Does it support type universes?

Yes, it implements universe levels (Type0, Type1, etc.) to prevent logical paradoxes like Russell's Paradox during formal proof verification.

What is bidirectional type checking?

It is an algorithm that splits type checking into two modes: 'Inference', where the system determines the type of an expression, and 'Check', where the system verifies that an expression matches a specific expected type.

How does this skill handle dependent types?

It supports Pi types (functions where return types depend on input values) and Sigma types (dependent pairs), allowing for extremely precise specifications like vectors of a specific length.

What is the GF(3) Trit role?

In this ecosystem, the Type Checker acts as a VALIDATOR (Trit -1), providing the necessary logical constraints to balance generative and coordinative code components.

Dependent Type Checker

Name: Dependent Type Checker
Author: plurigrid

byplurigrid

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Developer Tools

Validates program correctness using bidirectional type checking and dependent type theory to catch errors at compile time.

About

The Type Checker skill implements a sophisticated bidirectional type system designed for formal verification and rigorous static analysis. By treating types as theorems and programs as proofs, it enables developers to enforce complex logical constraints using Pi and Sigma types. It features a unique GF(3) balance verification system that classifies code components as generators, coordinators, or validators to ensure structural conservation. This skill is essential for developers building domain-specific languages, formalizing mathematical proofs, or ensuring the absolute correctness of critical code paths.

Key Features

Advanced error formatting with fix suggestions and context analysis
Type equality checking via beta-reduction and normalization
GF(3) trit-based conservation and balance verification
Bidirectional type checking (Inference vs. Check modes)
Support for dependent types including Pi and Sigma types
2 GitHub stars

Use Cases

Validating mathematical proofs and topological computations
Implementing type-safe domain-specific languages (DSLs)
Formal verification of mission-critical software and smart contracts

About

Key Features

Advanced error formatting with fix suggestions and context analysis
Type equality checking via beta-reduction and normalization
GF(3) trit-based conservation and balance verification
Bidirectional type checking (Inference vs. Check modes)
Support for dependent types including Pi and Sigma types
2 GitHub stars

Use Cases

Validating mathematical proofs and topological computations
Implementing type-safe domain-specific languages (DSLs)
Formal verification of mission-critical software and smart contracts