Compositional characterisations of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi>λ</mml:mi></mml:math>-terms using intersection types

Dezani‐Ciancaglini, Mariangiola; Honsell, Furio; Motohama, Yoko

doi:10.1016/j.tcs.2005.03.011

Cited by 23 publications

(3 citation statements)

References 16 publications

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“…A feature of intersection types is the ability to characterise computational properties of λ-terms [37,69], properties which are widely studied in the literature. In particular we recall the following classes of λ-terms:…”

Section: The Birth Of Intersection Typesmentioning

confidence: 99%

“…Other classes of λ-terms are characterised in [37]. Notably intersection types can then be considered the first example of behavioural types, i.e., types able to represent the behaviour of terms.…”

Section: The Birth Of Intersection Typesmentioning

confidence: 99%

“…The second rule depicts the co-variant and contra-variant behaviour of the arrow type constructor with respect to subtyping. Many subtyping relations have been shown to be useful for characterising computational properties of λ-terms [37] and/or for building λ-models, see Section 6. Subtyping can also modify the set of basic types.…”

Section: Type Theoriesmentioning

confidence: 99%

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A tale of intersection types

Bono

Dezani‐Ciancaglini

2020

Proceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science

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Intersection types have come a long way since their introduction in the Seventies. They have been exploited for characterising behaviours of λ-terms and π-calculus processes, building λ-models, verifying properties of higher-order programs, synthesising code, and enriching the expressivity of programming languages. This paper is a light overview of intersection types and some of their applications. CCS Concepts: • Theory of computation → Type theory.

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Section: The Birth Of Intersection Typesmentioning

confidence: 99%

Section: The Birth Of Intersection Typesmentioning

confidence: 99%

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A tale of intersection types

Bono

Dezani‐Ciancaglini

2020

Proceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science

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Recursive Domain Equations of Filter Models

Alessi

Severi

SOFSEM 2008: Theory and Practice of Computer Science

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Abstract. Filter models and (solutions of) recursive domain equations are two different ways of constructing lambda models. Many partial results have been shown about the equivalence between these two constructions (in some specific cases). This paper deepens the connection by showing that the equivalence can be shown in a general framework. We will introduce the class of disciplined intersection type theories and its four subclasses: natural split, lazy split, natural equated and lazy equated. We will prove that each class corresponds to a different recursive domain equation. For this result, we are extracting the essence of the specific proofs for the particular cases of intersection type theories and making one general construction that encompasses all of them. This general approach puts together all these results which may appear scattered and sometimes with incomplete proofs in the literature.

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Types for Hereditary Head Normalizing Terms

Tatsuta¹

Functional and Logic Programming

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Compositional characterisations of λ-terms using intersection types

Cited by 23 publications

References 16 publications

A tale of intersection types

A tale of intersection types

Recursive Domain Equations of Filter Models

Types for Hereditary Head Normalizing Terms

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