What is algebraic about algebraic effects?
5 hours ago
- #abstract-algebra
- #algebraic-effects
- #programming-languages
- Algebraic in programming refers to a specific kind of compositionality with structured properties.
- Abstract algebra pairs mathematical objects with operations that follow certain laws, providing structure.
- Groups in algebra are structures with closure, associativity, identity, and inverse properties.
- CRDTs use algebraic structures like semi-lattices to ensure data consistency over unreliable networks.
- Monads provide compositional properties in code but may require transformers for interoperation.
- Algebraic effects allow composable effects with guaranteed properties, unlike arbitrary effect handling.
- Key/value store operations can be designed with algebraic properties like idempotence and commutativity.
- Dependent type languages like Coq and Lean can enforce algebraic properties through proofs.
- Alan Kay's analogy compares unstructured code to piles of rocks, advocating for mathematical structure in software.