one_line_proof_text 0 one_line_params

     val isar_proof =

       if debug then

         isar_proof_of ()

       else

         (case try isar_proof_of () of

           SOME s => s

         | NONE =>

           if isar_proofs = SOME true then "\nWarning: Isar proof construction failed." else "")

   in one_line_proof ^ isar_proof end

 fun isar_proof_would_be_a_good_idea smt_proofs (meth, play) =

   (case play of

     Played _ => meth = SMT2_Method andalso smt_proofs <> SOME true

   | Play_Timed_Out time => Time.> (time, Time.zeroTime)

   | Play_Failed => true)

 fun proof_text ctxt debug isar_proofs smt_proofs isar_params num_chained

     (one_line_params as (preplay, _, _, _, _, _)) =

   (if isar_proofs = SOME true orelse

       (isar_proofs = NONE andalso isar_proof_would_be_a_good_idea smt_proofs preplay) then

      isar_proof_text ctxt debug isar_proofs smt_proofs isar_params

    else

      one_line_proof_text num_chained) one_line_params

 end;