Typology is a work in progress attempt to implement type checking of Swift in Swift itself. Currently it uses SwiftSyntax as a parser, but is ready to switch to other pure Swift parsers in the future when any are available.

• Education: understanding how type checking can be implemented in a Swift compiler
• User Experience: finding the best way to report type errors and to improve related developer tools
• Research and Experimentation: prototyping advanced features that could be fully developed within Swift's type system.

Same as the type checker in Apple's Swift compiler, Typology relies on the fact that you can express type systems with a set of constraints on types that are resolved through unification.

• Apple's Swift Compiler Type Checker Design and Implementation by multiple contributors
• A Type System From Scratch by @CodaFi
• Write You a Haskell: Hindley-Milner Inference by @sdiehl
• Typing Haskell in Haskell by Mark P Jones
• “What part of Hindley-Milner do you not understand?” question and answers on StackOverflow
• So you want to write a type checker... by @psygnisfive
• Exponential time complexity in the Swift type checker by @mattgallagher
• A Swift Playground containing Martin Grabmüller's "Algorithm W Step-by-Step" by @CodaFi

• Compiler Errors for Humans on Elm blog
• Shape of errors to come in Rust compiler by Jonathan Turner

• Apple's Swift Compiler Dependency Analysis by multiple contributors