Harnessing ML F with the Power of System F

On the power of coercion abstraction

“…The language F p ι subsumes Fη, F<:, and MLF ( §6); it also fixes and extends a previous language of coercions designed for modeling MLF alone [Manzonetto and Tranquilli 2010]. Our subset of F p ι that coincides with MLF is well-behaved: it satisfies the subject reduction and progress lemmas and strongly normalizes.…”

“…The termination of reduction for Fι can be piggybacked on the termination of reduction in System F: following Manzonetto and Tranquilli [2010], we show a forward simulation between Fι and System F, by translating Fι into System F so that every reduction step in Fι is simulated by at least one reduction step in System F.…”

A Church-Style Intermediate Language for ML F

“…The soundness proof of x ML F has been mechanized in the Coq proof assistant 1 and is briefly discussed in Appendix A. Other interesting proofs of §1 and §2 can be found in Appendix B, except for two results, which have already been proved by Manzonetto and Tranquilli (2010). Detailed proofs of §3 can all be found in the dissertation of Yakobowski (2008, Chapters 14 & 15), although for a slightly different-but equivalentpresentation.…”

“…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. They show that the elaboration preserves well-typedness and the dynamic semantics via a simulation between the reduction of source terms and target terms.…”

“…In x ML F , retyping functions are at the level of types. However, the translation of type instantiations back into coercion functions as done by Manzonetto and Tranquilli (2010) allows one to also see them at the level of terms, bringing x ML F and F η even closer. While the two languages differ in their coercions, they can be combined together as shown in recent work by Cretin and Rémy (2012), allowing a form of abstraction (as in x ML F ) over retyping functions (as in F η ).…”