add more flexibility to the monotonicity calculus: instead of hardcoding F-arrows, also allow G-arrows, simulating applications of the Sub rule
(* Title: HOL/Tools/Nitpick/nitpick_mono.ML
Author: Jasmin Blanchette, TU Muenchen
Copyright 2009, 2010
Monotonicity inference for higher-order logic.
*)
signature NITPICK_MONO =
sig
type hol_context = Nitpick_HOL.hol_context
val trace : bool Unsynchronized.ref
val formulas_monotonic :
hol_context -> bool -> typ -> term list * term list -> bool
val finitize_funs :
hol_context -> bool -> (typ option * bool option) list -> typ
-> term list * term list -> term list * term list
end;
structure Nitpick_Mono : NITPICK_MONO =
struct
open Nitpick_Util
open Nitpick_HOL
structure PL = PropLogic
datatype sign = Plus | Minus
type var = int
datatype annotation = Gen | New | Fls | Tru
datatype annotation_atom = A of annotation | V of var
type assign_literal = var * (sign * annotation)
datatype mtyp =
MAlpha |
MFun of mtyp * annotation_atom * mtyp |
MPair of mtyp * mtyp |
MType of string * mtyp list |
MRec of string * typ list
datatype mterm =
MRaw of term * mtyp |
MAbs of string * typ * mtyp * annotation_atom * mterm |
MApp of mterm * mterm
type mdata =
{hol_ctxt: hol_context,
binarize: bool,
alpha_T: typ,
no_harmless: bool,
max_fresh: int Unsynchronized.ref,
datatype_mcache: ((string * typ list) * mtyp) list Unsynchronized.ref,
constr_mcache: (styp * mtyp) list Unsynchronized.ref}
exception UNSOLVABLE of unit
exception MTYPE of string * mtyp list * typ list
exception MTERM of string * mterm list
val trace = Unsynchronized.ref false
fun trace_msg msg = if !trace then tracing (msg ()) else ()
fun string_for_sign Plus = "+"
| string_for_sign Minus = "-"
fun negate_sign Plus = Minus
| negate_sign Minus = Plus
val string_for_var = signed_string_of_int
fun string_for_vars sep [] = "0\<^bsub>" ^ sep ^ "\<^esub>"
| string_for_vars sep xs = space_implode sep (map string_for_var xs)
fun subscript_string_for_vars sep xs =
if null xs then "" else "\<^bsub>" ^ string_for_vars sep xs ^ "\<^esub>"
fun string_for_annotation Gen = "G"
| string_for_annotation New = "N"
| string_for_annotation Fls = "F"
| string_for_annotation Tru = "T"
fun string_for_annotation_atom (A a) = string_for_annotation a
| string_for_annotation_atom (V x) = string_for_var x
fun string_for_assign_literal (x, (sn, a)) =
string_for_var x ^ (case sn of Plus => " = " | Minus => " \<noteq> ") ^
string_for_annotation a
val bool_M = MType (@{type_name bool}, [])
val dummy_M = MType (nitpick_prefix ^ "dummy", [])
fun is_MRec (MRec _) = true
| is_MRec _ = false
fun dest_MFun (MFun z) = z
| dest_MFun M = raise MTYPE ("Nitpick_Mono.dest_MFun", [M], [])
val no_prec = 100
fun precedence_of_mtype (MFun _) = 1
| precedence_of_mtype (MPair _) = 2
| precedence_of_mtype _ = no_prec
val string_for_mtype =
let
fun aux outer_prec M =
let
val prec = precedence_of_mtype M
val need_parens = (prec < outer_prec)
in
(if need_parens then "(" else "") ^
(if M = dummy_M then
"_"
else case M of
MAlpha => "\<alpha>"
| MFun (M1, aa, M2) =>
aux (prec + 1) M1 ^ " \<Rightarrow>\<^bsup>" ^
string_for_annotation_atom aa ^ "\<^esup> " ^ aux prec M2
| MPair (M1, M2) => aux (prec + 1) M1 ^ " \<times> " ^ aux prec M2
| MType (s, []) =>
if s = @{type_name prop} orelse s = @{type_name bool} then "o"
else s
| MType (s, Ms) => "(" ^ commas (map (aux 0) Ms) ^ ") " ^ s
| MRec (s, _) => "[" ^ s ^ "]") ^
(if need_parens then ")" else "")
end
in aux 0 end
fun flatten_mtype (MPair (M1, M2)) = maps flatten_mtype [M1, M2]
| flatten_mtype (MType (_, Ms)) = maps flatten_mtype Ms
| flatten_mtype M = [M]
fun precedence_of_mterm (MRaw _) = no_prec
| precedence_of_mterm (MAbs _) = 1
| precedence_of_mterm (MApp _) = 2
fun string_for_mterm ctxt =
let
fun mtype_annotation M = "\<^bsup>" ^ string_for_mtype M ^ "\<^esup>"
fun aux outer_prec m =
let
val prec = precedence_of_mterm m
val need_parens = (prec < outer_prec)
in
(if need_parens then "(" else "") ^
(case m of
MRaw (t, M) => Syntax.string_of_term ctxt t ^ mtype_annotation M
| MAbs (s, _, M, aa, m) =>
"\<lambda>" ^ s ^ mtype_annotation M ^ ".\<^bsup>" ^
string_for_annotation_atom aa ^ "\<^esup> " ^ aux prec m
| MApp (m1, m2) => aux prec m1 ^ " " ^ aux (prec + 1) m2) ^
(if need_parens then ")" else "")
end
in aux 0 end
fun mtype_of_mterm (MRaw (_, M)) = M
| mtype_of_mterm (MAbs (_, _, M, aa, m)) = MFun (M, aa, mtype_of_mterm m)
| mtype_of_mterm (MApp (m1, _)) =
case mtype_of_mterm m1 of
MFun (_, _, M12) => M12
| M1 => raise MTYPE ("Nitpick_Mono.mtype_of_mterm", [M1], [])
fun strip_mcomb (MApp (m1, m2)) = strip_mcomb m1 ||> (fn ms => append ms [m2])
| strip_mcomb m = (m, [])
fun initial_mdata hol_ctxt binarize no_harmless alpha_T =
({hol_ctxt = hol_ctxt, binarize = binarize, alpha_T = alpha_T,
no_harmless = no_harmless, max_fresh = Unsynchronized.ref 0,
datatype_mcache = Unsynchronized.ref [],
constr_mcache = Unsynchronized.ref []} : mdata)
fun could_exist_alpha_subtype alpha_T (T as Type (_, Ts)) =
T = alpha_T orelse (not (is_fp_iterator_type T) andalso
exists (could_exist_alpha_subtype alpha_T) Ts)
| could_exist_alpha_subtype alpha_T T = (T = alpha_T)
fun could_exist_alpha_sub_mtype _ (alpha_T as TFree _) T =
could_exist_alpha_subtype alpha_T T
| could_exist_alpha_sub_mtype ctxt alpha_T T =
(T = alpha_T orelse is_datatype ctxt [(NONE, true)] T)
fun exists_alpha_sub_mtype MAlpha = true
| exists_alpha_sub_mtype (MFun (M1, _, M2)) =
exists exists_alpha_sub_mtype [M1, M2]
| exists_alpha_sub_mtype (MPair (M1, M2)) =
exists exists_alpha_sub_mtype [M1, M2]
| exists_alpha_sub_mtype (MType (_, Ms)) = exists exists_alpha_sub_mtype Ms
| exists_alpha_sub_mtype (MRec _) = true
fun exists_alpha_sub_mtype_fresh MAlpha = true
| exists_alpha_sub_mtype_fresh (MFun (_, V _, _)) = true
| exists_alpha_sub_mtype_fresh (MFun (_, _, M2)) =
exists_alpha_sub_mtype_fresh M2
| exists_alpha_sub_mtype_fresh (MPair (M1, M2)) =
exists exists_alpha_sub_mtype_fresh [M1, M2]
| exists_alpha_sub_mtype_fresh (MType (_, Ms)) =
exists exists_alpha_sub_mtype_fresh Ms
| exists_alpha_sub_mtype_fresh (MRec _) = true
fun constr_mtype_for_binders z Ms =
fold_rev (fn M => curry3 MFun M (A Gen)) Ms (MRec z)
fun repair_mtype _ _ MAlpha = MAlpha
| repair_mtype cache seen (MFun (M1, aa, M2)) =
MFun (repair_mtype cache seen M1, aa, repair_mtype cache seen M2)
| repair_mtype cache seen (MPair Mp) =
MPair (pairself (repair_mtype cache seen) Mp)
| repair_mtype cache seen (MType (s, Ms)) =
MType (s, maps (flatten_mtype o repair_mtype cache seen) Ms)
| repair_mtype cache seen (MRec (z as (s, _))) =
case AList.lookup (op =) cache z |> the of
MRec _ => MType (s, [])
| M => if member (op =) seen M then MType (s, [])
else repair_mtype cache (M :: seen) M
fun repair_datatype_mcache cache =
let
fun repair_one (z, M) =
Unsynchronized.change cache
(AList.update (op =) (z, repair_mtype (!cache) [] M))
in List.app repair_one (rev (!cache)) end
fun repair_constr_mcache dtype_cache constr_mcache =
let
fun repair_one (x, M) =
Unsynchronized.change constr_mcache
(AList.update (op =) (x, repair_mtype dtype_cache [] M))
in List.app repair_one (!constr_mcache) end
fun is_fin_fun_supported_type @{typ prop} = true
| is_fin_fun_supported_type @{typ bool} = true
| is_fin_fun_supported_type (Type (@{type_name option}, _)) = true
| is_fin_fun_supported_type _ = false
(* TODO: clean this up *)
fun fin_fun_body _ _ (t as @{term False}) = SOME t
| fin_fun_body _ _ (t as Const (@{const_name None}, _)) = SOME t
| fin_fun_body dom_T ran_T
((t0 as Const (@{const_name If}, _))
$ (t1 as Const (@{const_name HOL.eq}, _) $ Bound 0 $ t1')
$ t2 $ t3) =
(if loose_bvar1 (t1', 0) then
NONE
else case fin_fun_body dom_T ran_T t3 of
NONE => NONE
| SOME t3 =>
SOME (t0 $ (Const (@{const_name is_unknown}, dom_T --> bool_T) $ t1')
$ (Const (@{const_name unknown}, ran_T)) $ (t0 $ t1 $ t2 $ t3)))
| fin_fun_body _ _ _ = NONE
(* ### FIXME: make sure well-annotated! *)
fun fresh_mfun_for_fun_type (mdata as {max_fresh, ...} : mdata) all_minus
T1 T2 =
let
val M1 = fresh_mtype_for_type mdata all_minus T1
val M2 = fresh_mtype_for_type mdata all_minus T2
val aa = if not all_minus andalso exists_alpha_sub_mtype_fresh M1 andalso
is_fin_fun_supported_type (body_type T2) then
V (Unsynchronized.inc max_fresh)
else
A Gen
in (M1, aa, M2) end
and fresh_mtype_for_type (mdata as {hol_ctxt as {ctxt, ...}, binarize, alpha_T,
datatype_mcache, constr_mcache, ...})
all_minus =
let
fun do_type T =
if T = alpha_T then
MAlpha
else case T of
Type (@{type_name fun}, [T1, T2]) =>
MFun (fresh_mfun_for_fun_type mdata all_minus T1 T2)
| Type (@{type_name prod}, [T1, T2]) => MPair (pairself do_type (T1, T2))
| Type (z as (s, _)) =>
if could_exist_alpha_sub_mtype ctxt alpha_T T then
case AList.lookup (op =) (!datatype_mcache) z of
SOME M => M
| NONE =>
let
val _ = Unsynchronized.change datatype_mcache (cons (z, MRec z))
val xs = binarized_and_boxed_datatype_constrs hol_ctxt binarize T
val (all_Ms, constr_Ms) =
fold_rev (fn (_, T') => fn (all_Ms, constr_Ms) =>
let
val binder_Ms = map do_type (binder_types T')
val new_Ms = filter exists_alpha_sub_mtype_fresh
binder_Ms
val constr_M = constr_mtype_for_binders z
binder_Ms
in
(union (op =) new_Ms all_Ms,
constr_M :: constr_Ms)
end)
xs ([], [])
val M = MType (s, all_Ms)
val _ = Unsynchronized.change datatype_mcache
(AList.update (op =) (z, M))
val _ = Unsynchronized.change constr_mcache
(append (xs ~~ constr_Ms))
in
if forall (not o is_MRec o snd) (!datatype_mcache) then
(repair_datatype_mcache datatype_mcache;
repair_constr_mcache (!datatype_mcache) constr_mcache;
AList.lookup (op =) (!datatype_mcache) z |> the)
else
M
end
else
MType (s, [])
| _ => MType (simple_string_of_typ T, [])
in do_type end
val ground_and_sole_base_constrs = [] (* FIXME: [@{const_name Nil}, @{const_name None}], cf. lists_empty *)
fun prodM_factors (MPair (M1, M2)) = maps prodM_factors [M1, M2]
| prodM_factors M = [M]
fun curried_strip_mtype (MFun (M1, _, M2)) =
curried_strip_mtype M2 |>> append (prodM_factors M1)
| curried_strip_mtype M = ([], M)
fun sel_mtype_from_constr_mtype s M =
let
val (arg_Ms, dataM) = curried_strip_mtype M
val a = if member (op =) ground_and_sole_base_constrs
(constr_name_for_sel_like s) then
Fls
else
Gen
in
MFun (dataM, A a,
case sel_no_from_name s of ~1 => bool_M | n => nth arg_Ms n)
end
fun mtype_for_constr (mdata as {hol_ctxt = {ctxt, ...}, alpha_T, constr_mcache,
...}) (x as (_, T)) =
if could_exist_alpha_sub_mtype ctxt alpha_T T then
case AList.lookup (op =) (!constr_mcache) x of
SOME M => M
| NONE => if T = alpha_T then
let val M = fresh_mtype_for_type mdata false T in
(Unsynchronized.change constr_mcache (cons (x, M)); M)
end
else
(fresh_mtype_for_type mdata false (body_type T);
AList.lookup (op =) (!constr_mcache) x |> the)
else
fresh_mtype_for_type mdata false T
fun mtype_for_sel (mdata as {hol_ctxt, binarize, ...}) (x as (s, _)) =
x |> binarized_and_boxed_constr_for_sel hol_ctxt binarize
|> mtype_for_constr mdata |> sel_mtype_from_constr_mtype s
fun resolve_annotation_atom asgs (V x) =
x |> AList.lookup (op =) asgs |> Option.map A |> the_default (V x)
| resolve_annotation_atom _ aa = aa
fun resolve_mtype asgs =
let
fun aux MAlpha = MAlpha
| aux (MFun (M1, aa, M2)) =
MFun (aux M1, resolve_annotation_atom asgs aa, aux M2)
| aux (MPair Mp) = MPair (pairself aux Mp)
| aux (MType (s, Ms)) = MType (s, map aux Ms)
| aux (MRec z) = MRec z
in aux end
datatype comp_op = Eq | Neq | Leq
type comp = annotation_atom * annotation_atom * comp_op * var list
type assign_clause = assign_literal list
type constraint_set = comp list * assign_clause list
fun string_for_comp_op Eq = "="
| string_for_comp_op Neq = "\<noteq>"
| string_for_comp_op Leq = "\<le>"
fun string_for_comp (aa1, aa2, cmp, xs) =
string_for_annotation_atom aa1 ^ " " ^ string_for_comp_op cmp ^
subscript_string_for_vars " \<and> " xs ^ " " ^ string_for_annotation_atom aa2
fun string_for_assign_clause NONE = "\<top>"
| string_for_assign_clause (SOME []) = "\<bot>"
| string_for_assign_clause (SOME asgs) =
space_implode " \<or> " (map string_for_assign_literal asgs)
fun add_assign_literal (x, (sn, a)) clauses =
if exists (fn [(x', (sn', a'))] =>
x = x' andalso ((sn = sn' andalso a <> a') orelse
(sn <> sn' andalso a = a'))
| _ => false) clauses then
NONE
else
SOME ([(x, a)] :: clauses)
fun add_assign_disjunct _ NONE = NONE
| add_assign_disjunct asg (SOME asgs) = SOME (insert (op =) asg asgs)
fun add_assign_clause NONE = I
| add_assign_clause (SOME clause) = insert (op =) clause
fun annotation_comp Eq a1 a2 = (a1 = a2)
| annotation_comp Neq a1 a2 = (a1 <> a2)
| annotation_comp Leq a1 a2 = (a1 = a2 orelse a2 = Gen)
fun sign_for_comp_op Eq = Plus
| sign_for_comp_op Neq = Minus
| sign_for_comp_op Leq = raise BAD ("sign_for_comp_op", "unexpected \"Leq\"")
fun do_annotation_atom_comp Leq [] aa1 aa2 (cset as (comps, clauses)) =
(case (aa1, aa2) of
(A a1, A a2) => if annotation_comp Leq a1 a2 then SOME cset else NONE
| _ => SOME (insert (op =) (aa1, aa2, Leq, []) comps, clauses))
| do_annotation_atom_comp cmp [] aa1 aa2 (cset as (comps, clauses)) =
(case (aa1, aa2) of
(A a1, A a2) => if annotation_comp cmp a1 a2 then SOME cset else NONE
| (V x1, A a2) =>
clauses |> add_assign_literal (x1, (sign_for_comp_op cmp, a2))
|> Option.map (pair comps)
| (A _, V _) => do_annotation_atom_comp cmp [] aa2 aa1 cset
| (V _, V _) => SOME (insert (op =) (aa1, aa2, cmp, []) comps, clauses))
| do_annotation_atom_comp cmp xs aa1 aa2 (comps, clauses) =
SOME (insert (op =) (aa1, aa2, cmp, xs) comps, clauses)
fun add_annotation_atom_comp cmp xs aa1 aa2 (comps, clauses) =
(trace_msg (fn () => "*** Add " ^ string_for_comp (aa1, aa2, cmp, xs));
case do_annotation_atom_comp cmp xs aa1 aa2 (comps, clauses) of
NONE => (trace_msg (K "**** Unsolvable"); raise UNSOLVABLE ())
| SOME cset => cset)
fun do_mtype_comp _ _ _ _ NONE = NONE
| do_mtype_comp _ _ MAlpha MAlpha cset = cset
| do_mtype_comp Eq xs (MFun (M11, aa1, M12)) (MFun (M21, aa2, M22))
(SOME cset) =
cset |> do_annotation_atom_comp Eq xs aa1 aa2
|> do_mtype_comp Eq xs M11 M21 |> do_mtype_comp Eq xs M12 M22
| do_mtype_comp Leq xs (MFun (M11, aa1, M12)) (MFun (M21, aa2, M22))
(SOME cset) =
(if exists_alpha_sub_mtype M11 then
cset |> do_annotation_atom_comp Leq xs aa1 aa2
|> do_mtype_comp Leq xs M21 M11
|> (case aa2 of
A Gen => I
| A _ => do_mtype_comp Leq xs M11 M21
| V x => do_mtype_comp Leq (x :: xs) M11 M21)
else
SOME cset)
|> do_mtype_comp Leq xs M12 M22
| do_mtype_comp cmp xs (M1 as MPair (M11, M12)) (M2 as MPair (M21, M22))
cset =
(cset |> fold (uncurry (do_mtype_comp cmp xs)) [(M11, M21), (M12, M22)]
handle Library.UnequalLengths =>
raise MTYPE ("Nitpick_Mono.do_mtype_comp", [M1, M2], []))
| do_mtype_comp _ _ (MType _) (MType _) cset =
cset (* no need to compare them thanks to the cache *)
| do_mtype_comp cmp _ M1 M2 _ =
raise MTYPE ("Nitpick_Mono.do_mtype_comp (" ^ string_for_comp_op cmp ^ ")",
[M1, M2], [])
fun add_mtype_comp cmp M1 M2 cset =
(trace_msg (fn () => "*** Add " ^ string_for_mtype M1 ^ " " ^
string_for_comp_op cmp ^ " " ^ string_for_mtype M2);
case SOME cset |> do_mtype_comp cmp [] M1 M2 of
NONE => (trace_msg (K "**** Unsolvable"); raise UNSOLVABLE ())
| SOME cset => cset)
val add_mtypes_equal = add_mtype_comp Eq
val add_is_sub_mtype = add_mtype_comp Leq
fun do_notin_mtype_fv _ _ _ NONE = NONE
| do_notin_mtype_fv Minus _ MAlpha cset = cset
| do_notin_mtype_fv Plus [] MAlpha _ = NONE
| do_notin_mtype_fv Plus [asg] MAlpha (SOME clauses) =
clauses |> add_assign_literal asg
| do_notin_mtype_fv Plus unless MAlpha (SOME clauses) =
SOME (insert (op =) unless clauses)
| do_notin_mtype_fv sn unless (MFun (M1, A a, M2)) cset =
cset |> (if a <> Gen andalso sn = Plus then do_notin_mtype_fv Plus unless M1
else I)
|> (if a = Gen orelse sn = Plus then do_notin_mtype_fv Minus unless M1
else I)
|> do_notin_mtype_fv sn unless M2
| do_notin_mtype_fv Plus unless (MFun (M1, V x, M2)) cset =
cset |> (case add_assign_disjunct (x, (Plus, Gen)) (SOME unless) of
NONE => I
| SOME unless' => do_notin_mtype_fv Plus unless' M1)
|> do_notin_mtype_fv Minus unless M1
|> do_notin_mtype_fv Plus unless M2
| do_notin_mtype_fv Minus unless (MFun (M1, V x, M2)) cset =
cset |> (case fold (fn a => add_assign_disjunct (x, (Plus, a))) [Fls, Tru]
(SOME unless) of
NONE => I
| SOME unless' => do_notin_mtype_fv Plus unless' M1)
|> do_notin_mtype_fv Minus unless M2
| do_notin_mtype_fv sn unless (MPair (M1, M2)) cset =
cset |> fold (do_notin_mtype_fv sn unless) [M1, M2]
| do_notin_mtype_fv sn unless (MType (_, Ms)) cset =
cset |> fold (do_notin_mtype_fv sn unless) Ms
| do_notin_mtype_fv _ _ M _ =
raise MTYPE ("Nitpick_Mono.do_notin_mtype_fv", [M], [])
fun add_notin_mtype_fv sn unless M (comps, clauses) =
(trace_msg (fn () => "*** Add " ^ string_for_mtype M ^ " is " ^
(case sn of Minus => "concrete" | Plus => "complete"));
case SOME clauses |> do_notin_mtype_fv sn unless M of
NONE => (trace_msg (K "**** Unsolvable"); raise UNSOLVABLE ())
| SOME clauses => (comps, clauses))
val add_mtype_is_concrete = add_notin_mtype_fv Minus
val add_mtype_is_complete = add_notin_mtype_fv Plus
val bool_table =
[(Gen, (false, false)),
(New, (false, true)),
(Fls, (true, false)),
(Tru, (true, true))]
fun fst_var n = 2 * n
fun snd_var n = 2 * n + 1
val bools_from_annotation = AList.lookup (op =) bool_table #> the
val annotation_from_bools = AList.find (op =) bool_table #> the_single
fun prop_for_bool b = if b then PL.True else PL.False
fun prop_for_bool_var_equality (v1, v2) =
PL.SAnd (PL.SOr (PL.BoolVar v1, PL.SNot (PL.BoolVar v2)),
PL.SOr (PL.SNot (PL.BoolVar v1), PL.BoolVar v2))
fun prop_for_assign (x, a) =
let val (b1, b2) = bools_from_annotation a in
PL.SAnd (PL.BoolVar (fst_var x) |> not b1 ? PL.SNot,
PL.BoolVar (snd_var x) |> not b2 ? PL.SNot)
end
fun prop_for_assign_literal (x, (Plus, a)) = prop_for_assign (x, a)
| prop_for_assign_literal (x, (Minus, a)) = PL.SNot (prop_for_assign (x, a))
fun prop_for_atom_assign (A a', a) = prop_for_bool (a = a')
| prop_for_atom_assign (V x, a) = prop_for_assign_literal (x, (Plus, a))
fun prop_for_atom_equality (aa1, A a2) = prop_for_atom_assign (aa1, a2)
| prop_for_atom_equality (A a1, aa2) = prop_for_atom_assign (aa2, a1)
| prop_for_atom_equality (V x1, V x2) =
PL.SAnd (prop_for_bool_var_equality (pairself fst_var (x1, x2)),
prop_for_bool_var_equality (pairself snd_var (x1, x2)))
val prop_for_assign_clause = PL.exists o map prop_for_assign_literal
fun prop_for_exists_var_assign_literal xs a =
PL.exists (map (fn x => prop_for_assign_literal (x, (Plus, a))) xs)
fun prop_for_comp (aa1, aa2, Eq, []) =
PL.SAnd (prop_for_comp (aa1, aa2, Leq, []),
prop_for_comp (aa2, aa1, Leq, []))
| prop_for_comp (aa1, aa2, Neq, []) =
PL.SNot (prop_for_comp (aa1, aa2, Eq, []))
| prop_for_comp (aa1, aa2, Leq, []) =
PL.SOr (prop_for_atom_equality (aa1, aa2), prop_for_atom_assign (aa2, Gen))
| prop_for_comp (aa1, aa2, cmp, xs) =
PL.SOr (prop_for_exists_var_assign_literal xs Gen,
prop_for_comp (aa1, aa2, cmp, []))
fun extract_assigns max_var assigns asgs =
fold (fn x => fn accum =>
if AList.defined (op =) asgs x then
accum
else case (fst_var x, snd_var x) |> pairself assigns of
(NONE, NONE) => accum
| bp => (x, annotation_from_bools (pairself (the_default false) bp))
:: accum)
(max_var downto 1) asgs
fun print_problem comps clauses =
trace_msg (fn () => "*** Problem:\n" ^
cat_lines (map string_for_comp comps @
map (string_for_assign_clause o SOME) clauses))
fun print_solution asgs =
trace_msg (fn () => "*** Solution:\n" ^
(asgs
|> map swap
|> AList.group (op =)
|> map (fn (a, xs) => string_for_annotation a ^ ": " ^
string_for_vars ", " (sort int_ord xs))
|> space_implode "\n"))
(* The ML solver timeout should correspond more or less to the overhead of
invoking an external prover. *)
val ml_solver_timeout = SOME (seconds 0.02)
fun solve tac_timeout max_var (comps, clauses) =
let
val asgs =
map_filter (fn [(x, (Plus, a))] => SOME (x, a) | _ => NONE) clauses
fun do_assigns assigns =
SOME (extract_assigns max_var assigns asgs |> tap print_solution)
val _ = print_problem comps clauses
val prop =
PL.all (map prop_for_comp comps @ map prop_for_assign_clause clauses)
in
if PL.eval (K false) prop then
do_assigns (K (SOME false))
else if PL.eval (K true) prop then
do_assigns (K (SOME true))
else
let
(* use the first ML solver (to avoid startup overhead) *)
val (ml_solvers, nonml_solvers) =
!SatSolver.solvers
|> List.partition (member (op =) ["dptsat", "dpll"] o fst)
val res =
if null nonml_solvers then
time_limit tac_timeout (snd (hd ml_solvers)) prop
else
time_limit ml_solver_timeout (snd (hd ml_solvers)) prop
handle TimeLimit.TimeOut =>
time_limit tac_timeout (SatSolver.invoke_solver "auto") prop
in
case res of
SatSolver.SATISFIABLE assigns => do_assigns assigns
| _ => (trace_msg (K "*** Unsolvable"); NONE)
end
handle TimeLimit.TimeOut => (trace_msg (K "*** Timed out"); NONE)
end
type mcontext =
{bound_Ts: typ list,
bound_Ms: mtyp list,
frame: (int * annotation_atom) list,
frees: (styp * mtyp) list,
consts: (styp * mtyp) list}
fun string_for_bound ctxt Ms (j, aa) =
Syntax.string_of_term ctxt (Bound (length Ms - j - 1)) ^ " :\<^bsup>" ^
string_for_annotation_atom aa ^ "\<^esup> " ^
string_for_mtype (nth Ms (length Ms - j - 1))
fun string_for_free relevant_frees ((s, _), M) =
if member (op =) relevant_frees s then SOME (s ^ " : " ^ string_for_mtype M)
else NONE
fun string_for_mcontext ctxt t {bound_Ms, frame, frees, ...} =
(map_filter (string_for_free (Term.add_free_names t [])) frees @
map (string_for_bound ctxt bound_Ms) frame)
|> commas |> enclose "[" "]"
val initial_gamma =
{bound_Ts = [], bound_Ms = [], frame = [], frees = [], consts = []}
fun push_bound aa T M {bound_Ts, bound_Ms, frame, frees, consts} =
{bound_Ts = T :: bound_Ts, bound_Ms = M :: bound_Ms,
frame = frame @ [(length bound_Ts, aa)], frees = frees, consts = consts}
fun pop_bound {bound_Ts, bound_Ms, frame, frees, consts} =
{bound_Ts = tl bound_Ts, bound_Ms = tl bound_Ms,
frame = frame |> filter_out (fn (j, _) => j = length bound_Ts - 1),
frees = frees, consts = consts}
handle List.Empty => initial_gamma (* FIXME: needed? *)
fun set_frame frame ({bound_Ts, bound_Ms, frees, consts, ...} : mcontext) =
{bound_Ts = bound_Ts, bound_Ms = bound_Ms, frame = frame, frees = frees,
consts = consts}
(* FIXME: make sure tracing messages are complete *)
fun add_comp_frame aa cmp = fold (add_annotation_atom_comp cmp [] aa o snd)
fun add_bound_frame j frame =
let
val (new_frame, gen_frame) = List.partition (curry (op =) j o fst) frame
in
add_comp_frame (A New) Leq new_frame
#> add_comp_frame (A Gen) Eq gen_frame
end
fun fresh_frame ({max_fresh, ...} : mdata) fls tru =
map (apsnd (fn aa =>
case (aa, fls, tru) of
(A Fls, SOME a, _) => A a
| (A Tru, _, SOME a) => A a
| (A Gen, _, _) => A Gen
| _ => V (Unsynchronized.inc max_fresh)))
fun conj_clauses res_aa aa1 aa2 =
[[(aa1, (Neq, Tru)), (aa2, (Neq, Tru)), (res_aa, (Eq, Tru))],
[(aa1, (Neq, Fls)), (res_aa, (Eq, Fls))],
[(aa2, (Neq, Fls)), (res_aa, (Eq, Fls))],
[(aa1, (Neq, Gen)), (aa2, (Eq, Fls)), (res_aa, (Eq, Gen))],
[(aa1, (Neq, New)), (aa2, (Eq, Fls)), (res_aa, (Eq, Gen))],
[(aa1, (Eq, Fls)), (aa2, (Neq, Gen)), (res_aa, (Eq, Gen))],
[(aa1, (Eq, Fls)), (aa2, (Neq, New)), (res_aa, (Eq, Gen))]]
fun disj_clauses res_aa aa1 aa2 =
[[(aa1, (Neq, Tru)), (res_aa, (Eq, Tru))],
[(aa2, (Neq, Tru)), (res_aa, (Eq, Tru))],
[(aa1, (Neq, Fls)), (aa2, (Neq, Fls)), (res_aa, (Eq, Fls))],
[(aa1, (Neq, Gen)), (aa2, (Eq, Tru)), (res_aa, (Eq, Gen))],
[(aa1, (Neq, New)), (aa2, (Eq, Tru)), (res_aa, (Eq, Gen))],
[(aa1, (Eq, Tru)), (aa2, (Neq, Gen)), (res_aa, (Eq, Gen))],
[(aa1, (Eq, Tru)), (aa2, (Neq, New)), (res_aa, (Eq, Gen))]]
fun imp_clauses res_aa aa1 aa2 =
[[(aa1, (Neq, Fls)), (res_aa, (Eq, Tru))],
[(aa2, (Neq, Tru)), (res_aa, (Eq, Tru))],
[(aa1, (Neq, Tru)), (aa2, (Neq, Fls)), (res_aa, (Eq, Fls))],
[(aa1, (Neq, Gen)), (aa2, (Eq, Tru)), (res_aa, (Eq, Gen))],
[(aa1, (Neq, New)), (aa2, (Eq, Tru)), (res_aa, (Eq, Gen))],
[(aa1, (Eq, Fls)), (aa2, (Neq, Gen)), (res_aa, (Eq, Gen))],
[(aa1, (Eq, Fls)), (aa2, (Neq, New)), (res_aa, (Eq, Gen))]]
val meta_conj_triple = ("\<and>", conj_clauses, @{const Pure.conjunction})
val meta_imp_triple = ("\<implies>", imp_clauses, @{const "==>"})
val conj_triple = ("\<and>", conj_clauses, @{const conj})
val disj_triple = ("\<or>", disj_clauses, @{const disj})
val imp_triple = ("\<implies>", imp_clauses, @{const implies})
fun add_annotation_clause_from_quasi_clause _ NONE = NONE
| add_annotation_clause_from_quasi_clause [] accum = accum
| add_annotation_clause_from_quasi_clause ((aa, (cmp, a)) :: rest) accum =
case aa of
A a' => if annotation_comp cmp a' a then NONE
else add_annotation_clause_from_quasi_clause rest accum
| V x => add_annotation_clause_from_quasi_clause rest accum
|> Option.map (cons (x, (sign_for_comp_op cmp, a)))
fun assign_clause_from_quasi_clause unless =
add_annotation_clause_from_quasi_clause unless (SOME [])
fun add_connective_var conn mk_quasi_clauses res_aa aa1 aa2 =
(trace_msg (fn () => "*** Add " ^ string_for_annotation_atom res_aa ^ " = " ^
string_for_annotation_atom aa1 ^ " " ^ conn ^ " " ^
string_for_annotation_atom aa2);
fold (add_assign_clause o assign_clause_from_quasi_clause)
(mk_quasi_clauses res_aa aa1 aa2))
fun add_connective_frames conn mk_quasi_clauses res_frame frame1 frame2 =
fold I (map3 (fn (_, res_aa) => fn (_, aa1) => fn (_, aa2) =>
add_connective_var conn mk_quasi_clauses res_aa aa1 aa2)
res_frame frame1 frame2)
fun kill_unused_in_frame is_in (accum as ({frame, ...}, _)) =
let val (used_frame, unused_frame) = List.partition is_in frame in
accum |>> set_frame used_frame
||> add_comp_frame (A Gen) Eq unused_frame
end
fun split_frame is_in_fun (gamma as {frame, ...}, cset) =
let
fun bubble fun_frame arg_frame [] cset =
((rev fun_frame, rev arg_frame), cset)
| bubble fun_frame arg_frame ((bound as (_, aa)) :: rest) cset =
if is_in_fun bound then
bubble (bound :: fun_frame) arg_frame rest
(cset |> add_comp_frame aa Leq arg_frame)
else
bubble fun_frame (bound :: arg_frame) rest cset
in cset |> bubble [] [] frame ||> pair gamma end
fun add_annotation_atom_comp_alt _ (A Gen) _ _ = I
| add_annotation_atom_comp_alt _ (A _) _ _ =
(trace_msg (K "*** Expected G"); raise UNSOLVABLE ())
| add_annotation_atom_comp_alt cmp (V x) aa1 aa2 =
add_annotation_atom_comp cmp [x] aa1 aa2
fun add_arg_order1 ((_, aa), (_, prev_aa)) = I
add_annotation_atom_comp_alt Neq prev_aa (A Gen) aa
fun add_app1 fun_aa ((_, res_aa), (_, arg_aa)) = I
let
val clause = [(arg_aa, (Eq, New)), (res_aa, (Eq, Gen))]
|> assign_clause_from_quasi_clause
in
trace_msg (fn () => "*** Add " ^ string_for_assign_clause clause);
apsnd (add_assign_clause clause)
#> add_annotation_atom_comp_alt Leq arg_aa fun_aa res_aa
end
fun add_app _ [] [] = I
| add_app fun_aa res_frame arg_frame =
add_comp_frame (A New) Leq arg_frame
#> fold add_arg_order1 (tl arg_frame ~~ (fst (split_last arg_frame)))
#> fold (add_app1 fun_aa) (res_frame ~~ arg_frame)
fun consider_connective mdata (conn, mk_quasi_clauses, t0) do_t1 do_t2
(accum as ({frame, ...}, _)) =
let
val mtype_for = fresh_mtype_for_type mdata false
val frame1 = fresh_frame mdata (SOME Tru) NONE frame
val frame2 = fresh_frame mdata (SOME Fls) NONE frame
val (m1, accum) = accum |>> set_frame frame1 |> do_t1
val (m2, accum) = accum |>> set_frame frame2 |> do_t2
in
(MApp (MApp (MRaw (t0, mtype_for (fastype_of t0)), m1), m2),
accum |>> set_frame frame
||> apsnd (add_connective_frames conn mk_quasi_clauses frame frame1
frame2))
end
fun consider_term (mdata as {hol_ctxt = {thy, ctxt, stds, ...}, alpha_T,
max_fresh, ...}) =
let
fun is_enough_eta_expanded t =
case strip_comb t of
(Const x, ts) => the_default 0 (arity_of_built_in_const thy stds x)
<= length ts
| _ => true
val mtype_for = fresh_mtype_for_type mdata false
fun do_all T (gamma, cset) =
let
val abs_M = mtype_for (domain_type (domain_type T))
val x = Unsynchronized.inc max_fresh
val body_M = mtype_for (body_type T)
in
(MFun (MFun (abs_M, V x, body_M), A Gen, body_M),
(gamma, cset |> add_mtype_is_complete [(x, (Plus, Tru))] abs_M))
end
fun do_equals T (gamma, cset) =
let
val M = mtype_for (domain_type T)
val x = Unsynchronized.inc max_fresh
in
(MFun (M, A Gen, MFun (M, V x, mtype_for (nth_range_type 2 T))),
(gamma, cset |> add_mtype_is_concrete [] M
|> add_annotation_atom_comp Leq [] (A Fls) (V x)))
end
fun do_robust_set_operation T (gamma, cset) =
let
val set_T = domain_type T
val M1 = mtype_for set_T
val M2 = mtype_for set_T
val M3 = mtype_for set_T
in
(MFun (M1, A Gen, MFun (M2, A Gen, M3)),
(gamma, cset |> add_is_sub_mtype M1 M3 |> add_is_sub_mtype M2 M3))
end
fun do_fragile_set_operation T (gamma, cset) =
let
val set_T = domain_type T
val set_M = mtype_for set_T
fun custom_mtype_for (T as Type (@{type_name fun}, [T1, T2])) =
if T = set_T then set_M
else MFun (custom_mtype_for T1, A Gen, custom_mtype_for T2)
| custom_mtype_for T = mtype_for T
in
(custom_mtype_for T, (gamma, cset |> add_mtype_is_concrete [] set_M))
end
fun do_pair_constr T accum =
case mtype_for (nth_range_type 2 T) of
M as MPair (a_M, b_M) =>
(MFun (a_M, A Gen, MFun (b_M, A Gen, M)), accum)
| M => raise MTYPE ("Nitpick_Mono.consider_term.do_pair_constr", [M], [])
fun do_nth_pair_sel n T =
case mtype_for (domain_type T) of
M as MPair (a_M, b_M) =>
pair (MFun (M, A Gen, if n = 0 then a_M else b_M))
| M => raise MTYPE ("Nitpick_Mono.consider_term.do_nth_pair_sel", [M], [])
and do_connect triple t1 t2 =
consider_connective mdata triple (do_term t1) (do_term t2)
and do_term t
(accum as (gamma as {bound_Ts, bound_Ms, frame, frees, consts},
cset)) =
(trace_msg (fn () => " " ^ string_for_mcontext ctxt t gamma ^
" \<turnstile> " ^ Syntax.string_of_term ctxt t ^
" : _?");
case t of
@{const False} =>
(MRaw (t, bool_M), accum ||> add_comp_frame (A Fls) Leq frame)
| Const (@{const_name None}, _) =>
(MRaw (t, bool_M), accum ||> add_comp_frame (A Fls) Leq frame)
| @{const True} =>
(MRaw (t, bool_M), accum ||> add_comp_frame (A Tru) Leq frame)
| Const (x as (s, T)) =>
(case AList.lookup (op =) consts x of
SOME M => (M, accum)
| NONE =>
if not (could_exist_alpha_subtype alpha_T T) then
(mtype_for T, accum)
else case s of
@{const_name all} => do_all T accum
| @{const_name "=="} => do_equals T accum
| @{const_name All} => do_all T accum
| @{const_name Ex} =>
let val set_T = domain_type T in
do_term (Abs (Name.uu, set_T,
@{const Not} $ (HOLogic.mk_eq
(Abs (Name.uu, domain_type set_T,
@{const False}),
Bound 0)))) accum
|>> mtype_of_mterm
end
| @{const_name HOL.eq} => do_equals T accum
| @{const_name The} =>
(trace_msg (K "*** The"); raise UNSOLVABLE ())
| @{const_name Eps} =>
(trace_msg (K "*** Eps"); raise UNSOLVABLE ())
| @{const_name If} =>
do_robust_set_operation (range_type T) accum
|>> curry3 MFun bool_M (A Gen)
| @{const_name Pair} => do_pair_constr T accum
| @{const_name fst} => do_nth_pair_sel 0 T accum
| @{const_name snd} => do_nth_pair_sel 1 T accum
| @{const_name Id} =>
(MFun (mtype_for (domain_type T), A Gen, bool_M), accum)
| @{const_name converse} =>
let
val x = Unsynchronized.inc max_fresh
fun mtype_for_set T =
MFun (mtype_for (domain_type T), V x, bool_M)
val ab_set_M = domain_type T |> mtype_for_set
val ba_set_M = range_type T |> mtype_for_set
in
(MFun (ab_set_M, A Gen, ba_set_M),
accum ||> add_annotation_atom_comp Neq [] (V x) (A New))
end
| @{const_name trancl} => do_fragile_set_operation T accum
| @{const_name rel_comp} =>
let
val x = Unsynchronized.inc max_fresh
fun mtype_for_set T =
MFun (mtype_for (domain_type T), V x, bool_M)
val bc_set_M = domain_type T |> mtype_for_set
val ab_set_M = domain_type (range_type T) |> mtype_for_set
val ac_set_M = nth_range_type 2 T |> mtype_for_set
in
(MFun (bc_set_M, A Gen, MFun (ab_set_M, A Gen, ac_set_M)),
accum ||> add_annotation_atom_comp Neq [] (V x) (A New))
end
| @{const_name image} =>
let
val x = Unsynchronized.inc max_fresh
val a_M = mtype_for (domain_type (domain_type T))
val b_M = mtype_for (range_type (domain_type T))
in
(MFun (MFun (a_M, A Gen, b_M), A Gen,
MFun (MFun (a_M, V x, bool_M), A Gen,
MFun (b_M, V x, bool_M))),
accum ||> add_annotation_atom_comp Neq [] (V x) (A New))
end
| @{const_name finite} =>
let
val M1 = mtype_for (domain_type (domain_type T))
val a = if exists_alpha_sub_mtype M1 then Fls else Gen
in (MFun (MFun (M1, A a, bool_M), A Gen, bool_M), accum) end
| @{const_name Sigma} =>
let
val x = Unsynchronized.inc max_fresh
fun mtype_for_set T =
MFun (mtype_for (domain_type T), V x, bool_M)
val a_set_T = domain_type T
val a_M = mtype_for (domain_type a_set_T)
val b_set_M =
mtype_for_set (range_type (domain_type (range_type T)))
val a_set_M = mtype_for_set a_set_T
val a_to_b_set_M = MFun (a_M, A Gen, b_set_M)
val ab_set_M = mtype_for_set (nth_range_type 2 T)
in
(MFun (a_set_M, A Gen, MFun (a_to_b_set_M, A Gen, ab_set_M)),
accum ||> add_annotation_atom_comp Neq [] (V x) (A New))
end
| _ =>
if s = @{const_name safe_The} then
let
val a_set_M = mtype_for (domain_type T)
val a_M = dest_MFun a_set_M |> #1
in (MFun (a_set_M, A Gen, a_M), accum) end
else if s = @{const_name ord_class.less_eq} andalso
is_set_type (domain_type T) then
do_fragile_set_operation T accum
else if is_sel s then
(mtype_for_sel mdata x, accum)
else if is_constr ctxt stds x then
(mtype_for_constr mdata x, accum)
else if is_built_in_const thy stds x then
(fresh_mtype_for_type mdata true T, accum)
else
let val M = mtype_for T in
(M, ({bound_Ts = bound_Ts, bound_Ms = bound_Ms, frame = frame,
frees = frees, consts = (x, M) :: consts}, cset))
end)
|>> curry MRaw t
||> apsnd (add_comp_frame (A Gen) Eq frame)
| Free (x as (_, T)) =>
(case AList.lookup (op =) frees x of
SOME M => (M, accum)
| NONE =>
let val M = mtype_for T in
(M, ({bound_Ts = bound_Ts, bound_Ms = bound_Ms, frame = frame,
frees = (x, M) :: frees, consts = consts}, cset))
end)
|>> curry MRaw t ||> apsnd (add_comp_frame (A Gen) Eq frame)
| Var _ => (trace_msg (K "*** Var"); raise UNSOLVABLE ())
| Bound j =>
(MRaw (t, nth bound_Ms j),
accum ||> add_bound_frame (length bound_Ts - j - 1) frame)
| Abs (s, T, t') =>
(case fin_fun_body T (fastype_of1 (T :: bound_Ts, t')) t' of
SOME t' =>
let
val M = mtype_for T
val x = Unsynchronized.inc max_fresh
val (m', accum) = do_term t' (accum |>> push_bound (V x) T M)
in
(MAbs (s, T, M, V x, m'),
accum |>> pop_bound
||> add_annotation_atom_comp Leq [] (A Fls) (V x))
end
| NONE =>
((case t' of
t1' $ Bound 0 =>
if not (loose_bvar1 (t1', 0)) andalso
is_enough_eta_expanded t1' then
do_term (incr_boundvars ~1 t1') accum
else
raise SAME ()
| (t11 as Const (@{const_name HOL.eq}, _)) $ Bound 0 $ t13 =>
if not (loose_bvar1 (t13, 0)) then
do_term (incr_boundvars ~1 (t11 $ t13)) accum
else
raise SAME ()
| _ => raise SAME ())
handle SAME () =>
let
val M = mtype_for T
val x = Unsynchronized.inc max_fresh
val (m', accum) =
do_term t' (accum |>> push_bound (V x) T M)
in (MAbs (s, T, M, V x, m'), accum |>> pop_bound) end))
| @{const Not} $ t1 => do_connect imp_triple t1 @{const False} accum
| @{const conj} $ t1 $ t2 => do_connect conj_triple t1 t2 accum
| @{const disj} $ t1 $ t2 => do_connect disj_triple t1 t2 accum
| @{const implies} $ t1 $ t2 => do_connect imp_triple t1 t2 accum
| Const (@{const_name Let}, _) $ t1 $ t2 =>
do_term (betapply (t2, t1)) accum
| t1 $ t2 =>
let
fun is_in t (j, _) = loose_bvar1 (t, length bound_Ts - j - 1)
val accum as ({frame, ...}, _) =
accum |> kill_unused_in_frame (is_in t)
val ((frame1a, frame1b), accum) = accum |> split_frame (is_in t1)
val frame2a = frame1a |> map (apsnd (K (A Gen)))
val frame2b =
frame1b |> map (apsnd (fn _ => V (Unsynchronized.inc max_fresh)))
val frame2 = frame2a @ frame2b
val (m1, accum) = accum |>> set_frame frame1a |> do_term t1
val (m2, accum) = accum |>> set_frame frame2 |> do_term t2
in
let
val (M11, aa, _) = mtype_of_mterm m1 |> dest_MFun
val M2 = mtype_of_mterm m2
in
(MApp (m1, m2),
accum |>> set_frame frame
||> add_is_sub_mtype M2 M11
||> add_app aa frame1b frame2b)
end
end)
|> tap (fn (m, (gamma, _)) =>
trace_msg (fn () => " " ^ string_for_mcontext ctxt t gamma ^
" \<turnstile> " ^
string_for_mterm ctxt m))
in do_term end
fun force_gen_funs 0 _ = I
| force_gen_funs n (M as MFun (M1, _, M2)) =
add_mtypes_equal M (MFun (M1, A Gen, M2)) #> force_gen_funs (n - 1) M2
| force_gen_funs _ M = raise MTYPE ("Nitpick_Mono.force_gen_funs", [M], [])
fun consider_general_equals mdata def (x as (_, T)) t1 t2 accum =
let
val (m1, accum) = consider_term mdata t1 accum
val (m2, accum) = consider_term mdata t2 accum
val M1 = mtype_of_mterm m1
val M2 = mtype_of_mterm m2
val accum = accum ||> add_mtypes_equal M1 M2
val body_M = fresh_mtype_for_type mdata false (nth_range_type 2 T)
val m = MApp (MApp (MRaw (Const x,
MFun (M1, A Gen, MFun (M2, A Gen, body_M))), m1), m2)
in
(m, (if def then
let val (head_m, arg_ms) = strip_mcomb m1 in
accum ||> force_gen_funs (length arg_ms) (mtype_of_mterm head_m)
end
else
accum))
end
fun consider_general_formula (mdata as {hol_ctxt = {ctxt, ...}, max_fresh,
...}) =
let
val mtype_for = fresh_mtype_for_type mdata false
val do_term = consider_term mdata
fun do_formula sn t (accum as (gamma, _)) =
let
fun do_quantifier (quant_x as (quant_s, _)) abs_s abs_T body_t =
let
val abs_M = mtype_for abs_T
val x = Unsynchronized.inc max_fresh
val side_cond = ((sn = Minus) = (quant_s = @{const_name Ex}))
fun ann () = if quant_s = @{const_name Ex} then Fls else Tru
val (body_m, accum) =
accum ||> side_cond
? add_mtype_is_complete [(x, (Plus, ann ()))] abs_M
|>> push_bound (V x) abs_T abs_M |> do_formula sn body_t
val body_M = mtype_of_mterm body_m
in
(MApp (MRaw (Const quant_x,
MFun (MFun (abs_M, A Gen, body_M), A Gen, body_M)),
MAbs (abs_s, abs_T, abs_M, A Gen, body_m)),
accum |>> pop_bound)
end
fun do_connect triple neg1 t1 t2 =
consider_connective mdata triple
(do_formula (sn |> neg1 ? negate_sign) t1) (do_formula sn t2)
fun do_equals x t1 t2 =
case sn of
Plus => do_term t accum
| Minus => consider_general_equals mdata false x t1 t2 accum
in
trace_msg (fn () => " " ^ string_for_mcontext ctxt t gamma ^
" \<turnstile> " ^ Syntax.string_of_term ctxt t ^
" : o\<^sup>" ^ string_for_sign sn ^ "?");
case t of
Const (x as (@{const_name all}, _)) $ Abs (s1, T1, t1) =>
do_quantifier x s1 T1 t1
| Const (x as (@{const_name "=="}, _)) $ t1 $ t2 => do_equals x t1 t2
| @{const Trueprop} $ t1 =>
let val (m1, accum) = do_formula sn t1 accum in
(MApp (MRaw (@{const Trueprop}, mtype_for (bool_T --> prop_T)), m1),
accum)
end
| Const (x as (@{const_name All}, _)) $ Abs (s1, T1, t1) =>
do_quantifier x s1 T1 t1
| Const (x0 as (@{const_name Ex}, T0)) $ (t1 as Abs (s1, T1, t1')) =>
(case sn of
Plus => do_quantifier x0 s1 T1 t1'
| Minus =>
(* FIXME: Move elsewhere *)
do_term (@{const Not}
$ (HOLogic.eq_const (domain_type T0) $ t1
$ Abs (Name.uu, T1, @{const False}))) accum)
| Const (x as (@{const_name HOL.eq}, _)) $ t1 $ t2 => do_equals x t1 t2
| Const (@{const_name Let}, _) $ t1 $ t2 =>
do_formula sn (betapply (t2, t1)) accum
| @{const Pure.conjunction} $ t1 $ t2 =>
do_connect meta_conj_triple false t1 t2 accum
| @{const "==>"} $ t1 $ t2 =>
do_connect meta_imp_triple true t1 t2 accum
| @{const Not} $ t1 =>
do_connect imp_triple true t1 @{const False} accum
| @{const conj} $ t1 $ t2 => do_connect conj_triple false t1 t2 accum
| @{const disj} $ t1 $ t2 => do_connect disj_triple false t1 t2 accum
| @{const implies} $ t1 $ t2 => do_connect imp_triple true t1 t2 accum
| _ => do_term t accum
end
|> tap (fn (m, (gamma, _)) =>
trace_msg (fn () => string_for_mcontext ctxt t gamma ^
" \<turnstile> " ^
string_for_mterm ctxt m ^ " : o\<^sup>" ^
string_for_sign sn))
in do_formula end
(* The harmless axiom optimization below is somewhat too aggressive in the face
of (rather peculiar) user-defined axioms. *)
val harmless_consts =
[@{const_name ord_class.less}, @{const_name ord_class.less_eq}]
val bounteous_consts = [@{const_name bisim}]
fun is_harmless_axiom ({no_harmless = true, ...} : mdata) _ = false
| is_harmless_axiom {hol_ctxt = {thy, stds, ...}, ...} t =
Term.add_consts t []
|> filter_out (is_built_in_const thy stds)
|> (forall (member (op =) harmless_consts o original_name o fst) orf
exists (member (op =) bounteous_consts o fst))
fun consider_nondefinitional_axiom mdata t =
if is_harmless_axiom mdata t then pair (MRaw (t, dummy_M))
else consider_general_formula mdata Plus t
fun consider_definitional_axiom (mdata as {hol_ctxt = {ctxt, ...}, ...}) t =
if not (is_constr_pattern_formula ctxt t) then
consider_nondefinitional_axiom mdata t
else if is_harmless_axiom mdata t then
pair (MRaw (t, dummy_M))
else
let
val mtype_for = fresh_mtype_for_type mdata false
val do_term = consider_term mdata
fun do_all quant_t abs_s abs_T body_t accum =
let
val abs_M = mtype_for abs_T
val (body_m, accum) =
accum |>> push_bound (A Gen) abs_T abs_M |> do_formula body_t
val body_M = mtype_of_mterm body_m
in
(MApp (MRaw (quant_t, MFun (MFun (abs_M, A Gen, body_M), A Gen,
body_M)),
MAbs (abs_s, abs_T, abs_M, A Gen, body_m)),
accum |>> pop_bound)
end
and do_conjunction t0 t1 t2 accum =
let
val (m1, accum) = do_formula t1 accum
val (m2, accum) = do_formula t2 accum
in
(MApp (MApp (MRaw (t0, mtype_for (fastype_of t0)), m1), m2), accum)
end
and do_implies t0 t1 t2 accum =
let
val (m1, accum) = do_term t1 accum
val (m2, accum) = do_formula t2 accum
in
(MApp (MApp (MRaw (t0, mtype_for (fastype_of t0)), m1), m2), accum)
end
and do_formula t accum =
case t of
(t0 as Const (@{const_name all}, _)) $ Abs (s1, T1, t1) =>
do_all t0 s1 T1 t1 accum
| @{const Trueprop} $ t1 =>
let val (m1, accum) = do_formula t1 accum in
(MApp (MRaw (@{const Trueprop}, mtype_for (bool_T --> prop_T)), m1),
accum)
end
| Const (x as (@{const_name "=="}, _)) $ t1 $ t2 =>
consider_general_equals mdata true x t1 t2 accum
| (t0 as @{const "==>"}) $ t1 $ t2 => do_implies t0 t1 t2 accum
| (t0 as @{const Pure.conjunction}) $ t1 $ t2 =>
do_conjunction t0 t1 t2 accum
| (t0 as Const (@{const_name All}, _)) $ Abs (s0, T1, t1) =>
do_all t0 s0 T1 t1 accum
| Const (x as (@{const_name HOL.eq}, _)) $ t1 $ t2 =>
consider_general_equals mdata true x t1 t2 accum
| (t0 as @{const conj}) $ t1 $ t2 => do_conjunction t0 t1 t2 accum
| (t0 as @{const implies}) $ t1 $ t2 => do_implies t0 t1 t2 accum
| _ => raise TERM ("Nitpick_Mono.consider_definitional_axiom.\
\do_formula", [t])
in do_formula t end
fun string_for_mtype_of_term ctxt asgs t M =
Syntax.string_of_term ctxt t ^ " : " ^ string_for_mtype (resolve_mtype asgs M)
fun print_mcontext ctxt asgs ({frees, consts, ...} : mcontext) =
trace_msg (fn () =>
map (fn (x, M) => string_for_mtype_of_term ctxt asgs (Free x) M) frees @
map (fn (x, M) => string_for_mtype_of_term ctxt asgs (Const x) M) consts
|> cat_lines)
fun amass f t (ms, accum) =
let val (m, accum) = f t accum in (m :: ms, accum) end
fun infer which no_harmless (hol_ctxt as {ctxt, tac_timeout, ...}) binarize
alpha_T (nondef_ts, def_ts) =
let
val _ = trace_msg (fn () => "****** " ^ which ^ " analysis: " ^
string_for_mtype MAlpha ^ " is " ^
Syntax.string_of_typ ctxt alpha_T)
val mdata as {max_fresh, constr_mcache, ...} =
initial_mdata hol_ctxt binarize no_harmless alpha_T
val accum = (initial_gamma, ([], []))
val (nondef_ms, accum) =
([], accum) |> amass (consider_general_formula mdata Plus) (hd nondef_ts)
|> fold (amass (consider_nondefinitional_axiom mdata))
(tl nondef_ts)
val (def_ms, (gamma, cset)) =
([], accum) |> fold (amass (consider_definitional_axiom mdata)) def_ts
in
case solve tac_timeout (!max_fresh) cset of
SOME asgs => (print_mcontext ctxt asgs gamma;
SOME (asgs, (nondef_ms, def_ms), !constr_mcache))
| _ => NONE
end
handle UNSOLVABLE () => NONE
| MTYPE (loc, Ms, Ts) =>
raise BAD (loc, commas (map string_for_mtype Ms @
map (Syntax.string_of_typ ctxt) Ts))
| MTERM (loc, ms) =>
raise BAD (loc, commas (map (string_for_mterm ctxt) ms))
val formulas_monotonic = is_some oooo infer "Monotonicity" false
fun fin_fun_constr T1 T2 =
(@{const_name FinFun}, (T1 --> T2) --> Type (@{type_name fin_fun}, [T1, T2]))
fun finitize_funs (hol_ctxt as {thy, ctxt, stds, constr_cache, ...}) binarize
finitizes alpha_T tsp =
case infer "Finiteness" true hol_ctxt binarize alpha_T tsp of
SOME (asgs, msp, constr_mtypes) =>
if forall (curry (op =) Gen o snd) asgs then
tsp
else
let
fun should_finitize T aa =
case triple_lookup (type_match thy) finitizes T of
SOME (SOME false) => false
| _ => resolve_annotation_atom asgs aa = A Fls
fun type_from_mtype T M =
case (M, T) of
(MAlpha, _) => T
| (MFun (M1, aa, M2), Type (@{type_name fun}, Ts)) =>
Type (if should_finitize T aa then @{type_name fin_fun}
else @{type_name fun}, map2 type_from_mtype Ts [M1, M2])
| (MPair (M1, M2), Type (@{type_name prod}, Ts)) =>
Type (@{type_name prod}, map2 type_from_mtype Ts [M1, M2])
| (MType _, _) => T
| _ => raise MTYPE ("Nitpick_Mono.finitize_funs.type_from_mtype",
[M], [T])
fun finitize_constr (x as (s, T)) =
(s, case AList.lookup (op =) constr_mtypes x of
SOME M => type_from_mtype T M
| NONE => T)
fun term_from_mterm new_Ts old_Ts m =
case m of
MRaw (t, M) =>
let
val T = fastype_of1 (old_Ts, t)
val T' = type_from_mtype T M
in
case t of
Const (x as (s, _)) =>
if s = @{const_name finite} then
case domain_type T' of
set_T' as Type (@{type_name fin_fun}, _) =>
Abs (Name.uu, set_T', @{const True})
| _ => Const (s, T')
else if s = @{const_name "=="} orelse
s = @{const_name HOL.eq} then
let
val T =
case T' of
Type (_, [T1, Type (_, [T2, T3])]) =>
T1 --> T2 --> T3
| _ => raise TYPE ("Nitpick_Mono.finitize_funs.\
\term_from_mterm", [T, T'], [])
in coerce_term hol_ctxt new_Ts T' T (Const (s, T)) end
else if is_built_in_const thy stds x then
coerce_term hol_ctxt new_Ts T' T t
else if is_constr ctxt stds x then
Const (finitize_constr x)
else if is_sel s then
let
val n = sel_no_from_name s
val x' =
x |> binarized_and_boxed_constr_for_sel hol_ctxt binarize
|> finitize_constr
val x'' =
binarized_and_boxed_nth_sel_for_constr hol_ctxt binarize
x' n
in Const x'' end
else
Const (s, T')
| Free (s, T) => Free (s, type_from_mtype T M)
| Bound _ => t
| _ => raise MTERM ("Nitpick_Mono.finitize_funs.term_from_mterm",
[m])
end
| MApp (m1, m2) =>
let
val (t1, t2) = pairself (term_from_mterm new_Ts old_Ts) (m1, m2)
val (T1, T2) = pairself (curry fastype_of1 new_Ts) (t1, t2)
val (t1', T2') =
case T1 of
Type (s, [T11, T12]) =>
(if s = @{type_name fin_fun} then
select_nth_constr_arg ctxt stds (fin_fun_constr T11 T12) t1
0 (T11 --> T12)
else
t1, T11)
| _ => raise TYPE ("Nitpick_Mono.finitize_funs.term_from_mterm",
[T1], [])
in betapply (t1', coerce_term hol_ctxt new_Ts T2' T2 t2) end
| MAbs (s, old_T, M, aa, m') =>
let
val new_T = type_from_mtype old_T M
val t' = term_from_mterm (new_T :: new_Ts) (old_T :: old_Ts) m'
val T' = fastype_of1 (new_T :: new_Ts, t')
in
Abs (s, new_T, t')
|> should_finitize (new_T --> T') aa
? construct_value ctxt stds (fin_fun_constr new_T T') o single
end
in
Unsynchronized.change constr_cache (map (apsnd (map finitize_constr)));
pairself (map (term_from_mterm [] [])) msp
end
| NONE => tsp
end;