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The Weak Call-By-Value λ-Calculus is Reasonable for Both Time and Space [article]

Yannick Forster, Fabian Kunze, Marc Roth
2019 arXiv   pre-print
We study the weak call-by-value λ-calculus as a model for computational complexity theory and establish the natural measures for time and space -- the number of beta-reductions and the size of the largest  ...  Our proof relies on a hybrid of two simulation strategies of reductions in the weak call-by-value λ-calculus by Turing machines, both of which are insufficient if taken alone.  ...  Result and Discussion We prove that the weak call-by-value λ-calculus is a reasonable machine with respect to the natural time and space measures defined above.  ... 
arXiv:1902.07515v1 fatcat:ozbtl4yzazet3kj7cumll45db4

Strong Call by Value is Reasonable for Time [article]

Małgorzata Biernacka
2021 arXiv   pre-print
In this paper we show that a family of strong call-by-value strategies in the λ-calculus are reasonable for time.  ...  The invariance thesis of Slot and van Emde Boas states that all reasonable models of computation simulate each other with polynomially bounded overhead in time and constant-factor overhead in space.  ...  Recently this question has been answered positively, for both time and space, with the weak call-by-value (CbV) [23] and, for time, with the strong call-by-name (CbN) [6] strategies.  ... 
arXiv:2102.05985v1 fatcat:bmxojntubjg4hadgjl2gzvbtgq

A calculus for java's reference objects

Yarom Gabay, Assaf J. Kfoury
2007 SIGPLAN notices  
In addition, we constrain garbage collection with the scarcity of two resources: time and space.  ...  Using our model, we reason about the program's evaluation and interaction with the garbage collector.  ...  In the style of λ weak and λ gc , it corresponds to a left-to-right, call-by-value reduction.  ... 
doi:10.1145/1294297.1294299 fatcat:fhluj2halzbutidyi4hnnqtcau

A Fresh Look at the lambda-Calculus (Invited Talk)

Beniamino Accattoli, Michael Wagner
2019 International Conference on Rewriting Techniques and Applications  
The (untyped) λ-calculus is almost 90 years old. And yet -we argue here -its study is far from being over.  ...  The paper is a bird's eye view of the questions the author worked on in the last few years: how to measure the complexity of λ-terms, how to decompose their evaluation, how to implement it, and how all  ...  a number of λ-calculi depending at least on whether evaluation is call-by-name, call-by-value, or call-by-need, and -orthogonally -whether evaluation is strong or weak (that is, whether abstraction bodies  ... 
doi:10.4230/lipics.fscd.2019.1 dblp:conf/rta/Accattoli19 fatcat:75swok72vvb6fdfl3fx5lu5sey

A Calculus for Link-Time Compilation [chapter]

Elena Machkasova, Franklyn A. Turbak
2000 Lecture Notes in Computer Science  
We present a module calculus for studying a simple model of link-time compilation. The calculus is stratified into a term calculus, a core module calculus, and a linking calculus.  ...  We also introduce the weak distributivity property for a transformation T operating on modules D1 and D2 linked by ⊕: T (D1 ⊕ D2) = T (T (D1) ⊕ T (D2)).  ...  Pragmatics: We plan to empirically evaluate if link-time compilation can give reasonable "bang for the buck" in the context of a simple prototype compiler.  ... 
doi:10.1007/3-540-46425-5_17 fatcat:c3hzc3h7lzfp3k7kocxqsytab4

Modeling, Sharing, and Recursion for Weak Reduction Strategies using Explicit Substitution

Zine-El-Abidine Benaissa, Pierre Lescanne, Kristoffer H. Rose
1996 BRICS Report Series  
Third, we formalize the notion of space leaks in lambda sigma^a_w<br />and use this to define a space leak free calculus; this suggests optimisations<br />for call-by-need reduction that prevent space  ...  <p>We present the lambda sigma^a_w calculus, a formal synthesis of the concepts of<br />sharing and explicit substitution for weak reduction.  ...  The authors would like to thank Eva Rose and the anonymous referees for useful suggestions to the manuscript.  ... 
doi:10.7146/brics.v3i56.18681 fatcat:kkds5hclfbgarikre5rtnu36pa

Multi types and reasonable space

Beniamino Accattoli, Ugo Dal Lago, Gabriele Vanoni
2022 Proceedings of the ACM on Programming Languages (PACMPL)  
Accattoli, Dal Lago, 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 λ-calculus accounting for  ...  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.  ...  Therefore, the Space KAM is reasonable for both time and space, even if for such a simultaneous reasonability one has to pick an unusual and low-level notion of time.  ... 
doi:10.1145/3547650 fatcat:tkgb7zisizci7kr2qkyuow45nm

A concrete framework for environment machines

Małgorzata Biernacka, Olivier Danvy
2007 ACM Transactions on Computational Logic  
we methodically derive a series of environment machines from the specification of two one-step reduction strategies for the λ-calculus: normal order and applicative order.  ...  We materialize the common belief that calculi with explicit substitutions provide an intermediate step between an abstract specification of substitution in the λcalculus and its concrete implementations  ...  This work is partially supported by the ESPRIT Working Group APPSEM II (http: // and by the Danish Natural Science Research Council, Grant no. 21-03-0545.  ... 
doi:10.1145/1297658.1297664 fatcat:ldjgznn3cvh5hiwwnavhd35izy

A Concrete Framework for Environment Machines

Malgorzata Biernacka, Olivier Danvy
2005 BRICS Report Series  
derive a series of environment machines from the specification of two one-step reduction strategies for the lambda-calculus: normal order and applicative order.  ...  The resulting environment machines include both the idealized and the original versions of Krivine's machine, Felleisen et al.'s CEK machine, and Leroy's Zinc abstract machine.  ...  This work is partially supported by the ESPRIT Working Group APPSEM II (http: // and by the Danish Natural Science Research Council, Grant no. 21-03-0545.  ... 
doi:10.7146/brics.v12i15.21881 fatcat:deygynjytbhkpb6ueqv7jo2aw4

Explaining the lazy Krivine machine using explicit substitution and addresses

Frédéric Lang
2007 Higher-Order and Symbolic Computation  
In a previous paper, Benaissa, Lescanne, and Rose, have extended the weak lambda-calculus of explicit substitution λσw with addresses, so that it gives an account of the sharing implemented by lazy functional  ...  We show in this paper that their calculus, called λσ a w , fits well to the lazy Krivine machine, which describes the core of a lazy (call-by-need) functional programming language implementation.  ...  The author is grateful to Andrea Asperti, Michel Mauny, and Laurence Puel who reviewed the thesis and made useful comments, to René David and Dehlia Kesner for their active participation in the board of  ... 
doi:10.1007/s10990-007-9013-1 fatcat:huyphkxj4vhqrauetvc626chum

Reasonable Space for the λ-Calculus, Logarithmically [article]

Beniamino Accattoli and Ugo Dal Lago and Gabriele Vanoni
2022 arXiv   pre-print
For the first time, this cost model is able to account for logarithmic space. Moreover, we study the time behavior of our machine and show how to transport our results to the call-by-value λ-calculus.  ...  Can the λ-calculus be considered as a reasonable computational model? Can we use it for measuring the time and space consumption of algorithms?  ...  that is reasonable for both space and time, by interleaving the two machines in a smart way.  ... 
arXiv:2203.00362v2 fatcat:3cxajldlbfajnpe7aijaoygpnu

Minimality in a Linear Calculus with Iteration

Sandra Alves, Mário Florido, Ian Mackie, François-Régis Sinot
2008 Electronical Notes in Theoretical Computer Science  
for the weak reduction relation: call-by-name, call-by-value, and call-by-need (emphasising this last one), proving that they are indeed strategies in a technical sense.  ...  It is well-known that there exists no computable minimal strategy for the λ-calculus [5] .  ...  Acknowledgement We are sincerely grateful to the anonymous referees for their numerous and judicious comments (some of which could unfortunately not be followed because of space and time constraints).  ... 
doi:10.1016/j.entcs.2008.03.060 fatcat:sf6f372ozvcsjp5yz7sse2fr7q

Weak Solutions of a Hyperbolic-Type Partial Dynamic Equation in Banach Spaces

Ahmet Yantır
2015 Hacettepe Journal of Mathematics and Statistics  
For this purpose, by generalizing the definitions and results of Cichoń we develop weak partial derivatives, double integrability and the mean value results for double integrals on time scales.  ...  In this article, we prove an existence theorem regarding the weak solutions to the hyperbolic-type partial dynamic equation in Banach spaces.  ...  The authors wish to acknowledge the anonymous reviewer for his/her detailed and helpful comments to the manuscript.  ... 
doi:10.15672/hjms.2015449412 fatcat:6hotdl6ny5ejfo3o7z6a7al3ji

Uniform confluence in concurrent computation

2000 Journal of functional programming  
We model eager functional programming in the λ-calculus with weak call-by-value reduction and lazy functional programming in the call-by-need λ-calculus with standard reduction.  ...  We encode the λ-calculus with both above reduction strategies into the applicative core of the π-calculus and show that time complexity is preserved.  ...  I am deeply in debt to Gert Smolka, who initiated this work and contributed ideas during many discussions. It is an honor for me to thank Phil Wadler's for his engaged support.  ... 
doi:10.1017/s0956796800003762 fatcat:gzayrpjptbhrbmsd5lpz4liuhm

The Complexity of Abstract Machines

Beniamino Accattoli
2017 Electronic Proceedings in Theoretical Computer Science  
It is conceived to be a tutorial, focusing on the case study of implementing the weak head (call-by-name) strategy, and yet it is an original re-elaboration of known results.  ...  There is an extensive literature about abstract machines for the lambda-calculus, and yet-quite mysteriously-the efficiency of these machines with respect to the strategy that they implement has almost  ...  The catch, however, is that its cost model are far from being evident. What should be taken as time and space measures for the λ -calculus?  ... 
doi:10.4204/eptcs.235.1 fatcat:gbvg5jfk65f3pi5uvae5lrdq6u
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