Theory: Techniques Corpus

12 documents filed under theory. Every one of them is retrievable by agents through rag_context. All categories.

• Algebraic Effects & Optics

  A uniform way for reducers, FSMs, and services to express fine-grained nested-state updates (optics) and real-world side effects (algebraic effects) without leaking IO into the domain core.

• Category Theory in PHP

  Practical implementations of category theory concepts (functors, monads, comonads, transformers, optics, free monads) in PHP 8+.

• Category Theory in Rust

  Practical Rust implementations of categorical abstractions using traits and associated types.

• Category Theory in TypeScript

  TypeScript implementations of categorical abstractions that leverage the type system for composable, type-safe code.

• Category Theory: Mathematical Composition and Abstraction

  The complete theoretical foundation of category theory applied to software engineering: functors, monads, natural transformations, optics, and more.

• Emergence as a Design Practice

  Grounding emergent design in practical steps: simple rules, strong constraints, rich feedback, and adaptation without losing identity.

• Formal Verification: Proving Software Correctness

  Mathematical techniques (Hoare logic, temporal logic, model checking, TLA+, SMT, proof assistants) for proving software satisfies its specification.

• Novel Theories: Original Mathematical Frameworks for Software

  Eight original theoretical frameworks applying topology, differential geometry, homological algebra, and higher category theory to software.

• Process Calculi: Formal Models of Concurrent Communication

  Mathematical frameworks (CSP, pi-calculus, session types, join calculus) for modeling and verifying concurrent communication.

• Software as Life: Computational Nature and Digital Evolution

  Explores how software systems mirror living organisms through physics, emergence, evolution, entropy, and ecosystems.

• Theory Map: Complete Integration Guide

  A master index connecting all theoretical foundations, showing how concepts relate and when to use each paradigm.

• Type Theory: Types as Specifications and Proofs

  A mathematical framework for typing systems (dependent, linear, session, refinement types) connecting types to logic and proofs.