bidirectional-type-checking

Bidirectional type checking improves compiler error messages by using mode-directed inference and checking to pinpoint exact type mismatches locally. This enables structured error reporting during elaboration from surface syntax to a typed core.

To implement bidirectional typing rules for lambda calculus, distinguish between inference and checking modes. This mode-directed approach allows the type checker to synthesize types from expressions or verify expressions against expected types.

Elaboration is the process of converting untyped surface syntax into a fully typed core language. By using bidirectional type checking, the compiler ensures this conversion is type-safe and generates structured errors for invalid programs.

Yes, implementing bidirectional type checking requires expertise in functional programming and type theory. The algorithm relies on concepts common in languages like Haskell and OCaml to manage mode-directed inference and elaboration.

Inference mode synthesizes a type from an expression, while checking mode verifies an expression against an expected type. Bidirectional type checking alternates between these modes to achieve precise type analysis and better local error reporting.

Use bidirectional type checking when building a compiler that needs better local error messages and support for advanced type system features. It handles complex rules by combining inference and checking modes during elaboration.