--- a/src/HOL/Tools/Nitpick/nitpick_hol.ML Tue Feb 09 13:54:27 2010 +0100
+++ b/src/HOL/Tools/Nitpick/nitpick_hol.ML Tue Feb 09 17:06:05 2010 +0100
@@ -13,7 +13,7 @@
type unrolled = styp * styp
type wf_cache = (styp * (bool * bool)) list
- type extended_context = {
+ type hol_context = {
thy: theory,
ctxt: Proof.context,
max_bisim_depth: int,
@@ -46,12 +46,24 @@
wf_cache: wf_cache Unsynchronized.ref,
constr_cache: (typ * styp list) list Unsynchronized.ref}
+ datatype fixpoint_kind = Lfp | Gfp | NoFp
+ datatype boxability =
+ InConstr | InSel | InExpr | InPair | InFunLHS | InFunRHS1 | InFunRHS2
+
val name_sep : string
val numeral_prefix : string
+ val ubfp_prefix : string
+ val lbfp_prefix : string
val skolem_prefix : string
+ val special_prefix : string
+ val uncurry_prefix : string
val eval_prefix : string
val original_name : string -> string
val s_conj : term * term -> term
+ val s_disj : term * term -> term
+ val strip_any_connective : term -> term list * term
+ val conjuncts_of : term -> term list
+ val disjuncts_of : term -> term list
val unbit_and_unbox_type : typ -> typ
val string_for_type : Proof.context -> typ -> string
val prefix_name : string -> string -> string
@@ -76,6 +88,7 @@
val is_record_type : typ -> bool
val is_number_type : theory -> typ -> bool
val const_for_iterator_type : typ -> styp
+ val strip_n_binders : int -> typ -> typ list * typ
val nth_range_type : int -> typ -> typ
val num_factors_in_type : typ -> int
val num_binder_types : typ -> int
@@ -96,16 +109,20 @@
val is_rep_fun : theory -> styp -> bool
val is_quot_abs_fun : Proof.context -> styp -> bool
val is_quot_rep_fun : Proof.context -> styp -> bool
+ val mate_of_rep_fun : theory -> styp -> styp
+ val is_constr_like : theory -> styp -> bool
+ val is_stale_constr : theory -> styp -> bool
val is_constr : theory -> styp -> bool
- val is_stale_constr : theory -> styp -> bool
val is_sel : string -> bool
val is_sel_like_and_no_discr : string -> bool
+ val box_type : hol_context -> boxability -> typ -> typ
val discr_for_constr : styp -> styp
val num_sels_for_constr_type : typ -> int
val nth_sel_name_for_constr_name : string -> int -> string
val nth_sel_for_constr : styp -> int -> styp
- val boxed_nth_sel_for_constr : extended_context -> styp -> int -> styp
+ val boxed_nth_sel_for_constr : hol_context -> styp -> int -> styp
val sel_no_from_name : string -> int
+ val close_form : term -> term
val eta_expand : typ list -> term -> int -> term
val extensionalize : term -> term
val distinctness_formula : typ -> term list -> term
@@ -113,19 +130,25 @@
val unregister_frac_type : string -> theory -> theory
val register_codatatype : typ -> string -> styp list -> theory -> theory
val unregister_codatatype : typ -> theory -> theory
- val datatype_constrs : extended_context -> typ -> styp list
- val boxed_datatype_constrs : extended_context -> typ -> styp list
- val num_datatype_constrs : extended_context -> typ -> int
+ val datatype_constrs : hol_context -> typ -> styp list
+ val boxed_datatype_constrs : hol_context -> typ -> styp list
+ val num_datatype_constrs : hol_context -> typ -> int
val constr_name_for_sel_like : string -> string
- val boxed_constr_for_sel : extended_context -> styp -> styp
+ val boxed_constr_for_sel : hol_context -> styp -> styp
+ val discriminate_value : hol_context -> styp -> term -> term
+ val select_nth_constr_arg : theory -> styp -> term -> int -> typ -> term
+ val construct_value : theory -> styp -> term list -> term
val card_of_type : (typ * int) list -> typ -> int
val bounded_card_of_type : int -> int -> (typ * int) list -> typ -> int
val bounded_exact_card_of_type :
- extended_context -> int -> int -> (typ * int) list -> typ -> int
- val is_finite_type : extended_context -> typ -> bool
+ hol_context -> int -> int -> (typ * int) list -> typ -> int
+ val is_finite_type : hol_context -> typ -> bool
+ val special_bounds : term list -> (indexname * typ) list
+ val is_funky_typedef : theory -> typ -> bool
val all_axioms_of : theory -> term list * term list * term list
val arity_of_built_in_const : bool -> styp -> int option
val is_built_in_const : bool -> styp -> bool
+ val term_under_def : term -> term
val case_const_names : theory -> (string * int) list
val const_def_table : Proof.context -> term list -> const_table
val const_nondef_table : term list -> const_table
@@ -134,22 +157,33 @@
val inductive_intro_table : Proof.context -> const_table -> const_table
val ground_theorem_table : theory -> term list Inttab.table
val ersatz_table : theory -> (string * string) list
+ val add_simps : const_table Unsynchronized.ref -> string -> term list -> unit
+ val inverse_axioms_for_rep_fun : theory -> styp -> term list
+ val optimized_typedef_axioms : theory -> string * typ list -> term list
+ val optimized_quot_type_axioms : theory -> string * typ list -> term list
val def_of_const : theory -> const_table -> styp -> term option
- val is_inductive_pred : extended_context -> styp -> bool
+ val fixpoint_kind_of_const :
+ theory -> const_table -> string * typ -> fixpoint_kind
+ val is_inductive_pred : hol_context -> styp -> bool
+ val is_equational_fun : hol_context -> styp -> bool
val is_constr_pattern_lhs : theory -> term -> bool
val is_constr_pattern_formula : theory -> term -> bool
+ val unfold_defs_in_term : hol_context -> term -> term
+ val codatatype_bisim_axioms : hol_context -> typ -> term list
+ val is_well_founded_inductive_pred : hol_context -> styp -> bool
+ val unrolled_inductive_pred_const : hol_context -> bool -> styp -> term
+ val equational_fun_axioms : hol_context -> styp -> term list
+ val is_equational_fun_surely_complete : hol_context -> styp -> bool
val merge_type_vars_in_terms : term list -> term list
- val ground_types_in_type : extended_context -> typ -> typ list
- val ground_types_in_terms : extended_context -> term list -> typ list
+ val ground_types_in_type : hol_context -> typ -> typ list
+ val ground_types_in_terms : hol_context -> term list -> typ list
val format_type : int list -> int list -> typ -> typ
val format_term_type :
theory -> const_table -> (term option * int list) list -> term -> typ
val user_friendly_const :
- extended_context -> string * string -> (term option * int list) list
+ hol_context -> string * string -> (term option * int list) list
-> styp -> term * typ
val assign_operator_for_const : styp -> string
- val preprocess_term :
- extended_context -> term -> ((term list * term list) * (bool * bool)) * term
end;
structure Nitpick_HOL : NITPICK_HOL =
@@ -162,7 +196,7 @@
type unrolled = styp * styp
type wf_cache = (styp * (bool * bool)) list
-type extended_context = {
+type hol_context = {
thy: theory,
ctxt: Proof.context,
max_bisim_depth: int,
@@ -195,6 +229,10 @@
wf_cache: wf_cache Unsynchronized.ref,
constr_cache: (typ * styp list) list Unsynchronized.ref}
+datatype fixpoint_kind = Lfp | Gfp | NoFp
+datatype boxability =
+ InConstr | InSel | InExpr | InPair | InFunLHS | InFunRHS1 | InFunRHS2
+
structure Data = Theory_Data(
type T = {frac_types: (string * (string * string) list) list,
codatatypes: (string * (string * styp list)) list}
@@ -222,20 +260,11 @@
val special_prefix = nitpick_prefix ^ "sp"
val uncurry_prefix = nitpick_prefix ^ "unc"
val eval_prefix = nitpick_prefix ^ "eval"
-val bound_var_prefix = "b"
-val cong_var_prefix = "c"
val iter_var_prefix = "i"
-val val_var_prefix = nitpick_prefix ^ "v"
val arg_var_prefix = "x"
(* int -> string *)
fun sel_prefix_for j = sel_prefix ^ string_of_int j ^ name_sep
-fun special_prefix_for j = special_prefix ^ string_of_int j ^ name_sep
-(* int -> int -> string *)
-fun skolem_prefix_for k j =
- skolem_prefix ^ string_of_int k ^ "@" ^ string_of_int j ^ name_sep
-fun uncurry_prefix_for k j =
- uncurry_prefix ^ string_of_int k ^ "@" ^ string_of_int j ^ name_sep
(* string -> string * string *)
val strip_first_name_sep =
@@ -260,9 +289,6 @@
| s_disj (t1, t2) =
if t1 = @{const True} orelse t2 = @{const True} then @{const True}
else HOLogic.mk_disj (t1, t2)
-(* term -> term -> term *)
-fun mk_exists v t =
- HOLogic.exists_const (fastype_of v) $ lambda v (incr_boundvars 1 t)
(* term -> term -> term list *)
fun strip_connective conn_t (t as (t0 $ t1 $ t2)) =
@@ -276,8 +302,8 @@
([t], @{const Not})
| strip_any_connective t = ([t], @{const Not})
(* term -> term list *)
-val conjuncts = strip_connective @{const "op &"}
-val disjuncts = strip_connective @{const "op |"}
+val conjuncts_of = strip_connective @{const "op &"}
+val disjuncts_of = strip_connective @{const "op |"}
(* When you add constants to these lists, make sure to handle them in
"Nitpick_Nut.nut_from_term", and perhaps in "Nitpick_Mono.consider_term" as
@@ -373,8 +399,6 @@
fun shortest_name s = List.last (space_explode "." s) handle List.Empty => ""
(* string -> term -> term *)
val prefix_abs_vars = Term.map_abs_vars o prefix_name
-(* term -> term *)
-val shorten_abs_vars = Term.map_abs_vars shortest_name
(* string -> string *)
fun short_name s =
case space_explode name_sep s of
@@ -441,7 +465,7 @@
| const_for_iterator_type T =
raise TYPE ("Nitpick_HOL.const_for_iterator_type", [T], [])
-(* int -> typ -> typ * typ *)
+(* int -> typ -> typ list * typ *)
fun strip_n_binders 0 T = ([], T)
| strip_n_binders n (Type ("fun", [T1, T2])) =
strip_n_binders (n - 1) T2 |>> cons T1
@@ -552,7 +576,7 @@
val is_real_datatype = is_some oo Datatype.get_info
(* theory -> typ -> bool *)
fun is_quot_type _ (Type ("IntEx.my_int", _)) = true (* FIXME *)
- | is_quot_type _ (Type ("FSet.fset", _)) = true (* FIXME *)
+ | is_quot_type _ (Type ("FSet.fset", _)) = true
| is_quot_type _ _ = false
fun is_codatatype thy (T as Type (s, _)) =
not (null (AList.lookup (op =) (#codatatypes (Data.get thy)) s
@@ -619,11 +643,11 @@
| NONE => false)
| is_rep_fun _ _ = false
(* Proof.context -> styp -> bool *)
-fun is_quot_abs_fun _ ("IntEx.abs_my_int", _) = true (* FIXME *)
- | is_quot_abs_fun _ ("FSet.abs_fset", _) = true (* FIXME *)
+fun is_quot_abs_fun _ ("IntEx.abs_my_int", _) = true
+ | is_quot_abs_fun _ ("FSet.abs_fset", _) = true
| is_quot_abs_fun _ _ = false
-fun is_quot_rep_fun _ ("IntEx.rep_my_int", _) = true (* FIXME *)
- | is_quot_rep_fun _ ("FSet.rep_fset", _) = true (* FIXME *)
+fun is_quot_rep_fun _ ("IntEx.rep_my_int", _) = true
+ | is_quot_rep_fun _ ("FSet.rep_fset", _) = true
| is_quot_rep_fun _ _ = false
(* theory -> styp -> styp *)
@@ -682,9 +706,6 @@
String.isPrefix sel_prefix
orf (member (op =) [@{const_name fst}, @{const_name snd}])
-datatype boxability =
- InConstr | InSel | InExpr | InPair | InFunLHS | InFunRHS1 | InFunRHS2
-
(* boxability -> boxability *)
fun in_fun_lhs_for InConstr = InSel
| in_fun_lhs_for _ = InFunLHS
@@ -693,8 +714,8 @@
| in_fun_rhs_for InFunRHS1 = InFunRHS2
| in_fun_rhs_for _ = InFunRHS1
-(* extended_context -> boxability -> typ -> bool *)
-fun is_boxing_worth_it (ext_ctxt : extended_context) boxy T =
+(* hol_context -> boxability -> typ -> bool *)
+fun is_boxing_worth_it (hol_ctxt : hol_context) boxy T =
case T of
Type ("fun", _) =>
(boxy = InPair orelse boxy = InFunLHS) andalso
@@ -702,31 +723,31 @@
| Type ("*", Ts) =>
boxy = InPair orelse boxy = InFunRHS1 orelse boxy = InFunRHS2 orelse
((boxy = InExpr orelse boxy = InFunLHS) andalso
- exists (is_boxing_worth_it ext_ctxt InPair)
- (map (box_type ext_ctxt InPair) Ts))
+ exists (is_boxing_worth_it hol_ctxt InPair)
+ (map (box_type hol_ctxt InPair) Ts))
| _ => false
-(* extended_context -> boxability -> string * typ list -> string *)
-and should_box_type (ext_ctxt as {thy, boxes, ...}) boxy (z as (s, Ts)) =
+(* hol_context -> boxability -> string * typ list -> string *)
+and should_box_type (hol_ctxt as {thy, boxes, ...}) boxy (z as (s, Ts)) =
case triple_lookup (type_match thy) boxes (Type z) of
SOME (SOME box_me) => box_me
- | _ => is_boxing_worth_it ext_ctxt boxy (Type z)
-(* extended_context -> boxability -> typ -> typ *)
-and box_type ext_ctxt boxy T =
+ | _ => is_boxing_worth_it hol_ctxt boxy (Type z)
+(* hol_context -> boxability -> typ -> typ *)
+and box_type hol_ctxt boxy T =
case T of
Type (z as ("fun", [T1, T2])) =>
if boxy <> InConstr andalso boxy <> InSel andalso
- should_box_type ext_ctxt boxy z then
+ should_box_type hol_ctxt boxy z then
Type (@{type_name fun_box},
- [box_type ext_ctxt InFunLHS T1, box_type ext_ctxt InFunRHS1 T2])
+ [box_type hol_ctxt InFunLHS T1, box_type hol_ctxt InFunRHS1 T2])
else
- box_type ext_ctxt (in_fun_lhs_for boxy) T1
- --> box_type ext_ctxt (in_fun_rhs_for boxy) T2
+ box_type hol_ctxt (in_fun_lhs_for boxy) T1
+ --> box_type hol_ctxt (in_fun_rhs_for boxy) T2
| Type (z as ("*", Ts)) =>
if boxy <> InConstr andalso boxy <> InSel
- andalso should_box_type ext_ctxt boxy z then
- Type (@{type_name pair_box}, map (box_type ext_ctxt InSel) Ts)
+ andalso should_box_type hol_ctxt boxy z then
+ Type (@{type_name pair_box}, map (box_type hol_ctxt InSel) Ts)
else
- Type ("*", map (box_type ext_ctxt
+ Type ("*", map (box_type hol_ctxt
(if boxy = InConstr orelse boxy = InSel then boxy
else InPair)) Ts)
| _ => T
@@ -747,9 +768,9 @@
| nth_sel_for_constr (s, T) n =
(nth_sel_name_for_constr_name s n,
body_type T --> nth (maybe_curried_binder_types T) n)
-(* extended_context -> styp -> int -> styp *)
-fun boxed_nth_sel_for_constr ext_ctxt =
- apsnd (box_type ext_ctxt InSel) oo nth_sel_for_constr
+(* hol_context -> styp -> int -> styp *)
+fun boxed_nth_sel_for_constr hol_ctxt =
+ apsnd (box_type hol_ctxt InSel) oo nth_sel_for_constr
(* string -> int *)
fun sel_no_from_name s =
@@ -762,6 +783,22 @@
else
0
+(* term -> term *)
+val close_form =
+ let
+ (* (indexname * typ) list -> (indexname * typ) list -> term -> term *)
+ fun close_up zs zs' =
+ fold (fn (z as ((s, _), T)) => fn t' =>
+ Term.all T $ Abs (s, T, abstract_over (Var z, t')))
+ (take (length zs' - length zs) zs')
+ (* (indexname * typ) list -> term -> term *)
+ fun aux zs (@{const "==>"} $ t1 $ t2) =
+ let val zs' = Term.add_vars t1 zs in
+ close_up zs zs' (Logic.mk_implies (t1, aux zs' t2))
+ end
+ | aux zs t = close_up zs (Term.add_vars t zs) t
+ in aux [] end
+
(* typ list -> term -> int -> term *)
fun eta_expand _ t 0 = t
| eta_expand Ts (Abs (s, T, t')) n =
@@ -791,8 +828,8 @@
fun zero_const T = Const (@{const_name zero_nat_inst.zero_nat}, T)
fun suc_const T = Const (@{const_name Suc}, T --> T)
-(* extended_context -> typ -> styp list *)
-fun uncached_datatype_constrs ({thy, stds, ...} : extended_context)
+(* hol_context -> typ -> styp list *)
+fun uncached_datatype_constrs ({thy, stds, ...} : hol_context)
(T as Type (s, Ts)) =
(case AList.lookup (op =) (#codatatypes (Data.get thy)) s of
SOME (_, xs' as (_ :: _)) => map (apsnd (repair_constr_type thy T)) xs'
@@ -829,49 +866,49 @@
else
[])
| uncached_datatype_constrs _ _ = []
-(* extended_context -> typ -> styp list *)
-fun datatype_constrs (ext_ctxt as {constr_cache, ...}) T =
+(* hol_context -> typ -> styp list *)
+fun datatype_constrs (hol_ctxt as {constr_cache, ...}) T =
case AList.lookup (op =) (!constr_cache) T of
SOME xs => xs
| NONE =>
- let val xs = uncached_datatype_constrs ext_ctxt T in
+ let val xs = uncached_datatype_constrs hol_ctxt T in
(Unsynchronized.change constr_cache (cons (T, xs)); xs)
end
-fun boxed_datatype_constrs ext_ctxt =
- map (apsnd (box_type ext_ctxt InConstr)) o datatype_constrs ext_ctxt
-(* extended_context -> typ -> int *)
+fun boxed_datatype_constrs hol_ctxt =
+ map (apsnd (box_type hol_ctxt InConstr)) o datatype_constrs hol_ctxt
+(* hol_context -> typ -> int *)
val num_datatype_constrs = length oo datatype_constrs
(* string -> string *)
fun constr_name_for_sel_like @{const_name fst} = @{const_name Pair}
| constr_name_for_sel_like @{const_name snd} = @{const_name Pair}
| constr_name_for_sel_like s' = original_name s'
-(* extended_context -> styp -> styp *)
-fun boxed_constr_for_sel ext_ctxt (s', T') =
+(* hol_context -> styp -> styp *)
+fun boxed_constr_for_sel hol_ctxt (s', T') =
let val s = constr_name_for_sel_like s' in
- AList.lookup (op =) (boxed_datatype_constrs ext_ctxt (domain_type T')) s
+ AList.lookup (op =) (boxed_datatype_constrs hol_ctxt (domain_type T')) s
|> the |> pair s
end
-(* extended_context -> styp -> term *)
-fun discr_term_for_constr ext_ctxt (x as (s, T)) =
+(* hol_context -> styp -> term *)
+fun discr_term_for_constr hol_ctxt (x as (s, T)) =
let val dataT = body_type T in
if s = @{const_name Suc} then
Abs (Name.uu, dataT,
@{const Not} $ HOLogic.mk_eq (zero_const dataT, Bound 0))
- else if num_datatype_constrs ext_ctxt dataT >= 2 then
+ else if num_datatype_constrs hol_ctxt dataT >= 2 then
Const (discr_for_constr x)
else
Abs (Name.uu, dataT, @{const True})
end
-(* extended_context -> styp -> term -> term *)
-fun discriminate_value (ext_ctxt as {thy, ...}) (x as (_, T)) t =
+(* hol_context -> styp -> term -> term *)
+fun discriminate_value (hol_ctxt as {thy, ...}) (x as (_, T)) t =
case strip_comb t of
(Const x', args) =>
if x = x' then @{const True}
else if is_constr_like thy x' then @{const False}
- else betapply (discr_term_for_constr ext_ctxt x, t)
- | _ => betapply (discr_term_for_constr ext_ctxt x, t)
+ else betapply (discr_term_for_constr hol_ctxt x, t)
+ | _ => betapply (discr_term_for_constr hol_ctxt x, t)
(* styp -> term -> term *)
fun nth_arg_sel_term_for_constr (x as (s, T)) n =
@@ -920,25 +957,9 @@
| _ => list_comb (Const x, args)
end
-(* extended_context -> typ -> term -> term *)
-fun constr_expand (ext_ctxt as {thy, ...}) T t =
- (case head_of t of
- Const x => if is_constr_like thy x then t else raise SAME ()
- | _ => raise SAME ())
- handle SAME () =>
- let
- val x' as (_, T') =
- if is_pair_type T then
- let val (T1, T2) = HOLogic.dest_prodT T in
- (@{const_name Pair}, T1 --> T2 --> T)
- end
- else
- datatype_constrs ext_ctxt T |> hd
- val arg_Ts = binder_types T'
- in
- list_comb (Const x', map2 (select_nth_constr_arg thy x' t)
- (index_seq 0 (length arg_Ts)) arg_Ts)
- end
+(* The higher this number is, the more nonstandard models can be generated. It's
+ not important enough to be a user option, though. *)
+val xi_card = 8
(* (typ * int) list -> typ -> int *)
fun card_of_type assigns (Type ("fun", [T1, T2])) =
@@ -949,6 +970,7 @@
| card_of_type _ @{typ prop} = 2
| card_of_type _ @{typ bool} = 2
| card_of_type _ @{typ unit} = 1
+ | card_of_type _ @{typ \<xi>} = xi_card
| card_of_type assigns T =
case AList.lookup (op =) assigns T of
SOME k => k
@@ -975,8 +997,8 @@
card_of_type assigns T
handle TYPE ("Nitpick_HOL.card_of_type", _, _) =>
default_card)
-(* extended_context -> int -> (typ * int) list -> typ -> int *)
-fun bounded_exact_card_of_type ext_ctxt max default_card assigns T =
+(* hol_context -> int -> (typ * int) list -> typ -> int *)
+fun bounded_exact_card_of_type hol_ctxt max default_card assigns T =
let
(* typ list -> typ -> int *)
fun aux avoid T =
@@ -1005,14 +1027,15 @@
| @{typ prop} => 2
| @{typ bool} => 2
| @{typ unit} => 1
+ | @{typ \<xi>} => xi_card
| Type _ =>
- (case datatype_constrs ext_ctxt T of
+ (case datatype_constrs hol_ctxt T of
[] => if is_integer_type T orelse is_bit_type T then 0
else raise SAME ()
| constrs =>
let
val constr_cards =
- datatype_constrs ext_ctxt T
+ datatype_constrs hol_ctxt T
|> map (Integer.prod o map (aux (T :: avoid)) o binder_types
o snd)
in
@@ -1024,9 +1047,9 @@
AList.lookup (op =) assigns T |> the_default default_card
in Int.min (max, aux [] T) end
-(* extended_context -> typ -> bool *)
-fun is_finite_type ext_ctxt =
- not_equal 0 o bounded_exact_card_of_type ext_ctxt 1 2 []
+(* hol_context -> typ -> bool *)
+fun is_finite_type hol_ctxt =
+ not_equal 0 o bounded_exact_card_of_type hol_ctxt 1 2 []
(* term -> bool *)
fun is_ground_term (t1 $ t2) = is_ground_term t1 andalso is_ground_term t2
@@ -1052,7 +1075,7 @@
member (op =) [@{type_name unit}, @{type_name "*"}, @{type_name "+"},
@{type_name int}] s orelse
is_frac_type thy (Type (s, []))
-(* theory -> term -> bool *)
+(* theory -> typ -> bool *)
fun is_funky_typedef thy (Type (s, _)) = is_funky_typedef_name thy s
| is_funky_typedef _ _ = false
(* term -> bool *)
@@ -1199,8 +1222,6 @@
|> normalized_rhs_of thy |> Option.map (prefix_abs_vars s)
handle List.Empty => NONE
-datatype fixpoint_kind = Lfp | Gfp | NoFp
-
(* term -> fixpoint_kind *)
fun fixpoint_kind_of_rhs (Abs (_, _, t)) = fixpoint_kind_of_rhs t
| fixpoint_kind_of_rhs (Const (@{const_name lfp}, _) $ Abs _) = Lfp
@@ -1299,35 +1320,6 @@
Unsynchronized.change simp_table
(Symtab.update (s, eqs @ these (Symtab.lookup (!simp_table) s)))
-(* Similar to "Refute.specialize_type" but returns all matches rather than only
- the first (preorder) match. *)
-(* theory -> styp -> term -> term list *)
-fun multi_specialize_type thy slack (x as (s, T)) t =
- let
- (* term -> (typ * term) list -> (typ * term) list *)
- fun aux (Const (s', T')) ys =
- if s = s' then
- ys |> (if AList.defined (op =) ys T' then
- I
- else
- cons (T', Refute.monomorphic_term
- (Sign.typ_match thy (T', T) Vartab.empty) t)
- handle Type.TYPE_MATCH => I
- | Refute.REFUTE _ =>
- if slack then
- I
- else
- raise NOT_SUPPORTED ("too much polymorphism in \
- \axiom involving " ^ quote s))
- else
- ys
- | aux _ ys = ys
- in map snd (fold_aterms aux t []) end
-
-(* theory -> bool -> const_table -> styp -> term list *)
-fun nondef_props_for_const thy slack table (x as (s, _)) =
- these (Symtab.lookup table s) |> maps (multi_specialize_type thy slack x)
-
(* theory -> styp -> term list *)
fun inverse_axioms_for_rep_fun thy (x as (_, T)) =
let val abs_T = domain_type T in
@@ -1336,7 +1328,7 @@
|> pairself (Refute.specialize_type thy x o prop_of o the)
||> single |> op ::
end
-(* theory -> styp list -> term list *)
+(* theory -> string * typ list -> term list *)
fun optimized_typedef_axioms thy (abs_z as (abs_s, abs_Ts)) =
let val abs_T = Type abs_z in
if is_univ_typedef thy abs_T then
@@ -1392,15 +1384,15 @@
list_comb (Bound j, map2 (select_nth_constr_arg thy x (Bound 0))
(index_seq 0 (length arg_Ts)) arg_Ts)
end
-(* extended_context -> typ -> int * styp -> term -> term *)
-fun add_constr_case (ext_ctxt as {thy, ...}) res_T (j, x) res_t =
+(* hol_context -> typ -> int * styp -> term -> term *)
+fun add_constr_case (hol_ctxt as {thy, ...}) res_T (j, x) res_t =
Const (@{const_name If}, bool_T --> res_T --> res_T --> res_T)
- $ discriminate_value ext_ctxt x (Bound 0) $ constr_case_body thy (j, x)
+ $ discriminate_value hol_ctxt x (Bound 0) $ constr_case_body thy (j, x)
$ res_t
-(* extended_context -> typ -> typ -> term *)
-fun optimized_case_def (ext_ctxt as {thy, ...}) dataT res_T =
+(* hol_context -> typ -> typ -> term *)
+fun optimized_case_def (hol_ctxt as {thy, ...}) dataT res_T =
let
- val xs = datatype_constrs ext_ctxt dataT
+ val xs = datatype_constrs hol_ctxt dataT
val xs' = filter_out (fn (s, _) => s = @{const_name NonStd}) xs
val func_Ts = map ((fn T => binder_types T ---> res_T) o snd) xs'
in
@@ -1409,19 +1401,19 @@
val (xs'', x) = split_last xs'
in
constr_case_body thy (1, x)
- |> fold_rev (add_constr_case ext_ctxt res_T)
+ |> fold_rev (add_constr_case hol_ctxt res_T)
(length xs' downto 2 ~~ xs'')
end
else
Const (@{const_name undefined}, dataT --> res_T) $ Bound 0
- |> fold_rev (add_constr_case ext_ctxt res_T)
+ |> fold_rev (add_constr_case hol_ctxt res_T)
(length xs' downto 1 ~~ xs'))
|> fold_rev (curry absdummy) (func_Ts @ [dataT])
end
-(* extended_context -> string -> typ -> typ -> term -> term *)
-fun optimized_record_get (ext_ctxt as {thy, ...}) s rec_T res_T t =
- let val constr_x = hd (datatype_constrs ext_ctxt rec_T) in
+(* hol_context -> string -> typ -> typ -> term -> term *)
+fun optimized_record_get (hol_ctxt as {thy, ...}) s rec_T res_T t =
+ let val constr_x = hd (datatype_constrs hol_ctxt rec_T) in
case no_of_record_field thy s rec_T of
~1 => (case rec_T of
Type (_, Ts as _ :: _) =>
@@ -1430,16 +1422,16 @@
val j = num_record_fields thy rec_T - 1
in
select_nth_constr_arg thy constr_x t j res_T
- |> optimized_record_get ext_ctxt s rec_T' res_T
+ |> optimized_record_get hol_ctxt s rec_T' res_T
end
| _ => raise TYPE ("Nitpick_HOL.optimized_record_get", [rec_T],
[]))
| j => select_nth_constr_arg thy constr_x t j res_T
end
-(* extended_context -> string -> typ -> term -> term -> term *)
-fun optimized_record_update (ext_ctxt as {thy, ...}) s rec_T fun_t rec_t =
+(* hol_context -> string -> typ -> term -> term -> term *)
+fun optimized_record_update (hol_ctxt as {thy, ...}) s rec_T fun_t rec_t =
let
- val constr_x as (_, constr_T) = hd (datatype_constrs ext_ctxt rec_T)
+ val constr_x as (_, constr_T) = hd (datatype_constrs hol_ctxt rec_T)
val Ts = binder_types constr_T
val n = length Ts
val special_j = no_of_record_field thy s rec_T
@@ -1450,7 +1442,7 @@
if j = special_j then
betapply (fun_t, t)
else if j = n - 1 andalso special_j = ~1 then
- optimized_record_update ext_ctxt s
+ optimized_record_update hol_ctxt s
(rec_T |> dest_Type |> snd |> List.last) fun_t t
else
t
@@ -1473,19 +1465,19 @@
fixpoint_kind_of_rhs (the (def_of_const thy table x))
handle Option.Option => NoFp
-(* extended_context -> styp -> bool *)
+(* hol_context -> styp -> bool *)
fun is_real_inductive_pred ({thy, fast_descrs, def_table, intro_table, ...}
- : extended_context) x =
+ : hol_context) x =
not (null (def_props_for_const thy fast_descrs intro_table x)) andalso
fixpoint_kind_of_const thy def_table x <> NoFp
fun is_real_equational_fun ({thy, fast_descrs, simp_table, psimp_table, ...}
- : extended_context) x =
+ : hol_context) x =
exists (fn table => not (null (def_props_for_const thy fast_descrs table x)))
[!simp_table, psimp_table]
-fun is_inductive_pred ext_ctxt =
- is_real_inductive_pred ext_ctxt andf (not o is_real_equational_fun ext_ctxt)
-fun is_equational_fun (ext_ctxt as {thy, def_table, ...}) =
- (is_real_equational_fun ext_ctxt orf is_real_inductive_pred ext_ctxt
+fun is_inductive_pred hol_ctxt =
+ is_real_inductive_pred hol_ctxt andf (not o is_real_equational_fun hol_ctxt)
+fun is_equational_fun (hol_ctxt as {thy, def_table, ...}) =
+ (is_real_equational_fun hol_ctxt orf is_real_inductive_pred hol_ctxt
orf (String.isPrefix ubfp_prefix orf String.isPrefix lbfp_prefix) o fst)
andf (not o has_trivial_definition thy def_table)
@@ -1522,11 +1514,11 @@
SOME t' => is_constr_pattern_lhs thy t'
| NONE => false
+(* Prevents divergence in case of cyclic or infinite definition dependencies. *)
val unfold_max_depth = 255
-val axioms_max_depth = 255
-(* extended_context -> term -> term *)
-fun unfold_defs_in_term (ext_ctxt as {thy, destroy_constrs, fast_descrs,
+(* hol_context -> term -> term *)
+fun unfold_defs_in_term (hol_ctxt as {thy, destroy_constrs, fast_descrs,
case_names, def_table, ground_thm_table,
ersatz_table, ...}) =
let
@@ -1600,7 +1592,7 @@
val (dataT, res_T) = nth_range_type n T
|> pairf domain_type range_type
in
- (optimized_case_def ext_ctxt dataT res_T
+ (optimized_case_def hol_ctxt dataT res_T
|> do_term (depth + 1) Ts, ts)
end
| _ =>
@@ -1628,11 +1620,11 @@
else if is_record_get thy x then
case length ts of
0 => (do_term depth Ts (eta_expand Ts t 1), [])
- | _ => (optimized_record_get ext_ctxt s (domain_type T)
+ | _ => (optimized_record_get hol_ctxt s (domain_type T)
(range_type T) (do_term depth Ts (hd ts)), tl ts)
else if is_record_update thy x then
case length ts of
- 2 => (optimized_record_update ext_ctxt
+ 2 => (optimized_record_update hol_ctxt
(unsuffix Record.updateN s) (nth_range_type 2 T)
(do_term depth Ts (hd ts))
(do_term depth Ts (nth ts 1)), [])
@@ -1645,7 +1637,7 @@
else
(Const x, ts)
end
- else if is_equational_fun ext_ctxt x then
+ else if is_equational_fun hol_ctxt x then
(Const x, ts)
else case def_of_const thy def_table x of
SOME def =>
@@ -1662,10 +1654,10 @@
in s_betapplys (const, map (do_term depth Ts) ts) |> Envir.beta_norm end
in do_term 0 [] end
-(* extended_context -> typ -> term list *)
-fun codatatype_bisim_axioms (ext_ctxt as {thy, ...}) T =
+(* hol_context -> typ -> term list *)
+fun codatatype_bisim_axioms (hol_ctxt as {thy, ...}) T =
let
- val xs = datatype_constrs ext_ctxt T
+ val xs = datatype_constrs hol_ctxt T
val set_T = T --> bool_T
val iter_T = @{typ bisim_iterator}
val bisim_const = Const (@{const_name bisim}, iter_T --> T --> T --> bool_T)
@@ -1688,14 +1680,14 @@
let
val arg_Ts = binder_types T
val core_t =
- discriminate_value ext_ctxt x y_var ::
+ discriminate_value hol_ctxt x y_var ::
map2 (nth_sub_bisim x) (index_seq 0 (length arg_Ts)) arg_Ts
|> foldr1 s_conj
in List.foldr absdummy core_t arg_Ts end
in
[HOLogic.eq_const bool_T $ (bisim_const $ n_var $ x_var $ y_var)
$ (@{term "op |"} $ (HOLogic.eq_const iter_T $ n_var $ zero_const iter_T)
- $ (betapplys (optimized_case_def ext_ctxt T bool_T,
+ $ (betapplys (optimized_case_def hol_ctxt T bool_T,
map case_func xs @ [x_var]))),
HOLogic.eq_const set_T $ (bisim_const $ bisim_max $ x_var)
$ (Const (@{const_name insert}, T --> set_T --> set_T)
@@ -1754,10 +1746,10 @@
val termination_tacs = [Lexicographic_Order.lex_order_tac true,
ScnpReconstruct.sizechange_tac]
-(* extended_context -> const_table -> styp -> bool *)
+(* hol_context -> const_table -> styp -> bool *)
fun uncached_is_well_founded_inductive_pred
({thy, ctxt, debug, fast_descrs, tac_timeout, intro_table, ...}
- : extended_context) (x as (_, T)) =
+ : hol_context) (x as (_, T)) =
case def_props_for_const thy fast_descrs intro_table x of
[] => raise TERM ("Nitpick_HOL.uncached_is_well_founded_inductive",
[Const x])
@@ -1797,11 +1789,11 @@
handle List.Empty => false
| NO_TRIPLE () => false
-(* The type constraint below is a workaround for a Poly/ML bug. *)
+(* The type constraint below is a workaround for a Poly/ML crash. *)
-(* extended_context -> styp -> bool *)
+(* hol_context -> styp -> bool *)
fun is_well_founded_inductive_pred
- (ext_ctxt as {thy, wfs, def_table, wf_cache, ...} : extended_context)
+ (hol_ctxt as {thy, wfs, def_table, wf_cache, ...} : hol_context)
(x as (s, _)) =
case triple_lookup (const_match thy) wfs x of
SOME (SOME b) => b
@@ -1811,7 +1803,7 @@
| NONE =>
let
val gfp = (fixpoint_kind_of_const thy def_table x = Gfp)
- val wf = uncached_is_well_founded_inductive_pred ext_ctxt x
+ val wf = uncached_is_well_founded_inductive_pred hol_ctxt x
in
Unsynchronized.change wf_cache (cons (x, (gfp, wf))); wf
end
@@ -1842,14 +1834,14 @@
| do_disjunct j t =
case num_occs_of_bound_in_term j t of
0 => true
- | 1 => exists (curry (op =) (Bound j) o head_of) (conjuncts t)
+ | 1 => exists (curry (op =) (Bound j) o head_of) (conjuncts_of t)
| _ => false
(* term -> bool *)
fun do_lfp_def (Const (@{const_name lfp}, _) $ t2) =
let val (xs, body) = strip_abs t2 in
case length xs of
1 => false
- | n => forall (do_disjunct (n - 1)) (disjuncts body)
+ | n => forall (do_disjunct (n - 1)) (disjuncts_of body)
end
| do_lfp_def _ = false
in do_lfp_def o strip_abs_body end
@@ -1887,7 +1879,7 @@
end
val (nonrecs, recs) =
List.partition (curry (op =) 0 o num_occs_of_bound_in_term j)
- (disjuncts body)
+ (disjuncts_of body)
val base_body = nonrecs |> List.foldl s_disj @{const False}
val step_body = recs |> map (repair_rec j)
|> List.foldl s_disj @{const False}
@@ -1901,8 +1893,8 @@
raise TERM ("Nitpick_HOL.linear_pred_base_and_step_rhss.aux", [t])
in aux end
-(* extended_context -> styp -> term -> term *)
-fun starred_linear_pred_const (ext_ctxt as {simp_table, ...}) (x as (s, T))
+(* hol_context -> styp -> term -> term *)
+fun starred_linear_pred_const (hol_ctxt as {simp_table, ...}) (x as (s, T))
def =
let
val j = maxidx_of_term def + 1
@@ -1933,11 +1925,11 @@
$ list_comb (Const step_x, outer_bounds)))
$ list_comb (Const base_x, outer_bounds)
|> ap_curry tuple_arg_Ts tuple_T bool_T)
- |> unfold_defs_in_term ext_ctxt
+ |> unfold_defs_in_term hol_ctxt
end
-(* extended_context -> bool -> styp -> term *)
-fun unrolled_inductive_pred_const (ext_ctxt as {thy, star_linear_preds,
+(* hol_context -> bool -> styp -> term *)
+fun unrolled_inductive_pred_const (hol_ctxt as {thy, star_linear_preds,
def_table, simp_table, ...})
gfp (x as (s, T)) =
let
@@ -1946,11 +1938,11 @@
val unrolled_const = Const x' $ zero_const iter_T
val def = the (def_of_const thy def_table x)
in
- if is_equational_fun ext_ctxt x' then
+ if is_equational_fun hol_ctxt x' then
unrolled_const (* already done *)
else if not gfp andalso is_linear_inductive_pred_def def andalso
star_linear_preds then
- starred_linear_pred_const ext_ctxt x def
+ starred_linear_pred_const hol_ctxt x def
else
let
val j = maxidx_of_term def + 1
@@ -1973,8 +1965,8 @@
in unrolled_const end
end
-(* extended_context -> styp -> term *)
-fun raw_inductive_pred_axiom ({thy, def_table, ...} : extended_context) x =
+(* hol_context -> styp -> term *)
+fun raw_inductive_pred_axiom ({thy, def_table, ...} : hol_context) x =
let
val def = the (def_of_const thy def_table x)
val (outer, fp_app) = strip_abs def
@@ -1992,24 +1984,29 @@
HOLogic.mk_eq (list_comb (Const x, bounds), naked_rhs)
|> HOLogic.mk_Trueprop |> curry subst_bounds (rev vars)
end
-fun inductive_pred_axiom ext_ctxt (x as (s, T)) =
+fun inductive_pred_axiom hol_ctxt (x as (s, T)) =
if String.isPrefix ubfp_prefix s orelse String.isPrefix lbfp_prefix s then
let val x' = (after_name_sep s, T) in
- raw_inductive_pred_axiom ext_ctxt x' |> subst_atomic [(Const x', Const x)]
+ raw_inductive_pred_axiom hol_ctxt x' |> subst_atomic [(Const x', Const x)]
end
else
- raw_inductive_pred_axiom ext_ctxt x
+ raw_inductive_pred_axiom hol_ctxt x
-(* extended_context -> styp -> term list *)
-fun raw_equational_fun_axioms (ext_ctxt as {thy, fast_descrs, simp_table,
+(* hol_context -> styp -> term list *)
+fun raw_equational_fun_axioms (hol_ctxt as {thy, fast_descrs, simp_table,
psimp_table, ...}) (x as (s, _)) =
case def_props_for_const thy fast_descrs (!simp_table) x of
[] => (case def_props_for_const thy fast_descrs psimp_table x of
- [] => [inductive_pred_axiom ext_ctxt x]
+ [] => [inductive_pred_axiom hol_ctxt x]
| psimps => psimps)
| simps => simps
-
val equational_fun_axioms = map extensionalize oo raw_equational_fun_axioms
+(* hol_context -> styp -> bool *)
+fun is_equational_fun_surely_complete hol_ctxt x =
+ case raw_equational_fun_axioms hol_ctxt x of
+ [@{const Trueprop} $ (Const (@{const_name "op ="}, _) $ t1 $ _)] =>
+ strip_comb t1 |> snd |> forall is_Var
+ | _ => false
(* term list -> term list *)
fun merge_type_vars_in_terms ts =
@@ -2028,1261 +2025,29 @@
| coalesce T = T
in map (map_types (map_atyps coalesce)) ts end
-(* extended_context -> typ -> typ list -> typ list *)
-fun add_ground_types ext_ctxt T accum =
+(* hol_context -> typ -> typ list -> typ list *)
+fun add_ground_types hol_ctxt T accum =
case T of
- Type ("fun", Ts) => fold (add_ground_types ext_ctxt) Ts accum
- | Type ("*", Ts) => fold (add_ground_types ext_ctxt) Ts accum
- | Type (@{type_name itself}, [T1]) => add_ground_types ext_ctxt T1 accum
+ Type ("fun", Ts) => fold (add_ground_types hol_ctxt) Ts accum
+ | Type ("*", Ts) => fold (add_ground_types hol_ctxt) Ts accum
+ | Type (@{type_name itself}, [T1]) => add_ground_types hol_ctxt T1 accum
| Type (_, Ts) =>
- if member (op =) (@{typ prop} :: @{typ bool} :: @{typ unit} :: accum) T then
+ if member (op =) (@{typ prop} :: @{typ bool} :: @{typ unit} ::
+ @{typ \<xi>} :: accum) T then
accum
else
T :: accum
- |> fold (add_ground_types ext_ctxt)
- (case boxed_datatype_constrs ext_ctxt T of
+ |> fold (add_ground_types hol_ctxt)
+ (case boxed_datatype_constrs hol_ctxt T of
[] => Ts
| xs => map snd xs)
| _ => insert (op =) T accum
-(* extended_context -> typ -> typ list *)
-fun ground_types_in_type ext_ctxt T = add_ground_types ext_ctxt T []
-(* extended_context -> term list -> typ list *)
-fun ground_types_in_terms ext_ctxt ts =
- fold (fold_types (add_ground_types ext_ctxt)) ts []
-(* typ list -> int -> term -> bool *)
-fun has_heavy_bounds_or_vars Ts level t =
- let
- (* typ list -> bool *)
- fun aux [] = false
- | aux [T] = is_fun_type T orelse is_pair_type T
- | aux _ = true
- in aux (map snd (Term.add_vars t []) @ map (nth Ts) (loose_bnos t)) end
-
-(* typ list -> int -> int -> int -> term -> term *)
-fun fresh_value_var Ts k n j t =
- Var ((val_var_prefix ^ nat_subscript (n - j), k), fastype_of1 (Ts, t))
-
-(* theory -> typ list -> bool -> int -> int -> term -> term list -> term list
- -> term * term list *)
-fun pull_out_constr_comb thy Ts relax k level t args seen =
- let val t_comb = list_comb (t, args) in
- case t of
- Const x =>
- if not relax andalso is_constr thy x andalso
- not (is_fun_type (fastype_of1 (Ts, t_comb))) andalso
- has_heavy_bounds_or_vars Ts level t_comb andalso
- not (loose_bvar (t_comb, level)) then
- let
- val (j, seen) = case find_index (curry (op =) t_comb) seen of
- ~1 => (0, t_comb :: seen)
- | j => (j, seen)
- in (fresh_value_var Ts k (length seen) j t_comb, seen) end
- else
- (t_comb, seen)
- | _ => (t_comb, seen)
- end
-
-(* (term -> term) -> typ list -> int -> term list -> term list *)
-fun equations_for_pulled_out_constrs mk_eq Ts k seen =
- let val n = length seen in
- map2 (fn j => fn t => mk_eq (fresh_value_var Ts k n j t, t))
- (index_seq 0 n) seen
- end
-
-(* theory -> bool -> term -> term *)
-fun pull_out_universal_constrs thy def t =
- let
- val k = maxidx_of_term t + 1
- (* typ list -> bool -> term -> term list -> term list -> term * term list *)
- fun do_term Ts def t args seen =
- case t of
- (t0 as Const (@{const_name "=="}, _)) $ t1 $ t2 =>
- do_eq_or_imp Ts true def t0 t1 t2 seen
- | (t0 as @{const "==>"}) $ t1 $ t2 =>
- if def then (t, []) else do_eq_or_imp Ts false def t0 t1 t2 seen
- | (t0 as Const (@{const_name "op ="}, _)) $ t1 $ t2 =>
- do_eq_or_imp Ts true def t0 t1 t2 seen
- | (t0 as @{const "op -->"}) $ t1 $ t2 =>
- do_eq_or_imp Ts false def t0 t1 t2 seen
- | Abs (s, T, t') =>
- let val (t', seen) = do_term (T :: Ts) def t' [] seen in
- (list_comb (Abs (s, T, t'), args), seen)
- end
- | t1 $ t2 =>
- let val (t2, seen) = do_term Ts def t2 [] seen in
- do_term Ts def t1 (t2 :: args) seen
- end
- | _ => pull_out_constr_comb thy Ts def k 0 t args seen
- (* typ list -> bool -> bool -> term -> term -> term -> term list
- -> term * term list *)
- and do_eq_or_imp Ts eq def t0 t1 t2 seen =
- let
- val (t2, seen) = if eq andalso def then (t2, seen)
- else do_term Ts false t2 [] seen
- val (t1, seen) = do_term Ts false t1 [] seen
- in (t0 $ t1 $ t2, seen) end
- val (concl, seen) = do_term [] def t [] []
- in
- Logic.list_implies (equations_for_pulled_out_constrs Logic.mk_equals [] k
- seen, concl)
- end
-
-(* extended_context -> bool -> term -> term *)
-fun destroy_pulled_out_constrs (ext_ctxt as {thy, ...}) axiom t =
- let
- (* styp -> int *)
- val num_occs_of_var =
- fold_aterms (fn Var z => (fn f => fn z' => f z' |> z = z' ? Integer.add 1)
- | _ => I) t (K 0)
- (* bool -> term -> term *)
- fun aux careful ((t0 as Const (@{const_name "=="}, _)) $ t1 $ t2) =
- aux_eq careful true t0 t1 t2
- | aux careful ((t0 as @{const "==>"}) $ t1 $ t2) =
- t0 $ aux false t1 $ aux careful t2
- | aux careful ((t0 as Const (@{const_name "op ="}, _)) $ t1 $ t2) =
- aux_eq careful true t0 t1 t2
- | aux careful ((t0 as @{const "op -->"}) $ t1 $ t2) =
- t0 $ aux false t1 $ aux careful t2
- | aux careful (Abs (s, T, t')) = Abs (s, T, aux careful t')
- | aux careful (t1 $ t2) = aux careful t1 $ aux careful t2
- | aux _ t = t
- (* bool -> bool -> term -> term -> term -> term *)
- and aux_eq careful pass1 t0 t1 t2 =
- ((if careful then
- raise SAME ()
- else if axiom andalso is_Var t2 andalso
- num_occs_of_var (dest_Var t2) = 1 then
- @{const True}
- else case strip_comb t2 of
- (* The first case is not as general as it could be. *)
- (Const (@{const_name PairBox}, _),
- [Const (@{const_name fst}, _) $ Var z1,
- Const (@{const_name snd}, _) $ Var z2]) =>
- if z1 = z2 andalso num_occs_of_var z1 = 2 then @{const True}
- else raise SAME ()
- | (Const (x as (s, T)), args) =>
- let val arg_Ts = binder_types T in
- if length arg_Ts = length args andalso
- (is_constr thy x orelse s = @{const_name Pair} orelse
- x = (@{const_name Suc}, nat_T --> nat_T)) andalso
- (not careful orelse not (is_Var t1) orelse
- String.isPrefix val_var_prefix (fst (fst (dest_Var t1)))) then
- discriminate_value ext_ctxt x t1 ::
- map3 (sel_eq x t1) (index_seq 0 (length args)) arg_Ts args
- |> foldr1 s_conj
- else
- raise SAME ()
- end
- | _ => raise SAME ())
- |> body_type (type_of t0) = prop_T ? HOLogic.mk_Trueprop)
- handle SAME () => if pass1 then aux_eq careful false t0 t2 t1
- else t0 $ aux false t2 $ aux false t1
- (* styp -> term -> int -> typ -> term -> term *)
- and sel_eq x t n nth_T nth_t =
- HOLogic.eq_const nth_T $ nth_t $ select_nth_constr_arg thy x t n nth_T
- |> aux false
- in aux axiom t end
-
-(* theory -> term -> term *)
-fun simplify_constrs_and_sels thy t =
- let
- (* term -> int -> term *)
- fun is_nth_sel_on t' n (Const (s, _) $ t) =
- (t = t' andalso is_sel_like_and_no_discr s andalso
- sel_no_from_name s = n)
- | is_nth_sel_on _ _ _ = false
- (* term -> term list -> term *)
- fun do_term (Const (@{const_name Rep_Frac}, _)
- $ (Const (@{const_name Abs_Frac}, _) $ t1)) [] = do_term t1 []
- | do_term (Const (@{const_name Abs_Frac}, _)
- $ (Const (@{const_name Rep_Frac}, _) $ t1)) [] = do_term t1 []
- | do_term (t1 $ t2) args = do_term t1 (do_term t2 [] :: args)
- | do_term (t as Const (x as (s, T))) (args as _ :: _) =
- ((if is_constr_like thy x then
- if length args = num_binder_types T then
- case hd args of
- Const (x' as (_, T')) $ t' =>
- if domain_type T' = body_type T andalso
- forall (uncurry (is_nth_sel_on t'))
- (index_seq 0 (length args) ~~ args) then
- t'
- else
- raise SAME ()
- | _ => raise SAME ()
- else
- raise SAME ()
- else if is_sel_like_and_no_discr s then
- case strip_comb (hd args) of
- (Const (x' as (s', T')), ts') =>
- if is_constr_like thy x' andalso
- constr_name_for_sel_like s = s' andalso
- not (exists is_pair_type (binder_types T')) then
- list_comb (nth ts' (sel_no_from_name s), tl args)
- else
- raise SAME ()
- | _ => raise SAME ()
- else
- raise SAME ())
- handle SAME () => betapplys (t, args))
- | do_term (Abs (s, T, t')) args =
- betapplys (Abs (s, T, do_term t' []), args)
- | do_term t args = betapplys (t, args)
- in do_term t [] end
-
-(* term -> term *)
-fun curry_assms (@{const "==>"} $ (@{const Trueprop}
- $ (@{const "op &"} $ t1 $ t2)) $ t3) =
- curry_assms (Logic.list_implies ([t1, t2] |> map HOLogic.mk_Trueprop, t3))
- | curry_assms (@{const "==>"} $ t1 $ t2) =
- @{const "==>"} $ curry_assms t1 $ curry_assms t2
- | curry_assms t = t
-
-(* term -> term *)
-val destroy_universal_equalities =
- let
- (* term list -> (indexname * typ) list -> term -> term *)
- fun aux prems zs t =
- case t of
- @{const "==>"} $ t1 $ t2 => aux_implies prems zs t1 t2
- | _ => Logic.list_implies (rev prems, t)
- (* term list -> (indexname * typ) list -> term -> term -> term *)
- and aux_implies prems zs t1 t2 =
- case t1 of
- Const (@{const_name "=="}, _) $ Var z $ t' => aux_eq prems zs z t' t1 t2
- | @{const Trueprop} $ (Const (@{const_name "op ="}, _) $ Var z $ t') =>
- aux_eq prems zs z t' t1 t2
- | @{const Trueprop} $ (Const (@{const_name "op ="}, _) $ t' $ Var z) =>
- aux_eq prems zs z t' t1 t2
- | _ => aux (t1 :: prems) (Term.add_vars t1 zs) t2
- (* term list -> (indexname * typ) list -> indexname * typ -> term -> term
- -> term -> term *)
- and aux_eq prems zs z t' t1 t2 =
- if not (member (op =) zs z) andalso
- not (exists_subterm (curry (op =) (Var z)) t') then
- aux prems zs (subst_free [(Var z, t')] t2)
- else
- aux (t1 :: prems) (Term.add_vars t1 zs) t2
- in aux [] [] end
-
-(* theory -> term -> term *)
-fun pull_out_existential_constrs thy t =
- let
- val k = maxidx_of_term t + 1
- (* typ list -> int -> term -> term list -> term list -> term * term list *)
- fun aux Ts num_exists t args seen =
- case t of
- (t0 as Const (@{const_name Ex}, _)) $ Abs (s1, T1, t1) =>
- let
- val (t1, seen') = aux (T1 :: Ts) (num_exists + 1) t1 [] []
- val n = length seen'
- (* unit -> term list *)
- fun vars () = map2 (fresh_value_var Ts k n) (index_seq 0 n) seen'
- in
- (equations_for_pulled_out_constrs HOLogic.mk_eq Ts k seen'
- |> List.foldl s_conj t1 |> fold mk_exists (vars ())
- |> curry3 Abs s1 T1 |> curry (op $) t0, seen)
- end
- | t1 $ t2 =>
- let val (t2, seen) = aux Ts num_exists t2 [] seen in
- aux Ts num_exists t1 (t2 :: args) seen
- end
- | Abs (s, T, t') =>
- let
- val (t', seen) = aux (T :: Ts) 0 t' [] (map (incr_boundvars 1) seen)
- in (list_comb (Abs (s, T, t'), args), map (incr_boundvars ~1) seen) end
- | _ =>
- if num_exists > 0 then
- pull_out_constr_comb thy Ts false k num_exists t args seen
- else
- (list_comb (t, args), seen)
- in aux [] 0 t [] [] |> fst end
-
-(* theory -> int -> term list -> term list -> (term * term list) option *)
-fun find_bound_assign _ _ _ [] = NONE
- | find_bound_assign thy j seen (t :: ts) =
- let
- (* bool -> term -> term -> (term * term list) option *)
- fun aux pass1 t1 t2 =
- (if loose_bvar1 (t2, j) then
- if pass1 then aux false t2 t1 else raise SAME ()
- else case t1 of
- Bound j' => if j' = j then SOME (t2, ts @ seen) else raise SAME ()
- | Const (s, Type ("fun", [T1, T2])) $ Bound j' =>
- if j' = j andalso s = sel_prefix_for 0 ^ @{const_name FunBox} then
- SOME (construct_value thy (@{const_name FunBox}, T2 --> T1) [t2],
- ts @ seen)
- else
- raise SAME ()
- | _ => raise SAME ())
- handle SAME () => find_bound_assign thy j (t :: seen) ts
- in
- case t of
- Const (@{const_name "op ="}, _) $ t1 $ t2 => aux true t1 t2
- | _ => find_bound_assign thy j (t :: seen) ts
- end
-
-(* int -> term -> term -> term *)
-fun subst_one_bound j arg t =
- let
- fun aux (Bound i, lev) =
- if i < lev then raise SAME ()
- else if i = lev then incr_boundvars (lev - j) arg
- else Bound (i - 1)
- | aux (Abs (a, T, body), lev) = Abs (a, T, aux (body, lev + 1))
- | aux (f $ t, lev) =
- (aux (f, lev) $ (aux (t, lev) handle SAME () => t)
- handle SAME () => f $ aux (t, lev))
- | aux _ = raise SAME ()
- in aux (t, j) handle SAME () => t end
-
-(* theory -> term -> term *)
-fun destroy_existential_equalities thy =
- let
- (* string list -> typ list -> term list -> term *)
- fun kill [] [] ts = foldr1 s_conj ts
- | kill (s :: ss) (T :: Ts) ts =
- (case find_bound_assign thy (length ss) [] ts of
- SOME (_, []) => @{const True}
- | SOME (arg_t, ts) =>
- kill ss Ts (map (subst_one_bound (length ss)
- (incr_bv (~1, length ss + 1, arg_t))) ts)
- | NONE =>
- Const (@{const_name Ex}, (T --> bool_T) --> bool_T)
- $ Abs (s, T, kill ss Ts ts))
- | kill _ _ _ = raise UnequalLengths
- (* string list -> typ list -> term -> term *)
- fun gather ss Ts ((t0 as Const (@{const_name Ex}, _)) $ Abs (s1, T1, t1)) =
- gather (ss @ [s1]) (Ts @ [T1]) t1
- | gather [] [] (Abs (s, T, t1)) = Abs (s, T, gather [] [] t1)
- | gather [] [] (t1 $ t2) = gather [] [] t1 $ gather [] [] t2
- | gather [] [] t = t
- | gather ss Ts t = kill ss Ts (conjuncts (gather [] [] t))
- in gather [] [] end
-
-(* term -> term *)
-fun distribute_quantifiers t =
- case t of
- (t0 as Const (@{const_name All}, T0)) $ Abs (s, T1, t1) =>
- (case t1 of
- (t10 as @{const "op &"}) $ t11 $ t12 =>
- t10 $ distribute_quantifiers (t0 $ Abs (s, T1, t11))
- $ distribute_quantifiers (t0 $ Abs (s, T1, t12))
- | (t10 as @{const Not}) $ t11 =>
- t10 $ distribute_quantifiers (Const (@{const_name Ex}, T0)
- $ Abs (s, T1, t11))
- | t1 =>
- if not (loose_bvar1 (t1, 0)) then
- distribute_quantifiers (incr_boundvars ~1 t1)
- else
- t0 $ Abs (s, T1, distribute_quantifiers t1))
- | (t0 as Const (@{const_name Ex}, T0)) $ Abs (s, T1, t1) =>
- (case distribute_quantifiers t1 of
- (t10 as @{const "op |"}) $ t11 $ t12 =>
- t10 $ distribute_quantifiers (t0 $ Abs (s, T1, t11))
- $ distribute_quantifiers (t0 $ Abs (s, T1, t12))
- | (t10 as @{const "op -->"}) $ t11 $ t12 =>
- t10 $ distribute_quantifiers (Const (@{const_name All}, T0)
- $ Abs (s, T1, t11))
- $ distribute_quantifiers (t0 $ Abs (s, T1, t12))
- | (t10 as @{const Not}) $ t11 =>
- t10 $ distribute_quantifiers (Const (@{const_name All}, T0)
- $ Abs (s, T1, t11))
- | t1 =>
- if not (loose_bvar1 (t1, 0)) then
- distribute_quantifiers (incr_boundvars ~1 t1)
- else
- t0 $ Abs (s, T1, distribute_quantifiers t1))
- | t1 $ t2 => distribute_quantifiers t1 $ distribute_quantifiers t2
- | Abs (s, T, t') => Abs (s, T, distribute_quantifiers t')
- | _ => t
-
-(* int -> int -> (int -> int) -> term -> term *)
-fun renumber_bounds j n f t =
- case t of
- t1 $ t2 => renumber_bounds j n f t1 $ renumber_bounds j n f t2
- | Abs (s, T, t') => Abs (s, T, renumber_bounds (j + 1) n f t')
- | Bound j' =>
- Bound (if j' >= j andalso j' < j + n then f (j' - j) + j else j')
- | _ => t
-
-val quantifier_cluster_threshold = 7
-
-(* theory -> term -> term *)
-fun push_quantifiers_inward thy =
- let
- (* string -> string list -> typ list -> term -> term *)
- fun aux quant_s ss Ts t =
- (case t of
- (t0 as Const (s0, _)) $ Abs (s1, T1, t1 as _ $ _) =>
- if s0 = quant_s then
- aux s0 (s1 :: ss) (T1 :: Ts) t1
- else if quant_s = "" andalso
- (s0 = @{const_name All} orelse s0 = @{const_name Ex}) then
- aux s0 [s1] [T1] t1
- else
- raise SAME ()
- | _ => raise SAME ())
- handle SAME () =>
- case t of
- t1 $ t2 =>
- if quant_s = "" then
- aux "" [] [] t1 $ aux "" [] [] t2
- else
- let
- val typical_card = 4
- (* ('a -> ''b list) -> 'a list -> ''b list *)
- fun big_union proj ps =
- fold (fold (insert (op =)) o proj) ps []
- val (ts, connective) = strip_any_connective t
- val T_costs =
- map (bounded_card_of_type 65536 typical_card []) Ts
- val t_costs = map size_of_term ts
- val num_Ts = length Ts
- (* int -> int *)
- val flip = curry (op -) (num_Ts - 1)
- val t_boundss = map (map flip o loose_bnos) ts
- (* (int list * int) list -> int list
- -> (int list * int) list *)
- fun merge costly_boundss [] = costly_boundss
- | merge costly_boundss (j :: js) =
- let
- val (yeas, nays) =
- List.partition (fn (bounds, _) =>
- member (op =) bounds j)
- costly_boundss
- val yeas_bounds = big_union fst yeas
- val yeas_cost = Integer.sum (map snd yeas)
- * nth T_costs j
- in merge ((yeas_bounds, yeas_cost) :: nays) js end
- (* (int list * int) list -> int list -> int *)
- val cost = Integer.sum o map snd oo merge
- (* Inspired by Claessen & Sörensson's polynomial binary
- splitting heuristic (p. 5 of their MODEL 2003 paper). *)
- (* (int list * int) list -> int list -> int list *)
- fun heuristically_best_permutation _ [] = []
- | heuristically_best_permutation costly_boundss js =
- let
- val (costly_boundss, (j, js)) =
- js |> map (`(merge costly_boundss o single))
- |> sort (int_ord
- o pairself (Integer.sum o map snd o fst))
- |> split_list |>> hd ||> pairf hd tl
- in
- j :: heuristically_best_permutation costly_boundss js
- end
- val js =
- if length Ts <= quantifier_cluster_threshold then
- all_permutations (index_seq 0 num_Ts)
- |> map (`(cost (t_boundss ~~ t_costs)))
- |> sort (int_ord o pairself fst) |> hd |> snd
- else
- heuristically_best_permutation (t_boundss ~~ t_costs)
- (index_seq 0 num_Ts)
- val back_js = map (fn j => find_index (curry (op =) j) js)
- (index_seq 0 num_Ts)
- val ts = map (renumber_bounds 0 num_Ts (nth back_js o flip))
- ts
- (* (term * int list) list -> term *)
- fun mk_connection [] =
- raise ARG ("Nitpick_HOL.push_quantifiers_inward.aux.\
- \mk_connection", "")
- | mk_connection ts_cum_bounds =
- ts_cum_bounds |> map fst
- |> foldr1 (fn (t1, t2) => connective $ t1 $ t2)
- (* (term * int list) list -> int list -> term *)
- fun build ts_cum_bounds [] = ts_cum_bounds |> mk_connection
- | build ts_cum_bounds (j :: js) =
- let
- val (yeas, nays) =
- List.partition (fn (_, bounds) =>
- member (op =) bounds j)
- ts_cum_bounds
- ||> map (apfst (incr_boundvars ~1))
- in
- if null yeas then
- build nays js
- else
- let val T = nth Ts (flip j) in
- build ((Const (quant_s, (T --> bool_T) --> bool_T)
- $ Abs (nth ss (flip j), T,
- mk_connection yeas),
- big_union snd yeas) :: nays) js
- end
- end
- in build (ts ~~ t_boundss) js end
- | Abs (s, T, t') => Abs (s, T, aux "" [] [] t')
- | _ => t
- in aux "" [] [] end
-
-(* polarity -> string -> bool *)
-fun is_positive_existential polar quant_s =
- (polar = Pos andalso quant_s = @{const_name Ex}) orelse
- (polar = Neg andalso quant_s <> @{const_name Ex})
-
-(* extended_context -> int -> term -> term *)
-fun skolemize_term_and_more (ext_ctxt as {thy, def_table, skolems, ...})
- skolem_depth =
- let
- (* int list -> int list *)
- val incrs = map (Integer.add 1)
- (* string list -> typ list -> int list -> int -> polarity -> term -> term *)
- fun aux ss Ts js depth polar t =
- let
- (* string -> typ -> string -> typ -> term -> term *)
- fun do_quantifier quant_s quant_T abs_s abs_T t =
- if not (loose_bvar1 (t, 0)) then
- aux ss Ts js depth polar (incr_boundvars ~1 t)
- else if depth <= skolem_depth andalso
- is_positive_existential polar quant_s then
- let
- val j = length (!skolems) + 1
- val sko_s = skolem_prefix_for (length js) j ^ abs_s
- val _ = Unsynchronized.change skolems (cons (sko_s, ss))
- val sko_t = list_comb (Const (sko_s, rev Ts ---> abs_T),
- map Bound (rev js))
- val abs_t = Abs (abs_s, abs_T, aux ss Ts (incrs js) depth polar t)
- in
- if null js then betapply (abs_t, sko_t)
- else Const (@{const_name Let}, abs_T --> quant_T) $ sko_t $ abs_t
- end
- else
- Const (quant_s, quant_T)
- $ Abs (abs_s, abs_T,
- if is_higher_order_type abs_T then
- t
- else
- aux (abs_s :: ss) (abs_T :: Ts) (0 :: incrs js)
- (depth + 1) polar t)
- in
- case t of
- Const (s0 as @{const_name all}, T0) $ Abs (s1, T1, t1) =>
- do_quantifier s0 T0 s1 T1 t1
- | @{const "==>"} $ t1 $ t2 =>
- @{const "==>"} $ aux ss Ts js depth (flip_polarity polar) t1
- $ aux ss Ts js depth polar t2
- | @{const Pure.conjunction} $ t1 $ t2 =>
- @{const Pure.conjunction} $ aux ss Ts js depth polar t1
- $ aux ss Ts js depth polar t2
- | @{const Trueprop} $ t1 =>
- @{const Trueprop} $ aux ss Ts js depth polar t1
- | @{const Not} $ t1 =>
- @{const Not} $ aux ss Ts js depth (flip_polarity polar) t1
- | Const (s0 as @{const_name All}, T0) $ Abs (s1, T1, t1) =>
- do_quantifier s0 T0 s1 T1 t1
- | Const (s0 as @{const_name Ex}, T0) $ Abs (s1, T1, t1) =>
- do_quantifier s0 T0 s1 T1 t1
- | @{const "op &"} $ t1 $ t2 =>
- @{const "op &"} $ aux ss Ts js depth polar t1
- $ aux ss Ts js depth polar t2
- | @{const "op |"} $ t1 $ t2 =>
- @{const "op |"} $ aux ss Ts js depth polar t1
- $ aux ss Ts js depth polar t2
- | @{const "op -->"} $ t1 $ t2 =>
- @{const "op -->"} $ aux ss Ts js depth (flip_polarity polar) t1
- $ aux ss Ts js depth polar t2
- | (t0 as Const (@{const_name Let}, T0)) $ t1 $ t2 =>
- t0 $ t1 $ aux ss Ts js depth polar t2
- | Const (x as (s, T)) =>
- if is_inductive_pred ext_ctxt x andalso
- not (is_well_founded_inductive_pred ext_ctxt x) then
- let
- val gfp = (fixpoint_kind_of_const thy def_table x = Gfp)
- val (pref, connective, set_oper) =
- if gfp then
- (lbfp_prefix,
- @{const "op |"},
- @{const_name semilattice_sup_fun_inst.sup_fun})
- else
- (ubfp_prefix,
- @{const "op &"},
- @{const_name semilattice_inf_fun_inst.inf_fun})
- (* unit -> term *)
- fun pos () = unrolled_inductive_pred_const ext_ctxt gfp x
- |> aux ss Ts js depth polar
- fun neg () = Const (pref ^ s, T)
- in
- (case polar |> gfp ? flip_polarity of
- Pos => pos ()
- | Neg => neg ()
- | Neut =>
- if is_fun_type T then
- let
- val ((trunk_arg_Ts, rump_arg_T), body_T) =
- T |> strip_type |>> split_last
- val set_T = rump_arg_T --> body_T
- (* (unit -> term) -> term *)
- fun app f =
- list_comb (f (),
- map Bound (length trunk_arg_Ts - 1 downto 0))
- in
- List.foldr absdummy
- (Const (set_oper, set_T --> set_T --> set_T)
- $ app pos $ app neg) trunk_arg_Ts
- end
- else
- connective $ pos () $ neg ())
- end
- else
- Const x
- | t1 $ t2 =>
- betapply (aux ss Ts [] (skolem_depth + 1) polar t1,
- aux ss Ts [] depth Neut t2)
- | Abs (s, T, t1) => Abs (s, T, aux ss Ts (incrs js) depth polar t1)
- | _ => t
- end
- in aux [] [] [] 0 Pos end
-
-(* extended_context -> styp -> (int * term option) list *)
-fun static_args_in_term ({ersatz_table, ...} : extended_context) x t =
- let
- (* term -> term list -> term list -> term list list *)
- fun fun_calls (Abs (_, _, t)) _ = fun_calls t []
- | fun_calls (t1 $ t2) args = fun_calls t2 [] #> fun_calls t1 (t2 :: args)
- | fun_calls t args =
- (case t of
- Const (x' as (s', T')) =>
- x = x' orelse (case AList.lookup (op =) ersatz_table s' of
- SOME s'' => x = (s'', T')
- | NONE => false)
- | _ => false) ? cons args
- (* term list list -> term list list -> term list -> term list list *)
- fun call_sets [] [] vs = [vs]
- | call_sets [] uss vs = vs :: call_sets uss [] []
- | call_sets ([] :: _) _ _ = []
- | call_sets ((t :: ts) :: tss) uss vs =
- OrdList.insert TermOrd.term_ord t vs |> call_sets tss (ts :: uss)
- val sets = call_sets (fun_calls t [] []) [] []
- val indexed_sets = sets ~~ (index_seq 0 (length sets))
- in
- fold_rev (fn (set, j) =>
- case set of
- [Var _] => AList.lookup (op =) indexed_sets set = SOME j
- ? cons (j, NONE)
- | [t as Const _] => cons (j, SOME t)
- | [t as Free _] => cons (j, SOME t)
- | _ => I) indexed_sets []
- end
-(* extended_context -> styp -> term list -> (int * term option) list *)
-fun static_args_in_terms ext_ctxt x =
- map (static_args_in_term ext_ctxt x)
- #> fold1 (OrdList.inter (prod_ord int_ord (option_ord TermOrd.term_ord)))
-
-(* term -> term list *)
-fun params_in_equation (@{const "==>"} $ _ $ t2) = params_in_equation t2
- | params_in_equation (@{const Trueprop} $ t1) = params_in_equation t1
- | params_in_equation (Const (@{const_name "op ="}, _) $ t1 $ _) =
- snd (strip_comb t1)
- | params_in_equation _ = []
-
-(* styp -> styp -> int list -> term list -> term list -> term -> term *)
-fun specialize_fun_axiom x x' fixed_js fixed_args extra_args t =
- let
- val k = fold Integer.max (map maxidx_of_term (fixed_args @ extra_args)) 0
- + 1
- val t = map_aterms (fn Var ((s, i), T) => Var ((s, k + i), T) | t' => t') t
- val fixed_params = filter_indices fixed_js (params_in_equation t)
- (* term list -> term -> term *)
- fun aux args (Abs (s, T, t)) = list_comb (Abs (s, T, aux [] t), args)
- | aux args (t1 $ t2) = aux (aux [] t2 :: args) t1
- | aux args t =
- if t = Const x then
- list_comb (Const x', extra_args @ filter_out_indices fixed_js args)
- else
- let val j = find_index (curry (op =) t) fixed_params in
- list_comb (if j >= 0 then nth fixed_args j else t, args)
- end
- in aux [] t end
-
-(* typ list -> term -> bool *)
-fun is_eligible_arg Ts t =
- let val bad_Ts = map snd (Term.add_vars t []) @ map (nth Ts) (loose_bnos t) in
- null bad_Ts orelse
- (is_higher_order_type (fastype_of1 (Ts, t)) andalso
- forall (not o is_higher_order_type) bad_Ts)
- end
-
-(* (int * term option) list -> (int * term) list -> int list *)
-fun overlapping_indices [] _ = []
- | overlapping_indices _ [] = []
- | overlapping_indices (ps1 as (j1, t1) :: ps1') (ps2 as (j2, t2) :: ps2') =
- if j1 < j2 then overlapping_indices ps1' ps2
- else if j1 > j2 then overlapping_indices ps1 ps2'
- else overlapping_indices ps1' ps2' |> the_default t2 t1 = t2 ? cons j1
-
-val special_depth = 20
-
-(* extended_context -> int -> term -> term *)
-fun specialize_consts_in_term (ext_ctxt as {thy, specialize, simp_table,
- special_funs, ...}) depth t =
- if not specialize orelse depth > special_depth then
- t
- else
- let
- val blacklist = if depth = 0 then []
- else case term_under_def t of Const x => [x] | _ => []
- (* term list -> typ list -> term -> term *)
- fun aux args Ts (Const (x as (s, T))) =
- ((if not (member (op =) blacklist x) andalso not (null args) andalso
- not (String.isPrefix special_prefix s) andalso
- is_equational_fun ext_ctxt x then
- let
- val eligible_args = filter (is_eligible_arg Ts o snd)
- (index_seq 0 (length args) ~~ args)
- val _ = not (null eligible_args) orelse raise SAME ()
- val old_axs = equational_fun_axioms ext_ctxt x
- |> map (destroy_existential_equalities thy)
- val static_params = static_args_in_terms ext_ctxt x old_axs
- val fixed_js = overlapping_indices static_params eligible_args
- val _ = not (null fixed_js) orelse raise SAME ()
- val fixed_args = filter_indices fixed_js args
- val vars = fold Term.add_vars fixed_args []
- |> sort (TermOrd.fast_indexname_ord o pairself fst)
- val bound_js = fold (fn t => fn js => add_loose_bnos (t, 0, js))
- fixed_args []
- |> sort int_ord
- val live_args = filter_out_indices fixed_js args
- val extra_args = map Var vars @ map Bound bound_js @ live_args
- val extra_Ts = map snd vars @ filter_indices bound_js Ts
- val k = maxidx_of_term t + 1
- (* int -> term *)
- fun var_for_bound_no j =
- Var ((bound_var_prefix ^
- nat_subscript (find_index (curry (op =) j) bound_js
- + 1), k),
- nth Ts j)
- val fixed_args_in_axiom =
- map (curry subst_bounds
- (map var_for_bound_no (index_seq 0 (length Ts))))
- fixed_args
- in
- case AList.lookup (op =) (!special_funs)
- (x, fixed_js, fixed_args_in_axiom) of
- SOME x' => list_comb (Const x', extra_args)
- | NONE =>
- let
- val extra_args_in_axiom =
- map Var vars @ map var_for_bound_no bound_js
- val x' as (s', _) =
- (special_prefix_for (length (!special_funs) + 1) ^ s,
- extra_Ts @ filter_out_indices fixed_js (binder_types T)
- ---> body_type T)
- val new_axs =
- map (specialize_fun_axiom x x' fixed_js
- fixed_args_in_axiom extra_args_in_axiom) old_axs
- val _ =
- Unsynchronized.change special_funs
- (cons ((x, fixed_js, fixed_args_in_axiom), x'))
- val _ = add_simps simp_table s' new_axs
- in list_comb (Const x', extra_args) end
- end
- else
- raise SAME ())
- handle SAME () => list_comb (Const x, args))
- | aux args Ts (Abs (s, T, t)) =
- list_comb (Abs (s, T, aux [] (T :: Ts) t), args)
- | aux args Ts (t1 $ t2) = aux (aux [] Ts t2 :: args) Ts t1
- | aux args _ t = list_comb (t, args)
- in aux [] [] t end
-
-(* theory -> term -> int Termtab.tab -> int Termtab.tab *)
-fun add_to_uncurry_table thy t =
- let
- (* term -> term list -> int Termtab.tab -> int Termtab.tab *)
- fun aux (t1 $ t2) args table =
- let val table = aux t2 [] table in aux t1 (t2 :: args) table end
- | aux (Abs (_, _, t')) _ table = aux t' [] table
- | aux (t as Const (x as (s, _))) args table =
- if is_built_in_const true x orelse is_constr_like thy x orelse
- is_sel s orelse s = @{const_name Sigma} then
- table
- else
- Termtab.map_default (t, 65536) (curry Int.min (length args)) table
- | aux _ _ table = table
- in aux t [] end
-
-(* int Termtab.tab term -> term *)
-fun uncurry_term table t =
- let
- (* term -> term list -> term *)
- fun aux (t1 $ t2) args = aux t1 (aux t2 [] :: args)
- | aux (Abs (s, T, t')) args = betapplys (Abs (s, T, aux t' []), args)
- | aux (t as Const (s, T)) args =
- (case Termtab.lookup table t of
- SOME n =>
- if n >= 2 then
- let
- val (arg_Ts, rest_T) = strip_n_binders n T
- val j =
- if hd arg_Ts = @{typ bisim_iterator} orelse
- is_fp_iterator_type (hd arg_Ts) then
- 1
- else case find_index (not_equal bool_T) arg_Ts of
- ~1 => n
- | j => j
- val ((before_args, tuple_args), after_args) =
- args |> chop n |>> chop j
- val ((before_arg_Ts, tuple_arg_Ts), rest_T) =
- T |> strip_n_binders n |>> chop j
- val tuple_T = HOLogic.mk_tupleT tuple_arg_Ts
- in
- if n - j < 2 then
- betapplys (t, args)
- else
- betapplys (Const (uncurry_prefix_for (n - j) j ^ s,
- before_arg_Ts ---> tuple_T --> rest_T),
- before_args @ [mk_flat_tuple tuple_T tuple_args] @
- after_args)
- end
- else
- betapplys (t, args)
- | NONE => betapplys (t, args))
- | aux t args = betapplys (t, args)
- in aux t [] end
-
-(* (term -> term) -> int -> term -> term *)
-fun coerce_bound_no f j t =
- case t of
- t1 $ t2 => coerce_bound_no f j t1 $ coerce_bound_no f j t2
- | Abs (s, T, t') => Abs (s, T, coerce_bound_no f (j + 1) t')
- | Bound j' => if j' = j then f t else t
- | _ => t
-
-(* extended_context -> bool -> term -> term *)
-fun box_fun_and_pair_in_term (ext_ctxt as {thy, fast_descrs, ...}) def orig_t =
- let
- (* typ -> typ *)
- fun box_relational_operator_type (Type ("fun", Ts)) =
- Type ("fun", map box_relational_operator_type Ts)
- | box_relational_operator_type (Type ("*", Ts)) =
- Type ("*", map (box_type ext_ctxt InPair) Ts)
- | box_relational_operator_type T = T
- (* typ -> typ -> term -> term *)
- fun coerce_bound_0_in_term new_T old_T =
- old_T <> new_T ? coerce_bound_no (coerce_term [new_T] old_T new_T) 0
- (* typ list -> typ -> term -> term *)
- and coerce_term Ts new_T old_T t =
- if old_T = new_T then
- t
- else
- case (new_T, old_T) of
- (Type (new_s, new_Ts as [new_T1, new_T2]),
- Type ("fun", [old_T1, old_T2])) =>
- (case eta_expand Ts t 1 of
- Abs (s, _, t') =>
- Abs (s, new_T1,
- t' |> coerce_bound_0_in_term new_T1 old_T1
- |> coerce_term (new_T1 :: Ts) new_T2 old_T2)
- |> Envir.eta_contract
- |> new_s <> "fun"
- ? construct_value thy (@{const_name FunBox},
- Type ("fun", new_Ts) --> new_T) o single
- | t' => raise TERM ("Nitpick_HOL.box_fun_and_pair_in_term.\
- \coerce_term", [t']))
- | (Type (new_s, new_Ts as [new_T1, new_T2]),
- Type (old_s, old_Ts as [old_T1, old_T2])) =>
- if old_s = @{type_name fun_box} orelse
- old_s = @{type_name pair_box} orelse old_s = "*" then
- case constr_expand ext_ctxt old_T t of
- Const (@{const_name FunBox}, _) $ t1 =>
- if new_s = "fun" then
- coerce_term Ts new_T (Type ("fun", old_Ts)) t1
- else
- construct_value thy
- (@{const_name FunBox}, Type ("fun", new_Ts) --> new_T)
- [coerce_term Ts (Type ("fun", new_Ts))
- (Type ("fun", old_Ts)) t1]
- | Const _ $ t1 $ t2 =>
- construct_value thy
- (if new_s = "*" then @{const_name Pair}
- else @{const_name PairBox}, new_Ts ---> new_T)
- [coerce_term Ts new_T1 old_T1 t1,
- coerce_term Ts new_T2 old_T2 t2]
- | t' => raise TERM ("Nitpick_HOL.box_fun_and_pair_in_term.\
- \coerce_term", [t'])
- else
- raise TYPE ("coerce_term", [new_T, old_T], [t])
- | _ => raise TYPE ("coerce_term", [new_T, old_T], [t])
- (* indexname * typ -> typ * term -> typ option list -> typ option list *)
- fun add_boxed_types_for_var (z as (_, T)) (T', t') =
- case t' of
- Var z' => z' = z ? insert (op =) T'
- | Const (@{const_name Pair}, _) $ t1 $ t2 =>
- (case T' of
- Type (_, [T1, T2]) =>
- fold (add_boxed_types_for_var z) [(T1, t1), (T2, t2)]
- | _ => raise TYPE ("Nitpick_HOL.box_fun_and_pair_in_term.\
- \add_boxed_types_for_var", [T'], []))
- | _ => exists_subterm (curry (op =) (Var z)) t' ? insert (op =) T
- (* typ list -> typ list -> term -> indexname * typ -> typ *)
- fun box_var_in_def new_Ts old_Ts t (z as (_, T)) =
- case t of
- @{const Trueprop} $ t1 => box_var_in_def new_Ts old_Ts t1 z
- | Const (s0, _) $ t1 $ _ =>
- if s0 = @{const_name "=="} orelse s0 = @{const_name "op ="} then
- let
- val (t', args) = strip_comb t1
- val T' = fastype_of1 (new_Ts, do_term new_Ts old_Ts Neut t')
- in
- case fold (add_boxed_types_for_var z)
- (fst (strip_n_binders (length args) T') ~~ args) [] of
- [T''] => T''
- | _ => T
- end
- else
- T
- | _ => T
- (* typ list -> typ list -> polarity -> string -> typ -> string -> typ
- -> term -> term *)
- and do_quantifier new_Ts old_Ts polar quant_s quant_T abs_s abs_T t =
- let
- val abs_T' =
- if polar = Neut orelse is_positive_existential polar quant_s then
- box_type ext_ctxt InFunLHS abs_T
- else
- abs_T
- val body_T = body_type quant_T
- in
- Const (quant_s, (abs_T' --> body_T) --> body_T)
- $ Abs (abs_s, abs_T',
- t |> do_term (abs_T' :: new_Ts) (abs_T :: old_Ts) polar)
- end
- (* typ list -> typ list -> string -> typ -> term -> term -> term *)
- and do_equals new_Ts old_Ts s0 T0 t1 t2 =
- let
- val (t1, t2) = pairself (do_term new_Ts old_Ts Neut) (t1, t2)
- val (T1, T2) = pairself (curry fastype_of1 new_Ts) (t1, t2)
- val T = [T1, T2] |> sort TermOrd.typ_ord |> List.last
- in
- list_comb (Const (s0, T --> T --> body_type T0),
- map2 (coerce_term new_Ts T) [T1, T2] [t1, t2])
- end
- (* string -> typ -> term *)
- and do_description_operator s T =
- let val T1 = box_type ext_ctxt InFunLHS (range_type T) in
- Const (s, (T1 --> bool_T) --> T1)
- end
- (* typ list -> typ list -> polarity -> term -> term *)
- and do_term new_Ts old_Ts polar t =
- case t of
- Const (s0 as @{const_name all}, T0) $ Abs (s1, T1, t1) =>
- do_quantifier new_Ts old_Ts polar s0 T0 s1 T1 t1
- | Const (s0 as @{const_name "=="}, T0) $ t1 $ t2 =>
- do_equals new_Ts old_Ts s0 T0 t1 t2
- | @{const "==>"} $ t1 $ t2 =>
- @{const "==>"} $ do_term new_Ts old_Ts (flip_polarity polar) t1
- $ do_term new_Ts old_Ts polar t2
- | @{const Pure.conjunction} $ t1 $ t2 =>
- @{const Pure.conjunction} $ do_term new_Ts old_Ts polar t1
- $ do_term new_Ts old_Ts polar t2
- | @{const Trueprop} $ t1 =>
- @{const Trueprop} $ do_term new_Ts old_Ts polar t1
- | @{const Not} $ t1 =>
- @{const Not} $ do_term new_Ts old_Ts (flip_polarity polar) t1
- | Const (s0 as @{const_name All}, T0) $ Abs (s1, T1, t1) =>
- do_quantifier new_Ts old_Ts polar s0 T0 s1 T1 t1
- | Const (s0 as @{const_name Ex}, T0) $ Abs (s1, T1, t1) =>
- do_quantifier new_Ts old_Ts polar s0 T0 s1 T1 t1
- | Const (s0 as @{const_name "op ="}, T0) $ t1 $ t2 =>
- do_equals new_Ts old_Ts s0 T0 t1 t2
- | @{const "op &"} $ t1 $ t2 =>
- @{const "op &"} $ do_term new_Ts old_Ts polar t1
- $ do_term new_Ts old_Ts polar t2
- | @{const "op |"} $ t1 $ t2 =>
- @{const "op |"} $ do_term new_Ts old_Ts polar t1
- $ do_term new_Ts old_Ts polar t2
- | @{const "op -->"} $ t1 $ t2 =>
- @{const "op -->"} $ do_term new_Ts old_Ts (flip_polarity polar) t1
- $ do_term new_Ts old_Ts polar t2
- | Const (s as @{const_name The}, T) => do_description_operator s T
- | Const (s as @{const_name Eps}, T) => do_description_operator s T
- | Const (@{const_name quot_normal}, Type ("fun", [_, T2])) =>
- let val T' = box_type ext_ctxt InSel T2 in
- Const (@{const_name quot_normal}, T' --> T')
- end
- | Const (s as @{const_name Tha}, T) => do_description_operator s T
- | Const (x as (s, T)) =>
- Const (s, if s = @{const_name converse} orelse
- s = @{const_name trancl} then
- box_relational_operator_type T
- else if is_built_in_const fast_descrs x orelse
- s = @{const_name Sigma} then
- T
- else if is_constr_like thy x then
- box_type ext_ctxt InConstr T
- else if is_sel s
- orelse is_rep_fun thy x then
- box_type ext_ctxt InSel T
- else
- box_type ext_ctxt InExpr T)
- | t1 $ Abs (s, T, t2') =>
- let
- val t1 = do_term new_Ts old_Ts Neut t1
- val T1 = fastype_of1 (new_Ts, t1)
- val (s1, Ts1) = dest_Type T1
- val T' = hd (snd (dest_Type (hd Ts1)))
- val t2 = Abs (s, T', do_term (T' :: new_Ts) (T :: old_Ts) Neut t2')
- val T2 = fastype_of1 (new_Ts, t2)
- val t2 = coerce_term new_Ts (hd Ts1) T2 t2
- in
- betapply (if s1 = "fun" then
- t1
- else
- select_nth_constr_arg thy
- (@{const_name FunBox}, Type ("fun", Ts1) --> T1) t1 0
- (Type ("fun", Ts1)), t2)
- end
- | t1 $ t2 =>
- let
- val t1 = do_term new_Ts old_Ts Neut t1
- val T1 = fastype_of1 (new_Ts, t1)
- val (s1, Ts1) = dest_Type T1
- val t2 = do_term new_Ts old_Ts Neut t2
- val T2 = fastype_of1 (new_Ts, t2)
- val t2 = coerce_term new_Ts (hd Ts1) T2 t2
- in
- betapply (if s1 = "fun" then
- t1
- else
- select_nth_constr_arg thy
- (@{const_name FunBox}, Type ("fun", Ts1) --> T1) t1 0
- (Type ("fun", Ts1)), t2)
- end
- | Free (s, T) => Free (s, box_type ext_ctxt InExpr T)
- | Var (z as (x, T)) =>
- Var (x, if def then box_var_in_def new_Ts old_Ts orig_t z
- else box_type ext_ctxt InExpr T)
- | Bound _ => t
- | Abs (s, T, t') =>
- Abs (s, T, do_term (T :: new_Ts) (T :: old_Ts) Neut t')
- in do_term [] [] Pos orig_t end
-
-(* int -> term -> term *)
-fun eval_axiom_for_term j t =
- Logic.mk_equals (Const (eval_prefix ^ string_of_int j, fastype_of t), t)
-
-(* extended_context -> styp -> bool *)
-fun is_equational_fun_surely_complete ext_ctxt x =
- case raw_equational_fun_axioms ext_ctxt x of
- [@{const Trueprop} $ (Const (@{const_name "op ="}, _) $ t1 $ _)] =>
- strip_comb t1 |> snd |> forall is_Var
- | _ => false
-
-type special = int list * term list * styp
-
-(* styp -> special -> special -> term *)
-fun special_congruence_axiom (s, T) (js1, ts1, x1) (js2, ts2, x2) =
- let
- val (bounds1, bounds2) = pairself (map Var o special_bounds) (ts1, ts2)
- val Ts = binder_types T
- val max_j = fold (fold Integer.max) [js1, js2] ~1
- val (eqs, (args1, args2)) =
- fold (fn j => case pairself (fn ps => AList.lookup (op =) ps j)
- (js1 ~~ ts1, js2 ~~ ts2) of
- (SOME t1, SOME t2) => apfst (cons (t1, t2))
- | (SOME t1, NONE) => apsnd (apsnd (cons t1))
- | (NONE, SOME t2) => apsnd (apfst (cons t2))
- | (NONE, NONE) =>
- let val v = Var ((cong_var_prefix ^ nat_subscript j, 0),
- nth Ts j) in
- apsnd (pairself (cons v))
- end) (max_j downto 0) ([], ([], []))
- in
- Logic.list_implies (eqs |> filter_out (op =) |> distinct (op =)
- |> map Logic.mk_equals,
- Logic.mk_equals (list_comb (Const x1, bounds1 @ args1),
- list_comb (Const x2, bounds2 @ args2)))
- |> Refute.close_form (* TODO: needed? *)
- end
-
-(* extended_context -> styp list -> term list *)
-fun special_congruence_axioms (ext_ctxt as {special_funs, ...}) xs =
- let
- val groups =
- !special_funs
- |> map (fn ((x, js, ts), x') => (x, (js, ts, x')))
- |> AList.group (op =)
- |> filter_out (is_equational_fun_surely_complete ext_ctxt o fst)
- |> map (fn (x, zs) => (x, zs |> member (op =) xs x ? cons ([], [], x)))
- (* special -> int *)
- fun generality (js, _, _) = ~(length js)
- (* special -> special -> bool *)
- fun is_more_specific (j1, t1, x1) (j2, t2, x2) =
- x1 <> x2 andalso OrdList.subset (prod_ord int_ord TermOrd.term_ord)
- (j2 ~~ t2, j1 ~~ t1)
- (* styp -> special list -> special list -> special list -> term list
- -> term list *)
- fun do_pass_1 _ [] [_] [_] = I
- | do_pass_1 x skipped _ [] = do_pass_2 x skipped
- | do_pass_1 x skipped all (z :: zs) =
- case filter (is_more_specific z) all
- |> sort (int_ord o pairself generality) of
- [] => do_pass_1 x (z :: skipped) all zs
- | (z' :: _) => cons (special_congruence_axiom x z z')
- #> do_pass_1 x skipped all zs
- (* styp -> special list -> term list -> term list *)
- and do_pass_2 _ [] = I
- | do_pass_2 x (z :: zs) =
- fold (cons o special_congruence_axiom x z) zs #> do_pass_2 x zs
- in fold (fn (x, zs) => do_pass_1 x [] zs zs) groups [] end
-
-(* term -> bool *)
-val is_trivial_equation = the_default false o try (op aconv o Logic.dest_equals)
-
-(* 'a Symtab.table -> 'a list *)
-fun all_table_entries table = Symtab.fold (append o snd) table []
-(* const_table -> string -> const_table *)
-fun extra_table table s = Symtab.make [(s, all_table_entries table)]
-
-(* extended_context -> term -> (term list * term list) * (bool * bool) *)
-fun axioms_for_term
- (ext_ctxt as {thy, max_bisim_depth, user_axioms, fast_descrs, evals,
- def_table, nondef_table, user_nondefs, ...}) t =
- let
- type accumulator = styp list * (term list * term list)
- (* (term list * term list -> term list)
- -> ((term list -> term list) -> term list * term list
- -> term list * term list)
- -> int -> term -> accumulator -> accumulator *)
- fun add_axiom get app depth t (accum as (xs, axs)) =
- let
- val t = t |> unfold_defs_in_term ext_ctxt
- |> skolemize_term_and_more ext_ctxt ~1
- in
- if is_trivial_equation t then
- accum
- else
- let val t' = t |> specialize_consts_in_term ext_ctxt depth in
- if exists (member (op aconv) (get axs)) [t, t'] then accum
- else add_axioms_for_term (depth + 1) t' (xs, app (cons t') axs)
- end
- end
- (* int -> term -> accumulator -> accumulator *)
- and add_def_axiom depth = add_axiom fst apfst depth
- and add_nondef_axiom depth = add_axiom snd apsnd depth
- and add_maybe_def_axiom depth t =
- (if head_of t <> @{const "==>"} then add_def_axiom
- else add_nondef_axiom) depth t
- and add_eq_axiom depth t =
- (if is_constr_pattern_formula thy t then add_def_axiom
- else add_nondef_axiom) depth t
- (* int -> term -> accumulator -> accumulator *)
- and add_axioms_for_term depth t (accum as (xs, axs)) =
- case t of
- t1 $ t2 => accum |> fold (add_axioms_for_term depth) [t1, t2]
- | Const (x as (s, T)) =>
- (if member (op =) xs x orelse is_built_in_const fast_descrs x then
- accum
- else
- let val accum as (xs, _) = (x :: xs, axs) in
- if depth > axioms_max_depth then
- raise TOO_LARGE ("Nitpick_HOL.axioms_for_term.\
- \add_axioms_for_term",
- "too many nested axioms (" ^
- string_of_int depth ^ ")")
- else if Refute.is_const_of_class thy x then
- let
- val class = Logic.class_of_const s
- val of_class = Logic.mk_of_class (TVar (("'a", 0), [class]),
- class)
- val ax1 = try (Refute.specialize_type thy x) of_class
- val ax2 = Option.map (Refute.specialize_type thy x o snd)
- (Refute.get_classdef thy class)
- in
- fold (add_maybe_def_axiom depth) (map_filter I [ax1, ax2])
- accum
- end
- else if is_constr thy x then
- accum
- else if is_equational_fun ext_ctxt x then
- fold (add_eq_axiom depth) (equational_fun_axioms ext_ctxt x)
- accum
- else if is_abs_fun thy x then
- if is_quot_type thy (range_type T) then
- raise NOT_SUPPORTED "\"Abs_\" function of quotient type"
- else
- accum |> fold (add_nondef_axiom depth)
- (nondef_props_for_const thy false nondef_table x)
- |> is_funky_typedef thy (range_type T)
- ? fold (add_maybe_def_axiom depth)
- (nondef_props_for_const thy true
- (extra_table def_table s) x)
- else if is_rep_fun thy x then
- if is_quot_type thy (domain_type T) then
- raise NOT_SUPPORTED "\"Rep_\" function of quotient type"
- else
- accum |> fold (add_nondef_axiom depth)
- (nondef_props_for_const thy false nondef_table x)
- |> is_funky_typedef thy (range_type T)
- ? fold (add_maybe_def_axiom depth)
- (nondef_props_for_const thy true
- (extra_table def_table s) x)
- |> add_axioms_for_term depth
- (Const (mate_of_rep_fun thy x))
- |> fold (add_def_axiom depth)
- (inverse_axioms_for_rep_fun thy x)
- else
- accum |> user_axioms <> SOME false
- ? fold (add_nondef_axiom depth)
- (nondef_props_for_const thy false nondef_table x)
- end)
- |> add_axioms_for_type depth T
- | Free (_, T) => add_axioms_for_type depth T accum
- | Var (_, T) => add_axioms_for_type depth T accum
- | Bound _ => accum
- | Abs (_, T, t) => accum |> add_axioms_for_term depth t
- |> add_axioms_for_type depth T
- (* int -> typ -> accumulator -> accumulator *)
- and add_axioms_for_type depth T =
- case T of
- Type ("fun", Ts) => fold (add_axioms_for_type depth) Ts
- | Type ("*", Ts) => fold (add_axioms_for_type depth) Ts
- | @{typ prop} => I
- | @{typ bool} => I
- | @{typ unit} => I
- | TFree (_, S) => add_axioms_for_sort depth T S
- | TVar (_, S) => add_axioms_for_sort depth T S
- | Type (z as (s, Ts)) =>
- fold (add_axioms_for_type depth) Ts
- #> (if is_pure_typedef thy T then
- fold (add_maybe_def_axiom depth) (optimized_typedef_axioms thy z)
- else if is_quot_type thy T then
- fold (add_def_axiom depth) (optimized_quot_type_axioms thy z)
- else if max_bisim_depth >= 0 andalso is_codatatype thy T then
- fold (add_maybe_def_axiom depth)
- (codatatype_bisim_axioms ext_ctxt T)
- else
- I)
- (* int -> typ -> sort -> accumulator -> accumulator *)
- and add_axioms_for_sort depth T S =
- let
- val supers = Sign.complete_sort thy S
- val class_axioms =
- maps (fn class => map prop_of (AxClass.get_info thy class |> #axioms
- handle ERROR _ => [])) supers
- val monomorphic_class_axioms =
- map (fn t => case Term.add_tvars t [] of
- [] => t
- | [(x, S)] =>
- Refute.monomorphic_term (Vartab.make [(x, (S, T))]) t
- | _ => raise TERM ("Nitpick_HOL.axioms_for_term.\
- \add_axioms_for_sort", [t]))
- class_axioms
- in fold (add_nondef_axiom depth) monomorphic_class_axioms end
- val (mono_user_nondefs, poly_user_nondefs) =
- List.partition (null o Term.hidden_polymorphism) user_nondefs
- val eval_axioms = map2 eval_axiom_for_term (index_seq 0 (length evals))
- evals
- val (xs, (defs, nondefs)) =
- ([], ([], [])) |> add_axioms_for_term 1 t
- |> fold_rev (add_def_axiom 1) eval_axioms
- |> user_axioms = SOME true
- ? fold (add_nondef_axiom 1) mono_user_nondefs
- val defs = defs @ special_congruence_axioms ext_ctxt xs
- in
- ((defs, nondefs), (user_axioms = SOME true orelse null mono_user_nondefs,
- null poly_user_nondefs))
- end
+(* hol_context -> typ -> typ list *)
+fun ground_types_in_type hol_ctxt T = add_ground_types hol_ctxt T []
+(* hol_context -> term list -> typ list *)
+fun ground_types_in_terms hol_ctxt ts =
+ fold (fold_types (add_ground_types hol_ctxt)) ts []
(* theory -> const_table -> styp -> int list *)
fun const_format thy def_table (x as (s, T)) =
@@ -3356,10 +2121,10 @@
|> map (rev o filter_out (member (op =) js))
|> filter_out null |> map length |> rev
-(* extended_context -> string * string -> (term option * int list) list
+(* hol_context -> string * string -> (term option * int list) list
-> styp -> term * typ *)
fun user_friendly_const ({thy, evals, def_table, skolems, special_funs, ...}
- : extended_context) (base_name, step_name) formats =
+ : hol_context) (base_name, step_name) formats =
let
val default_format = the (AList.lookup (op =) formats NONE)
(* styp -> term * typ *)
@@ -3460,7 +2225,7 @@
(t, format_term_type thy def_table formats t)
end)
|>> map_types unbit_and_unbox_type
- |>> shorten_names_in_term |>> shorten_abs_vars
+ |>> shorten_names_in_term |>> Term.map_abs_vars shortest_name
in do_const end
(* styp -> string *)
@@ -3474,84 +2239,4 @@
else
"="
-val binary_int_threshold = 4
-
-(* term -> bool *)
-fun may_use_binary_ints (t1 $ t2) =
- may_use_binary_ints t1 andalso may_use_binary_ints t2
- | may_use_binary_ints (t as Const (s, _)) =
- t <> @{const Suc} andalso
- not (member (op =) [@{const_name Abs_Frac}, @{const_name Rep_Frac},
- @{const_name nat_gcd}, @{const_name nat_lcm},
- @{const_name Frac}, @{const_name norm_frac}] s)
- | may_use_binary_ints (Abs (_, _, t')) = may_use_binary_ints t'
- | may_use_binary_ints _ = true
-fun should_use_binary_ints (t1 $ t2) =
- should_use_binary_ints t1 orelse should_use_binary_ints t2
- | should_use_binary_ints (Const (s, _)) =
- member (op =) [@{const_name times_nat_inst.times_nat},
- @{const_name div_nat_inst.div_nat},
- @{const_name times_int_inst.times_int},
- @{const_name div_int_inst.div_int}] s orelse
- (String.isPrefix numeral_prefix s andalso
- let val n = the (Int.fromString (unprefix numeral_prefix s)) in
- n <= ~ binary_int_threshold orelse n >= binary_int_threshold
- end)
- | should_use_binary_ints (Abs (_, _, t')) = should_use_binary_ints t'
- | should_use_binary_ints _ = false
-
-(* typ -> typ *)
-fun binarize_nat_and_int_in_type @{typ nat} = @{typ "unsigned_bit word"}
- | binarize_nat_and_int_in_type @{typ int} = @{typ "signed_bit word"}
- | binarize_nat_and_int_in_type (Type (s, Ts)) =
- Type (s, map binarize_nat_and_int_in_type Ts)
- | binarize_nat_and_int_in_type T = T
-(* term -> term *)
-val binarize_nat_and_int_in_term = map_types binarize_nat_and_int_in_type
-
-(* extended_context -> term
- -> ((term list * term list) * (bool * bool)) * term *)
-fun preprocess_term (ext_ctxt as {thy, binary_ints, destroy_constrs, boxes,
- skolemize, uncurry, ...}) t =
- let
- val skolem_depth = if skolemize then 4 else ~1
- val (((def_ts, nondef_ts), (got_all_mono_user_axioms, no_poly_user_axioms)),
- core_t) = t |> unfold_defs_in_term ext_ctxt
- |> Refute.close_form
- |> skolemize_term_and_more ext_ctxt skolem_depth
- |> specialize_consts_in_term ext_ctxt 0
- |> `(axioms_for_term ext_ctxt)
- val binarize =
- case binary_ints of
- SOME false => false
- | _ =>
- forall may_use_binary_ints (core_t :: def_ts @ nondef_ts) andalso
- (binary_ints = SOME true orelse
- exists should_use_binary_ints (core_t :: def_ts @ nondef_ts))
- val box = exists (not_equal (SOME false) o snd) boxes
- val table =
- Termtab.empty |> uncurry
- ? fold (add_to_uncurry_table thy) (core_t :: def_ts @ nondef_ts)
- (* bool -> bool -> term -> term *)
- fun do_rest def core =
- binarize ? binarize_nat_and_int_in_term
- #> uncurry ? uncurry_term table
- #> box ? box_fun_and_pair_in_term ext_ctxt def
- #> destroy_constrs ? (pull_out_universal_constrs thy def
- #> pull_out_existential_constrs thy
- #> destroy_pulled_out_constrs ext_ctxt def)
- #> curry_assms
- #> destroy_universal_equalities
- #> destroy_existential_equalities thy
- #> simplify_constrs_and_sels thy
- #> distribute_quantifiers
- #> push_quantifiers_inward thy
- #> not core ? Refute.close_form
- #> shorten_abs_vars
- in
- (((map (do_rest true false) def_ts, map (do_rest false false) nondef_ts),
- (got_all_mono_user_axioms, no_poly_user_axioms)),
- do_rest false true core_t)
- end
-
end;