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A Curry-style Semantics of Interaction: From Untyped to Second-Order Lazy $$\lambda \mu $$-Calculus [chapter]

James Laird
2020 Lecture Notes in Computer Science  
This is built on an abstract machine for CPS evaluation of λμ-terms: we first give a basic typing system for this LTS which characterizes acyclicity of the environment and local control flow, and then  ...  results for typed bisimulation, and secondly via an example which captures the hiding of implementations in abstract data types: a typed bisimulation for the (Curry-style) lazy λμ-calculus with polymorphic  ...  Examples of typed LTS (in the form of models of the lazy λμ-calculus and lazy λμ2-calculus) follow in the rest of the paper.  ... 
doi:10.1007/978-3-030-45231-5_22 fatcat:m5vz6r2of5h7lhlnasujbnbc5i

On laziness and optimality in lambda interpreters: tools for specification and analysis

John Field
1990 Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '90  
However, we can improve matters considerably by extending the model of reduction a bit.  ...  To provide a more sophisticated tool for modeling Areduction using environments, 1 will define a new Z-sorted equational theory, ACCL, akin to Curien's theory CCLB.  ...  The Lambda Calculus, volume 103 of Studies in Logic and the Foundations of Mathematics. North-Holland, Amsterdam, 1984. H.P. Barendregt  ... 
doi:10.1145/96709.96710 dblp:conf/popl/Field90 fatcat:jpiles3shjdnngvjxsftddkqfm

A Calculus of Coroutines [chapter]

J. Laird
2004 Lecture Notes in Computer Science  
By contrast, in domain theory programs are modelled extensionally using sets (with certain order-theoretic structure) and functions (preserving that structure).  ...  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  ...  This leads to a full abstraction theorem for the biorder model of unary PCF, and by moving to bicpos, fully abstract models of the lazy λ-calculus and the call-by-value λcalculus are obtained.  ... 
doi:10.1007/978-3-540-27836-8_74 fatcat:hrcyftg22bcc3mw52qs3vbyr5y

RPO, Second-Order Contexts, and λ-Calculus [chapter]

Pietro Di Gianantonio, Furio Honsell, Marina Lenisa
2008 Lecture Notes in Computer Science  
We apply Leifer-Milner RPO approach to the λ-calculus, endowed with lazy and call by value reduction strategies.  ...  We show that, contrary to process calculi, one can deal directly with the λ-calculus syntax and apply Leifer-Milner technique to a category of contexts, provided that we work in the framework of weak bisimilarities  ...  Lambda Calculus as a Reactive System Both lazy and cbv λ-calculus can be endowed with a structure of reactive system in the sense of Definition 1, by considering a suitable variant of context category.  ... 
doi:10.1007/978-3-540-78499-9_24 fatcat:pf7no7ubovesxag35ylphb3p5y

A calculus for probabilistic languages

Sungwoo Park
2003 SIGPLAN notices  
In this paper, we develop a probabilistic calculus by extending the traditional lambda calculus. In our calculus, every expression denotes a probability distribution yet evaluates to a regular value.  ...  The most notable feature of our calculus is that it is founded upon sampling functions, which map the unit interval to probability domains.  ...  I thank Jonathan Moody and Aleks Nanevski for their helpful discussion, Sebastian Thrun and Mike Montemerlo for setting up the experiment environment, and three anonymous reviewers for their insightful  ... 
doi:10.1145/640136.604180 fatcat:ulzxymhtvzbntbb6glaritp7eu

A calculus for probabilistic languages

Sungwoo Park
2003 Proceedings of the 2003 ACM SIGPLAN international workshop on Types in languages design and implementation - TLDI '03  
In this paper, we develop a probabilistic calculus by extending the traditional lambda calculus. In our calculus, every expression denotes a probability distribution yet evaluates to a regular value.  ...  The most notable feature of our calculus is that it is founded upon sampling functions, which map the unit interval to probability domains.  ...  I thank Jonathan Moody and Aleks Nanevski for their helpful discussion, Sebastian Thrun and Mike Montemerlo for setting up the experiment environment, and three anonymous reviewers for their insightful  ... 
doi:10.1145/604174.604180 dblp:conf/tldi/Park03 fatcat:g37ka5mfp5ajbltq6gpws22fwe

A calculus for probabilistic languages

Sungwoo Park
2003 Proceedings of the 2003 ACM SIGPLAN international workshop on Types in languages design and implementation - TLDI '03  
In this paper, we develop a probabilistic calculus by extending the traditional lambda calculus. In our calculus, every expression denotes a probability distribution yet evaluates to a regular value.  ...  The most notable feature of our calculus is that it is founded upon sampling functions, which map the unit interval to probability domains.  ...  I thank Jonathan Moody and Aleks Nanevski for their helpful discussion, Sebastian Thrun and Mike Montemerlo for setting up the experiment environment, and three anonymous reviewers for their insightful  ... 
doi:10.1145/604178.604180 fatcat:nlqb7hxpbjhtfkcmgvdusfycoe

A calculus for reasoning about software composition

Franz Achermann, Oscar Nierstrasz
2005 Theoretical Computer Science  
The Piccola calculus is a process calculus, based on the asynchronous -calculus, extended with explicit namespaces.  ...  We motivate and present the calculus, and outline how it is used to specify the semantics of Piccola, a small composition language.  ...  Acknowledgements We gratefully acknowledge the financial support of the Swiss National Science Foundation for projects No. 20-61655.00, "Meta-models and Tools for Evolution Towards Component Systems'',  ... 
doi:10.1016/j.tcs.2004.09.022 fatcat:k52e3hrenzdttbene4zqqernje

RPO, Second-order Contexts, and Lambda-calculus

Pietro Di Gianantonio, Furio Honsell, Marina Lenisa, Roberto Amadio
2009 Logical Methods in Computer Science  
Then, we apply such extended RPO technique to the lambda-calculus, endowed with lazy and call by value reduction strategies.  ...  First, we extend Leifer-Milner RPO theory, by giving general conditions to obtain IPO labelled transition systems (and bisimilarities) with a reduced set of transitions, and possibly finitely branching  ...  Lambda Calculus as a Reactive System. Both lazy and cbv λ-calculus can be endowed with a structure of reactive system in the sense of Definition 2.1, by considering corresponding context categories.  ... 
doi:10.2168/lmcs-5(3:6)2009 fatcat:h5ez25kfvfffvmlfhdlgobv3hq

Nondeterministic Extensions of Untyped λ-Calculus

U. Deliguoro, A. Piperno
1995 Information and Computation  
We further prove conservativity theorems for the equational theory of the model and for other theories, related to non deterministic -calculus, with respect to classical -theories.  ...  of functional application and abstraction.  ...  Acknowledgements We are grateful to Corrado B ohm, Mariangiola Dezani-Ciancaglini, Rocco De Nicola, Gianfranco Mascari and Eugenio Moggi for helpful discussions and suggestions about 62 the topics of this  ... 
doi:10.1006/inco.1995.1145 fatcat:quhqqxpefzawxohsxhjqnxwx74

The Impact of the Lambda Calculus in Logic and Computer Science

Henk Barendregt
1997 Bulletin of Symbolic Logic  
Church to logic is his invention of the lambda calculus.  ...  We present the genesis of this theory and its two major areas of application: the representation of computations and the resulting functional programming languages on the one hand and the representation  ...  The sets of variables and terms of the lambda calculus are defined by the following abstract syntax.  ... 
doi:10.2307/421013 fatcat:v7nedk3s3vfk3mob6ao5sl4b74

Linear Lambda Calculus and Deep Inference [chapter]

Luca Roversi
2011 Lecture Notes in Computer Science  
The proof-search inside SBVr and BVr is complete with respect to the evaluation of linear λ-calculus with explicit substitutions. Instead, only soundness of proof-search in SBVr holds.  ...  We introduce a deep inference logical system SBVr which extends SBV [6] with Rename, a self-dual atom-renaming operator. We prove that the cut free subsystem BVr of SBVr exists.  ...  Extended version. This work is an extended abstract and contains a single full detailed proof. The technical report [13] contains all proofs of the coming statements, and a richer bibliography.  ... 
doi:10.1007/978-3-642-21691-6_16 fatcat:ehxpjhbmj5fklkfohmehdlbzp4

Linear lambda Calculus with Explicit Substitutions as Proof-Search in Deep Inference [article]

Luca Roversi
2011 arXiv   pre-print
SBVr and its cut free subsystem BVr are complete and sound with respect to linear lambda calculus with explicit substitutions.  ...  Despite SBVr is a minimal extension of SBV its proof-search can compute all boolean functions, as linear lambda-calculus with explicit substitutions can compute all boolean functions as well.  ...  We like to thanks Paola Bruscoli and Alessio Guglielmi for stimulating questions and comments that helped improving the presentation of this work.  ... 
arXiv:1011.3668v4 fatcat:37lyyg6q6veunpe2xprflhnsca

A Lambda Calculus with Forms [chapter]

Markus Lumpe
2005 Lecture Notes in Computer Science  
More precisely, we study a substitution-free variant of the lambda-calculus, called λF , where names are replaced with forms and parameter passing is modeled using explicit contexts and show how the λF  ...  The need to use position-dependent parameters often hampers the definition of flexible, extensible, and reusable abstractions for software composition.  ...  The author thanks Jean-Guy Schneider, Oscar Nierstrasz, and the anonymous reviewers for their valuable comments and discussions.  ... 
doi:10.1007/11550679_7 fatcat:hmrkjlea3vd7dbi44uhcgsow6m

EOLANG and φ-calculus [article]

Yegor Bugayenko
2022 arXiv   pre-print
We have made yet another attempt and created φ-calculus. We also created EOLANG (also called EO), an experimental programming language based on φ-calculus.  ...  However, despite its industrial and academic popularity, OOP is still missing a formal apparatus similar to λ-calculus, which functional programming is based on.  ...  Santos, Alex Semenyuk, Violetta Sim, Sergei Skliar, Stian Soiland-Reyes, Viacheslav Tradunskyi, Ilya Trub, César Soto Valero, and David West for their contribution to the development of EO and -calculus  ... 
arXiv:2111.13384v4 fatcat:zzfwytzhg5h3fm4dt6rwqklkde
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