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(* Title: HOL/Tools/Predicate_Compile/predicate_compile_aux.ML
Author: Lukas Bulwahn, TU Muenchen
Auxilary functions for predicate compiler.
*)
signature PREDICATE_COMPILE_AUX =
sig
val find_indices : ('a -> bool) -> 'a list -> int list
(* mode *)
datatype mode = Bool | Input | Output | Pair of mode * mode | Fun of mode * mode
val eq_mode : mode * mode -> bool
val mode_ord: mode ord
val list_fun_mode : mode list -> mode
val strip_fun_mode : mode -> mode list
val dest_fun_mode : mode -> mode list
val dest_tuple_mode : mode -> mode list
val all_modes_of_typ : typ -> mode list
val all_smodes_of_typ : typ -> mode list
val fold_map_aterms_prodT : ('a -> 'a -> 'a) -> (typ -> 'b -> 'a * 'b) -> typ -> 'b -> 'a * 'b
val map_filter_prod : (term -> term option) -> term -> term option
val replace_ho_args : mode -> term list -> term list -> term list
val ho_arg_modes_of : mode -> mode list
val ho_argsT_of : mode -> typ list -> typ list
val ho_args_of : mode -> term list -> term list
val ho_args_of_typ : typ -> term list -> term list
val ho_argsT_of_typ : typ list -> typ list
val split_map_mode : (mode -> term -> term option * term option)
-> mode -> term list -> term list * term list
val split_map_modeT : (mode -> typ -> typ option * typ option)
-> mode -> typ list -> typ list * typ list
val split_mode : mode -> term list -> term list * term list
val split_modeT : mode -> typ list -> typ list * typ list
val string_of_mode : mode -> string
val ascii_string_of_mode : mode -> string
(* premises *)
datatype indprem = Prem of term | Negprem of term | Sidecond of term
| Generator of (string * typ)
val dest_indprem : indprem -> term
val map_indprem : (term -> term) -> indprem -> indprem
(* general syntactic functions *)
val is_equationlike : thm -> bool
val is_pred_equation : thm -> bool
val is_intro : string -> thm -> bool
val is_predT : typ -> bool
val lookup_constr : Proof.context -> (string * typ) -> int option
val is_constrt : Proof.context -> term -> bool
val strip_ex : term -> (string * typ) list * term
val focus_ex : term -> Name.context -> ((string * typ) list * term) * Name.context
val strip_all : term -> (string * typ) list * term
val strip_intro_concl : thm -> term * term list
(* introduction rule combinators *)
val map_atoms : (term -> term) -> term -> term
val fold_atoms : (term -> 'a -> 'a) -> term -> 'a -> 'a
val fold_map_atoms : (term -> 'a -> term * 'a) -> term -> 'a -> term * 'a
val maps_premises : (term -> term list) -> term -> term
val map_concl : (term -> term) -> term -> term
val map_term : theory -> (term -> term) -> thm -> thm
(* split theorems of case expressions *)
val prepare_split_thm : Proof.context -> thm -> thm
val find_split_thm : theory -> term -> thm option
(* datastructures and setup for generic compilation *)
datatype compilation_funs = CompilationFuns of {
mk_monadT : typ -> typ,
dest_monadT : typ -> typ,
mk_empty : typ -> term,
mk_single : term -> term,
mk_bind : term * term -> term,
mk_plus : term * term -> term,
mk_if : term -> term,
mk_iterate_upto : typ -> term * term * term -> term,
mk_not : term -> term,
mk_map : typ -> typ -> term -> term -> term
};
val mk_monadT : compilation_funs -> typ -> typ
val dest_monadT : compilation_funs -> typ -> typ
val mk_empty : compilation_funs -> typ -> term
val mk_single : compilation_funs -> term -> term
val mk_bind : compilation_funs -> term * term -> term
val mk_plus : compilation_funs -> term * term -> term
val mk_if : compilation_funs -> term -> term
val mk_iterate_upto : compilation_funs -> typ -> term * term * term -> term
val mk_not : compilation_funs -> term -> term
val mk_map : compilation_funs -> typ -> typ -> term -> term -> term
val funT_of : compilation_funs -> mode -> typ -> typ
(* Different compilations *)
datatype compilation = Pred | Depth_Limited | Random | Depth_Limited_Random | DSeq | Annotated
| Pos_Random_DSeq | Neg_Random_DSeq | New_Pos_Random_DSeq | New_Neg_Random_DSeq
| Pos_Generator_DSeq | Neg_Generator_DSeq | Pos_Generator_CPS | Neg_Generator_CPS
val negative_compilation_of : compilation -> compilation
val compilation_for_polarity : bool -> compilation -> compilation
val is_depth_limited_compilation : compilation -> bool
val string_of_compilation : compilation -> string
val compilation_names : (string * compilation) list
val non_random_compilations : compilation list
val random_compilations : compilation list
(* Different options for compiler *)
datatype options = Options of {
expected_modes : (string * mode list) option,
proposed_modes : (string * mode list) list,
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,
show_invalid_clauses : bool,
skip_proof : bool,
no_topmost_reordering : bool,
function_flattening : bool,
fail_safe_function_flattening : bool,
specialise : bool,
no_higher_order_predicate : string list,
inductify : bool,
detect_switches : bool,
smart_depth_limiting : bool,
compilation : compilation
};
val expected_modes : options -> (string * mode list) option
val proposed_modes : options -> string -> mode list option
val proposed_names : options -> string -> mode -> string option
val show_steps : options -> bool
val show_proof_trace : options -> bool
val show_intermediate_results : options -> bool
val show_mode_inference : options -> bool
val show_modes : options -> bool
val show_compilation : options -> bool
val show_caught_failures : options -> bool
val show_invalid_clauses : options -> bool
val skip_proof : options -> bool
val no_topmost_reordering : options -> bool
val function_flattening : options -> bool
val fail_safe_function_flattening : options -> bool
val specialise : options -> bool
val no_higher_order_predicate : options -> string list
val is_inductify : options -> bool
val detect_switches : options -> bool
val smart_depth_limiting : options -> bool
val compilation : options -> compilation
val default_options : options
val bool_options : string list
val print_step : options -> string -> unit
(* conversions *)
val imp_prems_conv : conv -> conv
(* simple transformations *)
val split_conjuncts_in_assms : Proof.context -> thm -> thm
val dest_conjunct_prem : thm -> thm list
val expand_tuples : theory -> thm -> thm
val case_betapply : theory -> term -> term
val eta_contract_ho_arguments : theory -> thm -> thm
val remove_equalities : theory -> thm -> thm
val remove_pointless_clauses : thm -> thm list
val peephole_optimisation : theory -> thm -> thm option
(* auxillary *)
val unify_consts : theory -> term list -> term list -> (term list * term list)
val mk_casesrule : Proof.context -> term -> thm list -> term
val preprocess_intro : theory -> thm -> thm
val define_quickcheck_predicate :
term -> theory -> (((string * typ) * (string * typ) list) * thm) * theory
end
structure Predicate_Compile_Aux : PREDICATE_COMPILE_AUX =
struct
(* general functions *)
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 | (_, false) => NONE) (map_index (apsnd f) xs)
(* 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
fun mode_ord (Input, Output) = LESS
| mode_ord (Output, Input) = GREATER
| mode_ord (Input, Input) = EQUAL
| mode_ord (Output, Output) = EQUAL
| mode_ord (Bool, Bool) = EQUAL
| mode_ord (Pair (m1, m2), Pair (m3, m4)) = prod_ord mode_ord mode_ord ((m1, m2), (m3, m4))
| mode_ord (Fun (m1, m2), Fun (m3, m4)) = prod_ord mode_ord mode_ord ((m1, m2), (m3, m4))
fun list_fun_mode [] = Bool
| list_fun_mode (m :: ms) = Fun (m, list_fun_mode ms)
(* name: binder_modes? *)
fun strip_fun_mode (Fun (mode, mode')) = mode :: strip_fun_mode mode'
| strip_fun_mode Bool = []
| strip_fun_mode _ = raise Fail "Bad mode for strip_fun_mode"
(* name: 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 (\<^type_name>\Product_Type.prod\, [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 = \<^typ>\<open>bool\<close> then
fold_rev (fn m1 => fn m2 => map_product (curry Fun) m1 m2)
(map all_modes_of_typ' S) [Bool]
else
raise Fail "Invocation of all_modes_of_typ with a non-predicate type"
end
| all_modes_of_typ \<^typ>\<open>bool\<close> = [Bool]
| all_modes_of_typ _ =
raise Fail "Invocation of all_modes_of_typ with a non-predicate type"
fun all_smodes_of_typ (T as Type ("fun", _)) =
let
val (S, U) = strip_type T
fun all_smodes (Type (\<^type_name>\<open>Product_Type.prod\<close>, [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
raise Fail "invalid type for predicate"
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 = raise Fail "mode and term do not match"
| ho_arg (Pair (m1, m2)) (SOME (Const (\<^const_name>\<open>Pair\<close>, _) $ 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
fun ho_args_of_typ T ts =
let
fun ho_arg (T as Type ("fun", [_, _])) (SOME t) =
if body_type T = \<^typ>\<open>bool\<close> then [t] else []
| ho_arg (Type ("fun", [_, _])) NONE = raise Fail "mode and term do not match"
| ho_arg (Type(\<^type_name>\<open>Product_Type.prod\<close>, [T1, T2]))
(SOME (Const (\<^const_name>\<open>Pair\<close>, _) $ t1 $ t2)) =
ho_arg T1 (SOME t1) @ ho_arg T2 (SOME t2)
| ho_arg (Type(\<^type_name>\<open>Product_Type.prod\<close>, [T1, T2])) NONE =
ho_arg T1 NONE @ ho_arg T2 NONE
| ho_arg _ _ = []
in
flat (map2_optional ho_arg (binder_types T) ts)
end
fun ho_argsT_of_typ Ts =
let
fun ho_arg (T as Type("fun", [_,_])) = if body_type T = \<^typ>\<open>bool\<close> then [T] else []
| ho_arg (Type (\<^type_name>\<open>Product_Type.prod\<close>, [T1, T2])) =
ho_arg T1 @ ho_arg T2
| ho_arg _ = []
in
maps ho_arg 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 (\<^const_name>\<open>Pair\<close>, T) $ t1 $ t2) hoargs =
let
val (t1', hoargs') = replace (m1, t1) hoargs
val (t2', hoargs'') = replace (m2, t2) hoargs'
in
(Const (\<^const_name>\<open>Pair\<close>, 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 (\<^type_name>\<open>Product_Type.prod\<close>, [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 (\<^const_name>\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 raise Fail "split_map_mode: mode and term do not match"
in
(apply2 (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 (\<^type_name>\Product_Type.prod\, [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' _ _ = raise Fail "split_modeT': mode and type do not match"
in
(apply2 (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 (\<^type_name>\<open>Product_Type.prod\<close>, [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 _ f T s = f T s
fun map_filter_prod f (Const (\<^const_name>\<open>Pair\<close>, _) $ t1 $ t2) =
comb_option HOLogic.mk_prod (map_filter_prod f t1, map_filter_prod f t2)
| map_filter_prod f t = f t
fun split_modeT mode Ts =
let
fun split_arg_mode (Fun _) _ = ([], [])
| split_arg_mode (Pair (m1, m2)) (Type (\<^type_name>\<open>Product_Type.prod\<close>, [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 _ _ = raise Fail "split_modeT: mode and type do not match"
in
(apply2 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)
fun dest_indprem (Prem t) = t
| dest_indprem (Negprem t) = t
| dest_indprem (Sidecond t) = t
| dest_indprem (Generator _) = raise Fail "cannot destruct generator"
fun map_indprem f (Prem t) = Prem (f t)
| map_indprem f (Negprem t) = Negprem (f t)
| map_indprem f (Sidecond t) = Sidecond (f t)
| map_indprem f (Generator (v, T)) = Generator (dest_Free (f (Free (v, T))))
(* general syntactic functions *)
fun is_equationlike_term (Const (\<^const_name>\<open>Pure.eq\<close>, _) $ _ $ _) = true
| is_equationlike_term
(Const (\<^const_name>\<open>Trueprop\<close>, _) $ (Const (\<^const_name>\<open>HOL.eq\<close>, _) $ _ $ _)) = true
| is_equationlike_term _ = false
val is_equationlike = is_equationlike_term o Thm.prop_of
fun is_pred_equation_term (Const (\<^const_name>\<open>Pure.eq\<close>, _) $ u $ v) =
(fastype_of u = \<^typ>\<open>bool\<close>) andalso (fastype_of v = \<^typ>\<open>bool\<close>)
| is_pred_equation_term _ = false
val is_pred_equation = is_pred_equation_term o Thm.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 (Thm.prop_of t)
fun is_predT (T as Type("fun", [_, _])) = (body_type T = \<^typ>\<open>bool\<close>)
| is_predT _ = false
fun lookup_constr ctxt =
let
val tab = Ctr_Sugar.ctr_sugars_of ctxt
|> maps (map_filter (try dest_Const) o #ctrs)
|> map (fn (c, T) => ((c, (fst o dest_Type o body_type) T), BNF_Util.num_binder_types T))
in fn (c, T) =>
case body_type T of
Type (Tname, _) => AList.lookup (op =) tab (c, Tname)
| _ => NONE
end;
fun is_constrt ctxt =
let
val lookup_constr = lookup_constr ctxt
fun check t =
(case strip_comb t of
(Var _, []) => true
| (Free _, []) => true
| (Const cT, ts) =>
(case lookup_constr cT of
SOME i =>
length ts = i andalso forall check ts
| _ => false)
| _ => false)
in check end
fun strip_all t = (Term.strip_all_vars t, Term.strip_all_body t)
fun strip_ex (Const (\<^const_name>\<open>Ex\<close>, _) $ 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') = fold_map Name.variant xs nctxt;
val ps' = xs' ~~ Ts;
val vs = map Free ps';
val t'' = Term.subst_bounds (rev vs, t');
in ((ps', t''), nctxt') end
val strip_intro_concl =
strip_comb o HOLogic.dest_Trueprop o Logic.strip_imp_concl o Thm.prop_of
(* introduction rule combinators *)
fun map_atoms f intro =
let
val (literals, head) = Logic.strip_horn intro
fun appl t =
(case t of
(\<^term>\<open>Not\<close> $ 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, _) = Logic.strip_horn intro
fun appl t s =
(case t of
(\<^term>\<open>Not\<close> $ 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>\<open>Not\<close> $ 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 map_filter_premises f intro =
let
val (premises, head) = Logic.strip_horn intro
in
Logic.list_implies (map_filter f premises, head)
end
fun maps_premises f intro =
let
val (premises, head) = Logic.strip_horn intro
in
Logic.list_implies (maps f premises, head)
end
fun map_concl f intro =
let
val (premises, head) = Logic.strip_horn intro
in
Logic.list_implies (premises, f head)
end
(* combinators to apply a function to all basic parts of nested products *)
fun map_products f (Const (\<^const_name>\<open>Pair\<close>, T) $ t1 $ t2) =
Const (\<^const_name>\<open>Pair\<close>, T) $ map_products f t1 $ map_products f t2
| map_products f t = f t
(* split theorems of case expressions *)
fun prepare_split_thm ctxt split_thm =
(split_thm RS @{thm iffD2})
|> Local_Defs.unfold0 ctxt [@{thm atomize_conjL[symmetric]},
@{thm atomize_all[symmetric]}, @{thm atomize_imp[symmetric]}]
fun find_split_thm thy (Const (name, _)) =
Option.map #split (Ctr_Sugar.ctr_sugar_of_case (Proof_Context.init_global thy) name)
| find_split_thm _ _ = NONE
(* lifting term operations to theorems *)
fun map_term thy f th =
Skip_Proof.make_thm thy (f (Thm.prop_of th))
(*
fun equals_conv lhs_cv rhs_cv ct =
case Thm.term_of ct of
Const (@{const_name Pure.eq}, _) $ _ $ _ => Conv.arg_conv cv ct
| _ => error "equals_conv"
*)
(* Different compilations *)
datatype compilation = Pred | Depth_Limited | Random | Depth_Limited_Random | DSeq | Annotated
| Pos_Random_DSeq | Neg_Random_DSeq | New_Pos_Random_DSeq | New_Neg_Random_DSeq |
Pos_Generator_DSeq | Neg_Generator_DSeq | Pos_Generator_CPS | Neg_Generator_CPS
fun negative_compilation_of Pos_Random_DSeq = Neg_Random_DSeq
| negative_compilation_of Neg_Random_DSeq = Pos_Random_DSeq
| negative_compilation_of New_Pos_Random_DSeq = New_Neg_Random_DSeq
| negative_compilation_of New_Neg_Random_DSeq = New_Pos_Random_DSeq
| negative_compilation_of Pos_Generator_DSeq = Neg_Generator_DSeq
| negative_compilation_of Neg_Generator_DSeq = Pos_Generator_DSeq
| negative_compilation_of Pos_Generator_CPS = Neg_Generator_CPS
| negative_compilation_of Neg_Generator_CPS = Pos_Generator_CPS
| negative_compilation_of c = c
fun compilation_for_polarity false Pos_Random_DSeq = Neg_Random_DSeq
| compilation_for_polarity false New_Pos_Random_DSeq = New_Neg_Random_DSeq
| compilation_for_polarity _ c = c
fun is_depth_limited_compilation c =
(c = New_Pos_Random_DSeq) orelse (c = New_Neg_Random_DSeq) orelse
(c = Pos_Generator_DSeq) orelse (c = Pos_Generator_DSeq)
fun string_of_compilation c =
(case c of
Pred => ""
| Random => "random"
| Depth_Limited => "depth limited"
| Depth_Limited_Random => "depth limited random"
| DSeq => "dseq"
| Annotated => "annotated"
| Pos_Random_DSeq => "pos_random dseq"
| Neg_Random_DSeq => "neg_random_dseq"
| New_Pos_Random_DSeq => "new_pos_random dseq"
| New_Neg_Random_DSeq => "new_neg_random_dseq"
| Pos_Generator_DSeq => "pos_generator_dseq"
| Neg_Generator_DSeq => "neg_generator_dseq"
| Pos_Generator_CPS => "pos_generator_cps"
| Neg_Generator_CPS => "neg_generator_cps")
val compilation_names =
[("pred", Pred),
("random", Random),
("depth_limited", Depth_Limited),
("depth_limited_random", Depth_Limited_Random),
(*("annotated", Annotated),*)
("dseq", DSeq),
("random_dseq", Pos_Random_DSeq),
("new_random_dseq", New_Pos_Random_DSeq),
("generator_dseq", Pos_Generator_DSeq),
("generator_cps", Pos_Generator_CPS)]
val non_random_compilations = [Pred, Depth_Limited, DSeq, Annotated]
val random_compilations = [Random, Depth_Limited_Random,
Pos_Random_DSeq, Neg_Random_DSeq, New_Pos_Random_DSeq, New_Neg_Random_DSeq,
Pos_Generator_CPS, Neg_Generator_CPS]
(* datastructures and setup for generic compilation *)
datatype compilation_funs = CompilationFuns of {
mk_monadT : typ -> typ,
dest_monadT : typ -> typ,
mk_empty : typ -> term,
mk_single : term -> term,
mk_bind : term * term -> term,
mk_plus : term * term -> term,
mk_if : term -> term,
mk_iterate_upto : typ -> term * term * term -> term,
mk_not : term -> term,
mk_map : typ -> typ -> term -> term -> term
}
fun mk_monadT (CompilationFuns funs) = #mk_monadT funs
fun dest_monadT (CompilationFuns funs) = #dest_monadT funs
fun mk_empty (CompilationFuns funs) = #mk_empty funs
fun mk_single (CompilationFuns funs) = #mk_single funs
fun mk_bind (CompilationFuns funs) = #mk_bind funs
fun mk_plus (CompilationFuns funs) = #mk_plus funs
fun mk_if (CompilationFuns funs) = #mk_if funs
fun mk_iterate_upto (CompilationFuns funs) = #mk_iterate_upto funs
fun mk_not (CompilationFuns funs) = #mk_not funs
fun mk_map (CompilationFuns funs) = #mk_map funs
(** function types and names of different compilations **)
fun funT_of compfuns mode T =
let
val Ts = binder_types T
val (inTs, outTs) =
split_map_modeT (fn m => fn T => (SOME (funT_of compfuns m T), NONE)) mode Ts
in
inTs ---> (mk_monadT compfuns (HOLogic.mk_tupleT outTs))
end
(* Different options for compiler *)
datatype options = Options of {
expected_modes : (string * mode list) option,
proposed_modes : (string * mode list) list,
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,
show_invalid_clauses : bool,
skip_proof : bool,
no_topmost_reordering : bool,
function_flattening : bool,
specialise : bool,
fail_safe_function_flattening : bool,
no_higher_order_predicate : string list,
inductify : bool,
detect_switches : bool,
smart_depth_limiting : bool,
compilation : compilation
}
fun expected_modes (Options opt) = #expected_modes opt
fun proposed_modes (Options opt) = AList.lookup (op =) (#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 show_invalid_clauses (Options opt) = #show_invalid_clauses 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 specialise (Options opt) = #specialise 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
fun detect_switches (Options opt) = #detect_switches opt
fun smart_depth_limiting (Options opt) = #smart_depth_limiting opt
val default_options = Options {
expected_modes = NONE,
proposed_modes = [],
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,
show_invalid_clauses = false,
skip_proof = true,
no_topmost_reordering = false,
function_flattening = false,
specialise = false,
fail_safe_function_flattening = false,
no_higher_order_predicate = [],
inductify = false,
detect_switches = true,
smart_depth_limiting = false,
compilation = Pred
}
val bool_options = ["show_steps", "show_intermediate_results", "show_proof_trace", "show_modes",
"show_mode_inference", "show_compilation", "show_invalid_clauses", "skip_proof", "inductify",
"no_function_flattening", "detect_switches", "specialise", "no_topmost_reordering",
"smart_depth_limiting"]
fun print_step options s =
if show_steps options then tracing s else ()
(* simple transformations *)
(** tuple processing **)
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
(_ :: _ :: _) =>
let
fun rewrite_arg'
(Const (\<^const_name>\<open>Pair\<close>, _) $ _ $ t2, Type (\<^type_name>\<open>Product_Type.prod\<close>, [_, T2]))
(args, (pats, intro_t, ctxt)) =
rewrite_arg' (t2, T2) (args, (pats, intro_t, ctxt))
| rewrite_arg'
(t, Type (\<^type_name>\<open>Product_Type.prod\<close>, [T1, T2])) (args, (pats, intro_t, ctxt)) =
let
val thy = Proof_Context.theory_of ctxt
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
fun split_conjuncts_in_assms ctxt th =
let
val ((_, [fixed_th]), ctxt') = Variable.import false [th] ctxt
fun split_conjs i nprems th =
if i > nprems then th
else
(case try (op RSN) (@{thm conjI}, (i, th)) of
SOME th' => split_conjs i (nprems + 1) th'
| NONE => split_conjs (i + 1) nprems th)
in
singleton (Variable.export ctxt' ctxt)
(split_conjs 1 (Thm.nprems_of fixed_th) fixed_th)
end
fun dest_conjunct_prem th =
(case HOLogic.dest_Trueprop (Thm.prop_of th) of
(Const (\<^const_name>\<open>HOL.conj\<close>, _) $ _ $ _) =>
dest_conjunct_prem (th RS @{thm conjunct1}) @
dest_conjunct_prem (th RS @{thm conjunct2})
| _ => [th])
fun expand_tuples thy intro =
let
val ctxt = Proof_Context.init_global thy (* FIXME proper context!? *)
val (((T_insts, t_insts), [intro']), ctxt1) = Variable.import false [intro] ctxt
val intro_t = Thm.prop_of intro'
val concl = Logic.strip_imp_concl intro_t
val (_, args) = strip_comb (HOLogic.dest_Trueprop concl)
val (pats', intro_t', ctxt2) = rewrite_args args ([], intro_t, ctxt1)
val (pats', _, ctxt3) = fold_atoms rewrite_prem intro_t' (pats', intro_t', ctxt2)
fun rewrite_pat (ct1, ct2) =
(ct1, Thm.cterm_of ctxt3 (Pattern.rewrite_term thy pats' [] (Thm.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
(put_simpset HOL_basic_ss ctxt
addsimps [@{thm fst_conv}, @{thm snd_conv}, @{thm prod.inject}])
intro'''
(* splitting conjunctions introduced by prod.inject*)
val intro''''' = split_conjuncts_in_assms ctxt intro''''
in
intro'''''
end
(** making case distributivity rules **)
(*** this should be part of the datatype package ***)
fun datatype_name_of_case_name thy =
Ctr_Sugar.ctr_sugar_of_case (Proof_Context.init_global thy)
#> the #> #ctrs #> hd #> fastype_of #> body_type #> dest_Type #> fst
fun make_case_comb thy Tcon =
let
val ctxt = Proof_Context.init_global thy
val SOME {casex, ...} = Ctr_Sugar.ctr_sugar_of ctxt Tcon
val casex' = Type.legacy_freeze casex
val Ts = BNF_Util.binder_fun_types (fastype_of casex')
in
list_comb (casex', map_index (fn (j, T) => Free ("f" ^ string_of_int j, T)) Ts)
end
fun make_case_distrib thy Tcon =
let
val comb = make_case_comb thy Tcon;
val Type ("fun", [T, T']) = fastype_of comb;
val (Const (case_name, _), fs) = strip_comb comb
val used = Term.add_tfree_names comb []
val U = TFree (singleton (Name.variant_list used) "'t", \<^sort>\<open>type\<close>)
val x = Free ("x", T)
val f = Free ("f", T' --> U)
fun apply_f f' =
let
val Ts = binder_types (fastype_of f')
val bs = map Bound ((length Ts - 1) downto 0)
in
fold_rev absdummy Ts (f $ (list_comb (f', bs)))
end
val fs' = map apply_f fs
val case_c' = Const (case_name, (map fastype_of fs') @ [T] ---> U)
in
HOLogic.mk_eq (f $ (comb $ x), list_comb (case_c', fs') $ x)
end
fun case_rewrite thy Tcon =
(Drule.export_without_context o Skip_Proof.make_thm thy o HOLogic.mk_Trueprop)
(make_case_distrib thy Tcon)
fun instantiated_case_rewrite thy Tcon =
let
val th = case_rewrite thy Tcon
val ctxt = Proof_Context.init_global thy
val f = fst (strip_comb (fst (HOLogic.dest_eq (HOLogic.dest_Trueprop (Thm.prop_of th)))))
val Type ("fun", [uninst_T, uninst_T']) = fastype_of f
val ([yname], ctxt') = Variable.add_fixes ["y"] ctxt
val T' = TFree ("'t'", \<^sort>\type\)
val U = TFree ("'u", \<^sort>\<open>type\<close>)
val y = Free (yname, U)
val f' = absdummy (U --> T') (Bound 0 $ y)
val th' =
Thm.instantiate
([(dest_TVar uninst_T, Thm.ctyp_of ctxt' (U --> T')),
(dest_TVar uninst_T', Thm.ctyp_of ctxt' T')],
[((fst (dest_Var f), (U --> T') --> T'), Thm.cterm_of ctxt' f')]) th
val [th'] = Variable.export (Variable.declare_thm th' ctxt') ctxt [th']
in
th'
end
fun case_betapply thy t =
let
val case_name = fst (dest_Const (fst (strip_comb t)))
val Tcon = datatype_name_of_case_name thy case_name
val th = instantiated_case_rewrite thy Tcon
in
Raw_Simplifier.rewrite_term thy [th RS @{thm eq_reflection}] [] t
end
(*** conversions ***)
fun imp_prems_conv cv ct =
(case Thm.term_of ct of
Const (\<^const_name>\<open>Pure.imp\<close>, _) $ _ $ _ =>
Conv.combination_conv (Conv.arg_conv cv) (imp_prems_conv cv) ct
| _ => Conv.all_conv ct)
(** eta contract higher-order arguments **)
fun eta_contract_ho_arguments thy intro =
let
fun f atom = list_comb (apsnd ((map o map_products) Envir.eta_contract) (strip_comb atom))
in
map_term thy (map_concl f o map_atoms f) intro
end
(** remove equalities **)
fun remove_equalities thy intro =
let
fun remove_eqs intro_t =
let
val (prems, concl) = Logic.strip_horn intro_t
fun remove_eq (prems, concl) =
let
fun removable_eq prem =
(case try (HOLogic.dest_eq o HOLogic.dest_Trueprop) prem of
SOME (lhs, rhs) =>
(case lhs of
Var _ => true
| _ => (case rhs of Var _ => true | _ => false))
| NONE => false)
in
(case find_first removable_eq prems of
NONE => (prems, concl)
| SOME eq =>
let
val (lhs, rhs) = HOLogic.dest_eq (HOLogic.dest_Trueprop eq)
val prems' = remove (op =) eq prems
val subst =
(case lhs of
(v as Var _) =>
(fn t => if t = v then rhs else t)
| _ => (case rhs of (v as Var _) => (fn t => if t = v then lhs else t)))
in
remove_eq (map (map_aterms subst) prems', map_aterms subst concl)
end)
end
in
Logic.list_implies (remove_eq (prems, concl))
end
in
map_term thy remove_eqs intro
end
(* Some last processing *)
fun remove_pointless_clauses intro =
if Logic.strip_imp_prems (Thm.prop_of intro) = [\<^prop>\<open>False\<close>] then
[]
else [intro]
(* some peephole optimisations *)
fun peephole_optimisation thy intro =
let
val ctxt = Proof_Context.init_global thy (* FIXME proper context!? *)
val process =
rewrite_rule ctxt (Named_Theorems.get ctxt \<^named_theorems>\<open>code_pred_simp\<close>)
fun process_False intro_t =
if member (op =) (Logic.strip_imp_prems intro_t) \<^prop>\<open>False\<close>
then NONE else SOME intro_t
fun process_True intro_t =
map_filter_premises (fn p => if p = \<^prop>\<open>True\<close> then NONE else SOME p) intro_t
in
Option.map (Skip_Proof.make_thm thy)
(process_False (process_True (Thm.prop_of (process intro))))
end
(* importing introduction rules *)
fun import_intros inp_pred [] ctxt =
let
val (outp_pred, ctxt') = yield_singleton (Variable.import_terms true) inp_pred ctxt
val T = fastype_of outp_pred
val paramTs = ho_argsT_of_typ (binder_types T)
val (param_names, _) = Variable.variant_fixes
(map (fn i => "p" ^ (string_of_int i)) (1 upto (length paramTs))) ctxt'
val params = map2 (curry Free) param_names paramTs
in
(((outp_pred, params), []), ctxt')
end
| import_intros inp_pred (th :: ths) ctxt =
let
val ((_, [th']), ctxt') = Variable.import true [th] ctxt
val thy = Proof_Context.theory_of ctxt'
val (pred, args) = strip_intro_concl th'
val T = fastype_of pred
val ho_args = ho_args_of_typ T args
fun subst_of (pred', pred) =
let
val subst = Sign.typ_match thy (fastype_of pred', fastype_of pred) Vartab.empty
handle Type.TYPE_MATCH =>
error ("Type mismatch of predicate " ^ fst (dest_Const pred) ^
" (trying to match " ^ Syntax.string_of_typ ctxt' (fastype_of pred') ^
" and " ^ Syntax.string_of_typ ctxt' (fastype_of pred) ^ ")" ^
" in " ^ Thm.string_of_thm ctxt' th)
in map (fn (xi, (S, T)) => ((xi, S), T)) (Vartab.dest subst) end
fun instantiate_typ th =
let
val (pred', _) = strip_intro_concl th
val _ =
if not (fst (dest_Const pred) = fst (dest_Const pred')) then
raise Fail "Trying to instantiate another predicate"
else ()
in Thm.instantiate (map (apsnd (Thm.ctyp_of ctxt')) (subst_of (pred', pred)), []) th end
fun instantiate_ho_args th =
let
val (_, args') =
(strip_comb o HOLogic.dest_Trueprop o Logic.strip_imp_concl o Thm.prop_of) th
val ho_args' = map dest_Var (ho_args_of_typ T args')
in Thm.instantiate ([], ho_args' ~~ map (Thm.cterm_of ctxt') ho_args) th end
val outp_pred =
Term_Subst.instantiate (subst_of (inp_pred, pred), []) inp_pred
val ((_, ths'), ctxt1) =
Variable.import false (map (instantiate_typ #> instantiate_ho_args) ths) ctxt'
in
(((outp_pred, ho_args), th' :: ths'), ctxt1)
end
(* generation of case rules from user-given introduction rules *)
fun mk_args2 (Type (\<^type_name>\<open>Product_Type.prod\<close>, [T1, T2])) st =
let
val (t1, st') = mk_args2 T1 st
val (t2, st'') = mk_args2 T2 st'
in
(HOLogic.mk_prod (t1, t2), st'')
end
(*| mk_args2 (T as Type ("fun", _)) (params, ctxt) =
let
val (S, U) = strip_type T
in
if U = HOLogic.boolT then
(hd params, (tl params, ctxt))
else
let
val ([x], ctxt') = Variable.variant_fixes ["x"] ctxt
in
(Free (x, T), (params, ctxt'))
end
end*)
| mk_args2 T (params, ctxt) =
let
val ([x], ctxt') = Variable.variant_fixes ["x"] ctxt
in
(Free (x, T), (params, ctxt'))
end
fun mk_casesrule ctxt pred introrules =
let
(* TODO: can be simplified if parameters are not treated specially ? *)
val (((pred, params), intros_th), ctxt1) = import_intros pred introrules ctxt
(* TODO: distinct required ? -- test case with more than one parameter! *)
val params = distinct (op aconv) params
val intros = map Thm.prop_of intros_th
val ([propname], ctxt2) = Variable.variant_fixes ["thesis"] ctxt1
val prop = HOLogic.mk_Trueprop (Free (propname, HOLogic.boolT))
val argsT = binder_types (fastype_of pred)
(* TODO: can be simplified if parameters are not treated specially ? <-- see uncommented code! *)
val (argvs, _) = fold_map mk_args2 argsT (params, ctxt2)
fun mk_case intro =
let
val (_, args) = (strip_comb o HOLogic.dest_Trueprop o Logic.strip_imp_concl) intro
val prems = Logic.strip_imp_prems intro
val eqprems =
map2 (HOLogic.mk_Trueprop oo (curry HOLogic.mk_eq)) argvs args
val frees = map Free (fold Term.add_frees (args @ prems) [])
in fold Logic.all frees (Logic.list_implies (eqprems @ prems, prop)) end
val assm = HOLogic.mk_Trueprop (list_comb (pred, argvs))
val cases = map mk_case intros
in Logic.list_implies (assm :: cases, prop) end;
(* unifying constants to have the same type variables *)
fun unify_consts thy cs intr_ts =
let
val add_term_consts_2 = fold_aterms (fn Const c => insert (op =) c | _ => I);
fun varify (t, (i, ts)) =
let val t' = map_types (Logic.incr_tvar (i + 1)) (#2 (Type.varify_global [] t))
in (maxidx_of_term t', t' :: ts) end
val (i, cs') = List.foldr varify (~1, []) cs
val (i', intr_ts') = List.foldr varify (i, []) intr_ts
val rec_consts = fold add_term_consts_2 cs' []
val intr_consts = fold add_term_consts_2 intr_ts' []
fun unify (cname, cT) =
let val consts = map snd (filter (fn c => fst c = cname) intr_consts)
in fold (Sign.typ_unify thy) ((replicate (length consts) cT) ~~ consts) end
val (env, _) = fold unify rec_consts (Vartab.empty, i')
val subst = map_types (Envir.norm_type env)
in (map subst cs', map subst intr_ts')
end handle Type.TUNIFY =>
(warning "Occurrences of recursive constant have non-unifiable types"; (cs, intr_ts))
(* preprocessing rules *)
fun preprocess_equality thy rule =
Conv.fconv_rule
(imp_prems_conv
(HOLogic.Trueprop_conv
(Conv.try_conv (Conv.rewr_conv (Thm.symmetric @{thm Predicate.eq_is_eq})))))
(Thm.transfer thy rule)
fun preprocess_intro thy = expand_tuples thy #> preprocess_equality thy
(* defining a quickcheck predicate *)
fun strip_imp_prems (Const(\<^const_name>\<open>HOL.implies\<close>, _) $ A $ B) = A :: strip_imp_prems B
| strip_imp_prems _ = [];
fun strip_imp_concl (Const(\<^const_name>\<open>HOL.implies\<close>, _) $ _ $ B) = strip_imp_concl B
| strip_imp_concl A = A;
fun strip_horn A = (strip_imp_prems A, strip_imp_concl A)
fun define_quickcheck_predicate t thy =
let
val (vs, t') = strip_abs t
val vs' = Variable.variant_frees (Proof_Context.init_global thy) [] vs (* FIXME proper context!? *)
val t'' = subst_bounds (map Free (rev vs'), t')
val (prems, concl) = strip_horn t''
val constname = "quickcheck"
val full_constname = Sign.full_bname thy constname
val constT = map snd vs' ---> \<^typ>\bool\
val thy1 = Sign.add_consts [(Binding.name constname, constT, NoSyn)] thy
val const = Const (full_constname, constT)
val t =
Logic.list_implies
(map HOLogic.mk_Trueprop (prems @ [HOLogic.mk_not concl]),
HOLogic.mk_Trueprop (list_comb (const, map Free vs')))
val intro =
Goal.prove (Proof_Context.init_global thy1) (map fst vs') [] t
(fn {context = ctxt, ...} => ALLGOALS (Skip_Proof.cheat_tac ctxt))
in
((((full_constname, constT), vs'), intro), thy1)
end
end
¤ Dauer der Verarbeitung: 0.53 Sekunden
(vorverarbeitet)
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