Type Theory

SkillAI & models

Expert skill in type theory foundations for implementing type systems including inference, checking, and subtyping

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What this skill tells your AI

The instructions your AI receives, as published by a5c-ai/babysitter in library/specializations/programming-languages/skills/type-theory/SKILL.md and read by ahel’s review.

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" }
    }
  }
}

Signals

GitHub stars: 2k
Forks: 112
Last commit: Sep 2026

Advanced

Item type: skill
Key: type-theory
Source: github.com/a5c-ai/babysitter

github.com/a5c-ai/babysitter