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Solvability in Resource Lambda-Calculus
[chapter]

2010
*
Lecture Notes in Computer Science
*

Because of the non-determinism, different definitions of

doi:10.1007/978-3-642-12032-9_25
fatcat:cantaak2ovdrfobag3rxgm22km
*solvability*are possible*in*the*resource**calculus*. ... The*resource**calculus*is an extension of the λ-*calculus*allowing to model*resource*consumption. ...*In*Section 5 there is the proof of the main theorem, showing all the characterizations of*solvability*.*In*Section 6 alternative notions of*solvability*are discussed.*Resource**Calculus*Syntax. ...##
###
A Semantical and Operational Account of Call-by-Value Solvability
[chapter]

2014
*
Lecture Notes in Computer Science
*

*In*Plotkin's call-by-value

*lambda*-

*calculus*,

*solvable*terms are characterized syntactically by means of call-by-name reductions and there is no neat semantical characterization of such terms. ... As a technical tool, we also use a

*resource*-sensitive

*calculus*

*in*which the elements of the model are definable. ... A relational model of (

*resource*) CBV

*lambda*-

*calculus*

*In*this section we present a relational model for both the λ σ v -

*calculus*and the

*resource*λ σ v -

*calculus*. ...

##
###
Standardization in resource lambda-calculus

2012
*
Electronic Proceedings in Theoretical Computer Science
*

The

doi:10.4204/eptcs.101.1
fatcat:bwuyv7qddrhcxh6fmpantjndoy
*resource**calculus*is an extension of the*lambda*-*calculus*allowing to model*resource*consumption. ... We prove that the non-deterministic reduction enjoys a notion of standardization, which is the natural extension with respect to the similar one*in*classical*lambda*-*calculus*. ... Introduction The*resource**calculus*(Λ r ) is an extension of the λ -*calculus*allowing to model*resource*consumption. ...##
###
Page 6020 of Mathematical Reviews Vol. , Issue 2000i
[page]

2000
*
Mathematical Reviews
*

*In*the last section, the simply typed

*lambda*

*calculus*is studied. The standard set theoretical model of STT is given. ...

*In*the second section, the untyped

*lambda*

*calculus*and the untyped universe are considered. Their connection with combinatory logic is shown. ...

##
###
Full Abstraction for the Resource Lambda Calculus with Tests, through Taylor Expansion

2012
*
Logical Methods in Computer Science
*

We study the semantics of a

doi:10.2168/lmcs-8(4:3)2012
fatcat:wea6gyv45ncxvixdwmtzp5kd3u
*resource*-sensitive extension of the*lambda**calculus**in*a canonical reflexive object of a category of sets and relations, a relational version of Scott's original model of the ... This*calculus*is related to Boudol's*resource**calculus*and is derived from Ehrhard and Regnier's differential extension of Linear Logic and of the*lambda**calculus*. ... FULL ABSTRACTION FOR*RESOURCE*CALCULI ...##
###
What is a categorical model of the differential and the resource lambda-calculi?
[article]

2010
*
arXiv
*
pre-print

*In*this paper we provide an abstract model theory for the untyped differential

*lambda*-

*calculus*and the

*resource*

*calculus*. ...

*In*particular we propose a general definition of model of these calculi, namely the notion of linear reflexive object

*in*a Cartesian closed differential category. ... May and must

*solvability*have been studied

*in*[ 30]

*in*the context of the

*resource*

*calculus*. ...

##
###
Resource Combinatory Algebras
[chapter]

2010
*
Lecture Notes in Computer Science
*

We initiate a purely algebraic study of Ehrhard and Regnier's

doi:10.1007/978-3-642-15155-2_22
fatcat:woy5rv5wwrfxzpebux6i3aog3a
*resource*λ-*calculus*, by introducing three equational classes of algebras:*resource*combinatory algebras,*resource**lambda*-algebras and*resource*... model of the classical λ-*calculus*raising from a*resource**lambda*-algebra determines a λ-theory which equates all terms having the same Böhm tree. ...*lambda**calculus*We will now briefly introduce the linear fragment of*resource*λ-*calculus*(rλ*calculus*, for short). ...##
###
A Survey of Quantum Programming Languages: History, Methods, and Tools
[article]

2008
*
arXiv
*
pre-print

Quantum computer programming is emerging as a new subject domain from multidisciplinary research

arXiv:0804.1118v1
fatcat:gyi6j6n6xnet7gubikizmrct3a
*in*quantum computing, computer science, mathematics (especially quantum logic,*lambda*calculi, and linear ... It is intended to provide an extensive but non-exhaustive look at work leading up to the current state-of-the-art*in*quantum computer programming. ...*In*1996 Maymin [24] proposed a quantum*lambda**calculus*to investigate the Turing computability of quantum algorithms. ...##
###
The Resource Lambda Calculus Is Short-Sighted in Its Relational Model
[chapter]

2013
*
Lecture Notes in Computer Science
*

As a by-product we achieve a context lemma for the

doi:10.1007/978-3-642-38946-7_9
fatcat:easeaqltqfa37m5jvfi3e5l5oi
*resource*λ-*calculus*. ... That particular object of MRel is also a model of the*resource*λ-*calculus*, deriving from Ehrhard and Regnier's differential extension of Linear Logic and related to Boudol's λ-*calculus*with multiplicities ... Notation: We denote N A for the set of finite multisetes of elements*in*the set A. Syntax ∂λ-*Calculus**In*this section we give some background on the ∂λ-*calculus*, a*lambda**calculus*with*resources*. ...##
###
What is a categorical model of the differential and the resource λ-calculi?

2012
*
Mathematical Structures in Computer Science
*

Therefore the

doi:10.1017/s0960129511000594
fatcat:oahkwj3ihndovlixd4tp5yflg4
*resource**calculus*can be interpreted by translation into every linear reflexive object living*in*a Cartesian closed differential category. ... Finally, we study the relationship between the differential λ-*calculus*and the*resource**calculus*, a functional programming language combining the ideas behind the differential λ-*calculus*with those behind ... From the*Resource*to the Differential*Lambda**Calculus*. . . ...##
###
Essential and relational models

2015
*
Mathematical Structures in Computer Science
*

Intersection type assignment systems can be used as a general framework for building logical models of λ-

doi:10.1017/s0960129515000316
fatcat:22iizaim4recji4fhecm3fkbmm
*calculus*that allow to reason about the denotation of terms*in*a finitary way. ... A similar technique has been used*in*Pagani and Ronchi Della Rocca (2010b) for charactering*solvability**in*the*resource*λ-*calculus*. ... Recently non idempotent intersection types have been used*in*Pagani and Ronchi Della Rocca (2010b,a) to characterize the*solvability**in*the*resource*λ-*calculus*. ...##
###
A Resource Aware Computational Interpretation for Herbelin's Syntax
[chapter]

2015
*
Lecture Notes in Computer Science
*

We investigate a new computational interpretation for an intuitionistic focused sequent

doi:10.1007/978-3-319-25150-9_23
fatcat:a4pnehwarnechmoedtf3bqrhma
*calculus*which is compatible with a*resource*aware semantics. ... For the sake of completeness, we also study typability (and the corresponding strong normalization characterization)*in*the reduction*calculus*obtained from the former one by projecting the explicit substitutions ... Non-idempotent types also appear*in*linearization of the*lambda*-*calculus*[28] , type inference [30, 38] , different characterizations of*solvability*[40] and verification of higher-order programs ...##
###
An Infinitary Affine Lambda-Calculus Isomorphic to the Full Lambda-Calculus

2012
*
2012 27th Annual IEEE Symposium on Logic in Computer Science
*

We also show how this construction brings interesting insights on some standard rewriting properties of the

doi:10.1109/lics.2012.57
dblp:conf/lics/Mazza12
fatcat:ldqkg5sxyzb75lfgmanlhbwsl4
*lambda*-*calculus*(finite developments, confluence, standardization, head normalization and*solvability*... relation is exactly the full (non-affine)*lambda*-*calculus*. ... An example might be Ehrhard and Regnier's*resource*λ-*calculus*(which is strongly related to Boudol's λ-*calculus*with multiplicities). ...##
###
Normalization, Taylor expansion and rigid approximation of λ-terms
[article]

2020
*
arXiv
*
pre-print

The aim of this work is to characterize three fundamental normalization proprieties

arXiv:2001.01619v1
fatcat:adg4ok4spngjrksyonx6w4g6fa
*in**lambda*-*calculus*trough the Taylor expansion of λ-terms. ... The general proof strategy consists*in*stating the dependence of ordinary reduction strategies on their*resource*counterparts and*in*finding a convenient*resource*term*in*the Taylor expansion that behaves ...*In*particular we have that M N 1 · · · N n → * β λx.x. We say that a generic M ∈ Λ is*solvable*if there exists a closure of M that is*solvable*. Theorem 3.14. M is*solvable*iff M is head-normalisable. ...##
###
The differential lambda-calculus

2003
*
Theoretical Computer Science
*

We state and prove some basic results (con uence, strong normalization

doi:10.1016/s0304-3975(03)00392-x
fatcat:4cbn3lmgnjefhcp7ogdau22ml4
*in*the typed case), and also a theorem relating the usual Taylor series of analysis to the linear head reduction of*lambda*-*calculus*... We present an extension of the*lambda*-*calculus*with di erential constructions. ... thank especially one of the referees of this paper, who made many insightful comments on an earlier version of this work and derived us to clarify several delicate syntactical aspects of the di erential*lambda*-*calculus*...
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