simply-typed-lambda-calculus

To implement the simply-typed lambda calculus, define syntax for types and terms, then implement typing judgments and small-step evaluation rules to prove progress and preservation properties.

The simply-typed lambda calculus is a foundational model for learning type systems and formalizing programming languages, providing a practical framework to implement and understand core type theory concepts.

Implement typing judgments for STLC by defining evaluation rules for base types, functions, products, sums, and unit types, ensuring the small-step evaluation respects the type system structure.

Prove progress and preservation by defining small-step evaluation rules and typing judgments, demonstrating that well-typed terms either evaluate to values or take valid steps without type errors.

Learning the simply-typed lambda calculus is an entry point for type theory, though familiarity with formal logic or basic interpreter construction helps grasp typing judgments and evaluation rules.