DisjointDomainAbstract domains for collections of elements from disjoint unions of domains. Formally, the elements form a cofibered domain from a discrete category.
Elements are grouped into disjoint buckets by a congruence or/and a projection. All operations on elements are performed bucket-wise and must be bucket-closed.
Examples of such domains are path-sensitivity and address sets.
module type Representative = sig ... endBuckets defined by projection. The module is the image (representative) of the projection function of_elt.
module ProjectiveSet
(E : Printable.S)
(B : SetDomain.S with type elt = E.t)
(R : Representative with type elt = E.t) :
sig ... endSet of elements E.t grouped into buckets by R, where each bucket is described by the set B.
module type MayEqualSetDomain = sig ... endmodule ProjectiveSetPairwiseMeet
(E : Printable.S)
(B : MayEqualSetDomain with type elt = E.t)
(R : Representative with type elt = E.t) :
SetDomain.S with type elt = E.tmodule type Congruence = sig ... endBuckets defined by congruence.
module PairwiseSet
(E : Printable.S)
(B : SetDomain.S with type elt = E.t)
(C : Congruence with type elt = E.t) :
SetDomain.S with type elt = E.tSet of elements E.t grouped into buckets by C, where each bucket is described by the set B.
module type RepresentativeCongruence = sig ... endBuckets defined by a coarse projection and a fine congruence. Congruent elements must have the same representative, but not vice versa (Representative would then suffice).
module CombinedSet
(E : Printable.S)
(B : SetDomain.S with type elt = E.t)
(RC : RepresentativeCongruence with type elt = E.t) :
sig ... endSet of elements E.t grouped into buckets by RC, where each bucket is described by the set B.
Generalization of above sets into maps, whose key set behaves like above sets, but each element can also be associated with a value.
module ProjectiveMap
(E : Printable.S)
(V : Printable.S)
(B : MapDomain.S with type key = E.t and type value = V.t)
(R : Representative with type elt = E.t) :
MapDomain.S with type key = E.t and type value = B.valueMap of keys E.t grouped into buckets by R, where each bucket is described by the map B with values V.t.
module PairwiseMap
(E : Printable.S)
(R : Printable.S)
(B : MapDomain.S with type key = E.t and type value = R.t)
(C : Congruence with type elt = E.t) :
MapDomain.S with type key = E.t and type value = B.valueMap of keys E.t grouped into buckets by C, where each bucket is described by the map B with values R.t.