polished Nitpick's binary integer support etc.;
etc. = improve inconsistent scope correction + sort values nicely in output
+ handle "mod" using the characterization "x mod y = x - x div y * y"
(instead of explicit code in Nitpick)
+ introduce KK = Kodkod as abbreviation
(* Title: HOL/Tools/Nitpick/nitpick_model.ML
Author: Jasmin Blanchette, TU Muenchen
Copyright 2009
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_skolems: bool,
show_datatypes: bool,
show_consts: bool}
structure NameTable : TABLE
val tuple_list_for_name :
nut NameTable.table -> Kodkod.raw_bound list -> nut -> int list list
val reconstruct_hol_model :
params -> scope -> (term option * int list) 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_skolems: bool,
show_datatypes: bool,
show_consts: bool}
val unknown = "?"
val unrep = "\<dots>"
val maybe_mixfix = "_\<^sup>?"
val base_mixfix = "_\<^bsub>base\<^esub>"
val step_mixfix = "_\<^bsub>step\<^esub>"
val abs_mixfix = "\<guillemotleft>_\<guillemotright>"
val non_opt_name = nitpick_prefix ^ "non_opt"
(* string -> int -> string *)
fun atom_suffix s j =
nat_subscript (j + 1)
|> (s <> "" andalso Symbol.is_ascii_digit (List.last (explode s)))
? prefix "\<^isub>,"
(* string -> typ -> int -> string *)
fun atom_name prefix (T as Type (s, _)) j =
prefix ^ substring (shortest_name s, 0, 1) ^ atom_suffix s j
| atom_name prefix (T as TFree (s, _)) j =
prefix ^ perhaps (try (unprefix "'")) s ^ atom_suffix s j
| atom_name _ T _ = raise TYPE ("Nitpick_Model.atom_name", [T], [])
(* bool -> typ -> int -> term *)
fun atom for_auto T j =
if for_auto then
Free (atom_name (hd (space_explode "." nitpick_prefix)) T j, T)
else
Const (atom_name "" T j, T)
(* term -> real *)
fun extract_real_number (Const (@{const_name HOL.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))
(* term * term -> order *)
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)
| _ => TermOrd.fast_term_ord tp
(* nut NameTable.table -> KK.raw_bound list -> nut -> int list list *)
fun tuple_list_for_name rel_table bounds name =
the (AList.lookup (op =) bounds (the_rel rel_table name)) handle NUT _ => [[]]
(* term -> term *)
fun unbit_and_unbox_term (Const (@{const_name FunBox}, _) $ t1) =
unbit_and_unbox_term t1
| unbit_and_unbox_term (Const (@{const_name PairBox},
Type ("fun", [T1, Type ("fun", [T2, T3])]))
$ t1 $ t2) =
let val Ts = map unbit_and_unbox_type [T1, T2] in
Const (@{const_name Pair}, Ts ---> Type ("*", Ts))
$ unbit_and_unbox_term t1 $ unbit_and_unbox_term t2
end
| unbit_and_unbox_term (Const (s, T)) = Const (s, unbit_and_unbox_type T)
| unbit_and_unbox_term (t1 $ t2) =
unbit_and_unbox_term t1 $ unbit_and_unbox_term t2
| unbit_and_unbox_term (Free (s, T)) = Free (s, unbit_and_unbox_type T)
| unbit_and_unbox_term (Var (x, T)) = Var (x, unbit_and_unbox_type T)
| unbit_and_unbox_term (Bound j) = Bound j
| unbit_and_unbox_term (Abs (s, T, t')) =
Abs (s, unbit_and_unbox_type T, unbit_and_unbox_term t')
(* typ -> typ -> (typ * typ) * (typ * typ) *)
fun factor_out_types (T1 as Type ("*", [T11, T12]))
(T2 as Type ("*", [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 ("*", [T11, T11']), opt_T12'),
(Type ("*", [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 ("*", [T22', T22]))))
else
swap (factor_out_types T2 T1)
end
| factor_out_types (Type ("*", [T11, T12])) T2 = ((T11, SOME T12), (T2, NONE))
| factor_out_types T1 (Type ("*", [T21, T22])) = ((T1, NONE), (T21, SOME T22))
| factor_out_types T1 T2 = ((T1, NONE), (T2, NONE))
(* bool -> typ -> typ -> (term * term) list -> term *)
fun make_plain_fun maybe_opt T1 T2 =
let
(* typ -> typ -> (term * term) list -> term *)
fun aux T1 T2 [] =
Const (if maybe_opt orelse T2 <> bool_T then @{const_name undefined}
else non_opt_name, T1 --> T2)
| aux T1 T2 ((t1, t2) :: ps) =
Const (@{const_name fun_upd}, (T1 --> T2) --> T1 --> T2 --> T1 --> T2)
$ aux T1 T2 ps $ t1 $ t2
in aux T1 T2 o rev end
(* term -> bool *)
fun is_plain_fun (Const (s, _)) =
(s = @{const_name undefined} orelse s = non_opt_name)
| is_plain_fun (Const (@{const_name fun_upd}, _) $ t0 $ _ $ _) =
is_plain_fun t0
| is_plain_fun _ = false
(* term -> bool * (term list * term list) *)
val dest_plain_fun =
let
(* term -> term list * term list *)
fun aux (Const (s, _)) = (s <> non_opt_name, ([], []))
| aux (Const (@{const_name fun_upd}, _) $ t0 $ t1 $ t2) =
let val (s, (ts1, ts2)) = aux t0 in (s, (t1 :: ts1, t2 :: ts2)) end
| aux t = raise TERM ("Nitpick_Model.dest_plain_fun", [t])
in apsnd (pairself rev) o aux end
(* typ -> typ -> typ -> term -> term * term *)
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
(* typ -> term -> term -> term *)
fun pair_up (Type ("*", [T1', T2']))
(t1 as Const (@{const_name Pair},
Type ("fun", [_, Type ("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)
(* typ -> term -> term list * term list -> (term * term) list*)
fun multi_pair_up T1 t1 (ts2, ts3) = map2 (pair o pair_up T1 t1) ts2 ts3
(* typ -> typ -> typ -> term -> term *)
fun typecast_fun (Type ("fun", [T1', T2'])) T1 T2 t =
let
(* typ -> typ -> typ -> typ -> term -> term *)
fun do_curry T1 T1a T1b T2 t =
let
val (maybe_opt, ps) = dest_plain_fun t
val ps =
ps |>> 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) ps end
(* typ -> typ -> term -> term *)
and do_uncurry T1 T2 t =
let
val (maybe_opt, tsp) = dest_plain_fun t
val ps =
tsp |> op ~~
|> maps (fn (t1, t2) =>
multi_pair_up T1 t1 (snd (dest_plain_fun t2)))
in make_plain_fun maybe_opt T1 T2 ps end
(* typ -> typ -> typ -> typ -> term -> term *)
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.typecast_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.typecast_fun.do_fun", [T1, T1'], [])
(* typ -> typ -> term -> term *)
and do_term (Type ("fun", [T1', T2'])) (Type ("fun", [T1, T2])) t =
do_fun T1' T2' T1 T2 t
| do_term (T' as Type ("*", Ts' as [T1', T2'])) (Type ("*", [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.typecast_fun.do_term", [T, T'], [])
in if T1' = T1 andalso T2' = T2 then t else do_fun T1' T2' T1 T2 t end
| typecast_fun T' _ _ _ = raise TYPE ("Nitpick_Model.typecast_fun", [T'], [])
(* term -> string *)
fun truth_const_sort_key @{const True} = "0"
| truth_const_sort_key @{const False} = "2"
| truth_const_sort_key _ = "1"
(* typ -> term list -> term *)
fun mk_tuple (Type ("*", [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], [])
(* string * string * string * string -> scope -> nut list -> nut list
-> nut list -> nut NameTable.table -> KK.raw_bound list -> typ -> typ -> rep
-> int list list -> term *)
fun reconstruct_term (maybe_name, base_name, step_name, abs_name)
({ext_ctxt as {thy, ctxt, ...}, card_assigns, bits, datatypes, ofs, ...}
: scope) sel_names rel_table bounds =
let
val for_auto = (maybe_name = "")
(* int list list -> int *)
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
(* bool -> typ -> typ -> (term * term) list -> term *)
fun make_set maybe_opt T1 T2 =
let
val empty_const = Const (@{const_name Set.empty}, T1 --> T2)
val insert_const = Const (@{const_name insert},
T1 --> (T1 --> T2) --> T1 --> T2)
(* (term * term) list -> term *)
fun aux [] =
if maybe_opt andalso not (is_complete_type datatypes T1) then
insert_const $ Const (unrep, T1) $ 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,
T1 --> T1))))
in aux end
(* typ -> typ -> typ -> (term * term) list -> term *)
fun make_map T1 T2 T2' =
let
val update_const = Const (@{const_name fun_upd},
(T1 --> T2) --> T1 --> T2 --> T1 --> T2)
(* (term * term) list -> term *)
fun aux' [] = Const (@{const_name Map.empty}, T1 --> T2)
| aux' ((t1, t2) :: ps) =
(case t2 of
Const (@{const_name None}, _) => aux' ps
| _ => update_const $ aux' ps $ t1 $ t2)
fun aux ps =
if not (is_complete_type datatypes T1) then
update_const $ aux' ps $ Const (unrep, T1)
$ (Const (@{const_name Some}, T2' --> T2) $ Const (unknown, T2'))
else
aux' ps
in aux end
(* typ list -> term -> term *)
fun setify_mapify_funs Ts t =
(case fastype_of1 (Ts, t) of
Type ("fun", [T1, T2]) =>
if is_plain_fun t then
case T2 of
@{typ bool} =>
let
val (maybe_opt, ts_pair) =
dest_plain_fun t ||> pairself (map (setify_mapify_funs Ts))
in
make_set maybe_opt T1 T2
(sort_wrt (truth_const_sort_key o snd) (op ~~ ts_pair))
end
| Type (@{type_name option}, [T2']) =>
let
val ts_pair = snd (dest_plain_fun t)
|> pairself (map (setify_mapify_funs Ts))
in make_map T1 T2 T2' (rev (op ~~ ts_pair)) end
| _ => raise SAME ()
else
raise SAME ()
| _ => raise SAME ())
handle SAME () =>
case t of
t1 $ t2 => setify_mapify_funs Ts t1 $ setify_mapify_funs Ts t2
| Abs (s, T, t') => Abs (s, T, setify_mapify_funs (T :: Ts) t')
| _ => t
(* bool -> typ -> typ -> typ -> term list -> term list -> term *)
fun make_fun maybe_opt T1 T2 T' ts1 ts2 =
ts1 ~~ ts2 |> sort (nice_term_ord o pairself fst)
|> make_plain_fun (maybe_opt andalso not for_auto) T1 T2
|> unbit_and_unbox_term
|> typecast_fun (unbit_and_unbox_type T')
(unbit_and_unbox_type T1)
(unbit_and_unbox_type T2)
(* (typ * int) list -> typ -> typ -> int -> term *)
fun term_for_atom seen (T as Type ("fun", [T1, T2])) T' j =
let
val k1 = card_of_type card_assigns T1
val k2 = card_of_type card_assigns T2
in
term_for_rep 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_atom",
signed_string_of_int j ^ " for " ^
string_for_rep (Vect (k1, Atom (k2, 0))))
end
| term_for_atom seen (Type ("*", [T1, T2])) _ j =
let val k1 = card_of_type card_assigns T1 in
list_comb (HOLogic.pair_const T1 T2,
map2 (fn T => term_for_atom seen T T) [T1, T2]
[j div k1, j mod k1])
end
| term_for_atom seen @{typ prop} _ j =
HOLogic.mk_Trueprop (term_for_atom seen bool_T bool_T j)
| term_for_atom _ @{typ bool} _ j =
if j = 0 then @{const False} else @{const True}
| term_for_atom _ @{typ unit} _ _ = @{const Unity}
| term_for_atom seen T _ j =
if T = nat_T then
HOLogic.mk_number nat_T j
else if T = int_T then
HOLogic.mk_number int_T
(int_for_atom (card_of_type card_assigns int_T, 0) j)
else if is_fp_iterator_type T then
HOLogic.mk_number nat_T (card_of_type card_assigns T - j - 1)
else if T = @{typ bisim_iterator} then
HOLogic.mk_number nat_T j
else case datatype_spec datatypes T of
NONE => atom for_auto T j
| SOME {shallow = true, ...} => atom for_auto T j
| SOME {co, constrs, ...} =>
let
(* styp -> int list *)
fun tuples_for_const (s, T) =
tuple_list_for_name rel_table bounds (ConstName (s, T, Any))
(* unit -> indexname * typ *)
fun var () = ((atom_name "" 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 (boxed_nth_sel_for_constr ext_ctxt 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
in
if co andalso member (op =) seen (T, j) then
Var (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 |> co ? cons (T, j)
val ts =
if length arg_Ts = 0 then
[]
else
map3 (fn Ts => term_for_rep 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
let
val num_T = body_type T
(* int -> term *)
val mk_num = HOLogic.mk_number num_T
in
case ts of
[Const (@{const_name Pair}, _) $ t1 $ t2] =>
(case snd (HOLogic.dest_number t1) of
0 => mk_num 0
| n1 => case HOLogic.dest_number t2 |> snd of
1 => mk_num n1
| n2 => Const (@{const_name HOL.divide},
num_T --> num_T --> num_T)
$ mk_num n1 $ mk_num n2)
| _ => raise TERM ("Nitpick_Model.reconstruct_term.term_\
\for_atom (Abs_Frac)", ts)
end
else if not for_auto andalso is_abs_fun thy constr_x then
Const (abs_name, constr_T) $ the_single ts
else
list_comb (Const constr_x, ts)
in
if co then
let val var = var () in
if exists_subterm (curry (op =) (Var var)) t then
Const (@{const_name The}, (T --> bool_T) --> T)
$ Abs ("\<omega>", T,
Const (@{const_name "op ="}, T --> T --> bool_T)
$ Bound 0 $ abstract_over (Var var, t))
else
t
end
else
t
end
end
(* (typ * int) list -> int -> rep -> typ -> typ -> typ -> int list
-> term *)
and term_for_vect seen k R T1 T2 T' js =
make_fun true T1 T2 T' (map (term_for_atom seen T1 T1) (index_seq 0 k))
(map (term_for_rep seen T2 T2 R o single)
(batch_list (arity_of_rep R) js))
(* (typ * int) list -> typ -> typ -> rep -> int list list -> term *)
and term_for_rep seen T T' Unit [[]] = term_for_atom seen T T' 0
| 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)
else raise REP ("Nitpick_Model.reconstruct_term.term_for_rep", [R])
| term_for_rep seen (Type ("*", [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 seen T T) [T1, T2] [R1, R2]
[[js1], [js2]])
end
| term_for_rep seen (Type ("fun", [T1, T2])) T' (R as Vect (k, R')) [js] =
term_for_vect seen k R' T1 T2 T' js
| term_for_rep seen (Type ("fun", [T1, T2])) T' (Func (R1, Formula Neut))
jss =
let
val jss1 = all_combinations_for_rep R1
val ts1 = map (term_for_rep seen T1 T1 R1 o single) jss1
val ts2 =
map (fn js => term_for_rep seen T2 T2 (Atom (2, 0))
[[int_for_bool (member (op =) jss js)]])
jss1
in make_fun false T1 T2 T' ts1 ts2 end
| term_for_rep seen (Type ("fun", [T1, T2])) T' (Func (R1, R2)) jss =
let
val arity1 = arity_of_rep R1
val jss1 = all_combinations_for_rep R1
val ts1 = map (term_for_rep seen T1 T1 R1 o single) jss1
val grouped_jss2 = AList.group (op =) (map (chop arity1) jss)
val ts2 = map (term_for_rep seen T2 T2 R2 o the_default []
o AList.lookup (op =) grouped_jss2) jss1
in make_fun true 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 seen T T' R jss
| term_for_rep seen T _ R jss =
raise ARG ("Nitpick_Model.reconstruct_term.term_for_rep",
Refute.string_of_typ T ^ " " ^ string_for_rep R ^ " " ^
string_of_int (length jss))
in
(not for_auto ? setify_mapify_funs []) o unbit_and_unbox_term
oooo term_for_rep []
end
(* scope -> nut list -> nut NameTable.table -> KK.raw_bound list -> nut
-> term *)
fun term_for_name scope sel_names rel_table bounds name =
let val T = type_of name in
tuple_list_for_name rel_table bounds name
|> reconstruct_term ("", "", "", "") scope sel_names rel_table bounds T T
(rep_of name)
end
(* Proof.context
-> (string * string * string * string * string) * Proof.context *)
fun add_wacky_syntax ctxt =
let
(* term -> string *)
val name_of = fst o dest_Const
val thy = ProofContext.theory_of ctxt |> Context.reject_draft
val (maybe_t, thy) =
Sign.declare_const ((@{binding nitpick_maybe}, @{typ "'a => 'a"}),
Mixfix (maybe_mixfix, [1000], 1000)) thy
val (base_t, thy) =
Sign.declare_const ((@{binding nitpick_base}, @{typ "'a => 'a"}),
Mixfix (base_mixfix, [1000], 1000)) thy
val (step_t, thy) =
Sign.declare_const ((@{binding nitpick_step}, @{typ "'a => 'a"}),
Mixfix (step_mixfix, [1000], 1000)) thy
val (abs_t, thy) =
Sign.declare_const ((@{binding nitpick_abs}, @{typ "'a => 'b"}),
Mixfix (abs_mixfix, [40], 40)) thy
in
((name_of maybe_t, name_of base_t, name_of step_t, name_of abs_t),
ProofContext.transfer_syntax thy ctxt)
end
(* term -> term *)
fun unfold_outer_the_binders (t as Const (@{const_name The}, _)
$ Abs (s, T, Const (@{const_name "op ="}, _)
$ Bound 0 $ t')) =
betapply (Abs (s, T, t'), t) |> unfold_outer_the_binders
| unfold_outer_the_binders t = t
(* typ list -> int -> term * term -> bool *)
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
(* params -> scope -> (term option * int list) list -> styp list -> nut list
-> nut list -> nut list -> nut NameTable.table -> KK.raw_bound list
-> Pretty.T * bool *)
fun reconstruct_hol_model {show_skolems, show_datatypes, show_consts}
({ext_ctxt as {thy, ctxt, max_bisim_depth, boxes, wfs, user_axioms,
debug, binary_ints, destroy_constrs, specialize,
skolemize, star_linear_preds, uncurry, fast_descrs,
tac_timeout, evals, case_names, def_table, nondef_table,
user_nondefs, simp_table, psimp_table, intro_table,
ground_thm_table, ersatz_table, skolems, special_funs,
unrolled_preds, wf_cache, constr_cache},
card_assigns, bits, bisim_depth, datatypes, ofs} : scope)
formats all_frees free_names sel_names nonsel_names rel_table bounds =
let
val (wacky_names as (_, base_name, step_name, _), ctxt) =
add_wacky_syntax ctxt
val ext_ctxt =
{thy = thy, ctxt = ctxt, max_bisim_depth = max_bisim_depth, boxes = boxes,
wfs = wfs, user_axioms = user_axioms, debug = debug,
binary_ints = binary_ints, destroy_constrs = destroy_constrs,
specialize = specialize, skolemize = skolemize,
star_linear_preds = star_linear_preds, uncurry = uncurry,
fast_descrs = fast_descrs, tac_timeout = tac_timeout, evals = evals,
case_names = case_names, def_table = def_table,
nondef_table = nondef_table, user_nondefs = user_nondefs,
simp_table = simp_table, psimp_table = psimp_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 = {ext_ctxt = ext_ctxt, card_assigns = card_assigns,
bits = bits, bisim_depth = bisim_depth, datatypes = datatypes,
ofs = ofs}
(* typ -> typ -> rep -> int list list -> term *)
val term_for_rep = reconstruct_term wacky_names scope sel_names rel_table
bounds
(* nat -> typ -> nat -> typ *)
fun nth_value_of_type card T n = term_for_rep T T (Atom (card, 0)) [[n]]
(* nat -> typ -> typ list *)
fun all_values_of_type card T =
index_seq 0 card |> map (nth_value_of_type card T) |> sort nice_term_ord
(* dtype_spec list -> dtype_spec -> bool *)
fun is_codatatype_wellformed (cos : dtype_spec list)
({typ, card, ...} : dtype_spec) =
let
val ts = all_values_of_type 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
(* string -> Pretty.T *)
fun pretty_for_assign name =
let
val (oper, (t1, T'), T) =
case name of
FreeName (s, T, _) =>
let val t = Free (s, unbit_and_unbox_type T) in
("=", (t, format_term_type thy def_table formats t), T)
end
| ConstName (s, T, _) =>
(assign_operator_for_const (s, T),
user_friendly_const ext_ctxt (base_name, step_name) 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 T T' (rep_of name)
in
Pretty.block (Pretty.breaks
[setmp_show_all_types (Syntax.pretty_term ctxt) t1,
Pretty.str oper, Syntax.pretty_term ctxt t2])
end
(* dtype_spec -> Pretty.T *)
fun pretty_for_datatype ({typ, card, complete, ...} : dtype_spec) =
Pretty.block (Pretty.breaks
[Syntax.pretty_typ ctxt (unbit_and_unbox_type typ), Pretty.str "=",
Pretty.enum "," "{" "}"
(map (Syntax.pretty_term ctxt) (all_values_of_type card typ)
@ (if complete then [] else [Pretty.str unrep]))])
(* typ -> dtype_spec list *)
fun integer_datatype T =
[{typ = T, card = card_of_type card_assigns T, co = false,
complete = false, concrete = true, shallow = false, constrs = []}]
handle TYPE ("Nitpick_HOL.card_of_type", _, _) => []
val (codatatypes, datatypes) =
datatypes |> filter_out #shallow
|> List.partition #co
||> append (integer_datatype nat_T @ integer_datatype int_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
[]
(* bool -> string -> nut list -> Pretty.T list *)
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
[]
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 (curry (op =) @{const_name bisim_iterator_max}
o nickname_of)
val free_names =
map (fn x as (s, T) =>
case filter (curry (op =) x
o pairf nickname_of (unbit_and_unbox_type o type_of))
free_names of
[name] => name
| [] => FreeName (s, T, Any)
| _ => raise TERM ("Nitpick_Model.reconstruct_hol_model",
[Const x])) all_frees
val chunks = block_of_names true "Free variable" 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
(* scope -> Time.time option -> nut list -> nut list -> nut NameTable.table
-> KK.raw_bound list -> term -> bool option *)
fun prove_hol_model (scope as {ext_ctxt as {thy, ctxt, ...}, card_assigns, ...})
auto_timeout free_names sel_names rel_table bounds prop =
let
(* typ * int -> term *)
fun free_type_assm (T, k) =
let
(* int -> term *)
val atom = atom true T
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 HOLogic.mk_conj (compreh_assm, distinct_assm) end
(* nut -> term *)
fun free_name_assm name =
HOLogic.mk_eq (Free (nickname_of name, type_of name),
term_for_name scope 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 = List.foldr HOLogic.mk_conj @{const True}
(freeT_assms @ model_assms)
(* bool -> bool *)
fun try_out negate =
let
val concl = (negate ? curry (op $) @{const Not})
(ObjectLogic.atomize_term thy prop)
val goal = HOLogic.mk_Trueprop (HOLogic.mk_imp (assm, concl))
|> map_types (map_type_tfree
(fn (s, []) => TFree (s, HOLogic.typeS)
| x => TFree x))
|> cterm_of thy |> Goal.init
in
(goal |> SINGLE (DETERM_TIMEOUT auto_timeout
(auto_tac (clasimpset_of 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;