(*  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 option * 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 ATP_Waldmeister

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>\<open>sledgehammer_isar_trace\<close> (K false)

val e_definition_rule = "definition"

val e_skolemize_rule = "skolemize"

val leo2_extcnf_forall_neg_rule = "extcnf_forall_neg"

val pirate_datatype_rule = "DT"

val satallax_skolemize_rule = "tab_ex"

val vampire_skolemisation_rule = "skolemisation"

val veriT_la_generic_rule = "la_generic"

val veriT_simp_arith_rule = "simp_arith"

val veriT_tmp_skolemize_rule = "tmp_skolemize"

val z3_skolemize_rule = Z3_Proof.string_of_rule Z3_Proof.Skolemize

val z3_th_lemma_rule_prefix = Z3_Proof.string_of_rule (Z3_Proof.Th_Lemma "")

val zipperposition_cnf_rule = "cnf"

val skolemize_rules =

  [e_definition_rule, e_skolemize_rule, leo2_extcnf_forall_neg_rule, satallax_skolemize_rule,

   spass_skolemize_rule, vampire_skolemisation_rule,

   veriT_tmp_skolemize_rule, waldmeister_skolemize_rule, z3_skolemize_rule, zipperposition_cnf_rule]

fun is_ext_rule rule = (rule = leo2_extcnf_equal_neg_rule)

val is_maybe_ext_rule = is_ext_rule orf String.isPrefix satallax_tab_rule_prefix

val is_skolemize_rule = member (op =) skolemize_rules

fun is_arith_rule rule =

  String.isPrefix z3_th_lemma_rule_prefix rule orelse rule = veriT_simp_arith_rule orelse

  rule = veriT_la_generic_rule

val is_datatype_rule = String.isPrefix 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_global_fact ss = apsnd (union (op =) ss)

fun add_fact_of_dependency [(_, ss as _ :: _)] = add_global_fact ss

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

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 = Conjecture orelse role = Negated_Conjecture then

      line :: lines

    else if t aconv \<^prop>\<open>True\<close> then

      map (replace_dependencies_in_line (name, [])) lines

    else if role = Lemma orelse role = Hypothesis orelse is_arith_rule rule then

      line :: lines

    else if role = Axiom then

      lines (* axioms (facts) need no proof lines *)

    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

      fun normalize role =

        role = Conjecture ? (HOLogic.dest_Trueprop #> s_not #> HOLogic.mk_Trueprop)

      val norm_t = normalize role t

      val is_duplicate =

        exists (fn (prev_name, prev_role, prev_t, _, _) =>

            (prev_role = Hypothesis andalso prev_t aconv t) orelse

            (member (op =) deps prev_name andalso

             Term.aconv_untyped (normalize prev_role prev_t, norm_t)))

          res

      fun looks_boring () = t aconv \<^prop>\<open>False\<close> orelse length deps < 2

      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 is_duplicate orelse

          (role = Plain andalso not (is_skolemize_rule rule) andalso

           not (is_ext_rule rule) andalso not (is_arith_rule rule) andalso

           not (is_datatype_rule rule) andalso not (null lines) andalso looks_boring () andalso

           not (is_before_skolemize_rule ())) then

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

      else

        add_lines_pass2 (line :: res) lines

    end

type isar_params =

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

  * (term, string) atp_step list * thm

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

val basic_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 @ basic_simp_based_methods @ basic_systematic_methods

val datatype_methods = [Simp_Method, Simp_Size_Method]

val systematic_methods =

  basic_systematic_methods @ basic_arith_methods @ basic_simp_based_methods @

  [Metis_Method (SOME full_typesN, NONE), Metis_Method (SOME no_typesN, NONE)]

val rewrite_methods = basic_simp_based_methods @ basic_systematic_methods @ basic_arith_methods

val skolem_methods = Moura_Method :: systematic_methods

fun isar_proof_text ctxt debug num_chained isar_proofs smt_proofs isar_params

    (one_line_params as ((used_facts, (_, one_line_play)), banner, subgoal, subgoal_count)) =

  let

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

    fun generate_proof_text () =

      let

        val (verbose, alt_metis_args, preplay_timeout, compress, try0, minimize, atp_proof0, goal) =

          isar_params ()

      in

        if null atp_proof0 then

          one_line_proof_text ctxt 0 one_line_params

        else

          let

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

            fun massage_methods (meths as meth :: _) =

              if not try0 then [meth]

              else if smt_proofs = SOME true then SMT_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 =

              (case compress of

                NONE => if isar_proofs = NONE andalso do_preplay then 1000.0 else 10.0

              | SOME n => n)

            fun is_fixed ctxt = Variable.is_declared ctxt orf Name.is_skolem

            fun skolems_of ctxt t = Term.add_frees t [] |> filter_out (is_fixed ctxt 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 =

              fold_rev add_line_pass1 atp_proof0 []

              |> 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

            fun add_lemma ((l, t), rule) ctxt =

              let

                val (skos, meths) =

                  (if is_skolemize_rule rule then (skolems_of ctxt t, skolem_methods)

                   else if is_arith_rule rule then ([], arith_methods)

                   else ([], rewrite_methods))

                  ||> massage_methods

              in

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

                 ctxt |> not (null skos) ? (Variable.add_fixes (map fst skos) #> snd))

              end

            val (lems, _) =

              fold_map add_lemma (map_filter (get_role (curry (op =) Lemma)) atp_proof) ctxt

            val bot = #1 (List.last atp_proof)

            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

            fun is_referenced_in_step _ (Let _) = false

              | is_referenced_in_step l (Prove (_, _, _, _, subs, (ls, _), _, _)) =

                member (op =) ls l orelse exists (is_referenced_in_proof l) subs

            and is_referenced_in_proof l (Proof (_, _, steps)) =

              exists (is_referenced_in_step l) steps

            fun insert_lemma_in_step lem

                (step as Prove (qs, fix, l, t, subs, (ls, gs), meths, comment)) =

              let val l' = the (label_of_isar_step lem) in

                if member (op =) ls l' then

                  [lem, step]

                else

                  let val refs = map (is_referenced_in_proof l') subs in

                    if length (filter I refs) = 1 then

                      let

                        val subs' = map2 (fn false => I | true => insert_lemma_in_proof lem) refs

                          subs

                      in

                        [Prove (qs, fix, l, t, subs', (ls, gs), meths, comment)]

                      end

                    else

                      [lem, step]

                  end

              end

            and insert_lemma_in_steps lem [] = [lem]

              | insert_lemma_in_steps lem (step :: steps) =

                if is_referenced_in_step (the (label_of_isar_step lem)) step then

                  insert_lemma_in_step lem step @ steps

                else

                  step :: insert_lemma_in_steps lem steps

            and insert_lemma_in_proof lem (Proof (fix, assms, steps)) =

              Proof (fix, assms, insert_lemma_in_steps lem steps)

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

            val finish_off = close_form #> rename_bound_vars

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

              | 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>\<open>False\<close>)

                end

                |> HOLogic.mk_Trueprop |> finish_off

            fun maybe_show outer c = if outer andalso eq_set (op =) (c, conjs) then [Show] else []

            fun isar_steps outer predecessor accum [] =

                accum

                |> (if tainted = [] then

                      (* e.g., trivial, empty proof by Z3 *)

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

                        sort_facts (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_dependency gamma

                    |> is_maybe_ext_rule rule ? add_global_fact [short_thm_name ctxt ext]

                    |> sort_facts

                  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 skos = skolems_of ctxt (prop_of_clause g)

                          val subproof = Proof (skos, [], 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

                         (case skolems_of ctxt t of

                           [] => prove [] deps

                         | skos => Prove ([], skos, 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),

                      sort_facts (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,

                fold_rev insert_lemma_in_steps 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:\n" o string_of_refute_graph)

              |> redirect_graph axioms tainted bot

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

              |> isar_proof true params assms lems

              |> postprocess_isar_proof_remove_show_stuttering

              |> 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 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 ctxt [] 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 compress 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 preplay_data)

              |> tap (trace_isar_proof "Minimized")

              |> `(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

                   #> rationalize_obtains_in_isar_proofs ctxt)

          in

            (case (num_chained, add_isar_steps (steps_of_isar_proof isar_proof) 0) of

              (0, 1) =>

              one_line_proof_text ctxt 0

                (if is_less (play_outcome_ord (play_outcome, one_line_play)) then

                   (case isar_proof of

                     Proof (_, _, [Prove (_, _, _, _, _, (_, gfs), meth :: _, _)]) =>

                     let

                       val used_facts' =

                         map_filter (fn s =>

                            if exists (fn (s', (sc, _)) => s' = s andalso sc = Chained)

                                used_facts then

                              NONE

                            else

                              SOME (s, (Global, General))) gfs

                     in

                       ((used_facts', (meth, play_outcome)), banner, subgoal, subgoal_count)

                     end)

                 else

                   one_line_params) ^

              (if isar_proofs = SOME true then "\n(No Isar proof available.)" else "")

            | (_, num_steps) =>

              let

                val msg =

                  (if verbose then [string_of_int num_steps ^ " step" ^ plural_s num_steps]

                   else []) @

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

              in

                one_line_proof_text ctxt 0 one_line_params ^

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

                Active.sendback_markup_command

                  (string_of_isar_proof ctxt subgoal subgoal_count isar_proof)

              end)

          end

      end

  in

    if debug then

      generate_proof_text ()

    else

      (case try generate_proof_text () of

        SOME s => s

      | NONE =>

        one_line_proof_text ctxt 0 one_line_params ^

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

  end

fun isar_proof_would_be_a_good_idea smt_proofs (meth, play) =

  (case play of

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

  | Play_Timed_Out 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 num_chained isar_proofs smt_proofs isar_params

   else

     one_line_proof_text ctxt num_chained) one_line_params

end;