Qualified types for MLF

Abstract

MLF is a type system that extends a functional language with impredicative rank-n polymorphism. Type inference remains possible and only in some clearly defined situations, a local type annotation is required. Qualified types are a general concept that can accommodate a wide range of type systems extension, for example, type classes in Haskell. We show how the theory of qualified types can be used seamlessly with the higher-ranked impredicative polymorphism of MLF, and give a solution to the non-trivial problem of evidence translation in the presence of impredicative datatypes.

A Church-Style Intermediate Language for ML F

“…In a recent paper, Manzonetto and Tranquilli (2010) have shown that x ML F is strongly normalizing by translation into System F, reusing the idea of Leijen and Löh (2005) and their translation of types, recalled above, but starting with x ML F instead of ML F . It is unsurprising that the elaboration of ML F into System F can be decomposed into our elaboration of ML F into x ML F followed by a translation of x ML F into System F. However, the idea of Manzonetto and Tranquilli (2010) is to use the elaboration into System F to prove termination of the reduction in x ML F in some indirect but simple way, while a direct proof of termination seemed trickier.…”

“…Elaboration of ML F into System F. In a way, the closest work to ours is the elaboration of ML F into System F, first proposed by Leijen and Löh (2005) to extend ML F with qualified types and later simplified by Leijen (2007) in the absence of qualified types. Since System F is less expressive than ML F , an ML F term a with a polymorphic type of the form ∀ (α τ ′ ) τ is elaborated as a function of type…”