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The Minimal Graph Model of Lambda Calculus
[chapter]

2003
*
Lecture Notes in Computer Science
*

A longstanding open problem in

doi:10.1007/978-3-540-45138-9_24
fatcat:dpc7xdg6qze7fj3ewmpinj5sky
*lambda*-*calculus*, raised by G.Plotkin, is whether there exists a continuous*model**of**the*untyped*lambda*-*calculus*whose theory is exactly*the*beta-theory or*the*beta-eta-theory ... In particular, we build a*graph**model**the*equational theory*of*which is exactly*the*set*of*equations satisfied in any*graph**model*. ¾ ¼*models*in each*of*them inducing pairwise distinct*lambda*theories ... A*lambda*theory Ì is*the**minimal**lambda*theory*of**the*class*of**graph**models*if there exists a*graph**model*´ Ôµ such that Ì Ì ´ Ôµ and Ì Ì ´ µ for all other*graph**modelś*µ. ...##
###
The sensible graph theories of lambda calculus

2004
*
Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004.
*

In this paper we give a positive answer to this question for

doi:10.1109/lics.2004.1319622
dblp:conf/lics/BucciarelliS04
fatcat:u6hslqrpgfftjontp6wtlxsk3y
*the*semantics*of**lambda**calculus*given in terms*of**graph**models*. ... non-existence*of*a*graph**model*whose equational theory is exactly*the**minimal**lambda*theory § ¦ (this result negatively answers Question 1 in [7, Section 6.2] for*the*restricted class*of**graph**models*). ... With regard to*the**lambda**calculus*we follow*the*notation and terminology*of*[4] .*Lambda**calculus**Graph**models**The*class*of**graph**models*belongs to Scott's continuous semantics. ...##
###
Topological incompleteness and order incompleteness of the lambda calculus

2003
*
ACM Transactions on Computational Logic
*

A

doi:10.1145/772062.772067
fatcat:ptvuocqvcbe5nawqmtj2ztltyu
*model**of**the*untyped*lambda**calculus*univocally induces a*lambda*theory (i.e., a congruence relation on λ-terms closed under α-and β-conversion) through*the*kernel congruence relation*of**the*interpretation ... A semantics*of**lambda**calculus*is (equationally) incomplete if there exists a*lambda*theory which is not induced by any*model*in*the*semantics. ... ACKNOWLEDGMENTS*The*author wishes to thank Gordon Plotkin and*the*referees for helpful comments and suggestions. ...##
###
Graph lambda theories

2008
*
Mathematical Structures in Computer Science
*

A longstanding open problem in

doi:10.1017/s0960129508006683
fatcat:an6ar3j6w5efzbqodnw7fxjdli
*lambda**calculus*is whether there exist continuous*models**of**the*untyped*lambda**calculus*whose theory is exactly*the*λβ or*the**the*least sensible λ-theory H (generated by ... Berline, is whether, given a class*of**lambda**models*, there are a*minimal*λ-theory and a*minimal*sensible λ-theory represented by it. ... Then one recasts classical recursion theory results in*the*framework*of**graph**models*, and this seems particularly compelling since those are*models**of**the*λ-*calculus*. ...##
###
Anagopos: A Reduction Graph Visualizer for Term Rewriting and Lambda Calculus

2011
*
International Conference on Rewriting Techniques and Applications
*

We present Anagopos, an open source tool for visualizing reduction

doi:10.4230/lipics.rta.2011.61
dblp:conf/rta/GrathwohlKPS11
fatcat:wjr3phbg6ne4zavrklslj37f4a
*graphs**of*terms in*lambda**calculus*and term rewriting. ... Anagopos allows step-by-step generation*of*reduction*graphs*under six different*graph*drawing algorithms. We provide ample examples*of**graphs*drawn with*the*tool. ... Acknowledgments*The*authors thank Jan Willem Klop, Peter Sestoft, and*the*anonymous referees for useful feedback. ...##
###
Molecular computers
[article]

2018
*
arXiv
*
pre-print

We propose

arXiv:1811.04960v1
fatcat:2spmzxhmpnaudibbuvie4jiloa
*the*chemlambda artificial chemistry, whose behavior strongly suggests that real molecules which embed Interaction Nets patterns and real chemical reactions which resemble Interaction Nets*graph*... rewrites could be a realistic path towards molecular computers, in*the*sense explained in*the*article. ... There is a github repository [15] where this*model*is implemented and various demos are available [9] , which show some features*of**the**model*: classical examples*of**lambda**calculus*computations, demos ...##
###
Molecular computers

2018
*
Figshare
*

rewrites could be a realistic path towards molecular computers, in

doi:10.6084/m9.figshare.7339103
fatcat:6t2whbifsjdzrp2vo26cf5qsaa
*the*sense explained in*the*article.This is a text version*of**the*article [7]. ... We propose*the*chemlambda artificial chemistry, whose behavior strongly suggests that real molecules which embed Interaction Nets patterns and real chemical reactions which resemble Interaction Nets*graph*... There is a github repository [15] where this*model*is implemented and various demos are available [9] , which show some features*of**the**model*: classical examples*of**lambda**calculus*computations, demos ...##
###
Easiness in graph models

2006
*
Theoretical Computer Science
*

In this paper we concentrate on

doi:10.1016/j.tcs.2005.11.005
fatcat:367kbdjdh5cerfzoybtblycmvi
*the*semantics G*of**lambda**calculus*given in terms*of**graph**models*,*graph*semantics for short. ...*of**lambda**calculus*. ...*model**of**lambda**calculus*. ...##
###
Foreword

1999
*
Theoretical Computer Science
*

Spreen is a fundamental study on enrichments and refinements

doi:10.1016/s0304-3975(98)00133-9
fatcat:ea62itnvanbttcep6sq5qojv5y
*of*dI-domains and related classes*of**models*.*Lambda**Calculus**of*Objects by V. Bono and M. ... On Functions Preserving Levels*of*Approximations: a Refined*Model*Construction for Various*Lambda*Calculi by D. ...##
###
Lambda calculus as a workflow model

2009
*
Concurrency and Computation
*

We discuss how these can be

doi:10.1002/cpe.1448
fatcat:446xuff7lfei3aa2co6kw25hwi
*modeled*using*lambda**calculus*, and how ideas from functional programming are applicable in*the*design*of*workflows. ... This paper explains why*lambda**calculus*is an appropriate*model*for workflow representation, and how a suitably efficient implementation can provide a wide range*of*capabilities to developers. ...*Lambda**calculus**Lambda**calculus*[2] is an abstract*model**of*computation which is*the*theoretical foundation*of*functional programming. ...##
###
Lambda Calculus as a Workflow Model

2008
*
2008 The 3rd International Conference on Grid and Pervasive Computing - Workshops
*

We discuss how these can be

doi:10.1109/gpc.workshops.2008.38
dblp:conf/gpc/KellyCW08
fatcat:usih6kyd6bhqjdsz3b5bbewcna
*modeled*using*lambda**calculus*, and how ideas from functional programming are applicable in*the*design*of*workflows. ... This paper explains why*lambda**calculus*is an appropriate*model*for workflow representation, and how a suitably efficient implementation can provide a wide range*of*capabilities to developers. ...*Lambda**calculus**Lambda**calculus*[2] is an abstract*model**of*computation which is*the*theoretical foundation*of*functional programming. ...##
###
Page 3623 of Mathematical Reviews Vol. , Issue 2000e
[page]

2000
*
Mathematical Reviews
*

It combines

*the*communication mechanism*of*chi*calculus*and*the*recursion mechanism*of*full*lambda**calculus*, and therefore extends both.” ... It is shown that chi calulus is capable*of**modeling*sequential computation in that it captures*the*operational semantics*of*call-by-name*lambda**calculus*. ...##
###
Page 459 of Mathematical Reviews Vol. , Issue 83b
[page]

1983
*
Mathematical Reviews
*

In Chapter 18 we get

*the*construction*of**the*projective*model*D,, and*the**graph**model*Pw. ... To be sure,*models*are not*the*only kind*of*reality to be considered;*the*computations encoded in*lambda**calculus*terms are also a reality, perhaps more fundamental than that*of**the*set-theoretic*models*...##
###
Page 016 of Mathematical Reviews Vol. , Issue 81I
[page]

1981
*
Mathematical Reviews
*

*The*representation

*of*

*the*

*lambda*

*calculus*which we give faithfully

*models*reduction to normal form

*of*terms

*of*

*the*classical

*lambda*

*calculus*which have normal forms; we prove for this representation that ... Roman Murawski (Heidelberg) Staples, John 81i1:03017 A

*graph*-like

*lambda*

*calculus*for which leftmost-outermost reduction is optimal. ...

##
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Graph easy sets of mute lambda terms

2016
*
Theoretical Computer Science
*

In this paper, we define for each natural number n, an infinite and recursive set M n

doi:10.1016/j.tcs.2015.12.024
fatcat:4ronvkej6vfw7lpptda55gql4q
*of*mute terms, and show that it is*graph*-easy: for any closed term t*of**the**lambda**calculus*there exists a*graph**model*... Among*the*unsolvable terms*of**the**lambda**calculus*,*the*mute ones are those having*the*highest degree*of*undefinedness. ...*Graph**models*are arguably*the*simplest*models**of**the**lambda**calculus*. There are two known methods for building*graph**models*, namely: by forcing or by canonical completion. ...
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