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Add unsat core explanations to the simplex

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This commit is contained in:
Guillaume Bury 2020-12-22 14:16:23 +01:00
parent a6f6a99fb3
commit 4be726db43
4 changed files with 99 additions and 52 deletions
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17
src/arith/lra/sidekick_arith_lra.ml
View file

@ -253,7 +253,9 @@ module Make(A : ARG) : S with module A = A = struct
let open LE.Infix in
let le = le - LE.monomial1 t in
let c = LConstr.eq0 le in
SimpSolver.add_constr simplex c)
let lit = assert false (* TODO: find the lit *) in
SimpSolver.add_constr simplex c lit
)
self.t_defs
end;
(* add trail *)
@ -274,7 +276,7 @@ module Make(A : ARG) : S with module A = A = struct
) else (
(* TODO: tag *)
let c = LConstr.of_expr LE.(a-b) pred in
SimpSolver.add_constr simplex c;
SimpSolver.add_constr simplex c lit;
)
end)
end;
@ -283,17 +285,18 @@ module Make(A : ARG) : S with module A = A = struct
| SimpSolver.Solution _m ->
Log.debug 5 "lra: solver returns SAT";
() (* TODO: get a model + model combination *)
| SimpSolver.Unsatisfiable _cert ->
(* we tagged assertions with their lit, so the certificate being an
unsat core translates directly into a conflict clause *)
assert false
| SimpSolver.Unsatisfiable cert ->
begin match SimpSolver.check_cert simplex cert with
| `Ok _unsat_core -> assert false (* TODO *)
| _ -> assert false (* some kind of fatal error ? *)
(* TODO
Log.debugf 5 (fun k->k"lra: solver returns UNSAT@ with cert %a"
(Fmt.Dump.list Lit.pp) lits);
let confl = List.rev_map Lit.neg lits in
(* TODO: produce and store a proper LRA resolution proof *)
SI.raise_conflict si acts confl SI.P.default
*)
*)
end
end;
()

110
src/arith/lra/simplex.ml
View file

@ -122,13 +122,18 @@ module Make_inner
let str_of_erat = Format.to_string Erat.pp
let str_of_q = Format.to_string Q.pp_print
type bound = {
value : Erat.t;
reason : lit option;
}
type t = {
param: param;
tab : Q.t Matrix.t; (* the matrix of coefficients *)
basic : basic_var Vec.vector; (* basic variables *)
nbasic : nbasic_var Vec.vector; (* non basic variables *)
mutable assign : Erat.t M.t; (* assignments *)
mutable bounds : (Erat.t * Erat.t) M.t; (* (lower, upper) bounds for variables *)
mutable bounds : (bound * bound) M.t; (* (lower, upper) bounds for variables *)
mutable idx_basic : int M.t; (* basic var -> its index in [basic] *)
mutable idx_nbasic : int M.t; (* non basic var -> its index in [nbasic] *)
}
@ -136,7 +141,6 @@ module Make_inner
type cert = {
cert_var: var;
cert_expr: (Q.t * var) list;
cert_core: lit list;
}
type res =
@ -239,17 +243,23 @@ module Make_inner
with Not_found -> value_basic t x
(* trivial bounds *)
let empty_bounds : Erat.t * Erat.t = Q.(Erat.make minus_inf zero, Erat.make inf zero)
let empty_bounds : bound * bound =
{ value = Erat.make Q.minus_inf Q.zero; reason = None; },
{ value = Erat.make Q.inf Q.zero; reason = None; }
(* find bounds of [x] *)
let[@inline] get_bounds (t:t) (x:var) : Erat.t * Erat.t =
let[@inline] get_bounds (t:t) (x:var) : bound * bound =
try M.find x t.bounds
with Not_found -> empty_bounds
let[@inline] get_bounds_values (t:t) (x:var) : Erat.t * Erat.t =
let l, u = get_bounds t x in
l.value, u.value
(* is [value x] within the bounds for [x]? *)
let is_within_bounds (t:t) (x:var) : bool * Erat.t =
let v = value t x in
let low, upp = get_bounds t x in
let low, upp = get_bounds_values t x in
if Erat.compare v low < 0 then
false, low
else if Erat.compare v upp > 0 then
@ -313,15 +323,21 @@ module Make_inner
()
(* add bounds to [x] in [t] *)
let add_bound_aux (t:t) (x:var) (low:Erat.t) (upp:Erat.t) : unit =
let add_bound_aux (t:t) (x:var)
(low:Erat.t) (low_reason:lit option)
(upp:Erat.t) (upp_reason:lit option) : unit =
add_vars t [x];
let l, u = get_bounds t x in
t.bounds <- M.add x (Erat.max l low, Erat.min u upp) t.bounds
let l' = if Erat.lt low l.value then l else { value = low; reason = low_reason; } in
let u' = if Erat.gt upp u.value then u else { value = upp; reason = upp_reason; } in
t.bounds <- M.add x (l', u') t.bounds
let add_bounds (t:t) ?strict_lower:(slow=false) ?strict_upper:(supp=false) (x, l, u) : unit =
let add_bounds (t:t)
?strict_lower:(slow=false) ?strict_upper:(supp=false)
?lower_reason ?upper_reason (x, l, u) : unit =
let e1 = if slow then Q.one else Q.zero in
let e2 = if supp then Q.neg Q.one else Q.zero in
add_bound_aux t x (Erat.make l e1) (Erat.make u e2);
add_bound_aux t x (Erat.make l e1) lower_reason (Erat.make u e2) upper_reason;
if mem_nbasic t x then (
let b, v = is_within_bounds t x in
if not b then (
@ -329,8 +345,11 @@ module Make_inner
)
)
let add_lower_bound t ?strict x l = add_bounds t ?strict_lower:strict (x,l,Q.inf)
let add_upper_bound t ?strict x u = add_bounds t ?strict_upper:strict (x,Q.minus_inf,u)
let add_lower_bound t ?strict ~reason x l =
add_bounds t ?strict_lower:strict ~lower_reason:reason (x,l,Q.inf)
let add_upper_bound t ?strict ~reason x u =
add_bounds t ?strict_upper:strict ~upper_reason:reason (x,Q.minus_inf,u)
(* full assignment *)
let full_assign (t:t) : (var * Erat.t) Iter.t =
@ -352,7 +371,8 @@ module Make_inner
let solve_epsilon (t:t) : Q.t =
let emax =
M.fold
(fun x ({base=low;eps_factor=e_low}, {base=upp;eps_factor=e_upp}) emax ->
(fun x ({ value = {base=low;eps_factor=e_low}; _},
{ value = {base=upp;eps_factor=e_upp}; _}) emax ->
let {base=v; eps_factor=e_v} = value t x in
(* lower bound *)
let emax =
@ -396,7 +416,7 @@ module Make_inner
let test (y:nbasic_var) (a:Q.t) : bool =
assert (mem_nbasic t y);
let v = value t y in
let low, upp = get_bounds t y in
let low, upp = get_bounds_values t y in
if b then (
(Erat.lt v upp && Q.compare a Q.zero > 0) ||
(Erat.gt v low && Q.compare a Q.zero < 0)
@ -489,7 +509,7 @@ module Make_inner
(* check bounds *)
let check_bounds (t:t) : unit =
M.iter (fun x (l, u) -> if Erat.gt l u then raise (AbsurdBounds x)) t.bounds
M.iter (fun x (l, u) -> if Erat.gt l.value u.value then raise (AbsurdBounds x)) t.bounds
(* actual solving algorithm *)
let solve_aux (t:t) : unit =
@ -534,9 +554,9 @@ module Make_inner
(Vec.to_list (find_expr_basic t x))
(Vec.to_list t.nbasic)
in
Unsatisfiable { cert_var=x; cert_expr; cert_core=[]; } (* FIXME *)
Unsatisfiable { cert_var=x; cert_expr; } (* FIXME *)
| AbsurdBounds x ->
Unsatisfiable { cert_var=x; cert_expr=[]; cert_core=[]; }
Unsatisfiable { cert_var=x; cert_expr=[]; }
(* add [c·x] to [m] *)
let add_expr_ (x:var) (c:Q.t) (m:Q.t M.t) =
@ -557,38 +577,54 @@ module Make_inner
!m
(* maybe invert bounds, if [c < 0] *)
let scale_bounds c (l,u) : erat * erat =
let scale_bounds c (l,u) : bound * bound =
match Q.compare c Q.zero with
| 0 -> Erat.zero, Erat.zero
| n when n<0 -> Erat.mul c u, Erat.mul c l
| _ -> Erat.mul c l, Erat.mul c u
| 0 ->
let b = { value = Erat.zero; reason = None; } in
b, b
| n when n<0 ->
{ u with value = Erat.mul c u.value; },
{ l with value = Erat.mul c l.value; }
| _ ->
{ l with value = Erat.mul c l.value; },
{ u with value = Erat.mul c u.value; }
let add_to_unsat_core acc = function
| None -> acc
| Some reason -> reason :: acc
let check_cert (t:t) (c:cert) =
let x = c.cert_var in
let low_x, up_x = get_bounds t x in
let { value = low_x; reason = low_x_reason; },
{ value = up_x; reason = upp_x_reason; } = get_bounds t x in
begin match c.cert_expr with
| [] ->
if Erat.compare low_x up_x > 0 then `Ok
if Erat.compare low_x up_x > 0
then `Ok (add_to_unsat_core (add_to_unsat_core [] low_x_reason) upp_x_reason)
else `Bad_bounds (str_of_erat low_x, str_of_erat up_x)
| expr ->
let e0 = deref_var_ t x (Q.neg Q.one) M.empty in
(* compute bounds for the expression [c.cert_expr],
and also compute [c.cert_expr - x] to check if it's 0] *)
let low, up, expr_minus_x =
let low, low_unsat_core, up, up_unsat_core, expr_minus_x =
List.fold_left
(fun (l,u,expr_minus_x) (c, y) ->
(fun (l, luc, u, uuc, expr_minus_x) (c, y) ->
let ly, uy = scale_bounds c (get_bounds t y) in
assert (Erat.compare ly uy <= 0);
assert (Erat.compare ly.value uy.value <= 0);
let expr_minus_x = deref_var_ t y c expr_minus_x in
Erat.sum l ly, Erat.sum u uy, expr_minus_x)
(Erat.zero, Erat.zero, e0)
let luc = add_to_unsat_core luc ly.reason in
let uuc = add_to_unsat_core uuc uy.reason in
Erat.sum l ly.value, luc, Erat.sum u uy.value, uuc, expr_minus_x)
(Erat.zero, [], Erat.zero, [], e0)
expr
in
(* check that the expanded expression is [x], and that
one of the bounds on [x] is incompatible with bounds of [c.cert_expr] *)
if M.is_empty expr_minus_x then (
if Erat.compare low_x up > 0 || Erat.compare up_x low < 0
then `Ok
if Erat.compare low_x up > 0
then `Ok (add_to_unsat_core up_unsat_core low_x_reason)
else if Erat.compare up_x low < 0
then `Ok (add_to_unsat_core low_unsat_core upp_x_reason)
else `Bad_bounds (str_of_erat low, str_of_erat up)
) else `Diff_not_0 expr_minus_x
end
@ -636,7 +672,7 @@ module Make_inner
let pp_bounds =
let open Format in
let pp_pairs out (x,(l,u)) =
fprintf out "(@[%a =< %a =< %a@])" Erat.pp l Var.pp x Erat.pp u
fprintf out "(@[%a =< %a =< %a@])" Erat.pp l.value Var.pp x Erat.pp u.value
in
map Var_map.to_seq @@ within "(" ")" @@ hvbox @@ seq pp_pairs
@ -668,16 +704,18 @@ module Make_full_for_expr(V : VAR_GEN)
type constr = L.Constr.t
(* add a constraint *)
let add_constr (t:t) (c:constr) : unit =
let add_constr (t:t) (c:constr) (reason:lit) : unit =
let (x:var) = V.Fresh.fresh t.param in
let e, op, q = L.Constr.split c in
add_eq t (x, L.Comb.to_list e);
begin match op with
| Leq -> add_upper_bound t ~strict:false x q
| Geq -> add_lower_bound t ~strict:false x q
| Lt -> add_upper_bound t ~strict:true x q
| Gt -> add_lower_bound t ~strict:true x q
| Eq -> add_bounds t ~strict_lower:false ~strict_upper:false (x,q,q)
| Leq -> add_upper_bound t ~strict:false ~reason x q
| Geq -> add_lower_bound t ~strict:false ~reason x q
| Lt -> add_upper_bound t ~strict:true ~reason x q
| Gt -> add_lower_bound t ~strict:true ~reason x q
| Eq -> add_bounds t (x,q,q)
~strict_lower:false ~strict_upper:false
~lower_reason:reason ~upper_reason:reason
| Neq -> assert false
end
end

16
src/arith/lra/simplex_intf.ml
View file

@ -35,7 +35,6 @@ module type S = sig
type cert = {
cert_var: var;
cert_expr: (Q.t * var) list;
cert_core: lit list;
}
(** Generic type returned when solving the simplex. A solution is a list of
@ -66,11 +65,14 @@ module type S = sig
[Q.inf].
Optional parameters allow to make the the bounds strict. Defaults to false,
so that bounds are large by default. *)
val add_bounds : t -> ?strict_lower:bool -> ?strict_upper:bool -> var * Q.t * Q.t -> unit
val add_bounds : t ->
?strict_lower:bool -> ?strict_upper:bool ->
?lower_reason:lit -> ?upper_reason:lit ->
var * Q.t * Q.t -> unit
val add_lower_bound : t -> ?strict:bool -> var -> Q.t -> unit
val add_lower_bound : t -> ?strict:bool -> reason:lit -> var -> Q.t -> unit
val add_upper_bound : t -> ?strict:bool -> var -> Q.t -> unit
val add_upper_bound : t -> ?strict:bool -> reason:lit -> var -> Q.t -> unit
(** {3 Simplex solving} *)
@ -85,10 +87,10 @@ module type S = sig
val check_cert :
t ->
cert ->
[`Ok | `Bad_bounds of string * string | `Diff_not_0 of Q.t Var_map.t]
[`Ok of lit list | `Bad_bounds of string * string | `Diff_not_0 of Q.t Var_map.t]
(** checks that the certificat indeed yields to a contradiction
in the current state of the simplex.
@return [`Ok] if the certificate is valid. *)
@return [`Ok unsat_core] if the certificate is valid. *)
(* TODO: push/pop? at least on bounds *)
@ -119,6 +121,6 @@ module type S_FULL = sig
type constr = L.Constr.t
val add_constr : t -> constr -> unit
val add_constr : t -> constr -> lit -> unit
(** Add a constraint to a simplex state. *)
end

8
src/arith/tests/test_simplex.ml
View file

@ -107,7 +107,11 @@ module Problem = struct
QC.list_of_size QC.Gen.(m -- n) @@ Constr.rand 10
end
let add_problem (t:Spl.t) (pb:Problem.t) : unit = List.iter (Spl.add_constr t) pb
let add_problem (t:Spl.t) (pb:Problem.t) : unit =
(* TODO: use an arbitrary litteral if the tests do not check the unsat core,
or else add litterals to the generated problem. *)
let lit = assert false in
List.iter (fun constr -> Spl.add_constr t constr lit) pb
let pp_subst : subst Fmt.printer =
Fmt.(map Spl.L.Var_map.to_seq @@
@ -150,7 +154,7 @@ let check_sound =
)
| Spl.Unsatisfiable cert ->
begin match Spl.check_cert simplex cert with
| `Ok -> true
| `Ok _ -> true
| `Bad_bounds (low, up) ->
QC.Test.fail_reportf
"(@[<hv>bad-certificat@ :problem %a@ :cert %a@ :low %s :up %s@ :simplex-after %a@ :simplex-before %a@])"