Tailoring Filter Models

Alessi, Fabio; Barbanera, Franco; Dezani‐Ciancaglini, Mariangiola

doi:10.1007/978-3-540-24849-1_2

Cited by 4 publications

(7 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We have then a family of λ-models, called filter models, one for each β-sound type theory. Note that β-soundness is not a necessary condition to obtain filter models; a counterexample is given in [3].…”

Section: λ-Modelsmentioning

confidence: 99%

“…A recursion scheme is a kind of tree grammar for generating a single, possibly infinite, ranked tree with the start symbol S as the root. As a running example, we use the following recursion scheme 3 :…”

Section: Model Checking = Type Checkingmentioning

confidence: 99%

“…q k , then k = Σ(a). An example is B = (Σ, {q 0 , q 1 }, δ, q 0 ), where 3 This example and the following ones are taken from [56]. Figure 11.…”

Section: Model Checking = Type Checkingmentioning

confidence: 99%

See 2 more Smart Citations

A tale of intersection types

Bono

Dezani‐Ciancaglini

2020

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

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: λ-Modelsmentioning

confidence: 99%

Section: Model Checking = Type Checkingmentioning

confidence: 99%

See 1 more Smart Citation

A tale of intersection types

Bono

Dezani‐Ciancaglini

2020

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

Self Cite

View full text Add to dashboard Cite

show abstract

“…By making subtle changes to the subtyping relation it is possible to capture alternate semantics [7] such as call-by-value [22,54] or lazy evaluation [2]. Barendregt et al [11] give a thorough survey of these type systems.…”

Section: Type Soundnessmentioning

confidence: 99%

Revisiting Elementary Denotational Semantics

Siek¹

2017

Preprint

View full text Add to dashboard Cite

Operational semantics have been enormously successful, in large part due to its flexibility and simplicity, but they are not compositional. Denotational semantics, on the other hand, are compositional but the lattice-theoretic models are complex and difficult to scale to large languages. However, there are elementary models of the λ-calculus that are much less complex: by Coppo, Dezani-Ciancaglini, and Salle (1979), Engeler (1981), and Plotkin (1993. This paper takes first steps toward answering the question: can elementary models be good for the day-to-day work of language specification, mechanization, and compiler correctness? The elementary models in the literature are simple, but they are not as intuitive as they could be. To remedy this, we create a new model that represents functions literally as finite graphs. Regarding mechanization, we give the first machinechecked proof of soundness and completeness of an elementary model with respect to an operational semantics. Regarding compiler correctness, we define a polyvariant inliner for the call-by-value λ-calculus and prove that its output is contextually equivalent to its input. Toward scaling elementary models to larger languages, we formulate our semantics in a monadic style, give a semantics for System F with general recursion, and mechanize the proof of type soundness.

show abstract

“…Problem 19 in the TLCA list was posed by Fabio Alessi and Mariangiola Dezani-Ciancaglini in 2002 (see [1]) and asks whether easiness implies simple easiness. In this paper we negatively answer the question, providing a non-empty co-r.e.…”

Section: Introductionmentioning

confidence: 99%

Easy lambda-terms are not always simple

Carraro

Salibra

2012

RAIRO-Theor. Inf. Appl.

View full text Add to dashboard Cite

Abstract. A closed λ-term M is easy if, for any other closed term N , the lambda theory generated by M = N is consistent. Recently, it has been introduced a general technique to prove the easiness of λ-terms through the semantical notion of simple easiness. Simple easiness implies easiness and allows to prove consistency results via construction of suitable filter models of λ-calculus living in the category of complete partial orderings: given a simple easy term M and an arbitrary closed term N , it is possible to build (in a canonical way) a non-trivial filter model which equates the interpretation of M and N . The question whether easiness implies simple easiness constitutes Problem 19 in the TLCA list of open problems. In this paper we negatively answer the question providing a non-empty co-r.e. (complement of a recursively enumerable) set of easy, but not simple easy, λ-terms.

show abstract

Tailoring Filter Models

Abstract: Abstract. Conditions on type preorders are provided in order to characterize the induced filter models for the λ-calculus and some of its restrictions. Besides, two examples are given of filter models in which not all the continuous functions are representable.

Cited by 4 publications

References 18 publications

A tale of intersection types

A tale of intersection types

Revisiting Elementary Denotational Semantics

Easy lambda-terms are not always simple

Contact Info

Product

Resources

About