(* Title: HOL/Tools/Nitpick/nitpick_model.ML
Author: Jasmin Blanchette, TU Muenchen
Copyright 2009, 2010
Model reconstruction for Nitpick.
*)
signature NITPICK_MODEL =
sig
type styp = Nitpick_Util.styp
type scope = Nitpick_Scope.scope
type rep = Nitpick_Rep.rep
type nut = Nitpick_Nut.nut
type params =
{show_datatypes: bool,
show_skolems: bool,
show_consts: bool}
type term_postprocessor =
Proof.context -> string -> (typ -> term list) -> typ -> term -> term
structure NameTable : TABLE
val irrelevant : string
val unknown : string
val unrep : unit -> string
val register_term_postprocessor :
typ -> term_postprocessor -> morphism -> Context.generic -> Context.generic
val register_term_postprocessor_global :
typ -> term_postprocessor -> theory -> theory
val unregister_term_postprocessor :
typ -> morphism -> Context.generic -> Context.generic
val unregister_term_postprocessor_global : typ -> theory -> theory
val tuple_list_for_name :
nut NameTable.table -> Kodkod.raw_bound list -> nut -> int list list
val dest_plain_fun : term -> bool * (term list * term list)
val reconstruct_hol_model :
params -> scope -> (term option * int list) list
-> (typ option * string list) list -> styp list -> styp list -> nut list
-> nut list -> nut list -> nut NameTable.table -> Kodkod.raw_bound list
-> Pretty.T * bool
val prove_hol_model :
scope -> Time.time option -> nut list -> nut list -> nut NameTable.table
-> Kodkod.raw_bound list -> term -> bool option
end;
structure Nitpick_Model : NITPICK_MODEL =
struct
open Nitpick_Util
open Nitpick_HOL
open Nitpick_Scope
open Nitpick_Peephole
open Nitpick_Rep
open Nitpick_Nut
structure KK = Kodkod
type params =
{show_datatypes: bool,
show_skolems: bool,
show_consts: bool}
type term_postprocessor =
Proof.context -> string -> (typ -> term list) -> typ -> term -> term
structure Data = Generic_Data
(
type T = (typ * term_postprocessor) list
val empty = []
val extend = I
fun merge data = AList.merge (op =) (K true) data
)
fun xsym s s' () = if print_mode_active Symbol.xsymbolsN then s else s'
val irrelevant = "_"
val unknown = "?"
val unrep = xsym "\<dots>" "..."
val maybe_mixfix = xsym "_\<^sup>?" "_?"
val base_mixfix = xsym "_\<^bsub>base\<^esub>" "_.base"
val step_mixfix = xsym "_\<^bsub>step\<^esub>" "_.step"
val abs_mixfix = xsym "\<guillemotleft>_\<guillemotright>" "\"_\""
val arg_var_prefix = "x"
val cyclic_co_val_name = xsym "\<omega>" "w"
val cyclic_const_prefix = xsym "\<xi>" "X"
fun cyclic_type_name () = nitpick_prefix ^ cyclic_const_prefix ()
val opt_flag = nitpick_prefix ^ "opt"
val non_opt_flag = nitpick_prefix ^ "non_opt"
type atom_pool = ((string * int) * int list) list
fun add_wacky_syntax ctxt =
let
val name_of = fst o dest_Const
val thy = Proof_Context.theory_of ctxt |> Context.reject_draft
val (maybe_t, thy) =
Sign.declare_const_global ((@{binding nitpick_maybe}, @{typ "'a => 'a"}),
Mixfix (maybe_mixfix (), [1000], 1000)) thy
val (abs_t, thy) =
Sign.declare_const_global ((@{binding nitpick_abs}, @{typ "'a => 'b"}),
Mixfix (abs_mixfix (), [40], 40)) thy
val (base_t, thy) =
Sign.declare_const_global ((@{binding nitpick_base}, @{typ "'a => 'a"}),
Mixfix (base_mixfix (), [1000], 1000)) thy
val (step_t, thy) =
Sign.declare_const_global ((@{binding nitpick_step}, @{typ "'a => 'a"}),
Mixfix (step_mixfix (), [1000], 1000)) thy
in
(pairself (pairself name_of) ((maybe_t, abs_t), (base_t, step_t)),
Proof_Context.transfer_syntax thy ctxt)
end
(** Term reconstruction **)
fun nth_atom_number pool T j =
case AList.lookup (op =) (!pool) T of
SOME js =>
(case find_index (curry (op =) j) js of
~1 => (Unsynchronized.change pool (cons (T, j :: js));
length js + 1)
| n => length js - n)
| NONE => (Unsynchronized.change pool (cons (T, [j])); 1)
fun atom_suffix s =
nat_subscript
#> (s <> "" andalso Symbol.is_ascii_digit (List.last (raw_explode s))) (* FIXME Symbol.explode (?) *)
? prefix "\<^isub>,"
fun nth_atom_name thy atomss pool prefix T j =
let
val ss = these (triple_lookup (type_match thy) atomss T)
val m = nth_atom_number pool T j
in
if m <= length ss then
nth ss (m - 1)
else case T of
Type (s, _) =>
let val s' = shortest_name s in
prefix ^
(if T = @{typ string} then "s"
else if String.isPrefix "\\" s' then s'
else substring (s', 0, 1)) ^ atom_suffix s m
end
| TFree (s, _) => prefix ^ perhaps (try (unprefix "'")) s ^ atom_suffix s m
| _ => raise TYPE ("Nitpick_Model.nth_atom_name", [T], [])
end
fun nth_atom thy atomss pool for_auto T j =
if for_auto then
Free (nth_atom_name thy atomss pool (hd (space_explode "." nitpick_prefix))
T j, T)
else
Const (nth_atom_name thy atomss pool "" T j, T)
fun extract_real_number (Const (@{const_name divide}, _) $ t1 $ t2) =
real (snd (HOLogic.dest_number t1)) / real (snd (HOLogic.dest_number t2))
| extract_real_number t = real (snd (HOLogic.dest_number t))
fun nice_term_ord (Abs (_, _, t1), Abs (_, _, t2)) = nice_term_ord (t1, t2)
| nice_term_ord tp = Real.compare (pairself extract_real_number tp)
handle TERM ("dest_number", _) =>
case tp of
(t11 $ t12, t21 $ t22) =>
(case nice_term_ord (t11, t21) of
EQUAL => nice_term_ord (t12, t22)
| ord => ord)
| _ => Term_Ord.fast_term_ord tp
fun register_term_postprocessor_generic T postproc =
Data.map (cons (T, postproc))
(* TODO: Consider morphism. *)
fun register_term_postprocessor T postproc (_ : morphism) =
register_term_postprocessor_generic T postproc
val register_term_postprocessor_global =
Context.theory_map oo register_term_postprocessor_generic
fun unregister_term_postprocessor_generic T = Data.map (AList.delete (op =) T)
(* TODO: Consider morphism. *)
fun unregister_term_postprocessor T (_ : morphism) =
unregister_term_postprocessor_generic T
val unregister_term_postprocessor_global =
Context.theory_map o unregister_term_postprocessor_generic
fun tuple_list_for_name rel_table bounds name =
the (AList.lookup (op =) bounds (the_rel rel_table name)) handle NUT _ => [[]]
fun unarize_unbox_etc_term (Const (@{const_name FunBox}, _) $ t1) =
unarize_unbox_etc_term t1
| unarize_unbox_etc_term
(Const (@{const_name PairBox},
Type (@{type_name fun}, [T1, Type (@{type_name fun}, [T2, _])]))
$ t1 $ t2) =
let val Ts = map uniterize_unarize_unbox_etc_type [T1, T2] in
Const (@{const_name Pair}, Ts ---> Type (@{type_name prod}, Ts))
$ unarize_unbox_etc_term t1 $ unarize_unbox_etc_term t2
end
| unarize_unbox_etc_term (Const (s, T)) =
Const (s, uniterize_unarize_unbox_etc_type T)
| unarize_unbox_etc_term (t1 $ t2) =
unarize_unbox_etc_term t1 $ unarize_unbox_etc_term t2
| unarize_unbox_etc_term (Free (s, T)) =
Free (s, uniterize_unarize_unbox_etc_type T)
| unarize_unbox_etc_term (Var (x, T)) =
Var (x, uniterize_unarize_unbox_etc_type T)
| unarize_unbox_etc_term (Bound j) = Bound j
| unarize_unbox_etc_term (Abs (s, T, t')) =
Abs (s, uniterize_unarize_unbox_etc_type T, unarize_unbox_etc_term t')
fun factor_out_types (T1 as Type (@{type_name prod}, [T11, T12]))
(T2 as Type (@{type_name prod}, [T21, T22])) =
let val (n1, n2) = pairself num_factors_in_type (T11, T21) in
if n1 = n2 then
let
val ((T11', opt_T12'), (T21', opt_T22')) = factor_out_types T12 T22
in
((Type (@{type_name prod}, [T11, T11']), opt_T12'),
(Type (@{type_name prod}, [T21, T21']), opt_T22'))
end
else if n1 < n2 then
case factor_out_types T1 T21 of
(p1, (T21', NONE)) => (p1, (T21', SOME T22))
| (p1, (T21', SOME T22')) =>
(p1, (T21', SOME (Type (@{type_name prod}, [T22', T22]))))
else
swap (factor_out_types T2 T1)
end
| factor_out_types (Type (@{type_name prod}, [T11, T12])) T2 =
((T11, SOME T12), (T2, NONE))
| factor_out_types T1 (Type (@{type_name prod}, [T21, T22])) =
((T1, NONE), (T21, SOME T22))
| factor_out_types T1 T2 = ((T1, NONE), (T2, NONE))
(* Term-encoded data structure for holding key-value pairs as well as an "opt"
flag indicating whether the function is approximated. *)
fun make_plain_fun maybe_opt T1 T2 =
let
fun aux T1 T2 [] =
Const (if maybe_opt then opt_flag else non_opt_flag, T1 --> T2)
| aux T1 T2 ((t1, t2) :: tps) =
Const (@{const_name fun_upd}, (T1 --> T2) --> T1 --> T2 --> T1 --> T2)
$ aux T1 T2 tps $ t1 $ t2
in aux T1 T2 o rev end
fun is_plain_fun (Const (s, _)) = (s = opt_flag orelse s = non_opt_flag)
| is_plain_fun (Const (@{const_name fun_upd}, _) $ t0 $ _ $ _) =
is_plain_fun t0
| is_plain_fun _ = false
val dest_plain_fun =
let
fun aux (Abs (_, _, Const (s, _))) = (s <> irrelevant, ([], []))
| aux (Const (s, _)) = (s <> non_opt_flag, ([], []))
| aux (Const (@{const_name fun_upd}, _) $ t0 $ t1 $ t2) =
let val (maybe_opt, (ts1, ts2)) = aux t0 in
(maybe_opt, (t1 :: ts1, t2 :: ts2))
end
| aux t = raise TERM ("Nitpick_Model.dest_plain_fun", [t])
in apsnd (pairself rev) o aux end
fun break_in_two T T1 T2 t =
let
val ps = HOLogic.flat_tupleT_paths T
val cut = length (HOLogic.strip_tupleT T1)
val (ps1, ps2) = pairself HOLogic.flat_tupleT_paths (T1, T2)
val (ts1, ts2) = t |> HOLogic.strip_ptuple ps |> chop cut
in (HOLogic.mk_ptuple ps1 T1 ts1, HOLogic.mk_ptuple ps2 T2 ts2) end
fun pair_up (Type (@{type_name prod}, [T1', T2']))
(t1 as Const (@{const_name Pair},
Type (@{type_name fun},
[_, Type (@{type_name fun}, [_, T1])]))
$ t11 $ t12) t2 =
if T1 = T1' then HOLogic.mk_prod (t1, t2)
else HOLogic.mk_prod (t11, pair_up T2' t12 t2)
| pair_up _ t1 t2 = HOLogic.mk_prod (t1, t2)
fun multi_pair_up T1 t1 (ts2, ts3) = map2 (pair o pair_up T1 t1) ts2 ts3
fun format_fun T' T1 T2 t =
let
val T1' = pseudo_domain_type T'
val T2' = pseudo_range_type T'
fun do_curry T1 T1a T1b T2 t =
let
val (maybe_opt, tsp) = dest_plain_fun t
val tps =
tsp |>> map (break_in_two T1 T1a T1b)
|> uncurry (map2 (fn (t1a, t1b) => fn t2 => (t1a, (t1b, t2))))
|> AList.coalesce (op =)
|> map (apsnd (make_plain_fun maybe_opt T1b T2))
in make_plain_fun maybe_opt T1a (T1b --> T2) tps end
and do_uncurry T1 T2 t =
let
val (maybe_opt, tsp) = dest_plain_fun t
val tps =
tsp |> op ~~
|> maps (fn (t1, t2) =>
multi_pair_up T1 t1 (snd (dest_plain_fun t2)))
in make_plain_fun maybe_opt T1 T2 tps end
and do_arrow T1' T2' _ _ (Const (s, _)) = Const (s, T1' --> T2')
| do_arrow T1' T2' T1 T2
(Const (@{const_name fun_upd}, _) $ t0 $ t1 $ t2) =
Const (@{const_name fun_upd},
(T1' --> T2') --> T1' --> T2' --> T1' --> T2')
$ do_arrow T1' T2' T1 T2 t0 $ do_term T1' T1 t1 $ do_term T2' T2 t2
| do_arrow _ _ _ _ t =
raise TERM ("Nitpick_Model.format_fun.do_arrow", [t])
and do_fun T1' T2' T1 T2 t =
case factor_out_types T1' T1 of
((_, NONE), (_, NONE)) => t |> do_arrow T1' T2' T1 T2
| ((_, NONE), (T1a, SOME T1b)) =>
t |> do_curry T1 T1a T1b T2 |> do_arrow T1' T2' T1a (T1b --> T2)
| ((T1a', SOME T1b'), (_, NONE)) =>
t |> do_arrow T1a' (T1b' --> T2') T1 T2 |> do_uncurry T1' T2'
| _ => raise TYPE ("Nitpick_Model.format_fun.do_fun", [T1, T1'], [])
and do_term (Type (@{type_name fun}, [T1', T2']))
(Type (@{type_name fun}, [T1, T2])) t =
do_fun T1' T2' T1 T2 t
| do_term (T' as Type (@{type_name prod}, Ts' as [T1', T2']))
(Type (@{type_name prod}, [T1, T2]))
(Const (@{const_name Pair}, _) $ t1 $ t2) =
Const (@{const_name Pair}, Ts' ---> T')
$ do_term T1' T1 t1 $ do_term T2' T2 t2
| do_term T' T t =
if T = T' then t
else raise TYPE ("Nitpick_Model.format_fun.do_term", [T, T'], [])
in if T1' = T1 andalso T2' = T2 then t else do_fun T1' T2' T1 T2 t end
fun truth_const_sort_key @{const True} = "0"
| truth_const_sort_key @{const False} = "2"
| truth_const_sort_key _ = "1"
fun mk_tuple (Type (@{type_name prod}, [T1, T2])) ts =
HOLogic.mk_prod (mk_tuple T1 ts,
mk_tuple T2 (List.drop (ts, length (HOLogic.flatten_tupleT T1))))
| mk_tuple _ (t :: _) = t
| mk_tuple T [] = raise TYPE ("Nitpick_Model.mk_tuple", [T], [])
fun varified_type_match ctxt (candid_T, pat_T) =
let val thy = Proof_Context.theory_of ctxt in
strict_type_match thy (candid_T, varify_type ctxt pat_T)
end
fun all_values_of_type pool wacky_names (scope as {card_assigns, ...} : scope)
atomss sel_names rel_table bounds card T =
let
val card = if card = 0 then card_of_type card_assigns T else card
fun nth_value_of_type n =
let
fun term unfold =
reconstruct_term true unfold pool wacky_names scope atomss sel_names
rel_table bounds T T (Atom (card, 0)) [[n]]
in
case term false of
t as Const (s, _) =>
if String.isPrefix (cyclic_const_prefix ()) s then
HOLogic.mk_eq (t, term true)
else
t
| t => t
end
in index_seq 0 card |> map nth_value_of_type |> sort nice_term_ord end
and reconstruct_term maybe_opt unfold pool
(wacky_names as ((maybe_name, abs_name), _))
(scope as {hol_ctxt as {thy, ctxt, stds, ...}, binarize, card_assigns,
bits, datatypes, ofs, ...})
atomss sel_names rel_table bounds =
let
val for_auto = (maybe_name = "")
fun value_of_bits jss =
let
val j0 = offset_of_type ofs @{typ unsigned_bit}
val js = map (Integer.add (~ j0) o the_single) jss
in
fold (fn j => Integer.add (reasonable_power 2 j |> j = bits ? op ~))
js 0
end
val all_values =
all_values_of_type pool wacky_names scope atomss sel_names rel_table
bounds 0
fun postprocess_term (Type (@{type_name fun}, _)) = I
| postprocess_term T =
case Data.get (Context.Proof ctxt) of
[] => I
| postprocs =>
case AList.lookup (varified_type_match ctxt) postprocs T of
SOME postproc => postproc ctxt maybe_name all_values T
| NONE => I
fun postprocess_subterms Ts (t1 $ t2) =
let val t = postprocess_subterms Ts t1 $ postprocess_subterms Ts t2 in
postprocess_term (fastype_of1 (Ts, t)) t
end
| postprocess_subterms Ts (Abs (s, T, t')) =
Abs (s, T, postprocess_subterms (T :: Ts) t')
| postprocess_subterms Ts t = postprocess_term (fastype_of1 (Ts, t)) t
fun make_set maybe_opt T tps =
let
val set_T = HOLogic.mk_setT T
val empty_const = Const (@{const_abbrev Set.empty}, set_T)
val insert_const = Const (@{const_name insert}, T --> set_T --> set_T)
fun aux [] =
if maybe_opt andalso not (is_complete_type datatypes false T) then
insert_const $ Const (unrep (), T) $ empty_const
else
empty_const
| aux ((t1, t2) :: zs) =
aux zs
|> t2 <> @{const False}
? curry (op $)
(insert_const
$ (t1 |> t2 <> @{const True}
? curry (op $)
(Const (maybe_name, T --> T))))
in
if forall (fn (_, t) => t <> @{const True} andalso t <> @{const False})
tps then
Const (unknown, set_T)
else
aux tps
end
fun make_map maybe_opt T1 T2 T2' =
let
val update_const = Const (@{const_name fun_upd},
(T1 --> T2) --> T1 --> T2 --> T1 --> T2)
fun aux' [] = Const (@{const_abbrev Map.empty}, T1 --> T2)
| aux' ((t1, t2) :: tps) =
(case t2 of
Const (@{const_name None}, _) => aux' tps
| _ => update_const $ aux' tps $ t1 $ t2)
fun aux tps =
if maybe_opt andalso not (is_complete_type datatypes false T1) then
update_const $ aux' tps $ Const (unrep (), T1)
$ (Const (@{const_name Some}, T2' --> T2) $ Const (unknown, T2'))
else
aux' tps
in aux end
fun polish_funs Ts t =
(case fastype_of1 (Ts, t) of
Type (@{type_name fun}, [T1, T2]) =>
if is_plain_fun t then
case T2 of
Type (@{type_name option}, [T2']) =>
let
val (maybe_opt, ts_pair) =
dest_plain_fun t ||> pairself (map (polish_funs Ts))
in make_map maybe_opt T1 T2 T2' (rev (op ~~ ts_pair)) end
| _ => raise SAME ()
else
raise SAME ()
| _ => raise SAME ())
handle SAME () =>
case t of
(t1 as Const (@{const_name fun_upd}, _) $ t11 $ _)
$ (t2 as Const (s, _)) =>
if s = unknown then polish_funs Ts t11
else polish_funs Ts t1 $ polish_funs Ts t2
| t1 $ t2 => polish_funs Ts t1 $ polish_funs Ts t2
| Abs (s, T, t') => Abs (s, T, polish_funs (T :: Ts) t')
| Const (s, Type (@{type_name fun}, [T1, T2])) =>
if s = opt_flag orelse s = non_opt_flag then
Abs ("x", T1,
Const (if is_complete_type datatypes false T1 then
irrelevant
else
unknown, T2))
else
t
| t => t
fun make_fun_or_set maybe_opt T T1 T2 T' ts1 ts2 =
ts1 ~~ ts2
|> sort (nice_term_ord o pairself fst)
|> (case T of
Type (@{type_name set}, _) =>
sort_wrt (truth_const_sort_key o snd)
#> make_set maybe_opt T'
| _ =>
make_plain_fun maybe_opt T1 T2
#> unarize_unbox_etc_term
#> format_fun (uniterize_unarize_unbox_etc_type T')
(uniterize_unarize_unbox_etc_type T1)
(uniterize_unarize_unbox_etc_type T2))
fun term_for_fun_or_set seen T T' j =
let
val k1 = card_of_type card_assigns (pseudo_domain_type T)
val k2 = card_of_type card_assigns (pseudo_range_type T)
in
term_for_rep true seen T T' (Vect (k1, Atom (k2, 0)))
[nth_combination (replicate k1 (k2, 0)) j]
handle General.Subscript =>
raise ARG ("Nitpick_Model.reconstruct_term.\
\term_for_fun_or_set",
signed_string_of_int j ^ " for " ^
string_for_rep (Vect (k1, Atom (k2, 0))))
end
and term_for_atom seen (T as Type (@{type_name fun}, _)) T' j _ =
term_for_fun_or_set seen T T' j
| term_for_atom seen (T as Type (@{type_name set}, _)) T' j _ =
term_for_fun_or_set seen T T' j
| term_for_atom seen (Type (@{type_name prod}, [T1, T2])) _ j k =
let
val k1 = card_of_type card_assigns T1
val k2 = k div k1
in
list_comb (HOLogic.pair_const T1 T2,
map3 (fn T => term_for_atom seen T T) [T1, T2]
(* ### k2 or k1? FIXME *)
[j div k2, j mod k2] [k1, k2])
end
| term_for_atom seen @{typ prop} _ j k =
HOLogic.mk_Trueprop (term_for_atom seen bool_T bool_T j k)
| term_for_atom _ @{typ bool} _ j _ =
if j = 0 then @{const False} else @{const True}
| term_for_atom seen T _ j k =
if T = nat_T andalso is_standard_datatype thy stds nat_T then
HOLogic.mk_number nat_T j
else if T = int_T then
HOLogic.mk_number int_T (int_for_atom (k, 0) j)
else if is_fp_iterator_type T then
HOLogic.mk_number nat_T (k - j - 1)
else if T = @{typ bisim_iterator} then
HOLogic.mk_number nat_T j
else case datatype_spec datatypes T of
NONE => nth_atom thy atomss pool for_auto T j
| SOME {deep = false, ...} => nth_atom thy atomss pool for_auto T j
| SOME {co, standard, constrs, ...} =>
let
fun tuples_for_const (s, T) =
tuple_list_for_name rel_table bounds (ConstName (s, T, Any))
fun cyclic_atom () =
nth_atom thy atomss pool for_auto (Type (cyclic_type_name (), []))
j
fun cyclic_var () =
Var ((nth_atom_name thy atomss pool "" T j, 0), T)
val discr_jsss = map (tuples_for_const o discr_for_constr o #const)
constrs
val real_j = j + offset_of_type ofs T
val constr_x as (constr_s, constr_T) =
get_first (fn (jss, {const, ...}) =>
if member (op =) jss [real_j] then SOME const
else NONE)
(discr_jsss ~~ constrs) |> the
val arg_Ts = curried_binder_types constr_T
val sel_xs =
map (binarized_and_boxed_nth_sel_for_constr hol_ctxt binarize
constr_x)
(index_seq 0 (length arg_Ts))
val sel_Rs =
map (fn x => get_first
(fn ConstName (s', T', R) =>
if (s', T') = x then SOME R else NONE
| u => raise NUT ("Nitpick_Model.reconstruct_\
\term.term_for_atom", [u]))
sel_names |> the) sel_xs
val arg_Rs = map (snd o dest_Func) sel_Rs
val sel_jsss = map tuples_for_const sel_xs
val arg_jsss =
map (map_filter (fn js => if hd js = real_j then SOME (tl js)
else NONE)) sel_jsss
val uncur_arg_Ts = binder_types constr_T
val maybe_cyclic = co orelse not standard
in
if maybe_cyclic andalso not (null seen) andalso
member (op =) (seen |> unfold ? (fst o split_last)) (T, j) then
cyclic_var ()
else if constr_s = @{const_name Word} then
HOLogic.mk_number
(if T = @{typ "unsigned_bit word"} then nat_T else int_T)
(value_of_bits (the_single arg_jsss))
else
let
val seen = seen |> maybe_cyclic ? cons (T, j)
val ts =
if length arg_Ts = 0 then
[]
else
map3 (fn Ts => term_for_rep true seen Ts Ts) arg_Ts arg_Rs
arg_jsss
|> mk_tuple (HOLogic.mk_tupleT uncur_arg_Ts)
|> dest_n_tuple (length uncur_arg_Ts)
val t =
if constr_s = @{const_name Abs_Frac} then
case ts of
[Const (@{const_name Pair}, _) $ t1 $ t2] =>
frac_from_term_pair (body_type T) t1 t2
| _ => raise TERM ("Nitpick_Model.reconstruct_term.\
\term_for_atom (Abs_Frac)", ts)
else if not for_auto andalso
(is_abs_fun ctxt constr_x orelse
constr_s = @{const_name Quot}) then
Const (abs_name, constr_T) $ the_single ts
else
list_comb (Const constr_x, ts)
in
if maybe_cyclic then
let val var = cyclic_var () in
if unfold andalso not standard andalso
length seen = 1 andalso
exists_subterm
(fn Const (s, _) =>
String.isPrefix (cyclic_const_prefix ()) s
| t' => t' = var) t then
subst_atomic [(var, cyclic_atom ())] t
else if exists_subterm (curry (op =) var) t then
if co then
Const (@{const_name The}, (T --> bool_T) --> T)
$ Abs (cyclic_co_val_name (), T,
Const (@{const_name HOL.eq}, T --> T --> bool_T)
$ Bound 0 $ abstract_over (var, t))
else
cyclic_atom ()
else
t
end
else
t
end
end
and term_for_vect seen k R T T' js =
let
val T1 = pseudo_domain_type T
val T2 = pseudo_range_type T
in
make_fun_or_set true T T1 T2 T'
(map (fn j => term_for_atom seen T1 T1 j k) (index_seq 0 k))
(map (term_for_rep true seen T2 T2 R o single)
(batch_list (arity_of_rep R) js))
end
and term_for_rep _ seen T T' (R as Atom (k, j0)) [[j]] =
if j >= j0 andalso j < j0 + k then term_for_atom seen T T' (j - j0) k
else raise REP ("Nitpick_Model.reconstruct_term.term_for_rep", [R])
| term_for_rep _ seen (Type (@{type_name prod}, [T1, T2])) _
(Struct [R1, R2]) [js] =
let
val arity1 = arity_of_rep R1
val (js1, js2) = chop arity1 js
in
list_comb (HOLogic.pair_const T1 T2,
map3 (fn T => term_for_rep true seen T T) [T1, T2] [R1, R2]
[[js1], [js2]])
end
| term_for_rep _ seen T T' (Vect (k, R')) [js] =
term_for_vect seen k R' T T' js
| term_for_rep maybe_opt seen T T' (Func (R1, Formula Neut)) jss =
let
val T1 = pseudo_domain_type T
val T2 = pseudo_range_type T
val jss1 = all_combinations_for_rep R1
val ts1 = map (term_for_rep true seen T1 T1 R1 o single) jss1
val ts2 =
map (fn js => term_for_rep true seen T2 T2 (Atom (2, 0))
[[int_from_bool (member (op =) jss js)]])
jss1
in make_fun_or_set maybe_opt T T1 T2 T' ts1 ts2 end
| term_for_rep maybe_opt seen T T' (Func (R1, R2)) jss =
let
val T1 = pseudo_domain_type T
val T2 = pseudo_range_type T
val arity1 = arity_of_rep R1
val jss1 = all_combinations_for_rep R1
val ts1 = map (term_for_rep false seen T1 T1 R1 o single) jss1
val grouped_jss2 = AList.group (op =) (map (chop arity1) jss)
val ts2 = map (term_for_rep false seen T2 T2 R2 o the_default []
o AList.lookup (op =) grouped_jss2) jss1
in make_fun_or_set maybe_opt T T1 T2 T' ts1 ts2 end
| term_for_rep _ seen T T' (Opt R) jss =
if null jss then Const (unknown, T)
else term_for_rep true seen T T' R jss
| term_for_rep _ _ T _ R jss =
raise ARG ("Nitpick_Model.reconstruct_term.term_for_rep",
Syntax.string_of_typ ctxt T ^ " " ^ string_for_rep R ^ " " ^
string_of_int (length jss))
in
postprocess_subterms [] o polish_funs [] o unarize_unbox_etc_term
oooo term_for_rep maybe_opt []
end
(** Constant postprocessing **)
fun dest_n_tuple_type 1 T = [T]
| dest_n_tuple_type n (Type (_, [T1, T2])) =
T1 :: dest_n_tuple_type (n - 1) T2
| dest_n_tuple_type _ T =
raise TYPE ("Nitpick_Model.dest_n_tuple_type", [T], [])
fun const_format thy def_tables (x as (s, T)) =
if String.isPrefix unrolled_prefix s then
const_format thy def_tables (original_name s, range_type T)
else if String.isPrefix skolem_prefix s then
let
val k = unprefix skolem_prefix s
|> strip_first_name_sep |> fst |> space_explode "@"
|> hd |> Int.fromString |> the
in [k, num_binder_types T - k] end
else if original_name s <> s then
[num_binder_types T]
else case def_of_const thy def_tables x of
SOME t' => if fixpoint_kind_of_rhs t' <> NoFp then
let val k = length (strip_abs_vars t') in
[k, num_binder_types T - k]
end
else
[num_binder_types T]
| NONE => [num_binder_types T]
fun intersect_formats _ [] = []
| intersect_formats [] _ = []
| intersect_formats ks1 ks2 =
let val ((ks1', k1), (ks2', k2)) = pairself split_last (ks1, ks2) in
intersect_formats (ks1' @ (if k1 > k2 then [k1 - k2] else []))
(ks2' @ (if k2 > k1 then [k2 - k1] else [])) @
[Int.min (k1, k2)]
end
fun lookup_format thy def_tables formats t =
case AList.lookup (fn (SOME x, SOME y) =>
(term_match thy) (x, y) | _ => false)
formats (SOME t) of
SOME format => format
| NONE => let val format = the (AList.lookup (op =) formats NONE) in
case t of
Const x => intersect_formats format
(const_format thy def_tables x)
| _ => format
end
fun format_type default_format format T =
let
val T = uniterize_unarize_unbox_etc_type T
val format = format |> filter (curry (op <) 0)
in
if forall (curry (op =) 1) format then
T
else
let
val (binder_Ts, body_T) = strip_type T
val batched =
binder_Ts
|> map (format_type default_format default_format)
|> rev |> chunk_list_unevenly (rev format)
|> map (HOLogic.mk_tupleT o rev)
in List.foldl (op -->) body_T batched end
end
fun format_term_type thy def_tables formats t =
format_type (the (AList.lookup (op =) formats NONE))
(lookup_format thy def_tables formats t) (fastype_of t)
fun repair_special_format js m format =
m - 1 downto 0 |> chunk_list_unevenly (rev format)
|> map (rev o filter_out (member (op =) js))
|> filter_out null |> map length |> rev
fun user_friendly_const ({thy, evals, def_tables, skolems, special_funs, ...}
: hol_context) (base_name, step_name) formats =
let
val default_format = the (AList.lookup (op =) formats NONE)
fun do_const (x as (s, T)) =
(if String.isPrefix special_prefix s then
let
val do_term = map_aterms (fn Const x => fst (do_const x) | t' => t')
val (x' as (_, T'), js, ts) =
AList.find (op =) (!special_funs) (s, unarize_unbox_etc_type T)
|> the_single
val max_j = List.last js
val Ts = List.take (binder_types T', max_j + 1)
val missing_js = filter_out (member (op =) js) (0 upto max_j)
val missing_Ts = filter_indices missing_js Ts
fun nth_missing_var n =
((arg_var_prefix ^ nat_subscript (n + 1), 0), nth missing_Ts n)
val missing_vars = map nth_missing_var (0 upto length missing_js - 1)
val vars = special_bounds ts @ missing_vars
val ts' =
map (fn j =>
case AList.lookup (op =) (js ~~ ts) j of
SOME t => do_term t
| NONE =>
Var (nth missing_vars
(find_index (curry (op =) j) missing_js)))
(0 upto max_j)
val t = do_const x' |> fst
val format =
case AList.lookup (fn (SOME t1, SOME t2) => term_match thy (t1, t2)
| _ => false) formats (SOME t) of
SOME format =>
repair_special_format js (num_binder_types T') format
| NONE =>
const_format thy def_tables x'
|> repair_special_format js (num_binder_types T')
|> intersect_formats default_format
in
(list_comb (t, ts') |> fold_rev abs_var vars,
format_type default_format format T)
end
else if String.isPrefix uncurry_prefix s then
let
val (ss, s') = unprefix uncurry_prefix s
|> strip_first_name_sep |>> space_explode "@"
in
if String.isPrefix step_prefix s' then
do_const (s', T)
else
let
val k = the (Int.fromString (hd ss))
val j = the (Int.fromString (List.last ss))
val (before_Ts, (tuple_T, rest_T)) =
strip_n_binders j T ||> (strip_n_binders 1 #>> hd)
val T' = before_Ts ---> dest_n_tuple_type k tuple_T ---> rest_T
in do_const (s', T') end
end
else if String.isPrefix unrolled_prefix s then
let val t = Const (original_name s, range_type T) in
(lambda (Free (iter_var_prefix, nat_T)) t,
format_type default_format
(lookup_format thy def_tables formats t) T)
end
else if String.isPrefix base_prefix s then
(Const (base_name, T --> T) $ Const (unprefix base_prefix s, T),
format_type default_format default_format T)
else if String.isPrefix step_prefix s then
(Const (step_name, T --> T) $ Const (unprefix step_prefix s, T),
format_type default_format default_format T)
else if String.isPrefix quot_normal_prefix s then
let val t = Const (nitpick_prefix ^ "quotient normal form", T) in
(t, format_term_type thy def_tables formats t)
end
else if String.isPrefix skolem_prefix s then
let
val ss = the (AList.lookup (op =) (!skolems) s)
val (Ts, Ts') = chop (length ss) (binder_types T)
val frees = map Free (ss ~~ Ts)
val s' = original_name s
in
(fold lambda frees (Const (s', Ts' ---> T)),
format_type default_format
(lookup_format thy def_tables formats (Const x)) T)
end
else if String.isPrefix eval_prefix s then
let
val t = nth evals (the (Int.fromString (unprefix eval_prefix s)))
in (t, format_term_type thy def_tables formats t) end
else
(* The selector case can occur in conjunction with fractional types.
It's not pretty. *)
let val t = Const (s |> not (is_sel s) ? original_name, T) in
(t, format_term_type thy def_tables formats t)
end)
|>> map_types uniterize_unarize_unbox_etc_type
|>> shorten_names_in_term |>> Term.map_abs_vars shortest_name
in do_const end
fun assign_operator_for_const (s, T) =
if String.isPrefix ubfp_prefix s then
xsym "\<le>" "<=" ()
else if String.isPrefix lbfp_prefix s then
xsym "\<ge>" ">=" ()
else if original_name s <> s then
assign_operator_for_const (strip_first_name_sep s |> snd, T)
else
"="
(** Model reconstruction **)
fun unfold_outer_the_binders (t as Const (@{const_name The}, _)
$ Abs (s, T, Const (@{const_name HOL.eq}, _)
$ Bound 0 $ t')) =
betapply (Abs (s, T, t'), t) |> unfold_outer_the_binders
| unfold_outer_the_binders t = t
fun bisimilar_values _ 0 _ = true
| bisimilar_values coTs max_depth (t1, t2) =
let val T = fastype_of t1 in
if exists_subtype (member (op =) coTs) T then
let
val ((head1, args1), (head2, args2)) =
pairself (strip_comb o unfold_outer_the_binders) (t1, t2)
val max_depth = max_depth - (if member (op =) coTs T then 1 else 0)
in
head1 = head2 andalso
forall (bisimilar_values coTs max_depth) (args1 ~~ args2)
end
else
t1 = t2
end
fun reconstruct_hol_model {show_datatypes, show_skolems, show_consts}
({hol_ctxt = {thy, ctxt, max_bisim_depth, boxes, stds, wfs, user_axioms,
debug, whacks, binary_ints, destroy_constrs, specialize,
star_linear_preds, total_consts, needs, tac_timeout,
evals, case_names, def_tables, nondef_table, nondefs,
simp_table, psimp_table, choice_spec_table, intro_table,
ground_thm_table, ersatz_table, skolems, special_funs,
unrolled_preds, wf_cache, constr_cache}, binarize,
card_assigns, bits, bisim_depth, datatypes, ofs} : scope)
formats atomss real_frees pseudo_frees free_names sel_names nonsel_names
rel_table bounds =
let
val pool = Unsynchronized.ref []
val (wacky_names as (_, base_step_names), ctxt) =
add_wacky_syntax ctxt
val hol_ctxt =
{thy = thy, ctxt = ctxt, max_bisim_depth = max_bisim_depth, boxes = boxes,
stds = stds, wfs = wfs, user_axioms = user_axioms, debug = debug,
whacks = whacks, binary_ints = binary_ints,
destroy_constrs = destroy_constrs, specialize = specialize,
star_linear_preds = star_linear_preds, total_consts = total_consts,
needs = needs, tac_timeout = tac_timeout, evals = evals,
case_names = case_names, def_tables = def_tables,
nondef_table = nondef_table, nondefs = nondefs, simp_table = simp_table,
psimp_table = psimp_table, choice_spec_table = choice_spec_table,
intro_table = intro_table, ground_thm_table = ground_thm_table,
ersatz_table = ersatz_table, skolems = skolems,
special_funs = special_funs, unrolled_preds = unrolled_preds,
wf_cache = wf_cache, constr_cache = constr_cache}
val scope =
{hol_ctxt = hol_ctxt, binarize = binarize, card_assigns = card_assigns,
bits = bits, bisim_depth = bisim_depth, datatypes = datatypes, ofs = ofs}
fun term_for_rep maybe_opt unfold =
reconstruct_term maybe_opt unfold pool wacky_names scope atomss
sel_names rel_table bounds
val all_values =
all_values_of_type pool wacky_names scope atomss sel_names rel_table
bounds
fun is_codatatype_wellformed (cos : datatype_spec list)
({typ, card, ...} : datatype_spec) =
let
val ts = all_values card typ
val max_depth = Integer.sum (map #card cos)
in
forall (not o bisimilar_values (map #typ cos) max_depth)
(all_distinct_unordered_pairs_of ts)
end
fun pretty_for_assign name =
let
val (oper, (t1, T'), T) =
case name of
FreeName (s, T, _) =>
let val t = Free (s, uniterize_unarize_unbox_etc_type T) in
("=", (t, format_term_type thy def_tables formats t), T)
end
| ConstName (s, T, _) =>
(assign_operator_for_const (s, T),
user_friendly_const hol_ctxt base_step_names formats (s, T), T)
| _ => raise NUT ("Nitpick_Model.reconstruct_hol_model.\
\pretty_for_assign", [name])
val t2 = if rep_of name = Any then
Const (@{const_name undefined}, T')
else
tuple_list_for_name rel_table bounds name
|> term_for_rep (not (is_fully_representable_set name)) false
T T' (rep_of name)
in
Pretty.block (Pretty.breaks
[Syntax.pretty_term (set_show_all_types ctxt) t1,
Pretty.str oper, Syntax.pretty_term ctxt t2])
end
fun pretty_for_datatype ({typ, card, complete, ...} : datatype_spec) =
Pretty.block (Pretty.breaks
(pretty_for_type ctxt typ ::
(case typ of
Type (@{type_name fun_box}, _) => [Pretty.str "[boxed]"]
| Type (@{type_name pair_box}, _) => [Pretty.str "[boxed]"]
| _ => []) @
[Pretty.str "=",
Pretty.enum "," "{" "}"
(map (Syntax.pretty_term ctxt) (all_values card typ) @
(if fun_from_pair complete false then []
else [Pretty.str (unrep ())]))]))
fun integer_datatype T =
[{typ = T, card = card_of_type card_assigns T, co = false,
standard = true, self_rec = true, complete = (false, false),
concrete = (true, true), deep = true, constrs = []}]
handle TYPE ("Nitpick_HOL.card_of_type", _, _) => []
val (codatatypes, datatypes) =
datatypes |> filter #deep |> List.partition #co
||> append (integer_datatype int_T
|> is_standard_datatype thy stds nat_T
? append (integer_datatype nat_T))
val block_of_datatypes =
if show_datatypes andalso not (null datatypes) then
[Pretty.big_list ("Datatype" ^ plural_s_for_list datatypes ^ ":")
(map pretty_for_datatype datatypes)]
else
[]
val block_of_codatatypes =
if show_datatypes andalso not (null codatatypes) then
[Pretty.big_list ("Codatatype" ^ plural_s_for_list codatatypes ^ ":")
(map pretty_for_datatype codatatypes)]
else
[]
fun block_of_names show title names =
if show andalso not (null names) then
Pretty.str (title ^ plural_s_for_list names ^ ":")
:: map (Pretty.indent indent_size o pretty_for_assign)
(sort_wrt (original_name o nickname_of) names)
else
[]
fun free_name_for_term keep_all (x as (s, T)) =
case filter (curry (op =) x
o pairf nickname_of (uniterize_unarize_unbox_etc_type
o type_of)) free_names of
[name] => SOME name
| [] => if keep_all then SOME (FreeName (s, T, Any)) else NONE
| _ => raise TERM ("Nitpick_Model.reconstruct_hol_model.\
\free_name_for_term", [Const x])
val (skolem_names, nonskolem_nonsel_names) =
List.partition is_skolem_name nonsel_names
val (eval_names, noneval_nonskolem_nonsel_names) =
List.partition (String.isPrefix eval_prefix o nickname_of)
nonskolem_nonsel_names
||> filter_out (member (op =) [@{const_name bisim},
@{const_name bisim_iterator_max}]
o nickname_of)
||> append (map_filter (free_name_for_term false) pseudo_frees)
val real_free_names = map_filter (free_name_for_term true) real_frees
val chunks = block_of_names true "Free variable" real_free_names @
block_of_names show_skolems "Skolem constant" skolem_names @
block_of_names true "Evaluated term" eval_names @
block_of_datatypes @ block_of_codatatypes @
block_of_names show_consts "Constant"
noneval_nonskolem_nonsel_names
in
(Pretty.chunks (if null chunks then [Pretty.str "Empty assignment"]
else chunks),
bisim_depth >= 0 orelse
forall (is_codatatype_wellformed codatatypes) codatatypes)
end
fun term_for_name pool scope atomss sel_names rel_table bounds name =
let val T = type_of name in
tuple_list_for_name rel_table bounds name
|> reconstruct_term (not (is_fully_representable_set name)) false pool
(("", ""), ("", "")) scope atomss sel_names rel_table
bounds T T (rep_of name)
end
fun prove_hol_model (scope as {hol_ctxt = {thy, ctxt, debug, ...},
card_assigns, ...})
auto_timeout free_names sel_names rel_table bounds prop =
let
val pool = Unsynchronized.ref []
val atomss = [(NONE, [])]
fun free_type_assm (T, k) =
let
fun atom j = nth_atom thy atomss pool true T j
fun equation_for_atom j = HOLogic.eq_const T $ Bound 0 $ atom j
val eqs = map equation_for_atom (index_seq 0 k)
val compreh_assm =
Const (@{const_name All}, (T --> bool_T) --> bool_T)
$ Abs ("x", T, foldl1 HOLogic.mk_disj eqs)
val distinct_assm = distinctness_formula T (map atom (index_seq 0 k))
in s_conj (compreh_assm, distinct_assm) end
fun free_name_assm name =
HOLogic.mk_eq (Free (nickname_of name, type_of name),
term_for_name pool scope atomss sel_names rel_table bounds
name)
val freeT_assms = map free_type_assm (filter (is_TFree o fst) card_assigns)
val model_assms = map free_name_assm free_names
val assm = foldr1 s_conj (freeT_assms @ model_assms)
fun try_out negate =
let
val concl = (negate ? curry (op $) @{const Not})
(Object_Logic.atomize_term thy prop)
val prop = HOLogic.mk_Trueprop (HOLogic.mk_imp (assm, concl))
|> map_types (map_type_tfree
(fn (s, []) => TFree (s, HOLogic.typeS)
| x => TFree x))
val _ =
if debug then
(if negate then "Genuineness" else "Spuriousness") ^ " goal: " ^
Syntax.string_of_term ctxt prop ^ "."
|> Output.urgent_message
else
()
val goal = prop |> cterm_of thy |> Goal.init
in
(goal |> SINGLE (DETERM_TIMEOUT auto_timeout (auto_tac ctxt))
|> the |> Goal.finish ctxt; true)
handle THM _ => false
| TimeLimit.TimeOut => false
end
in
if try_out false then SOME true
else if try_out true then SOME false
else NONE
end
end;