Algebraic structure
An algebraic structure is a set of elements equipped with operations and laws governing those operations.
Functional Programming in Scala, Second Edition
An algebra is an abstract system consisting of operations on elements together with laws that specify how those operations behave.
- How it is used
- Guides functional API design by treating operations and laws as a manipulable interface before implementation.
- How deep it goes
- Defines operations and laws, derives combinators, and tests expressiveness; defers concrete representation during design.
- Examples
- Uses parallel computations, parser construction, monoid operations, map and flatMap, join, choice, and automatically checked API properties.
- What you can do after
- Build it from scratch by specifying primitives, laws, derived combinators, and implementation-independent client programs.
Read how Functional Programming in Scala, Second Edition explains algebraic structure →
Geometry for Programmers
An algebraic system is a set of mathematical entities together with defined operations and rules for manipulating them.
- How it is used
- Frames numbers, vectors, and matrices as sets with operations and rules useful for geometric and computational reasoning.
- How deep it goes
- Defines structures through closure, associativity, commutativity, identity, and inverses, then stops short of formal classification.
- Examples
- Uses integer addition, vector addition and scalar multiplication, and matrix multiplication as concrete structures.
- What you can do after
- Evaluate whether a set of entities and operations share recognizable algebraic properties.
Read how Geometry for Programmers explains algebraic structure →
Related concepts
- Monoidincludes · A monoid is an algebraic structure consisting of a set with an associative binary operation and an identity element.
- groupincludes · A group is a set with a closed associative binary operation, an identity element, and an inverse for every element.
- grid containerincludes · A grid container is an element whose display mode establishes a CSS Grid formatting context for laying out its child elements as grid items.
- contractincludes · An API contract is a specification of the operations, data, and behavioral expectations that govern interactions between software components.
- algebraic lawhas part · An algebraic law is a general equation or behavioral property that an operation or implementation is expected to satisfy for applicable values.
These guides are generated from the text of Manning books by Manning's knowledge graph and link to the sections they draw on. The full books are available on liveBook and at manning.com.