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semilattices
This Haskell package defines typeclasses for join- and meet-semilattices, and for upper and lower bounds, and a variety of instances for each.
Usage
Semilattices are idempotent commutative semigroups, and come in two flavours: Join
and Meet
. This presentation of them doesn’t inherit from Semigroup
however, since Semigroup
s already exist and the relationships between the various classes here warrant their own operators.
Join semilattices can be combined using the \/
operator (pronounced “lub,” for “least upper bound”). Meet semilattices can be combined with the /\
operator (pronounced “glb,” for “greatest lower bound”). They have opposite relationships to Lower
and Upper
bounds (which are optional; in general, there are more lower bounds than upper ones).
Related work
lattices
also offers join & meet semilattices, & their respective bounds. Relative tolattices
,semilattices
primarily offers a different class hierarchy, e.g.Lower
&Upper
do not haveJoin
&Meet
as superclasses. Relative tosemilattices
,lattices
offers classes for lattices (both bounded and un-), partial orderings, a variety of operations for instances.