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Page 2530 of Mathematical Reviews Vol. , Issue 84g
[page]

1984
*
Mathematical Reviews
*

This is

*for*the Af-calculus;*for*the*An*-calculus, the required structure is*an*extensional*combinatory**model*, which is like a*combinatory**model*without e which satisfies: if,*for*all dE D, d):d=d,-d, then ... The author shows that every lambda*model*is a lambda*algebra*and, given any lambda*algebra*, the free*combinatory**algebra*generated by*an*infinite set of variables over the lambda*algebra*is a lambda*model*...##
###
The Fixpoint Combinator in Combinatory Logic – A Step towards Autonomous Real-time Testing of Software?

2022
*
Athens Journal of Sciences
*

*Combinatory*Logic is

*an*elegant and powerful logical theory that is used in computer science as a theoretical

*model*

*for*computation. ... A Neural

*Algebra*,

*modeling*the way we think, constitutes

*an*interesting

*model*of

*Combinatory*Logic. There are other

*models*, also based on the Graph

*Model*(Engeler 1981), such as software testing. ... Graph

*Model*that he did. ...

##
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Scott Is Always Simple
[chapter]

2012
*
Lecture Notes in Computer Science
*

In this paper we give

doi:10.1007/978-3-642-32589-2_3
fatcat:jqadnhzb5jcudfucqdvxbirasa
*an*outline of recent*algebraic*results concerning theories and*models*of the untyped lambda calculus. ... Of course,*an*unorderable*model*can still arise from*an*order-theoretic construction,*for*instance as a subalgebra of some orderable*model*. ... A function f : C → C is representable in a*combinatory**algebra*C if there exists*an*element c ∈ C such that cz = f (z)*for*all z ∈ C. ...##
###
Models and theories of lambda calculus
[article]

2009
*
arXiv
*
pre-print

*algebras*; (iii) a proof that no effective lambda-

*model*can have lambda-beta or lambda-beta-eta as its equational theory (this can be seen as a partial answer to

*an*open

*problem*introduced by Honsell-Ronchi ... The main research achievements include: (i) a general construction of lambda-

*models*from reflexive objects in (possibly non-well-pointed) categories; (ii) a Stone-style representation theorem

*for*

*combinatory*... [35, Thm. 4.3.7 ] (Stone's representation theorem

*for*

*combinatory*

*algebras*) Every

*combinatory*

*algebra*C can be represented as a weak Boolean product of indecomposable

*combinatory*

*algebras*C x (

*for*x ...

##
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Page 4360 of Mathematical Reviews Vol. , Issue 84j
[page]

1984
*
Mathematical Reviews
*

“In Section 5 we consider a

*problem*in which the*combinatorial*structure (flows) is generalized in*an**algebraic*setting. ... Thus a second direction of further research is the discussion of reasonable*algebraic*generalizations of*combinatorial*structures.*For*example, the dual of*an**algebraic*linear program (cf. ...##
###
Heisenberg-Weyl algebra revisited: Combinatorics of words and paths
[article]

2009
*
arXiv
*
pre-print

We provide a concrete

arXiv:0904.1506v1
fatcat:vfs2s5wclzc47agmrdrxqxkvf4
*model*of the*algebra*in terms of paths on a lattice with some decomposition rules. ... The Heisenberg-Weyl*algebra*, which underlies virtually all physical representations of Quantum Theory, is considered from the*combinatorial*point of view. ... Acknowledgments We thank Hayat Cheballah*for*useful discussions. ...##
###
Book Review: Linear and combinatorial optimization in ordered algebraic structures

1985
*
Bulletin of the American Mathematical Society
*

Many

doi:10.1090/s0273-0979-1985-15325-x
fatcat:lfnlvbmtjfgu3gpi7ituv6yqni
*combinatorial*optimization*problems*assume, under such reformulation, the appearance of*problems*of linear*algebra*over*an*ordered system of scalars. ... This application is made relevant by the fact that many optimization questions depend essentially on the presence of two features:*an**algebraic*language within which a system can be*modelled*and*an*algorithm ...##
###
Extension of combinatory logic to a theory of combinatory representation

1992
*
Theoretical Computer Science
*

., Extension of

doi:10.1016/0304-3975(92)90392-s
fatcat:iogen6fsz5gs5eurzfsfp6mjr4
*combinatory*logic to a theory of*combinatory*representation, Theoretical Computer Science 97 (1992) 157-173. ... On one hand, a solution (h, f;-c,YI) of r' in a*combinatory**model*M should render*an*inner Y-*algebra*M[! ... By adding this property to a semi-universal*combinatory**model*, the resulting universal*combinatory**model*can now deal with the entire representation*problem*. ...##
###
Relations between Generalization, Reasoning and Combinatorial Thinking in Solving Mathematical Open-Ended Problems within Mathematical Contest

2020
*
Mathematics
*

*Algebraic*generalization is

*an*important prerequisite to prove mathematically and to solve

*combinatorial*

*problem*at higher levels, i.e., using expressions and formulas, therefore a special focus should ... mathematical

*problems*Specific relations between these three abilities, manifested in the solving of

*an*open-ended ill-structured

*problem*aimed at mathematical

*modeling*, were investigated. ... As stated by Ericson and Lockwood [49] in order to prove a

*combinatorial*identity various cognitive

*models*are needed in order to understand the

*algebraic*notations. ...

##
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Algebraic, logical and network representations in the design of software for combinatorial optimization

1996
*
Proceedings of HICSS-29: 29th Hawaii International Conference on System Sciences
*

We survey three

doi:10.1109/hicss.1996.495425
dblp:conf/hicss/CoullardF96
fatcat:63vhji73snbnbomgngy47ag7eq
*problem*representations that are popularly applied in*combinatorial*optimization:*algebraic**modeling*languages, constraint logic programming languages, and network diagrams. ... We focus especially on the possibility that general-purpose system designs, which are highly successful in other areas, might be extended to*combinatorial*optimization. ...*For*the user who has a difficult*combinatorial*optim ization*problem*,*algebraic**modeling*languages offer*an*appealing environment in which to devise and test new formulations that may provide tighter bounds ...##
###
The lambda calculus is algebraic

2002
*
Journal of functional programming
*

In particular, it solves the

doi:10.1017/s0956796801004294
fatcat:n34nmya5tfbbjddyepeomcwgjq
*problem*of the notorious ξ-rule, which asserts that equations should be preserved under binders, and which fails to be sound*for*the usual interpretation. ... This paper serves as a self-contained, tutorial introduction to*combinatory**models*of the untyped lambda calculus. We focus particularly on the interpretation of free variables. ... Acknowledgments I would like to thank the three anonymous referees*for*their valuable suggestions. ...##
###
Combinatorial Strand Algebra in Insertion Modeling System

2012
*
International Conference on Information and Communication Technologies in Education, Research, and Industrial Applications
*

We focus on the basic strand

dblp:conf/icteri/Klionov12
fatcat:l5xhot75cja6lfeqsdcvrtxemy
*algebra*-*combinatorial*strand*algebra*, which is equivalent to the place-transition Petri nets, and on the version of the*model*driver of the Insertion*Modeling*System, based ... Letichevsky in 1987. and on the way of implementation of strand*algebras*-a process*algebra**for*DNA computing devised by Luca Cardelli in order to compile other formal systems into the*algebra*, and compilation ... Some solution of this*problem*, based on the*combinatorial*DNA*algebra*, was given by Cardelli in paper [10] . ...##
###
Applying Universal Algebra to Lambda Calculus

2008
*
Journal of Logic and Computation
*

In fact the Stone representation theorem

doi:10.1093/logcom/exn085
fatcat:muo26iplxbe2diepxtlnnutdxi
*for*Boolean*algebras*can be generalized to*combinatory**algebras*and λ-abstraction*algebras*. ... , and 26 open*problems*. ... In*an**algebraic*setting the*problem*of the order-incompleteness can be expressed as follows: (P19) Is there*an*n-permutable variety of LAAs*for*some n ≥ 2 (see [53]*for*the definition of n-permutability ...##
###
Page 1477 of Mathematical Reviews Vol. , Issue 99c
[page]

1991
*
Mathematical Reviews
*

Functional lambda abstraction

*algebras*arise as the ‘coordinatizations’ of environment*models*or lambda*models*, the natural*combinatory**models*of the lambda calculus. ... to*combinatory**algebras*in this regard. ...##
###
New constructs for the description of combinatorial optimization problems in algebraic modeling languages

1996
*
Computational optimization and applications
*

We show in this paper, through a series of examples, how

doi:10.1007/bf00248011
fatcat:pkxo4vvsjnhadim7jlmgv52dsm
*an**algebraic**modeling*language might be extended to help with a greater variety of*combinatorial*optimization*problems*. ...*Algebraic*languages are at the heart of many successful optimization*modeling*systems, yet they have been used with only limited success*for**combinatorial*(or discrete) optimization. ... Decision sets in*algebraic**modeling*languages Our examples from previous sections suggest that*algebraic**modeling*languages have several strengths*for*the specification of*combinatorial*optimization*problems*...
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