(* 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 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 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", test_goals))
end;