The Structural λ-Calculus

Accattoli, Beniamino; Kesner, Delia

doi:10.1007/978-3-642-15205-4_30

Cited by 53 publications

(75 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We shall see that each is Cauchy-continuous; then, by a standard result of analysis, each uniquely extends to a continuous function on the completion Λ ∞ , i.e., the Cauchy-continuity of reduction on Λ p automatically implies the existence of a (unique) notion of reduction on Λ ∞ (note that simple continuity would not be enough). 2 Of course we already know this (we can define directly on Λ ∞ ), but what we want to stress here is that, even if we were not able to explicitly describe the terms of Λ ∞ , we would still know how to reduce them.…”

Section: Cauchy-continuity Of Reductionmentioning

confidence: 96%

“…Since then, it has influenced many aspects of the development of the theory of functional languages: from denotational semantics, categorical semantics, and computational interpretations of classical logic [10], to higher-order languages for quantum computation [14], passing through a number of important pragmatic aspects, such as optimal reduction [4], constant-size programming [17] and explicit substitutions [2].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An Infinitary Affine Lambda-Calculus Isomorphic to the Full Lambda-Calculus

Mazza¹

2012

2012 27th Annual IEEE Symposium on Logic in Computer Science

View full text Add to dashboard Cite

It is well known that the real numbers arise from the metric completion of the rational numbers, with the metric induced by the usual absolute value. We seek a computational version of this phenomenon, with the idea that the role of the rationals should be played by the affine lambda-calculus, whose dynamics is finitary; the full lambda-calculus should then appear as a suitable metric completion of the affine lambda-calculus. This paper proposes a technical realization of this idea: an affine lambda-calculus is introduced, based on a fragment of intuitionistic multiplicative linear logic; the calculus is endowed with a notion of distance making the set of terms an incomplete metric space; the completion of this space is shown to yield an infinitary affine lambda-calculus, whose quotient under a suitable partial equivalence relation is exactly the full (non-affine) lambda-calculus. We also show how this construction brings interesting insights on some standard rewriting properties of the lambda-calculus (finite developments, confluence, standardization, head normalization and solvability).

show abstract

Section: Cauchy-continuity Of Reductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

An Infinitary Affine Lambda-Calculus Isomorphic to the Full Lambda-Calculus

Mazza¹

2012

2012 27th Annual IEEE Symposium on Logic in Computer Science

View full text Add to dashboard Cite

show abstract

“…Our calculus borrows ideas from two existing calculi, Herbelin and Zimmerman's λ CBV -calculus [11] and Accattoli and Kesner's λ sub -calculus [4], as we explain in Section 2. In particular, it is a reformulation at a distance [5,4]-i.e. without commutative rules-of λ CBV .…”

Section: λ-Theories a Term T Is Solvable If There Exists A Head Contmentioning

confidence: 99%

Call-by-Value Solvability, Revisited

Accattoli

Paolini

2012

Functional and Logic Programming

Self Cite

View full text Add to dashboard Cite

Abstract. In the call-by-value lambda-calculus solvable terms have been characterised by means of call-by-name reductions, which is disappointing and requires complex reasonings. We introduce the valuesubstitution lambda-calculus, a simple calculus borrowing ideas from Herbelin and Zimmerman's call-by-value λCBV calculus and from Accattoli and Kesner's substitution calculus λsub. In this new setting, we characterise solvable terms as those terms having normal form with respect to a suitable restriction of the rewriting relation.

show abstract

“…These two features of LL have influenced the theory of explicit substitutions in various ways [12,16,23,24], culminating in the design of the structural λ-calculus [8], a calculus isomorphic (more precisely strongly bisimilar 1 ) to its representation in a variant of LL proof nets [7,1]. Such a calculus can be seen as an algebraic reformulation of proof nets for λ-calculus [14,36], and turned out to have a simpler meta-theory than previous calculi with explicit substitutions.…”

Section: Introductionmentioning

confidence: 99%

“…7.b would be rejected by the original version of the criterion, which is based on a different orientation. But the original orientation cannot be applied to the fragment under study 8. Just replace each sequence of a !…”

mentioning

confidence: 99%

Proof nets and the call-by-value λ-calculus

Accattoli

2015

Theoretical Computer Science

Self Cite

View full text Add to dashboard Cite

Please cite this article in press as: B. Accattoli, Proof nets and the call-by-value λ-calculus, Theoret. Comput. Sci. (2015), http://dx. AbstractThis paper gives a detailed account of the relationship between (a variant of) the call-by-value lambda calculus and linear logic proof nets. The presentation is carefully tuned in order to realize an isomorphism between the two systems: every single rewriting step on the calculus maps to a single step on proof nets, and viceversa. In this way, we obtain an algebraic reformulation of proof nets. Moreover, we provide a simple correctness criterion for our proof nets, which employ boxes in an unusual way, and identify a subcalculus that is shown to be as expressive as the full calculus.

show abstract

The Structural λ-Calculus

Cited by 53 publications

References 18 publications

An Infinitary Affine Lambda-Calculus Isomorphic to the Full Lambda-Calculus

An Infinitary Affine Lambda-Calculus Isomorphic to the Full Lambda-Calculus

Call-by-Value Solvability, Revisited

Proof nets and the call-by-value λ-calculus

Contact Info

Product

Resources

About