(*  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 "Generated_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 Generated_Code;\n\n" ^

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

           "}\n"

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

           (unprefix "module Generated_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\" " ^ Code_Haskell.language_params ^ " " ^

           (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 ("[Quickcheck-Narrowing] 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} $ t)

   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 (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_t)

       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' = fold_rev absfree (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. "

         ^ "To deactivate narrowing-based quickcheck, set quickcheck_narrowing_active to false.");

       [Quickcheck.empty_result])

 (* setup *)

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

 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;