A tale of intersection types

Bono, Viviana; Dezani‐Ciancaglini, Mariangiola

doi:10.1145/3373718.3394733

Cited by 5 publications

(2 citation statements)

References 61 publications

(84 reference statements)

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“…In the opposite direction we have Intersection Type Systems [10,11,6]. They characterise exactly the set of strongly normalising terms and thus they type more terms than the Curry type system [12] or the type system of pure ML or core Haskell [14].…”

Section: Introductionmentioning

confidence: 99%

Structural Rules and Algebraic Properties of Intersection Types

Alves¹,

Florido²

2022

Preprint

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In this paper we define several notions of term expansion, used to define terms with less sharing, but with the same computational properties of terms typable in an intersection type system. Expansion relates terms typed by associative, commutative and idempotent intersections with terms typed in the Curry type system and the relevant type system; terms typed by non-idempotent intersections with terms typed in the affine and linear type systems; and terms typed by non-idempotent and non-commutative intersections with terms typed in an ordered type system. Finally, we show how idempotent intersection is related with the contraction rule, commutative intersection with the exchange rule and associative intersection with the lack of structural rules in a type system.

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Section: Introductionmentioning

confidence: 99%

Structural Rules and Algebraic Properties of Intersection Types

Alves¹,

Florido²

2022

Preprint

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“…At first sight, such types are simply a slight variation on simple types, in which one can assign a finite set of types to a term, thus providing a form of finite polymorphism. While some forms of intersection types can be used for programming purposes (see Dezani-Ciancaglini et al [28], Freeman and Pfenning [30], Frisch et al [32], Pierce [41] or the recent survey by Bono and Dezani-Ciancaglini [17]), they have mainly played a more theoretical role, so far.…”

Section: Introductionmentioning

confidence: 99%

Multi Types and Reasonable Space (Long Version)

Accattoli¹,

Lago²,

Vanoni³

2022

Preprint

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and Vanoni have recently proved that the space used by the Space KAM, a variant of the Krivine abstract machine, is a reasonable space cost model for the -calculus accounting for logarithmic space, solving a longstanding open problem. In this paper, we provide a new system of multi types (a variant of intersection types) and extract from multi type derivations the space used by the Space KAM, capturing into a type system the space complexity of the abstract machine. Additionally, we show how to capture also the time of the Space KAM, which is a reasonable time cost model, via minor changes to the type system.

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Structural Rules and Algebraic Properties of Intersection Types

Alves

Florido²

2022

Lecture Notes in Computer Science

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A tale of intersection types

Cited by 5 publications

References 61 publications

Structural Rules and Algebraic Properties of Intersection Types

Structural Rules and Algebraic Properties of Intersection Types

Multi Types and Reasonable Space (Long Version)

Structural Rules and Algebraic Properties of Intersection Types

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