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Intersection Types and Computational Effects
, 2000
"... We show that standard formulations of intersection type systems are unsound in the presence of computational effects, and propose a solution similar to the value restriction for polymorphism adopted in the revised definition of Standard ML. It differs in that it is not tied to letexpressions and re ..."
Abstract

Cited by 65 (6 self)
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We show that standard formulations of intersection type systems are unsound in the presence of computational effects, and propose a solution similar to the value restriction for polymorphism adopted in the revised definition of Standard ML. It differs in that it is not tied to letexpressions and requires an additional weakening of the usual subtyping rules. We also present a bidirectional typechecking algorithm for the resulting language that does not require an excessive amount of type annotations and illustrate it through some examples. We further show that the type assignment system can be extended to incorporate parametric polymorphism. Taken together, we see our system and associated typechecking algorithm as a significant step towards the introduction of intersection types into realistic programming languages. The added expressive power would allow many more properties of programs to be stated by the programmer and statically verified by a compiler.
Typability is undecidable for F+eta
, 1995
"... System F is the wellknown polymorphicallytypedcalculus with universal quanti ers (\8"). F+ is System F extended with the eta rule, which says that if term M can be given type and Mreduces to N, then N can also be given the type. Adding the eta rule to System F is equivalent to adding the subsump ..."
Abstract

Cited by 9 (6 self)
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System F is the wellknown polymorphicallytypedcalculus with universal quanti ers (\8"). F+ is System F extended with the eta rule, which says that if term M can be given type and Mreduces to N, then N can also be given the type. Adding the eta rule to System F is equivalent to adding the subsumption rule using the subtyping (\containment") relation that Mitchell de ned and axiomatized [Mit88]. The subsumption rule says that if M can be given type and is a subtype of type,thenMcan be given type. Mitchell's subtyping relation involves no extensions to the syntaxoftypes, i.e., no bounded polymorphism and no supertype of all types, and is thus unrelated to the system F (\Fsub"). Typability for F+ is the problem of determining for any termMwhether there is any type that can be given to it using the type inference rules of F+. Typability has been proven undecidable for System F [Wel94] (without the eta rule), but the decidability oftypability has been an open problem for F+. Mitchell's subtyping relation has recently been proven undecidable [TU95, Wel95b], implying the undecidability of\type checking " for F+. This paper reduces the problem of subtyping to the problem of typability for F+,thus proving the undecidability oftypability. The proof methods are similar in outline to those used to prove the undecidability oftypability for System F, but the ne details di er greatly. 1