Type Theory Skill
Overview
Expert skill in type theory foundations for implementing type systems including inference, checking, and subtyping.
Capabilities
- Implement Hindley-Milner type inference with Algorithm W
- Implement constraint-based type inference with unification
- Design and implement bidirectional type checking
- Implement structural and nominal subtyping
- Handle variance (covariant, contravariant, invariant)
- Implement row polymorphism and record types
- Design flow-sensitive type narrowing
- Implement type error message generation
Target Processes
- type-system-implementation.js
- semantic-analysis.js
- generics-polymorphism.js
- effect-system-design.js
Dependencies
Academic type theory literature (TAPL, ATTAPL)
Usage Guidelines
- Algorithm Selection: Choose between HM inference and bidirectional checking based on language features
- Constraint Generation: Separate constraint generation from solving for cleaner implementation
- Error Localization: Track constraint origins for accurate error location
- Variance: Document variance rules explicitly for all generic positions
- Gradual Typing: Consider gradual typing for mixed typed/untyped codebases
Output Schema
{
"type": "object",
"properties": {
"inferenceAlgorithm": {
"type": "string",
"enum": ["hindley-milner", "bidirectional", "constraint-based", "flow-sensitive"]
},
"subtypingKind": {
"type": "string",
"enum": ["structural", "nominal", "mixed"]
},
"features": {
"type": "array",
"items": { "type": "string" }
},
"generatedFiles": {
"type": "array",
"items": { "type": "string" }
}
}
}