Type Theory

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

1. Algorithm Selection: Choose between HM inference and bidirectional checking based on language features
2. Constraint Generation: Separate constraint generation from solving for cleaner implementation
3. Error Localization: Track constraint origins for accurate error location
4. Variance: Document variance rules explicitly for all generic positions
5. 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" }
    }
  }
}