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On the Power of Coercion Abstraction

Abstract : Erasable coercions in System F-eta, also known as retyping functions, are well-typed eta-expansions of the identity. They may change the type of terms without changing their behavior and can thus be erased before reduction. Coercions in F-eta can model subtyping of known types and some displacement of quantifiers, but not subtyping assumptions nor certain forms of delayed type instantiation. We generalize F-eta by allowing abstraction over retyping functions. We follow a general approach where computing with coercions can be seen as computing in the lambda-calculus but keeping track of which parts of terms are coercions. We obtain a language where coercions do not contribute to the reduction but may block it and are thus not erasable. We recover erasable coercions by choosing a weak reduction strategy and restricting coercion abstraction to value-forms or by restricting abstraction to coercions that are polymorphic in their domain or codomain. The latter variant subsumes F-eta, F-sub, and MLF in a unified framework.
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Submitted on : Monday, December 12, 2011 - 2:14:37 PM
Last modification on : Friday, January 21, 2022 - 3:15:34 AM
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  • HAL Id : inria-00582570, version 3



Julien Cretin, Didier Rémy. On the Power of Coercion Abstraction. [Research Report] RR-7587, INRIA. 2011, pp.59. ⟨inria-00582570v3⟩



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