File ‹Tools/Quickcheck/narrowing_generators.ML›
signature NARROWING_GENERATORS =
sig
val allow_existentials : bool Config.T
val finite_functions : bool Config.T
val overlord : bool Config.T
val ghc_options : string Config.T
val active : bool Config.T
datatype counterexample = Universal_Counterexample of (term * counterexample)
| Existential_Counterexample of (term * counterexample) list
| Empty_Assignment
val put_counterexample: (unit -> (bool * term list) option) -> Proof.context -> Proof.context
val put_existential_counterexample : (unit -> counterexample option) ->
Proof.context -> Proof.context
end
structure Narrowing_Generators : NARROWING_GENERATORS =
struct
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)
val ghc_options = Attrib.setup_config_string \<^binding>‹quickcheck_narrowing_ghc_options› (K "")
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›) $ Logic.mk_type T $ x
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 (fn ctxt => Class.intro_classes_tac ctxt [])
end
fun ensure_partial_term_of (tyco, (raw_vs, _)) thy =
let
val need_inst = not (Sorts.has_instance (Sign.classes_of thy) tyco \<^sort>‹partial_term_of›)
andalso Sorts.has_instance (Sign.classes_of thy) tyco \<^sort>‹typerep›
in if need_inst then add_partial_term_of tyco raw_vs thy else thy end
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.Narrowing_constructor› $ HOLogic.mk_number \<^typ>‹integer› 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.global_cterm_of thy o Logic.unvarify_types_global o Logic.varify_global)
[Free ("ty", Term.itselfT ty), narrowing_term, rhs]
val cty = Thm.global_ctyp_of thy ty
in
@{thm partial_term_of_anything}
|> Thm.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.global_cterm_of thy o Logic.unvarify_types_global o Logic.varify_global)
[Free ("ty", Term.itselfT ty), \<^term>‹Quickcheck_Narrowing.Narrowing_variable p tt›,
\<^term>‹Code_Evaluation.Free (STR ''_'')› $ HOLogic.mk_typerep ty]
val var_eq =
@{thm partial_term_of_anything}
|> Thm.instantiate' [SOME (Thm.global_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.declare_default_eqns_global (map (rpair true) eqs)
end
fun ensure_partial_term_of_code (tyco, (raw_vs, cs)) thy =
let val has_inst = Sorts.has_instance (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
exception FUNCTION_TYPE
val narrowingN = "narrowing"
fun narrowingT T = \<^typ>‹integer› --> Type (\<^type_name>‹Quickcheck_Narrowing.narrowing_cons›, [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
fun mk_equations descr vs narrowings =
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 =
Old_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 Old_Datatype_Aux.strip_dtyp dT of (_ :: _, Old_Datatype_Aux.DtRec _) => true | _ => false)))) xs
fun instantiate_narrowing_datatype config descr vs tycos prfx (names, auxnames) (Ts, Us) thy =
let
val _ = Old_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 narrowings, NONE)
prfx [] narrowingsN (map narrowingT (Ts @ Us))
|> Class.prove_instantiation_exit (fn ctxt => Class.intro_classes_tac ctxt [])
else thy
end
val target = "Haskell_Quickcheck"
val narrowing_engine =
File.read 🗏‹~~/src/HOL/Tools/Quickcheck/Narrowing_Engine.hs›
val pnf_narrowing_engine =
File.read 🗏‹~~/src/HOL/Tools/Quickcheck/PNF_Narrowing_Engine.hs›
fun exec verbose code =
ML_Context.exec (fn () =>
ML_Compiler0.ML ML_Env.context
{line = 0, file = "generated code", verbose = verbose, debug = false} code)
fun with_overlord_dir name f =
(Path.explode "$ISABELLE_HOME_USER" + Path.basic (name ^ serial_string ()))
|> Isabelle_System.make_directory
|> f
fun value (contains_existentials, ((genuine_only, (quiet, verbose)), size))
ctxt cookie (code_modules_bytes, _) =
let
val code_modules = (map o apsnd) Bytes.content code_modules_bytes
val ((is_genuine, counterexample_of), (get, put, put_ml)) = cookie
fun message s = if quiet then () else writeln s
fun verbose_message s = if not quiet andalso verbose then writeln s else ()
val current_size = Unsynchronized.ref 0
val current_result = Unsynchronized.ref Quickcheck.empty_result
val tmp_prefix = "Quickcheck_Narrowing"
val ghc_options = Config.get ctxt ghc_options
val with_tmp_dir =
if Config.get ctxt overlord then with_overlord_dir else Isabelle_System.with_tmp_dir
fun run in_path =
let
fun mk_code_file module =
let
val (paths, base) = split_last module
in Path.appends (in_path :: map Path.basic (paths @ [suffix ".hs" base])) end;
val generatedN_suffix = suffix ".hs" Code_Target.generatedN;
val includes = AList.delete (op =) [generatedN_suffix] code_modules
|> (map o apfst) mk_code_file
val code = the (AList.lookup (op =) code_modules [generatedN_suffix])
val code_file = mk_code_file [Code_Target.generatedN]
val narrowing_engine_file = mk_code_file ["Narrowing_Engine"]
val main_file = mk_code_file ["Main"]
val main =
"module Main where {\n\n" ^
"import System.IO;\n" ^
"import System.Environment;\n" ^
"import Narrowing_Engine;\n" ^
"import " ^ Code_Target.generatedN ^ " ;\n\n" ^
"main = getArgs >>= \\[potential, size] -> " ^
"Narrowing_Engine.depthCheck (read potential) (read size) (" ^ Code_Target.generatedN ^
".value ())\n\n}\n"
val _ =
map (uncurry File.write)
(includes @
[(narrowing_engine_file,
if contains_existentials then pnf_narrowing_engine else narrowing_engine),
(code_file, code), (main_file, main)])
val executable = in_path + Path.basic "isabelle_quickcheck_narrowing"
val cmd =
"exec \"$ISABELLE_GHC\" " ^ Code_Haskell.language_params ^ " " ^ ghc_options ^ " " ^
(space_implode " "
(map File.bash_platform_path
(map fst includes @ [code_file, narrowing_engine_file, main_file]))) ^
" -o " ^ File.bash_platform_path executable ^ ";"
val compilation_time =
Isabelle_System.bash_process (Bash.script cmd)
|> Process_Result.check
|> Process_Result.timing_elapsed |> Time.toMilliseconds
handle ERROR msg => cat_error "Compilation with GHC failed" msg
val _ = Quickcheck.add_timing ("Haskell compilation", compilation_time) current_result
fun haskell_string_of_bool v = if v then "True" else "False"
fun with_size genuine_only k =
if k > size then (NONE, !current_result)
else
let
val _ = verbose_message ("[Quickcheck-narrowing] Test data size: " ^ string_of_int k)
val _ = current_size := k
val res =
Isabelle_System.bash_process (Bash.script
(File.bash_path executable ^ " " ^ haskell_string_of_bool genuine_only ^ " " ^
string_of_int k))
|> Process_Result.check
val response = Process_Result.out res
val timing = res |> Process_Result.timing_elapsed |> Time.toMilliseconds;
val _ =
Quickcheck.add_timing
("execution of size " ^ string_of_int k, timing) current_result
in
if response = "NONE" then with_size genuine_only (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)
val ml_code =
"\nval _ = Context.put_generic_context (SOME (Context.map_proof (" ^ put_ml
^ " (fn () => " ^ output_value ^ ")) (Context.the_generic_context ())))"
val ctxt' = ctxt
|> put (fn () => error ("Bad evaluation for " ^ quote put_ml))
|> Context.proof_map (exec false ml_code)
val counterexample = get ctxt' ()
in
if is_genuine counterexample then
(counterexample, !current_result)
else
let
val cex = Option.map (rpair []) (counterexample_of counterexample)
val _ = message (Pretty.string_of (Quickcheck.pretty_counterex ctxt false cex))
val _ = message "Quickcheck continues to find a genuine counterexample..."
in with_size true (k + 1) end
end
end
in with_size genuine_only 0 end
in with_tmp_dir tmp_prefix run end
fun dynamic_value_strict opts cookie ctxt postproc t =
let
fun evaluator program _ vs_ty_t deps =
Exn.result (value opts ctxt cookie)
(Code_Target.compilation_text ctxt target program deps true vs_ty_t)
in Exn.release (Code_Thingol.dynamic_value ctxt (Exn.map_res o postproc) evaluator t) end
datatype counterexample =
Universal_Counterexample of (term * counterexample)
| Existential_Counterexample of (term * counterexample) list
| Empty_Assignment
fun map_counterexample _ 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 Data = Proof_Data
(
type T =
(unit -> (bool * term list) option) *
(unit -> counterexample option)
val empty: T =
(fn () => raise Fail "counterexample",
fn () => raise Fail "existential_counterexample")
fun init _ = empty
)
val get_counterexample = #1 o Data.get;
val get_existential_counterexample = #2 o Data.get;
val put_counterexample = Data.map o @{apply 2(1)} o K
val put_existential_counterexample = Data.map o @{apply 2(2)} o K
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 (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 as Type (\<^type_name>‹prod›, [fT, sT])) =
let
val (ft', fT') = eval_function fT
val (st', sT') = eval_function sT
val T' = Type (\<^type_name>‹prod›, [fT', sT'])
val map_const = Const (\<^const_name>‹map_prod›, (fT' --> fT) --> (sT' --> sT) --> T' --> T)
fun apply_dummy T t = absdummy T (t (Bound 0))
in
(fn t => list_comb (map_const, [apply_dummy fT' ft', apply_dummy sT' st', t]), T')
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
fun dest_ffun (Type (\<^type_name>‹Quickcheck_Narrowing.ffun›, [dT, rT])) = (dT, rT)
fun eval_finite_functions (Const (\<^const_name>‹Quickcheck_Narrowing.ffun.Constant›, T) $ value) =
absdummy (fst (dest_ffun (body_type T))) (eval_finite_functions value)
| eval_finite_functions (Const (\<^const_name>‹Quickcheck_Narrowing.ffun.Update›, T) $ a $ b $ f) =
let
val (T1, T2) = dest_ffun (body_type T)
in
Quickcheck_Common.mk_fun_upd T1 T2
(eval_finite_functions a, eval_finite_functions b) (eval_finite_functions f)
end
| eval_finite_functions t = t
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},
@{thm meta_eq_to_obj_eq [OF Ex1_def]}]
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) =
Case_Translation.make_case ctxt Case_Translation.Quiet Name.context (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›, _) :: qs') (Universal_Counterexample (t, c)) =
if p = 0 then t else mk_case_term ctxt (p - 1) qs' c
val post_process =
perhaps (try Quickcheck_Common.post_process_term) o eval_finite_functions
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, _))) => (x, mk_case_term ctxt p qs result)) ps
|> map (apsnd post_process)
end
fun test_term ctxt catch_code_errors (t, _) =
let
fun dest_result (Quickcheck.Result r) = r
val opts =
((Config.get ctxt Quickcheck.genuine_only,
(Config.get ctxt Quickcheck.quiet, Config.get ctxt Quickcheck.verbose)),
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 act = if catch_code_errors then try else (fn f => SOME o f)
val execute =
dynamic_value_strict (true, opts)
((K true, fn _ => error ""),
(get_existential_counterexample, put_existential_counterexample,
"Narrowing_Generators.put_existential_counterexample"))
ctxt (apfst o Option.map o map_counterexample)
in
(case act execute (mk_property qs prop_t) of
SOME (counterexample, result) => Quickcheck.Result
{counterexample = Option.map (pair true o mk_terms ctxt qs) counterexample,
evaluation_terms = Option.map (K []) counterexample,
timings = #timings (dest_result result), reports = #reports (dest_result result)}
| NONE =>
(Quickcheck.message ctxt "Conjecture is not executable with Quickcheck-narrowing";
Quickcheck.empty_result))
end
else
let
val frees = Term.add_frees t []
val t' = fold_rev absfree frees t
fun wrap f t = uncurry (fold_rev Term.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
fun is_genuine (SOME (true, _)) = true
| is_genuine _ = false
val counterexample_of =
Option.map (apsnd (curry (op ~~) (map fst frees) o map post_process))
val act = if catch_code_errors then try else (fn f => SOME o f)
val execute =
dynamic_value_strict (false, opts)
((is_genuine, counterexample_of),
(get_counterexample, put_counterexample,
"Narrowing_Generators.put_counterexample"))
ctxt (apfst o Option.map o apsnd o map)
in
(case act execute (ensure_testable (finitize t')) of
SOME (counterexample, result) =>
Quickcheck.Result
{counterexample = counterexample_of counterexample,
evaluation_terms = Option.map (K []) counterexample,
timings = #timings (dest_result result),
reports = #reports (dest_result result)}
| NONE =>
(Quickcheck.message ctxt "Conjecture is not executable with Quickcheck-narrowing";
Quickcheck.empty_result))
end
end
fun test_goals ctxt catch_code_errors insts goals =
if not (getenv "ISABELLE_GHC" = "") then
let
val _ = Quickcheck.message ctxt "Testing conjecture with Quickcheck-narrowing..."
val correct_inst_goals = Quickcheck_Common.instantiate_goals ctxt insts goals
in
Quickcheck_Common.collect_results (test_term ctxt catch_code_errors)
(maps (map snd) correct_inst_goals) []
end
else
(if Config.get ctxt Quickcheck.quiet then () else writeln
("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])
val active = Attrib.setup_config_bool \<^binding>‹quickcheck_narrowing_active› (K false)
val _ =
Theory.setup
(Code.datatype_interpretation ensure_partial_term_of
#> Code.datatype_interpretation ensure_partial_term_of_code
#> Quickcheck_Common.datatype_interpretation \<^plugin>‹quickcheck_narrowing›
(\<^sort>‹narrowing›, instantiate_narrowing_datatype)
#> Context.theory_map (Quickcheck.add_tester ("narrowing", (active, test_goals))))
end