A Type Checking Algorithm for Higher-rank, Impredicative and Second-order Types
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We study a type checking algorithm that is able to type check a nontrivial subclass of functional programs that use features such as higher-rank, impredicative and second-order types. The only place the algorithm requires type annotation is before each function declaration. We prove the soundness of the type checking algorithm with respect to System F_ω, i.e. if the program is type checked, then the type checker will produce a well-typed annotated System F_ω term. We extend the basic algorithm to handle pattern matching and let-bindings. We implement a prototype type checker and test it on a variety of functional programs.
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