Pattern concepts are everywhere in our world—from design patterns in software architecture, to musical patterns in composition, to literary patterns in poetry, to behavioral patterns in psychology. The Pattern data structure is designed to support this intuitive way of thinking about pattern concepts as first-class entities.
This guide will help you understand the Pattern data structure, learn how to use it effectively, and explore its powerful capabilities through category-theoretic foundations.
A Pattern is a decorated sequence: the elements form the pattern concept itself, and the value provides decoration about that pattern concept.
For example, consider a musical pattern like "A B B A" (an enclosed rhyme pattern). In Pattern notation:
["Enclosed rhyme" | A, B, B, A]
Here:
- The elements (
A, B, B, A) are the pattern concept—they form the sequence that defines the pattern concept - The value (
"Enclosed rhyme") provides decoration—it describes what kind of pattern concept this is
This simple structure enables powerful ways to represent, manipulate, and reason about pattern concepts.
Many systems represent pattern concepts implicitly. For example, knowledge graphs encode pattern concepts as implicit traversals of the graph structure. A classic example is "Route 66"—it's both a sequence of road segments and information about the entire route (history, pop culture, etc.). In a knowledge graph, Route 66 might be represented as nodes connected by relationships, but the pattern concept itself (the sequence) is implicit—you have to traverse the graph to discover it.
The Pattern data structure makes pattern concepts explicit. Route 66 as a Pattern would explicitly represent both:
- The sequence of road segments (as elements)
- The decoration about the route (history, pop culture) as the value
In agentic systems, workflows and reasoning traces can be thought of as equivalent pattern concepts when they achieve the same outcome, even though the approaches and individual steps may differ. The Pattern data structure gives us a way to:
- Compare equivalent pattern concepts (same outcome, different approaches)
- Compose pattern structures to build more complex structures
- Factor pattern structures to extract common elements
Pattern concepts align with how we naturally think about patterns in the world. Whether you're working with:
- Design patterns in software architecture
- Architectural patterns in building design
- Musical patterns in composition
- Literary patterns in poetry
- Behavioral patterns in psychology
The Pattern data structure provides a consistent, powerful way to represent and work with these pattern concepts.
This guide progresses from basic concepts to advanced topics:
- Basic Concepts - Understanding the Pattern data structure as decorated sequences
- Construction - Creating Pattern data structures with construction functions
- Basic Operations - Accessing components and querying Pattern data structures
- Typeclass Instances - Advanced operations (Functor, Foldable, Traversable, etc.)
- Advanced Morphisms - Category theory foundations
- Use Cases - Real-world applications
Each section builds on previous knowledge, with examples that progress from simple conceptual sketches to complete working code.
Throughout this guide, we use gram notation as the standard representation of Patterns. Gram notation provides a concise, readable way to express Pattern structures:
- Atomic pattern:
["value"]- A pattern with no elements - Pattern with elements:
["value" | elem1, elem2]- A pattern with value and elements - Nested patterns:
["outer" | ["inner" | elem]]- Patterns containing other patterns
All examples include both gram notation and Haskell code, so you can see both the conceptual representation and the implementation.
Ready to dive in? Start with Basic Concepts to understand how the Pattern data structure works as decorated sequences.