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Fork algebraic datatypes

1998
*
Logic Journal of the IGPL
*

*Fork*

*algebras*have been proposed as an

*algebraic*basis for the construction of a program synthesis environment. ... ; these results make

*fork*

*algebras*a sound and powerful framework for this task. ... Abstract

*fork*

*algebras*(AFAs for short) are one attempt to give the

*algebraic*description of proper

*fork*

*algebras*. ...

##
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Algebraic multigrid fork-form Laplacians

2008
*
Numerical Linear Algebra with Applications
*

In this paper we describe an aggregation-based

doi:10.1002/nla.577
fatcat:iqmd4kki2bbl5itvn3xpm4ukca
*algebraic*multigrid method for the solution of discrete k-form Laplacians. ... Linear*Algebra*Appl. 2000; 00:1-6 Prepared using nlaauth.cls ... Lastly, we have initiated a study of*algebraic*multigrid for the Hodge decomposition of general k-forms. ...##
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Forked Temperley-Lieb Algebras and Intermediate Subfactors
[article]

2006
*
arXiv
*
pre-print

We consider noncommuting pairs P,Q of intermediate subfactors of an irreducible, finite-index inclusion N in M of II_1 factors such that P and Q are supertransitive with Jones index less than 4 over N. We show that up to isomorphism of the standard invariant, there is a unique such pair corresponding to each even value [P:N]=4cos^2(pi/2n) but none for the odd values [P:N]=4cos^2 (pi/(2n+1)). We also classify the angle values which occur between pairs of intermediate subfactors with small index

arXiv:math/0607335v4
fatcat:ptizx5hn6bbzhbxrxprsxnyt74
## more »

... ver their intersection: if [P:N] < 4, then the unique nontrivial angle value is always cos^-1 (1/([P:N]-1)).##
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Representability and program construction within fork algebras

1998
*
Logic Journal of the IGPL
*

This result makes

doi:10.1093/jigpal/6.2.227
fatcat:4uwwwngqo5e7jedeeq3wsy4uum
*fork**algebras*a programming calculus by far more powerful than it was previously thought. ... The representation theorem for*fork**algebras*was always misunderstood regarding its applications in program construction. ... Proper and Abstract*Fork**Algebras*Proper*fork**algebras*(PFAs for short) are extensions of*algebras*of binary relations [17] with a new operator called*fork*, and denoted by ∇. ...##
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Forked Temperley–Lieb algebras and intermediate subfactors

2007
*
Journal of Functional Analysis
*

I would also like to thank David Evans for pointing out the results on

doi:10.1016/j.jfa.2007.03.014
fatcat:mnpedmjglrgo5aua5ljywy626i
*algebras*associated to T -graphs. ... The*forked*Temperley-Lieb*algebras*in the above definition are a special case of*algebras*associated to T -shaped graphs which were studied by Evans and Gould in [5] . ... Subfactors coming from*forked*Temperley-Lieb*algebras*Definition We note some properties of the example in the preceeding section. . ...##
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th-Forking, Algebraic Independence and Examples of Rosy Theories
[article]

2003
*
arXiv
*
pre-print

We proved that rosy theories include simple and o-minimal theories and that for any theory for which the stable

arXiv:math/0306003v1
fatcat:c7pwohzlnrhnjmiekdtacbdbya
*forking*conjecture was true, \th-*forking*coincides with*forking*independence. ... In this article, we continue to study properties of th-*forking*and find more examples of rosy theories. ...##
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A short proof of representability of fork algebras

1997
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Theoretical Computer Science
*

In this paper a strong relationship is demonstrated between

doi:10.1016/s0304-3975(96)00299-x
fatcat:4cckbcd2mjgsbnekemv52dgvai
*fork**algebras*and quasi-projective relation*algebras*. ... With the help of Tarski's classical representation theorem for quasi-projective relation*algebras*, a short proof is given for the representation theorem of*fork**algebras*. ... the notion pre-*fork**algebra*to denote the class we call here*fork**algebra*. ...##
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Fork-Resilient Cross-Blockchain Transactions through Algebraic Topology
[article]

2020
*
arXiv
*
pre-print

However, state-of-the-art CBT models do not address the effect of the possible local

arXiv:2004.08473v2
fatcat:zmelwdyvlvhjvfxz24k6oxcuoa
*fork*suspension that might invalidate the entire CBT. ... This paper takes an*algebraic*-topological approach to abstract the blockchains and their transactions into simplicial complexes and shows that CBTs cannot complete in either a committed or an aborted status ... We take an*algebraic*-topological approach to abstract the blockchains and their transactions into simplicial complexes, and show that CBTs cannot complete in either a committed or an aborted status by ...##
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Fork Algebras as a Sufficiently Rich Universal Institution
[chapter]

2006
*
Lecture Notes in Computer Science
*

Therefore, formulas are equations and

doi:10.1007/11784180_19
fatcat:xtppciowrbca3kfwjqhymqcoay
*fork*is equational reasoning in the theory of*fork**algebras*(to be introduced later). This makes reasoning in*fork**algebras*simple. ...*Algebraization*of computational logics in the theory of*fork**algebras*has been a research topic for a while. ... Full Closure*Fork**algebras*Full Closure*Fork**Algebras*with Urelements (denoted by FCFAU) are extensions of relation*algebras*[12] , that is, they possess a relation*algebra*reduct. ...##
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Forking and stability in the representations of a C*-algebra
[article]

2012
*
arXiv
*
pre-print

We show that the theory of a non-degenerate representation of a C*-

arXiv:1211.7155v1
fatcat:2e3xwfmlobd2vb3caisuwyba74
*algebra*A over a Hilbert space H is superstable. ... Also, we characterize*forking*, orthogonality and domination of types and show that the theory has weak elimination of imaginaries. ... introduction Let A be a unital C * -*algebra*and let π : A → B(H) be a C * -*algebra*nondegenerate isometric homomorphism, where B(H) is the*algebra*of bounded operators over a Hilbert space H. ...##
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Algebraic Modelling and Performance Evaluation of Acyclic Fork-Join Queueing Networks
[chapter]

2000
*
Advances in Stochastic Simulation Methods
*

Simple lower and upper bounds on mean cycle time in stochastic acyclic

doi:10.1007/978-1-4612-1318-5_5
fatcat:f3dszexwavhrjofhr4ufwaa4bu
*fork*-join queueing networks are derived using a (max,+)-*algebra*based representation of network dynamics. ... A (max,+)-*algebra*representation of the*fork*-join network dynamics and related examples are given in Section 4. ... In this paper we propose an approach to get bounds on the mean cycle time, which exploits the (max,+)-*algebra*representation of acyclic*fork*-join network dynamics derived in [8, 9] . ...##
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Interpretability of first-order linear temporal logics in fork algebras

2006
*
The Journal of Logic and Algebraic Programming
*

In this paper we prove theorems on the interpretability of the first-order temporal logics LT L and T L into

doi:10.1016/j.jlap.2005.04.005
fatcat:wq7kq57wxjfc3eocmb3t6susci
*fork**algebras*. ... This result is part of a research project on the interpretability of logics in*fork**algebras*, and has important applications towards the relational specification of properties of systems within the Ar ... A "proper closure*fork**algebra*on S, T " is a proper closure*fork**algebra*A for which U A = T (S, T ) ૽ , and*fork*is defined by U ∇ V = { t 1 , t 2 ૽t 3 : t 1 , t 2 ∈ U ∧ t 1 , t 3 ∈ V } . ...##
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Some classes containing a fork algebra equivalent variety involving projections

1998
*
Logic Journal of the IGPL
*

The classes have as a subvariety the abstract

doi:10.1093/jigpal/6.2.203
fatcat:njkcxjz5zfhateifoyy2kowzfa
*fork**algebra*(AFA) equivalent variety involving projections. They are obtained by weakening some laws valid in AFA. ... Finally, the existence of equivalent classes with a binary operation like*fork*is studied. ... For example the comparison of direct products of heterogeneous relation*algebras*with*fork**algebras*[3] ,groupoid representable*fork**algebras*with set*fork**algebras*[25] and AFA with Q-relation*algebras*...##
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On Previdi's delooping conjecture forK-theory

2015
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Algebra & Number Theory
*

His main results are formulated in terms of

doi:10.2140/ant.2015.9.1
fatcat:6ogqgr3qpbaxlgnnruxbekpdne
*algebraic*K-theory, and he observes a certain relation between the K-groups K i .A/ and K i C1 . lim ! ... Denote by K the sheaf of group-like E 1 -spaces on the Nisnevich site of Spec R, that sends an étale R-*algebra*S to the space 1 .ދS /. ...*Algebra*& Number Theory ...##
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Squares in Fork Arrow Logic

2003
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Journal of Philosophical Logic
*

FAL is the modal logic of

doi:10.1023/a:1024847106313
fatcat:2fpe5w6f3bchzpy575rogr6yyq
*fork**algebras*(FAs) just as arrow logic is the modal logic of relation*algebras*(RAs). ... A proper FA is an*algebra*of relations where the*fork*is induced by an injective operation coding pair formation. ... of*fork**algebras*. ...
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