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Understanding the Expressive Power of Unhygienic Substitution in Metaprogramming via Combinatory Logic [article]

Martin Lester
2019 arXiv   pre-print
Recent work on combinatory logic demonstrates a compositional translation from lambda calculus that gives meaning to open terms.  ...  Kiselyov calls this a denotational semantics.  ...  However, there is a simple translation of the calculus into unaugmented lambda calculus, essentially by treating code values as thunks.  ... 
arXiv:1910.03217v1 fatcat:hc6t6tptrzdxjjpfl66ptaigqy

Sharing Continuations: Proofnets for Languages with Explicit Control [chapter]

Julia L. Lawall, Harry G. Mairson
2000 Lecture Notes in Computer Science  
We propose a family of translations, produced uniformly by beginning with a continuation-passing style semantics for the languages, employing standard codings into proofnets using call-by-value, call-by-name-or  ...  to yield a new understanding of sharable values.  ...  A λ-calculus program can be converted to CPS automatically using a CPS transformation. Furthermore, the control operator call/cc can be translated into CPS.  ... 
doi:10.1007/3-540-46425-5_16 fatcat:3jevx7qevzahhehomccscbwvum

Towards a Semantic Measure of the Execution Time in Call-by-Value lambda-Calculus

Giulio Guerrieri
2019 Electronic Proceedings in Theoretical Computer Science  
We investigate the possibility of a semantic account of the execution time (i.e. the number of beta-steps leading to the normal form, if any) for the shuffling calculus, an extension of Plotkin's call-by-value  ...  To get a truly semantic measure of execution time in a call-by-value setting, we conjecture that a refinement of its syntax and operational semantics is needed.  ...  of LL than call-by-value (as said in Sect. 1, call-by-name and call-by-value λ -calculi are translated into LL via two distinct embeddings).  ... 
doi:10.4204/eptcs.293.5 fatcat:jzmth6wunvfaxcbaixhdsb5xmq

On the Representation of McCarthy's amb in the π-calculus

Arnaud Carayol, Daniel Hirschkoff, Davide Sangiorgi
2004 Electronical Notes in Theoretical Computer Science  
We study the encoding of λ [] , the call by name λ-calculus enriched with McCarthy's amb operator, into the π-calculus.  ...  We prove that, under a certain interpretation of divergence in the λ-calculus (weak divergence), a faithful encoding is impossible.  ...  This work has been supported by the european FET -Global Computing project Profundis.  ... 
doi:10.1016/j.entcs.2004.04.022 fatcat:lx53osustvdmzg342lfkva6vbm

Visualizing the turing tarpit

Jason Hemann, Eric Holk
2013 Proceedings of the first ACM SIGPLAN workshop on Functional art, music, modeling & design - FARM '13  
In the same way that research into fractals yielded new mathematical insights, visualizations such as those presented here could yield new insights into the structure and nature of computation.  ...  This is a shame, as the simplicity of these languages ascribes to them an inherent beauty and provides deep insight into the nature of computation.  ...  The semantics are defined in terms of the λ calculus, and reference implementations use a call-by-value evaluation strategy. Syntax Semantics [F ] ⇒ ϵ λx.x ⇒ 0 [F ]SK ⇒ 1 λxy.  ... 
doi:10.1145/2505341.2505348 dblp:conf/icfp/HemannH13 fatcat:kjjncvt7x5ay3dn7e6kbb5hvv4

The Call-by-need Lambda Calculus, Revisited [article]

Stephen Chang, Matthias Felleisen
2012 arXiv   pre-print
The existing call-by-need lambda calculi describe lazy evaluation via equational logics.  ...  Like its predecessors, our new calculus satisfies consistency and standardization properties and is thus suitable for reasoning about behavioral equivalence.  ...  This work was supported in part by NSF Infrastructure grant CNS-0855140 and AFOSR grant FA9550-09-1-0110.  ... 
arXiv:1201.3907v1 fatcat:iyovi4zeane3jgymmopmirt3yi

The Call-by-Need Lambda Calculus, Revisited [chapter]

Stephen Chang, Matthias Felleisen
2012 Lecture Notes in Computer Science  
The existing call-by-need λ calculi describe lazy evaluation via equational logics.  ...  Like its predecessors, our new calculus satisfies consistency and standardization properties and is thus suitable for reasoning about behavioral equivalence.  ...  This work was supported in part by NSF Infrastructure grant CNS-0855140 and AFOSR grant FA9550-09-1-0110.  ... 
doi:10.1007/978-3-642-28869-2_7 fatcat:h4q73ulv6rec7cowidt6dork24

Static typing for a substructural lambda calculus

Baojian Hua
2011 Frontiers of Computer Science in China  
The new calculus λ SL can guarantee much more safety invariants than the traditional lambda calculus, which is demonstrated by showing that the λ SL calculus can serve as an idealized type intermediate  ...  language, and defining a type-preserving translation from ordinary typed lambda calculus into λ SL .  ...  And this section presents the operational semantics for λ SL , which gives rules for reducing a term to a value. The reduction uses a small-step call-by-value strategy, and is from left to right.  ... 
doi:10.1007/s11704-011-9106-1 fatcat:petvji2x4fevrcim3v6qitgmde

Functions as Session-Typed Processes [chapter]

Bernardo Toninho, Luis Caires, Frank Pfenning
2012 Lecture Notes in Computer Science  
Milner [17] presented two translations of the λ-calculus into the π-calculus: one capturing call-by-name and one capturing call-by-value.  ...  Van Bakel and Vigliotti [21] give a partial answer by providing a conceptually different translation into the asynchronous π-calculus where the image of simply-typed λ-terms can be assigned types in Gentzen's  ...  For instance, the redex (λx.M ) N can be translated into the following linear terms (we denote by −→ the linear λ calculus operational semantics, as given in Def. 3.1 -by-name application, by-value let  ... 
doi:10.1007/978-3-642-28729-9_23 fatcat:lnqf2iy6mjbbffe5evhb2gzdie

Open Call-by-Value [chapter]

Beniamino Accattoli, Giulio Guerrieri
2016 Lecture Notes in Computer Science  
Four, we introduce a new simple abstract machine, and prove it a reasonable implementation of Open Call-by-Value with respect to its cost model.  ...  The elegant theory of the call-by-value lambda-calculus relies on weak evaluation and closed terms, that are natural hypotheses in the study of programming languages.  ...  Plotkin's call-by-value λ -calculus [18] is at the heart of programming languages such as Ocaml and proof assistants such as Coq.  ... 
doi:10.1007/978-3-319-47958-3_12 fatcat:b2muwpevj5bptd32xvsjnogo4q

Equational axiomatization of call-by-name delimited control

Yukiyoshi Kameyama, Asami Tanaka
2010 Proceedings of the 12th international ACM SIGPLAN symposium on Principles and practice of declarative programming - PPDP '10  
While many works in the literature study them in call-by-value, several recent works have shown call-by-name delimited control operators are also worth studying.  ...  In this paper, we study semantic foundation of the call-by-name variant of the delimited-control operators "shift" and "reset".  ...  The first author was partly supported by JSPS Grant-in-Aid for Scientific Research (B) 21300005.  ... 
doi:10.1145/1836089.1836100 dblp:conf/ppdp/KameyamaT10 fatcat:nxoi2vib2fgcvlc3g6hmhabkhe

A Calculus of Coroutines [chapter]

J. Laird
2004 Lecture Notes in Computer Science  
In particular, Laird showed that the bistable functions (a new notion) gave rise to a universal model of the λ-calculus with two constants, and that CPS-translations allowed this to be extended to programming  ...  Domains have formed the basis for much research in denotational semantics by virtue of their conceptual simplicity, and now form a wide-ranging mathematical theory.  ...  call-by-value variants.  ... 
doi:10.1007/978-3-540-27836-8_74 fatcat:hrcyftg22bcc3mw52qs3vbyr5y

Reduction in a Linear Lambda-Calculus with Applications to Operational Semantics [chapter]

Alex Simpson
2005 Lecture Notes in Computer Science  
We apply these results to the operational semantics of Lily, a second-order linear lambda-calculus with recursion, introduced by Bierman, Pitts and Russo, for which we give simple proofs that call-by-value  ...  , call-by-name and call-by-need contextual equivalences coincide.  ...  of) β-reduction simulates both call-by-value and call-by-name operational semantics.  ... 
doi:10.1007/978-3-540-32033-3_17 fatcat:4ueyxjhavbdmzks6mvxmkvkmc4

A concrete framework for environment machines

Małgorzata Biernacka, Olivier Danvy
2007 ACM Transactions on Computational Logic  
The derivation extends Danvy and Nielsen's refocusing-based construction of abstract machines with two new steps: one for coalescing two successive transitions into one, and the other for unfolding a closure  ...  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.  ...  This work is partially supported by the ESPRIT Working Group APPSEM II (http: //www.appsem.org) 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  
The derivation extends Danvy and Nielsen's refocusing-based construction of abstract machines with two new steps: one for coalescing two successive transitions into one, and one for unfolding a closure  ...  into a term and an environment in the resulting abstract machine.  ...  This work is partially supported by the ESPRIT Working Group APPSEM II (http: //www.appsem.org) and by the Danish Natural Science Research Council, Grant no. 21-03-0545.  ... 
doi:10.7146/brics.v12i15.21881 fatcat:deygynjytbhkpb6ueqv7jo2aw4
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