Note: This document accompanies the paper “Practical type inference for arbitrary-rank types ” [6]. Prior reading of the main paper is required. 1 Contents

apport de recherche ISSN 0249-6399 ISRN INRIA/RR--????--FR+ENG A graphical presentation of MLF types with a linear-time local unification algorithm.

HMF is a conservative extension of Hindley-Milner type inference with first-class polymorphism. In contrast to other proposals, HML uses regular System F types and has a simple type inference algorithm that is just a small extension of the usual Damas-Milner algorithm W. Given the relative simplicity and expressive power, we feel that HMF can be an attractive type system in practice. There is a reference implementation of the type system available online together with

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MLF is a type system that seamlessly merges ML-style implicit but second-class polymorphism with System F explicit first-class polymorphism. We present xMLF, a Church-style version of MLF with full type information that can easily be maintained during reduction. All parameters of functions are explicitly typed and both type abstraction and type instantiation are explicit. However, type instantiation in xMLF is more general than type application in System F. We equip xMLF with a small-step reduction semantics that allows reduction in any context and show that this relation is confluent and type preserving. We also show that both subject reduction and progress hold for weak-reduction strategies, including call-byvalue with the value-restriction. We exhibit a type preserving encoding of MLF into xMLF, which ensures type soundness for the most general version of MLF. We observe that xMLF is a calculus of retyping functions at the type level.

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Languages supporting polymorphism typically have ad-hoc restrictions on where polymorphic types may occur. Supporting “firstclass” polymorphism, by lifting those restrictions, is obviously desirable, but it is hard to achieve this without sacrificing type inference. We present a new type system for higher-rank and impredicative polymorphism that improves on earlier proposals: it is an extension of Damas-Milner; it relies only on System F types; it has a simple, declarative specification; it is robust to program transformations; and it enjoys a complete and decidable type inference algorithm. 1.

apport de recherche ISSN 0249-6399 ISRN INRIA/RR--????--FR+ENGA graphical presentation of MLF types with a linear-time local unification algorithm.

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