(*  Title:      HOL/Tools/Quickcheck/narrowing_generators.ML

    Author:     Lukas Bulwahn, TU Muenchen

Narrowing-based counterexample generation.

*)

signature NARROWING_GENERATORS =

sig

  val allow_existentials : bool Config.T

  val finite_functions : bool Config.T

  val overlord : bool Config.T

  val active : bool Config.T

  val test_term: Proof.context -> bool * bool -> term * term list -> Quickcheck.result

  datatype counterexample = Universal_Counterexample of (term * counterexample)

    | Existential_Counterexample of (term * counterexample) list

    | Empty_Assignment

  val put_counterexample: (unit -> term list option) -> Proof.context -> Proof.context

  val put_existential_counterexample : (unit -> counterexample option) -> Proof.context -> Proof.context

  val setup: theory -> theory

end;

structure Narrowing_Generators : NARROWING_GENERATORS =

struct

(* configurations *)

val allow_existentials = Attrib.setup_config_bool @{binding quickcheck_allow_existentials} (K true)

val finite_functions = Attrib.setup_config_bool @{binding quickcheck_finite_functions} (K true)

val overlord = Attrib.setup_config_bool @{binding quickcheck_narrowing_overlord} (K false)

(* partial_term_of instances *)

fun mk_partial_term_of (x, T) =

  Const (@{const_name Quickcheck_Narrowing.partial_term_of_class.partial_term_of},

    Term.itselfT T --> @{typ narrowing_term} --> @{typ Code_Evaluation.term})

      $ Const ("TYPE", Term.itselfT T) $ x

(** formal definition **)

fun add_partial_term_of tyco raw_vs thy =

  let

    val vs = map (fn (v, _) => (v, @{sort typerep})) raw_vs;

    val ty = Type (tyco, map TFree vs);

    val lhs = Const (@{const_name partial_term_of},

        Term.itselfT ty --> @{typ narrowing_term} --> @{typ Code_Evaluation.term})

      $ Free ("x", Term.itselfT ty) $ Free ("t", @{typ narrowing_term});

    val rhs = @{term "undefined :: Code_Evaluation.term"};

    val eq = HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs, rhs));

    fun triv_name_of t = (fst o dest_Free o fst o strip_comb o fst

      o HOLogic.dest_eq o HOLogic.dest_Trueprop) t ^ "_triv";

  in

    thy

    |> Class.instantiation ([tyco], vs, @{sort partial_term_of})

    |> `(fn lthy => Syntax.check_term lthy eq)

    |-> (fn eq => Specification.definition (NONE, ((Binding.name (triv_name_of eq), []), eq)))

    |> snd

    |> Class.prove_instantiation_exit (K (Class.intro_classes_tac []))

  end;

fun ensure_partial_term_of (tyco, (raw_vs, _)) thy =

  let

    val need_inst = not (can (Sorts.mg_domain (Sign.classes_of thy) tyco) @{sort partial_term_of})

      andalso can (Sorts.mg_domain (Sign.classes_of thy) tyco) @{sort typerep};

  in if need_inst then add_partial_term_of tyco raw_vs thy else thy end;

(** code equations for datatypes **)

fun mk_partial_term_of_eq thy ty (i, (c, (_, tys))) =

  let

    val frees = map Free (Name.invent_names Name.context "a" (map (K @{typ narrowing_term}) tys))

    val narrowing_term = @{term "Quickcheck_Narrowing.Ctr"} $ HOLogic.mk_number @{typ code_int} i

      $ (HOLogic.mk_list @{typ narrowing_term} (rev frees))

    val rhs = fold (fn u => fn t => @{term "Code_Evaluation.App"} $ t $ u)

        (map mk_partial_term_of (frees ~~ tys))

        (@{term "Code_Evaluation.Const"} $ HOLogic.mk_literal c $ HOLogic.mk_typerep (tys ---> ty))

    val insts =

      map (SOME o Thm.cterm_of thy o map_types Logic.unvarifyT_global o Logic.varify_global)

        [Free ("ty", Term.itselfT ty), narrowing_term, rhs]

    val cty = Thm.ctyp_of thy ty;

  in

    @{thm partial_term_of_anything}

    |> Drule.instantiate' [SOME cty] insts

    |> Thm.varifyT_global

  end

fun add_partial_term_of_code tyco raw_vs raw_cs thy =

  let

    val algebra = Sign.classes_of thy;

    val vs = map (fn (v, sort) =>

      (v, curry (Sorts.inter_sort algebra) @{sort typerep} sort)) raw_vs;

    val ty = Type (tyco, map TFree vs);

    val cs = (map o apsnd o apsnd o map o map_atyps)

      (fn TFree (v, _) => TFree (v, (the o AList.lookup (op =) vs) v)) raw_cs;

    val const = AxClass.param_of_inst thy (@{const_name partial_term_of}, tyco);

    val var_insts = map (SOME o Thm.cterm_of thy o map_types Logic.unvarifyT_global o Logic.varify_global)

        [Free ("ty", Term.itselfT ty), @{term "Quickcheck_Narrowing.Var p tt"},

          @{term "Code_Evaluation.Free (STR ''_'')"} $ HOLogic.mk_typerep ty]

    val var_eq =

      @{thm partial_term_of_anything}

      |> Drule.instantiate' [SOME (Thm.ctyp_of thy ty)] var_insts

      |> Thm.varifyT_global

    val eqs = var_eq :: map_index (mk_partial_term_of_eq thy ty) cs;

 in

    thy

    |> Code.del_eqns const

    |> fold Code.add_eqn eqs

  end;

fun ensure_partial_term_of_code (tyco, (raw_vs, cs)) thy =

  let

    val has_inst = can (Sorts.mg_domain (Sign.classes_of thy) tyco) @{sort partial_term_of};

  in if has_inst then add_partial_term_of_code tyco raw_vs cs thy else thy end;

(* narrowing generators *)

(** narrowing specific names and types **)

exception FUNCTION_TYPE;

val narrowingN = "narrowing";

fun narrowingT T =

  @{typ Quickcheck_Narrowing.code_int} --> Type (@{type_name Quickcheck_Narrowing.cons}, [T])

fun mk_empty T = Const (@{const_name Quickcheck_Narrowing.empty}, narrowingT T)

fun mk_cons c T = Const (@{const_name Quickcheck_Narrowing.cons}, T --> narrowingT T) $ Const (c, T)

fun mk_apply (T, t) (U, u) =

  let

    val (_, U') = dest_funT U

  in

    (U', Const (@{const_name Quickcheck_Narrowing.apply},

      narrowingT U --> narrowingT T --> narrowingT U') $ u $ t)

  end

fun mk_sum (t, u) =

  let

    val T = fastype_of t

  in

    Const (@{const_name Quickcheck_Narrowing.sum}, T --> T --> T) $ t $ u

  end

(** deriving narrowing instances **)

fun mk_equations descr vs tycos narrowings (Ts, Us) =

  let

    fun mk_call T =

      (T, Const (@{const_name "Quickcheck_Narrowing.narrowing_class.narrowing"}, narrowingT T))

    fun mk_aux_call fTs (k, _) (tyco, Ts) =

      let

        val T = Type (tyco, Ts)

        val _ = if not (null fTs) then raise FUNCTION_TYPE else ()

      in

        (T, nth narrowings k)

      end

    fun mk_consexpr simpleT (c, xs) =

      let

        val Ts = map fst xs

      in snd (fold mk_apply xs (Ts ---> simpleT, mk_cons c (Ts ---> simpleT))) end

    fun mk_rhs exprs = foldr1 mk_sum exprs

    val rhss =

      Datatype_Aux.interpret_construction descr vs

        { atyp = mk_call, dtyp = mk_aux_call }

      |> (map o apfst) Type

      |> map (fn (T, cs) => map (mk_consexpr T) cs)

      |> map mk_rhs

    val lhss = narrowings

    val eqs = map (HOLogic.mk_Trueprop o HOLogic.mk_eq) (lhss ~~ rhss)

  in

    eqs

  end

fun contains_recursive_type_under_function_types xs =

  exists (fn (_, (_, _, cs)) => cs |> exists (snd #> exists (fn dT =>

    (case Datatype_Aux.strip_dtyp dT of (_ :: _, Datatype.DtRec _) => true | _ => false)))) xs

fun instantiate_narrowing_datatype config descr vs tycos prfx (names, auxnames) (Ts, Us) thy =

  let

    val _ = Datatype_Aux.message config "Creating narrowing generators ...";

    val narrowingsN = map (prefix (narrowingN ^ "_")) (names @ auxnames);

  in

    if not (contains_recursive_type_under_function_types descr) then

      thy

      |> Class.instantiation (tycos, vs, @{sort narrowing})

      |> Quickcheck_Common.define_functions

        (fn narrowings => mk_equations descr vs tycos narrowings (Ts, Us), NONE)

        prfx [] narrowingsN (map narrowingT (Ts @ Us))

      |> Class.prove_instantiation_exit (K (Class.intro_classes_tac []))

    else

      thy

  end;

(* testing framework *)

val target = "Haskell_Quickcheck"

(** invocation of Haskell interpreter **)

val narrowing_engine =

  Context.>>> (Context.map_theory_result

    (Thy_Load.use_file (Path.explode "Tools/Quickcheck/Narrowing_Engine.hs")))

val pnf_narrowing_engine =

  Context.>>> (Context.map_theory_result

    (Thy_Load.use_file (Path.explode "Tools/Quickcheck/PNF_Narrowing_Engine.hs")))

fun exec verbose code =

  ML_Context.exec (fn () => Secure.use_text ML_Env.local_context (0, "generated code") verbose code)

fun with_overlord_dir name f =

  let

    val path =

      Path.append (Path.explode "$ISABELLE_HOME_USER") (Path.basic (name ^ serial_string ()))

    val _ = Isabelle_System.mkdirs path;

  in Exn.release (Exn.capture f path) end;

fun elapsed_time description e =

  let val ({elapsed, ...}, result) = Timing.timing e ()

  in (result, (description, Time.toMilliseconds elapsed)) end

fun value (contains_existentials, opts) ctxt cookie (code, value_name) =

  let

    val (limit_time, is_interactive, timeout, quiet, size) = opts

    val (get, put, put_ml) = cookie

    fun message s = if quiet then () else Output.urgent_message s

    val current_size = Unsynchronized.ref 0

    val current_result = Unsynchronized.ref Quickcheck.empty_result 

    fun excipit () =

      "Quickcheck ran out of time while testing at size " ^ string_of_int (!current_size)

    val tmp_prefix = "Quickcheck_Narrowing"

    val with_tmp_dir =

      if Config.get ctxt overlord then with_overlord_dir else Isabelle_System.with_tmp_dir 

    fun run in_path = 

      let

        val code_file = Path.append in_path (Path.basic "Code.hs")

        val narrowing_engine_file = Path.append in_path (Path.basic "Narrowing_Engine.hs")

        val main_file = Path.append in_path (Path.basic "Main.hs")

        val main = "module Main where {\n\n" ^

          "import System;\n" ^

          "import Narrowing_Engine;\n" ^

          "import Code;\n\n" ^

          "main = getArgs >>= \\[size] -> Narrowing_Engine.depthCheck (read size) (Code.value ())\n\n" ^

          "}\n"

        val code' = prefix "module Code where {\n\ndata Typerep = Typerep String [Typerep];\n"

          (unprefix "module Code where {" code)

        val _ = File.write code_file code'

        val _ = File.write narrowing_engine_file

          (if contains_existentials then pnf_narrowing_engine else narrowing_engine)

        val _ = File.write main_file main

        val executable = File.shell_path (Path.append in_path (Path.basic "isabelle_quickcheck_narrowing"))

        val cmd = "exec \"$ISABELLE_GHC\" -fglasgow-exts " ^

          (space_implode " " (map File.shell_path [code_file, narrowing_engine_file, main_file])) ^

          " -o " ^ executable ^ ";"

        val (result, compilation_time) =

          elapsed_time "Haskell compilation" (fn () => Isabelle_System.bash cmd) 

        val _ = Quickcheck.add_timing compilation_time current_result

        val _ = if Isabelle_System.bash cmd <> 0 then error "Compilation with GHC failed" else ()

        fun with_size k =

          if k > size then

            (NONE, !current_result)

          else

            let

              val _ = message ("Test data size: " ^ string_of_int k)

              val _ = current_size := k

              val ((response, _), timing) = elapsed_time ("execution of size " ^ string_of_int k)

                (fn () => Isabelle_System.bash_output (executable ^ " " ^ string_of_int k))

              val _ = Quickcheck.add_timing timing current_result

            in

              if response = "NONE\n" then

                with_size (k + 1)

              else

                let

                  val output_value = the_default "NONE"

                    (try (snd o split_last o filter_out (fn s => s = "") o split_lines) response)

                    |> translate_string (fn s => if s = "\\" then "\\\\" else s)

                  val ml_code = "\nval _ = Context.set_thread_data (SOME (Context.map_proof (" ^ put_ml

                    ^ " (fn () => " ^ output_value ^ ")) (ML_Context.the_generic_context ())))";

                  val ctxt' = ctxt

                    |> put (fn () => error ("Bad evaluation for " ^ quote put_ml))

                    |> Context.proof_map (exec false ml_code);

                in (get ctxt' (), !current_result) end

            end 

      in with_size 0 end

  in

    Quickcheck.limit timeout (limit_time, is_interactive) 

      (fn () => with_tmp_dir tmp_prefix run)

      (fn () => (message (excipit ()); (NONE, !current_result))) ()

  end;

fun dynamic_value_strict opts cookie thy postproc t =

  let

    val ctxt = Proof_Context.init_global thy

    fun evaluator naming program ((_, vs_ty), t) deps = Exn.interruptible_capture (value opts ctxt cookie)

      (Code_Target.evaluator thy target naming program deps (vs_ty, t));    

  in Exn.release (Code_Thingol.dynamic_value thy (Exn.map_result o postproc) evaluator t) end;

(** counterexample generator **)

structure Counterexample = Proof_Data

(

  type T = unit -> term list option

  fun init _ () = error "Counterexample"

)

datatype counterexample = Universal_Counterexample of (term * counterexample)

  | Existential_Counterexample of (term * counterexample) list

  | Empty_Assignment

fun map_counterexample f Empty_Assignment = Empty_Assignment

  | map_counterexample f (Universal_Counterexample (t, c)) =

      Universal_Counterexample (f t, map_counterexample f c)

  | map_counterexample f (Existential_Counterexample cs) =

      Existential_Counterexample (map (fn (t, c) => (f t, map_counterexample f c)) cs)

structure Existential_Counterexample = Proof_Data

(

  type T = unit -> counterexample option

  fun init _ () = error "Counterexample"

)

val put_existential_counterexample = Existential_Counterexample.put

val put_counterexample = Counterexample.put

fun finitize_functions (xTs, t) =

  let

    val (names, boundTs) = split_list xTs

    fun mk_eval_ffun dT rT =

      Const (@{const_name "Quickcheck_Narrowing.eval_ffun"}, 

        Type (@{type_name "Quickcheck_Narrowing.ffun"}, [dT, rT]) --> dT --> rT)

    fun mk_eval_cfun dT rT =

      Const (@{const_name "Quickcheck_Narrowing.eval_cfun"}, 

        Type (@{type_name "Quickcheck_Narrowing.cfun"}, [rT]) --> dT --> rT)

    fun eval_function (T as Type (@{type_name fun}, [dT, rT])) =

      let

        val (rt', rT') = eval_function rT

      in

        case dT of

          Type (@{type_name fun}, _) =>

            (fn t => absdummy (dT, rt' (mk_eval_cfun dT rT' $ incr_boundvars 1 t $ Bound 0)),

            Type (@{type_name "Quickcheck_Narrowing.cfun"}, [rT']))

        | _ => (fn t => absdummy (dT, rt' (mk_eval_ffun dT rT' $ incr_boundvars 1 t $ Bound 0)),

            Type (@{type_name "Quickcheck_Narrowing.ffun"}, [dT, rT']))

      end

      | eval_function T = (I, T)

    val (tt, boundTs') = split_list (map eval_function boundTs)

    val t' = subst_bounds (map2 (fn f => fn x => f x) (rev tt) (map_index (Bound o fst) boundTs), t)

  in

    (names ~~ boundTs', t')

  end

(** tester **)

val rewrs =

    map (swap o HOLogic.dest_eq o HOLogic.dest_Trueprop o Thm.prop_of)

      (@{thms all_simps} @ @{thms ex_simps})

    @ map (HOLogic.dest_eq o HOLogic.dest_Trueprop o Thm.prop_of)

        [@{thm iff_conv_conj_imp}, @{thm not_ex}, @{thm not_all}]

fun make_pnf_term thy t = Pattern.rewrite_term thy rewrs [] t

fun strip_quantifiers (Const (@{const_name Ex}, _) $ Abs (x, T, t)) =

    apfst (cons (@{const_name Ex}, (x, T))) (strip_quantifiers t)

  | strip_quantifiers (Const (@{const_name All}, _) $ Abs (x, T, t)) =

    apfst (cons (@{const_name All}, (x, T))) (strip_quantifiers t)

  | strip_quantifiers t = ([], t)

fun contains_existentials t = exists (fn (Q, _) => Q = @{const_name Ex}) (fst (strip_quantifiers t))

fun mk_property qs t =

  let

    fun enclose (@{const_name Ex}, (x, T)) t =

        Const (@{const_name Quickcheck_Narrowing.exists}, (T --> @{typ property}) --> @{typ property})

          $ Abs (x, T, t)

      | enclose (@{const_name All}, (x, T)) t =

        Const (@{const_name Quickcheck_Narrowing.all}, (T --> @{typ property}) --> @{typ property})

          $ Abs (x, T, t)

  in

    fold_rev enclose qs (@{term Quickcheck_Narrowing.Property} $

      (list_comb (t , map Bound (((length qs) - 1) downto 0))))

  end

fun mk_case_term ctxt p ((@{const_name Ex}, (x, T)) :: qs') (Existential_Counterexample cs) =

    Datatype.make_case ctxt Datatype_Case.Quiet [] (Free (x, T)) (map (fn (t, c) =>

      (t, mk_case_term ctxt (p - 1) qs' c)) cs)

  | mk_case_term ctxt p ((@{const_name All}, (x, T)) :: qs') (Universal_Counterexample (t, c)) =

    if p = 0 then t else mk_case_term ctxt (p - 1) qs' c

fun mk_terms ctxt qs result =

  let

    val

      ps = filter (fn (_, (@{const_name All}, _)) => true | _ => false) (map_index I qs)

    in

      map (fn (p, (_, (x, T))) => (x, mk_case_term ctxt p qs result)) ps

    end

fun test_term ctxt (limit_time, is_interactive) (t, eval_terms) =

  let

    fun dest_result (Quickcheck.Result r) = r 

    val opts =

      (limit_time, is_interactive, seconds (Config.get ctxt Quickcheck.timeout),

        Config.get ctxt Quickcheck.quiet, Config.get ctxt Quickcheck.size)

    val thy = Proof_Context.theory_of ctxt

    val t' = fold_rev (fn (x, T) => fn t => HOLogic.mk_all (x, T, t)) (Term.add_frees t []) t

    val pnf_t = make_pnf_term thy t'

  in

    if Config.get ctxt allow_existentials andalso contains_existentials pnf_t then

      let

        fun wrap f (qs, t) =

          let val (qs1, qs2) = split_list qs in

          apfst (map2 pair qs1) (f (qs2, t)) end

        val finitize = if Config.get ctxt finite_functions then wrap finitize_functions else I

        val (qs, prop_t) = finitize (strip_quantifiers pnf_t)

        val prop_term = fold_rev (fn (_, (x, T)) => fn t => Abs (x, T, t)) qs prop_t

        (* FIXME proper naming convention for local_theory *)

        val ((prop_def, _), ctxt') =

          Local_Theory.define ((Binding.conceal @{binding test_property}, NoSyn),

            ((Binding.conceal Binding.empty, [Code.add_default_eqn_attrib]), prop_term)) ctxt

        val (prop_def', thy') = Local_Theory.exit_result_global Morphism.term (prop_def, ctxt') 

        val (counterexample, result) = dynamic_value_strict (true, opts)

          (Existential_Counterexample.get, Existential_Counterexample.put,

            "Narrowing_Generators.put_existential_counterexample")

          thy' (apfst o Option.map o map_counterexample) (mk_property qs prop_def')

      in

        Quickcheck.Result

         {counterexample = Option.map (mk_terms ctxt' qs) counterexample,

          evaluation_terms = Option.map (K []) counterexample,

          timings = #timings (dest_result result), reports = #reports (dest_result result)}

      end

    else

      let

        val t' = Term.list_abs_free (Term.add_frees t [], t)

        fun wrap f t = list_abs (f (strip_abs t))

        val finitize = if Config.get ctxt finite_functions then wrap finitize_functions else I

        fun ensure_testable t =

          Const (@{const_name Quickcheck_Narrowing.ensure_testable}, fastype_of t --> fastype_of t) $ t

        val (counterexample, result) = dynamic_value_strict (false, opts)

          (Counterexample.get, Counterexample.put, "Narrowing_Generators.put_counterexample")

          thy (apfst o Option.map o map) (ensure_testable (finitize t'))

      in

        Quickcheck.Result

         {counterexample = Option.map ((curry (op ~~)) (Term.add_free_names t [])) counterexample,

          evaluation_terms = Option.map (K []) counterexample,

          timings = #timings (dest_result result), reports = #reports (dest_result result)}

      end

  end;

fun test_goals ctxt (limit_time, is_interactive) insts goals =

  if (not (getenv "ISABELLE_GHC" = "")) then

    let

      val correct_inst_goals = Quickcheck.instantiate_goals ctxt insts goals

    in

      Quickcheck.collect_results (test_term ctxt (limit_time, is_interactive)) (maps (map snd) correct_inst_goals) []

    end

  else

    (if Config.get ctxt Quickcheck.quiet then () else Output.urgent_message

      ("Environment variable ISABELLE_GHC is not set. To use narrowing-based quickcheck, please set "

        ^ "this variable to your GHC Haskell compiler in your settings file."); [Quickcheck.empty_result])

(* setup *)

val active = Attrib.setup_config_bool @{binding quickcheck_narrowing_active} (K false);

val setup =

  Code.datatype_interpretation ensure_partial_term_of

  #> Code.datatype_interpretation ensure_partial_term_of_code

  #> Datatype.interpretation (Quickcheck_Common.ensure_sort_datatype

    (((@{sort typerep}, @{sort term_of}), @{sort narrowing}), instantiate_narrowing_datatype))

  #> Context.theory_map (Quickcheck.add_tester ("narrowing", (active, test_goals)))

end;