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

2020
*
Lecture Notes in Computer Science
*

This is built on an

doi:10.1007/978-3-030-45231-5_22
fatcat:m5vz6r2of5h7lhlnasujbnbc5i
*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. ...##
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On laziness and optimality in lambda interpreters: tools for specification and analysis

1990
*
Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '90
*

However, we can improve matters considerably by

doi:10.1145/96709.96710
dblp:conf/popl/Field90
fatcat:jpiles3shjdnngvjxsftddkqfm
*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 ...##
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A Calculus of Coroutines
[chapter]

2004
*
Lecture Notes in Computer Science
*

By contrast, in domain

doi:10.1007/978-3-540-27836-8_74
fatcat:hrcyftg22bcc3mw52qs3vbyr5y
*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 λ*calculus*are obtained. ...##
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RPO, Second-Order Contexts, and λ-Calculus
[chapter]

2008
*
Lecture Notes in Computer Science
*

We apply Leifer-Milner RPO approach to the λ-

doi:10.1007/978-3-540-78499-9_24
fatcat:pf7no7ubovesxag35ylphb3p5y
*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. ...##
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A calculus for probabilistic languages

2003
*
SIGPLAN notices
*

In this paper, we develop a probabilistic

doi:10.1145/640136.604180
fatcat:ulzxymhtvzbntbb6glaritp7eu
*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 ...##
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A calculus for probabilistic languages

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

doi:10.1145/604174.604180
dblp:conf/tldi/Park03
fatcat:g37ka5mfp5ajbltq6gpws22fwe
*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 ...##
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A calculus for probabilistic languages

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

doi:10.1145/604178.604180
fatcat:nlqb7hxpbjhtfkcmgvdusfycoe
*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 ...##
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A calculus for reasoning about software composition

2005
*
Theoretical Computer Science
*

The Piccola

doi:10.1016/j.tcs.2004.09.022
fatcat:k52e3hrenzdttbene4zqqernje
*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'', ...##
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RPO, Second-order Contexts, and Lambda-calculus

2009
*
Logical Methods in Computer Science
*

Then, we apply such

doi:10.2168/lmcs-5(3:6)2009
fatcat:h5ez25kfvfffvmlfhdlgobv3hq
*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. ...##
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Nondeterministic Extensions of Untyped λ-Calculus

1995
*
Information and Computation
*

We further prove conservativity theorems for the equational

doi:10.1006/inco.1995.1145
fatcat:quhqqxpefzawxohsxhjqnxwx74
*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 ...##
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The Impact of the Lambda Calculus in Logic and Computer Science

1997
*
Bulletin of Symbolic Logic
*

Church to logic is his invention of the

doi:10.2307/421013
fatcat:v7nedk3s3vfk3mob6ao5sl4b74
*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. ...##
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Linear Lambda Calculus and Deep Inference
[chapter]

2011
*
Lecture Notes in Computer Science
*

The proof-search inside SBVr

doi:10.1007/978-3-642-21691-6_16
fatcat:ehxpjhbmj5fklkfohmehdlbzp4
*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. ...##
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Linear lambda Calculus with Explicit Substitutions as Proof-Search in Deep Inference
[article]

2011
*
arXiv
*
pre-print

SBVr

arXiv:1011.3668v4
fatcat:37lyyg6q6veunpe2xprflhnsca
*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. ...##
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A Lambda Calculus with Forms
[chapter]

2005
*
Lecture Notes in Computer Science
*

More precisely, we study a substitution-free variant of the

doi:10.1007/11550679_7
fatcat:hmrkjlea3vd7dbi44uhcgsow6m
*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. ...##
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EOLANG and φ-calculus
[article]

2022
*
arXiv
*
pre-print

We have made yet another attempt

arXiv:2111.13384v4
fatcat:zzfwytzhg5h3fm4dt6rwqklkde
*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*...
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