semilattices: Semilattices

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Join- and meet-semilattices, with optional upper and lower bounds, and a variety of instances for each.

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Versions	0.0.0.0, 0.0.0.1, 0.0.0.2, 0.0.0.3, 0.0.0.4, 0.0.0.5, 0.0.0.5, 0.0.0.6, 0.0.0.7, 0.0.0.8
Change log	ChangeLog.md
Dependencies	base (>=4.9 && <5), containers (>=0.5 && <0.7), unordered-containers (>=0.2 && <0.3) [details]
License	BSD-3-Clause
Copyright	2017-2024 Rob Rix
Author	Rob Rix
Maintainer	rob.rix@me.com
Category	Algebra, Data, Data Structures, Math
Home page	https://github.com/robrix/semilattices
Source repo	head: git clone https://github.com/robrix/semilattices
Uploaded	by robrix at 2024-03-04T17:05:22Z

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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 Semigroups 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).

lattices also offers join & meet semilattices, & their respective bounds. Relative to lattices, semilattices primarily offers a different class hierarchy, e.g. Lower & Upper do not have Join & Meet as superclasses. Relative to semilattices, lattices offers classes for lattices (both bounded and un-), partial orderings, a variety of operations for instances.