adopting mutabelle and quickcheck to return timing information; exporting make_case_combs in datatype package for predicate compiler; adding Spec_Rules declaration for tail recursive functions; improving the predicate compiler and function flattening
(* Title: HOL/Tools/Predicate_Compile/predicate_compile_aux.ML
Author: Lukas Bulwahn, TU Muenchen
Auxilary functions for predicate compiler.
*)
(* FIXME proper signature *)
structure TermGraph = Graph(type key = term val ord = TermOrd.fast_term_ord);
structure Predicate_Compile_Aux =
struct
(* general functions *)
fun apfst3 f (x, y, z) = (f x, y, z)
fun apsnd3 f (x, y, z) = (x, f y, z)
fun aptrd3 f (x, y, z) = (x, y, f z)
fun comb_option f (SOME x1, SOME x2) = SOME (f (x1, x2))
| comb_option f (NONE, SOME x2) = SOME x2
| comb_option f (SOME x1, NONE) = SOME x1
| comb_option f (NONE, NONE) = NONE
fun map2_optional f (x :: xs) (y :: ys) = (f x (SOME y)) :: (map2_optional f xs ys)
| map2_optional f (x :: xs) [] = (f x NONE) :: (map2_optional f xs [])
| map2_optional f [] [] = []
fun find_indices f xs =
map_filter (fn (i, true) => SOME i | (i, false) => NONE) (map_index (apsnd f) xs)
fun assert check = if check then () else error "Assertion failed!"
(* mode *)
datatype mode = Bool | Input | Output | Pair of mode * mode | Fun of mode * mode
(* equality of instantiatedness with respect to equivalences:
Pair Input Input == Input and Pair Output Output == Output *)
fun eq_mode (Fun (m1, m2), Fun (m3, m4)) = eq_mode (m1, m3) andalso eq_mode (m2, m4)
| eq_mode (Pair (m1, m2), Pair (m3, m4)) = eq_mode (m1, m3) andalso eq_mode (m2, m4)
| eq_mode (Pair (m1, m2), Input) = eq_mode (m1, Input) andalso eq_mode (m2, Input)
| eq_mode (Pair (m1, m2), Output) = eq_mode (m1, Output) andalso eq_mode (m2, Output)
| eq_mode (Input, Pair (m1, m2)) = eq_mode (Input, m1) andalso eq_mode (Input, m2)
| eq_mode (Output, Pair (m1, m2)) = eq_mode (Output, m1) andalso eq_mode (Output, m2)
| eq_mode (Input, Input) = true
| eq_mode (Output, Output) = true
| eq_mode (Bool, Bool) = true
| eq_mode _ = false
(* name: binder_modes? *)
fun strip_fun_mode (Fun (mode, mode')) = mode :: strip_fun_mode mode'
| strip_fun_mode Bool = []
| strip_fun_mode _ = error "Bad mode for strip_fun_mode"
fun dest_fun_mode (Fun (mode, mode')) = mode :: dest_fun_mode mode'
| dest_fun_mode mode = [mode]
fun dest_tuple_mode (Pair (mode, mode')) = mode :: dest_tuple_mode mode'
| dest_tuple_mode _ = []
fun all_modes_of_typ' (T as Type ("fun", _)) =
let
val (S, U) = strip_type T
in
if U = HOLogic.boolT then
fold_rev (fn m1 => fn m2 => map_product (curry Fun) m1 m2)
(map all_modes_of_typ' S) [Bool]
else
[Input, Output]
end
| all_modes_of_typ' (Type ("*", [T1, T2])) =
map_product (curry Pair) (all_modes_of_typ' T1) (all_modes_of_typ' T2)
| all_modes_of_typ' _ = [Input, Output]
fun all_modes_of_typ (T as Type ("fun", _)) =
let
val (S, U) = strip_type T
in
if U = HOLogic.boolT then
fold_rev (fn m1 => fn m2 => map_product (curry Fun) m1 m2)
(map all_modes_of_typ' S) [Bool]
else
[Input, Output]
end
| all_modes_of_typ (Type ("bool", [])) = [Bool]
| all_modes_of_typ T = all_modes_of_typ' T
fun all_smodes_of_typ (T as Type ("fun", _)) =
let
val (S, U) = strip_type T
fun all_smodes (Type ("*", [T1, T2])) =
map_product (curry Pair) (all_smodes T1) (all_smodes T2)
| all_smodes _ = [Input, Output]
in
if U = HOLogic.boolT then
fold_rev (fn m1 => fn m2 => map_product (curry Fun) m1 m2) (map all_smodes S) [Bool]
else
error "all_smodes_of_typ: invalid type for predicate"
end
(*
fun extract_params arg =
case fastype_of arg of
(T as Type ("fun", _)) =>
(if (body_type T = HOLogic.boolT) then
(case arg of
Free _ => [arg] | _ => error "extract_params: Unexpected term")
else [])
| (Type ("*", [T1, T2])) =>
let
val (t1, t2) = HOLogic.dest_prod arg
in
extract_params t1 @ extract_params t2
end
| _ => []
*)
fun ho_arg_modes_of mode =
let
fun ho_arg_mode (m as Fun _) = [m]
| ho_arg_mode (Pair (m1, m2)) = ho_arg_mode m1 @ ho_arg_mode m2
| ho_arg_mode _ = []
in
maps ho_arg_mode (strip_fun_mode mode)
end
fun ho_args_of mode ts =
let
fun ho_arg (Fun _) (SOME t) = [t]
| ho_arg (Fun _) NONE = error "ho_arg_of"
| ho_arg (Pair (m1, m2)) (SOME (Const ("Pair", _) $ t1 $ t2)) =
ho_arg m1 (SOME t1) @ ho_arg m2 (SOME t2)
| ho_arg (Pair (m1, m2)) NONE = ho_arg m1 NONE @ ho_arg m2 NONE
| ho_arg _ _ = []
in
flat (map2_optional ho_arg (strip_fun_mode mode) ts)
end
(* temporary function should be replaced by unsplit_input or so? *)
fun replace_ho_args mode hoargs ts =
let
fun replace (Fun _, _) (arg' :: hoargs') = (arg', hoargs')
| replace (Pair (m1, m2), Const ("Pair", T) $ t1 $ t2) hoargs =
let
val (t1', hoargs') = replace (m1, t1) hoargs
val (t2', hoargs'') = replace (m2, t2) hoargs'
in
(Const ("Pair", T) $ t1' $ t2', hoargs'')
end
| replace (_, t) hoargs = (t, hoargs)
in
fst (fold_map replace ((strip_fun_mode mode) ~~ ts) hoargs)
end
fun ho_argsT_of mode Ts =
let
fun ho_arg (Fun _) T = [T]
| ho_arg (Pair (m1, m2)) (Type ("*", [T1, T2])) = ho_arg m1 T1 @ ho_arg m2 T2
| ho_arg _ _ = []
in
flat (map2 ho_arg (strip_fun_mode mode) Ts)
end
(* splits mode and maps function to higher-order argument types *)
fun split_map_mode f mode ts =
let
fun split_arg_mode' (m as Fun _) t = f m t
| split_arg_mode' (Pair (m1, m2)) (Const ("Pair", _) $ t1 $ t2) =
let
val (i1, o1) = split_arg_mode' m1 t1
val (i2, o2) = split_arg_mode' m2 t2
in
(comb_option HOLogic.mk_prod (i1, i2), comb_option HOLogic.mk_prod (o1, o2))
end
| split_arg_mode' m t =
if eq_mode (m, Input) then (SOME t, NONE)
else if eq_mode (m, Output) then (NONE, SOME t)
else error "split_map_mode: mode and term do not match"
in
(pairself (map_filter I) o split_list) (map2 split_arg_mode' (strip_fun_mode mode) ts)
end
(* splits mode and maps function to higher-order argument types *)
fun split_map_modeT f mode Ts =
let
fun split_arg_mode' (m as Fun _) T = f m T
| split_arg_mode' (Pair (m1, m2)) (Type ("*", [T1, T2])) =
let
val (i1, o1) = split_arg_mode' m1 T1
val (i2, o2) = split_arg_mode' m2 T2
in
(comb_option HOLogic.mk_prodT (i1, i2), comb_option HOLogic.mk_prodT (o1, o2))
end
| split_arg_mode' Input T = (SOME T, NONE)
| split_arg_mode' Output T = (NONE, SOME T)
| split_arg_mode' _ _ = error "split_modeT': mode and type do not match"
in
(pairself (map_filter I) o split_list) (map2 split_arg_mode' (strip_fun_mode mode) Ts)
end
fun split_mode mode ts = split_map_mode (fn _ => fn _ => (NONE, NONE)) mode ts
fun fold_map_aterms_prodT comb f (Type ("*", [T1, T2])) s =
let
val (x1, s') = fold_map_aterms_prodT comb f T1 s
val (x2, s'') = fold_map_aterms_prodT comb f T2 s'
in
(comb x1 x2, s'')
end
| fold_map_aterms_prodT comb f T s = f T s
fun map_filter_prod f (Const ("Pair", _) $ t1 $ t2) =
comb_option HOLogic.mk_prod (map_filter_prod f t1, map_filter_prod f t2)
| map_filter_prod f t = f t
(* obviously, split_mode' and split_modeT' do not match? where does that cause problems? *)
fun split_modeT' mode Ts =
let
fun split_arg_mode' (Fun _) T = ([], [])
| split_arg_mode' (Pair (m1, m2)) (Type ("*", [T1, T2])) =
let
val (i1, o1) = split_arg_mode' m1 T1
val (i2, o2) = split_arg_mode' m2 T2
in
(i1 @ i2, o1 @ o2)
end
| split_arg_mode' Input T = ([T], [])
| split_arg_mode' Output T = ([], [T])
| split_arg_mode' _ _ = error "split_modeT': mode and type do not match"
in
(pairself flat o split_list) (map2 split_arg_mode' (strip_fun_mode mode) Ts)
end
fun string_of_mode mode =
let
fun string_of_mode1 Input = "i"
| string_of_mode1 Output = "o"
| string_of_mode1 Bool = "bool"
| string_of_mode1 mode = "(" ^ (string_of_mode3 mode) ^ ")"
and string_of_mode2 (Pair (m1, m2)) = string_of_mode3 m1 ^ " * " ^ string_of_mode2 m2
| string_of_mode2 mode = string_of_mode1 mode
and string_of_mode3 (Fun (m1, m2)) = string_of_mode2 m1 ^ " => " ^ string_of_mode3 m2
| string_of_mode3 mode = string_of_mode2 mode
in string_of_mode3 mode end
fun ascii_string_of_mode mode' =
let
fun ascii_string_of_mode' Input = "i"
| ascii_string_of_mode' Output = "o"
| ascii_string_of_mode' Bool = "b"
| ascii_string_of_mode' (Pair (m1, m2)) =
"P" ^ ascii_string_of_mode' m1 ^ ascii_string_of_mode'_Pair m2
| ascii_string_of_mode' (Fun (m1, m2)) =
"F" ^ ascii_string_of_mode' m1 ^ ascii_string_of_mode'_Fun m2 ^ "B"
and ascii_string_of_mode'_Fun (Fun (m1, m2)) =
ascii_string_of_mode' m1 ^ (if m2 = Bool then "" else "_" ^ ascii_string_of_mode'_Fun m2)
| ascii_string_of_mode'_Fun Bool = "B"
| ascii_string_of_mode'_Fun m = ascii_string_of_mode' m
and ascii_string_of_mode'_Pair (Pair (m1, m2)) =
ascii_string_of_mode' m1 ^ ascii_string_of_mode'_Pair m2
| ascii_string_of_mode'_Pair m = ascii_string_of_mode' m
in ascii_string_of_mode'_Fun mode' end
(* premises *)
datatype indprem = Prem of term | Negprem of term | Sidecond of term
| Generator of (string * typ);
(* general syntactic functions *)
(*Like dest_conj, but flattens conjunctions however nested*)
fun conjuncts_aux (Const ("op &", _) $ t $ t') conjs = conjuncts_aux t (conjuncts_aux t' conjs)
| conjuncts_aux t conjs = t::conjs;
fun conjuncts t = conjuncts_aux t [];
fun is_equationlike_term (Const ("==", _) $ _ $ _) = true
| is_equationlike_term (Const ("Trueprop", _) $ (Const ("op =", _) $ _ $ _)) = true
| is_equationlike_term _ = false
val is_equationlike = is_equationlike_term o prop_of
fun is_pred_equation_term (Const ("==", _) $ u $ v) =
(fastype_of u = @{typ bool}) andalso (fastype_of v = @{typ bool})
| is_pred_equation_term _ = false
val is_pred_equation = is_pred_equation_term o prop_of
fun is_intro_term constname t =
the_default false (try (fn t => case fst (strip_comb (HOLogic.dest_Trueprop (Logic.strip_imp_concl t))) of
Const (c, _) => c = constname
| _ => false) t)
fun is_intro constname t = is_intro_term constname (prop_of t)
fun is_pred thy constname =
let
val T = (Sign.the_const_type thy constname)
in body_type T = @{typ "bool"} end;
fun is_predT (T as Type("fun", [_, _])) = (snd (strip_type T) = HOLogic.boolT)
| is_predT _ = false
(*** check if a term contains only constructor functions ***)
(* TODO: another copy in the core! *)
(* FIXME: constructor terms are supposed to be seen in the way the code generator
sees constructors.*)
fun is_constrt thy =
let
val cnstrs = flat (maps
(map (fn (_, (Tname, _, cs)) => map (apsnd (rpair Tname o length)) cs) o #descr o snd)
(Symtab.dest (Datatype.get_all thy)));
fun check t = (case strip_comb t of
(Free _, []) => true
| (Const (s, T), ts) => (case (AList.lookup (op =) cnstrs s, body_type T) of
(SOME (i, Tname), Type (Tname', _)) => length ts = i andalso Tname = Tname' andalso forall check ts
| _ => false)
| _ => false)
in check end;
fun is_funtype (Type ("fun", [_, _])) = true
| is_funtype _ = false;
fun is_Type (Type _) = true
| is_Type _ = false
(* returns true if t is an application of an datatype constructor *)
(* which then consequently would be splitted *)
(* else false *)
(*
fun is_constructor thy t =
if (is_Type (fastype_of t)) then
(case DatatypePackage.get_datatype thy ((fst o dest_Type o fastype_of) t) of
NONE => false
| SOME info => (let
val constr_consts = maps (fn (_, (_, _, constrs)) => map fst constrs) (#descr info)
val (c, _) = strip_comb t
in (case c of
Const (name, _) => name mem_string constr_consts
| _ => false) end))
else false
*)
val is_constr = Code.is_constr;
fun strip_ex (Const ("Ex", _) $ Abs (x, T, t)) =
let
val (xTs, t') = strip_ex t
in
((x, T) :: xTs, t')
end
| strip_ex t = ([], t)
fun focus_ex t nctxt =
let
val ((xs, Ts), t') = apfst split_list (strip_ex t)
val (xs', nctxt') = Name.variants xs nctxt;
val ps' = xs' ~~ Ts;
val vs = map Free ps';
val t'' = Term.subst_bounds (rev vs, t');
in ((ps', t''), nctxt') end;
(* introduction rule combinators *)
(* combinators to apply a function to all literals of an introduction rules *)
fun map_atoms f intro =
let
val (literals, head) = Logic.strip_horn intro
fun appl t = (case t of
(@{term "Not"} $ t') => HOLogic.mk_not (f t')
| _ => f t)
in
Logic.list_implies
(map (HOLogic.mk_Trueprop o appl o HOLogic.dest_Trueprop) literals, head)
end
fun fold_atoms f intro s =
let
val (literals, head) = Logic.strip_horn intro
fun appl t s = (case t of
(@{term "Not"} $ t') => f t' s
| _ => f t s)
in fold appl (map HOLogic.dest_Trueprop literals) s end
fun fold_map_atoms f intro s =
let
val (literals, head) = Logic.strip_horn intro
fun appl t s = (case t of
(@{term "Not"} $ t') => apfst HOLogic.mk_not (f t' s)
| _ => f t s)
val (literals', s') = fold_map appl (map HOLogic.dest_Trueprop literals) s
in
(Logic.list_implies (map HOLogic.mk_Trueprop literals', head), s')
end;
fun maps_premises f intro =
let
val (premises, head) = Logic.strip_horn intro
in
Logic.list_implies (maps f premises, head)
end
(* split theorems of case expressions *)
(*
fun has_split_rule_cname @{const_name "nat_case"} = true
| has_split_rule_cname @{const_name "list_case"} = true
| has_split_rule_cname _ = false
fun has_split_rule_term thy (Const (@{const_name "nat_case"}, _)) = true
| has_split_rule_term thy (Const (@{const_name "list_case"}, _)) = true
| has_split_rule_term thy _ = false
fun has_split_rule_term' thy (Const (@{const_name "If"}, _)) = true
| has_split_rule_term' thy (Const (@{const_name "Let"}, _)) = true
| has_split_rule_term' thy c = has_split_rule_term thy c
*)
fun prepare_split_thm ctxt split_thm =
(split_thm RS @{thm iffD2})
|> LocalDefs.unfold ctxt [@{thm atomize_conjL[symmetric]},
@{thm atomize_all[symmetric]}, @{thm atomize_imp[symmetric]}]
fun find_split_thm thy (Const (name, typ)) =
let
fun split_name str =
case first_field "." str
of (SOME (field, rest)) => field :: split_name rest
| NONE => [str]
val splitted_name = split_name name
in
if length splitted_name > 0 andalso
String.isSuffix "_case" (List.last splitted_name)
then
(List.take (splitted_name, length splitted_name - 1)) @ ["split"]
|> space_implode "."
|> PureThy.get_thm thy
|> SOME
handle ERROR msg => NONE
else NONE
end
| find_split_thm _ _ = NONE
(* TODO: split rules for let and if are different *)
fun find_split_thm' thy (Const (@{const_name "If"}, _)) = SOME @{thm split_if}
| find_split_thm' thy (Const (@{const_name "Let"}, _)) = SOME @{thm refl} (* TODO *)
| find_split_thm' thy c = find_split_thm thy c
fun has_split_thm thy t = is_some (find_split_thm thy t)
fun strip_all t = (Term.strip_all_vars t, Term.strip_all_body t)
(* lifting term operations to theorems *)
fun map_term thy f th =
Skip_Proof.make_thm thy (f (prop_of th))
(*
fun equals_conv lhs_cv rhs_cv ct =
case Thm.term_of ct of
Const ("==", _) $ _ $ _ => Conv.arg_conv cv ct
| _ => error "equals_conv"
*)
(* Different options for compiler *)
datatype compilation = Pred | Random | Depth_Limited | DSeq | Annotated
| Pos_Random_DSeq | Neg_Random_DSeq
fun negative_compilation_of Pos_Random_DSeq = Neg_Random_DSeq
| negative_compilation_of Neg_Random_DSeq = Pos_Random_DSeq
| negative_compilation_of c = c
fun compilation_for_polarity false Pos_Random_DSeq = Neg_Random_DSeq
| compilation_for_polarity _ c = c
fun string_of_compilation c = case c of
Pred => ""
| Random => "random"
| Depth_Limited => "depth limited"
| DSeq => "dseq"
| Annotated => "annotated"
| Pos_Random_DSeq => "pos_random dseq"
| Neg_Random_DSeq => "neg_random_dseq"
(*datatype compilation_options =
Pred | Random of int | Depth_Limited of int | DSeq of int | Annotated*)
datatype options = Options of {
expected_modes : (string * mode list) option,
proposed_modes : (string * mode list) option,
proposed_names : ((string * mode) * string) list,
show_steps : bool,
show_proof_trace : bool,
show_intermediate_results : bool,
show_mode_inference : bool,
show_modes : bool,
show_compilation : bool,
show_caught_failures : bool,
skip_proof : bool,
no_topmost_reordering : bool,
function_flattening : bool,
fail_safe_function_flattening : bool,
no_higher_order_predicate : string list,
inductify : bool,
compilation : compilation
};
fun expected_modes (Options opt) = #expected_modes opt
fun proposed_modes (Options opt) = #proposed_modes opt
fun proposed_names (Options opt) name mode = AList.lookup (eq_pair (op =) eq_mode)
(#proposed_names opt) (name, mode)
fun show_steps (Options opt) = #show_steps opt
fun show_intermediate_results (Options opt) = #show_intermediate_results opt
fun show_proof_trace (Options opt) = #show_proof_trace opt
fun show_modes (Options opt) = #show_modes opt
fun show_mode_inference (Options opt) = #show_mode_inference opt
fun show_compilation (Options opt) = #show_compilation opt
fun show_caught_failures (Options opt) = #show_caught_failures opt
fun skip_proof (Options opt) = #skip_proof opt
fun function_flattening (Options opt) = #function_flattening opt
fun fail_safe_function_flattening (Options opt) = #fail_safe_function_flattening opt
fun no_topmost_reordering (Options opt) = #no_topmost_reordering opt
fun no_higher_order_predicate (Options opt) = #no_higher_order_predicate opt
fun is_inductify (Options opt) = #inductify opt
fun compilation (Options opt) = #compilation opt
val default_options = Options {
expected_modes = NONE,
proposed_modes = NONE,
proposed_names = [],
show_steps = false,
show_intermediate_results = false,
show_proof_trace = false,
show_modes = false,
show_mode_inference = false,
show_compilation = false,
show_caught_failures = false,
skip_proof = true,
no_topmost_reordering = false,
function_flattening = false,
fail_safe_function_flattening = false,
no_higher_order_predicate = [],
inductify = false,
compilation = Pred
}
val bool_options = ["show_steps", "show_intermediate_results", "show_proof_trace", "show_modes",
"show_mode_inference", "show_compilation", "skip_proof", "inductify", "no_function_flattening"]
val compilation_names = [("pred", Pred),
(*("random", Random), ("depth_limited", Depth_Limited), ("annotated", Annotated),*)
("dseq", DSeq), ("random_dseq", Pos_Random_DSeq)]
fun print_step options s =
if show_steps options then tracing s else ()
(* tuple processing *)
fun expand_tuples thy intro =
let
fun rewrite_args [] (pats, intro_t, ctxt) = (pats, intro_t, ctxt)
| rewrite_args (arg::args) (pats, intro_t, ctxt) =
(case HOLogic.strip_tupleT (fastype_of arg) of
(Ts as _ :: _ :: _) =>
let
fun rewrite_arg' (Const ("Pair", _) $ _ $ t2, Type ("*", [_, T2]))
(args, (pats, intro_t, ctxt)) = rewrite_arg' (t2, T2) (args, (pats, intro_t, ctxt))
| rewrite_arg' (t, Type ("*", [T1, T2])) (args, (pats, intro_t, ctxt)) =
let
val ([x, y], ctxt') = Variable.variant_fixes ["x", "y"] ctxt
val pat = (t, HOLogic.mk_prod (Free (x, T1), Free (y, T2)))
val intro_t' = Pattern.rewrite_term thy [pat] [] intro_t
val args' = map (Pattern.rewrite_term thy [pat] []) args
in
rewrite_arg' (Free (y, T2), T2) (args', (pat::pats, intro_t', ctxt'))
end
| rewrite_arg' _ (args, (pats, intro_t, ctxt)) = (args, (pats, intro_t, ctxt))
val (args', (pats, intro_t', ctxt')) = rewrite_arg' (arg, fastype_of arg)
(args, (pats, intro_t, ctxt))
in
rewrite_args args' (pats, intro_t', ctxt')
end
| _ => rewrite_args args (pats, intro_t, ctxt))
fun rewrite_prem atom =
let
val (_, args) = strip_comb atom
in rewrite_args args end
val ctxt = ProofContext.init thy
val (((T_insts, t_insts), [intro']), ctxt1) = Variable.import false [intro] ctxt
val intro_t = prop_of intro'
val concl = Logic.strip_imp_concl intro_t
val (p, args) = strip_comb (HOLogic.dest_Trueprop concl)
val (pats', intro_t', ctxt2) = rewrite_args args ([], intro_t, ctxt1)
val (pats', intro_t', ctxt3) =
fold_atoms rewrite_prem intro_t' (pats', intro_t', ctxt2)
fun rewrite_pat (ct1, ct2) =
(ct1, cterm_of thy (Pattern.rewrite_term thy pats' [] (term_of ct2)))
val t_insts' = map rewrite_pat t_insts
val intro'' = Thm.instantiate (T_insts, t_insts') intro
val [intro'''] = Variable.export ctxt3 ctxt [intro'']
val intro'''' = Simplifier.full_simplify
(HOL_basic_ss addsimps [@{thm fst_conv}, @{thm snd_conv}, @{thm Pair_eq}])
intro'''
(* splitting conjunctions introduced by Pair_eq*)
fun split_conj prem =
map HOLogic.mk_Trueprop (conjuncts (HOLogic.dest_Trueprop prem))
val intro''''' = map_term thy (maps_premises split_conj) intro''''
in
intro'''''
end
end;