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Cool: A control-flow generator for system analysis
[chapter]

1998
*
Lecture Notes in Computer Science
*

It uniformly supports the automatic generation

doi:10.1007/bfb0026442
fatcat:nnuxqtmp45hrpgoiksmasbyieq
*of*transition systems and flow*graphs*from process*algebra*terms and*programs**of**programming*languages. ... As a side-effect*of*the unifying view*of*process*algebra*and*programming*language*programs*, Coot supports the automatic*construction**of*CFA-components*of*optimizing compilers, which are usually still handcoded ... In both cases the application*of*the relevant analysis and verification procedures relies on transforming the process*algebra*or*programming*language*program*into appropriate graphical*representations*, ...##
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A Robust Algebraic Framework For High-Level Music Programming

2016
*
Zenodo
*

In this paper, we present a new

doi:10.5281/zenodo.1289575
fatcat:sreircw63fdh7lwxlglv7ialom
*algebraic*model for music*programming*: tiled musical*graphs*. ... This leads to the definition*of*an*algebra**of*music objects~: tiled music*graphs*, which can be combined by a single operator : the tiled product, that is neither sequential nor parallel but both. ... Any (mental or explicit)*representation*induced by the usage*of*these functions converges to a single and coherent*representation**of*the elements*of*this*algebra*. ...##
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Finally, a Polymorphic Linear Algebra Language (Pearl)

2019
*
European Conference on Object-Oriented Programming
*

This design enables us to change the behaviour

doi:10.4230/lipics.ecoop.2019.25
dblp:conf/ecoop/ShaikhhaP19
fatcat:uw35z2shozcs3lghnngzenfrwe
*of*arithmetic operations to express matrix*algebra*,*graph*algorithms, logical probabilistic*programs*, and differentiable*programs*. ... The design*of*this domain-specific language (DSL) is inspired by both mathematics and*programming*languages: its basic*constructs*are borrowed from abstract*algebra*, whereas the key technology behind its ... 1 We used Scala as the implementation language for Pilatus, but other*programming*languages with support for lambda expressions and multi-stage*programming*could be used as well; most*of*the techniques ...##
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Version Space Algebras are Acyclic Tree Automata
[article]

2021
*
arXiv
*
pre-print

Version space

arXiv:2107.12568v1
fatcat:7mhjl7lnufckpfhtkwlyrztvgi
*algebras*are ways*of*representing spaces*of**programs*which can be combined using union, intersection, and cross-product/"join" operators. ... We present a linear-time semantics-preserving*constructive*embedding from version space*algebras*into nondeterministic finite tree automata, showing that the former are but a special case*of*the latter ... Though works involving VSAs, e-*graphs*, and tree automata typically*construct*and use them very differently, their*representational*capabilities appear quite similar. ...##
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Algebraic graphs with class (functional pearl)

2017
*
SIGPLAN notices
*

The flexibility

doi:10.1145/3156695.3122956
fatcat:w33jwwrf5rb4fac6p27urqjjmi
*of*the approach is demonstrated by developing a library for*constructing*and transforming polymorphic*graphs*. ... It is built on a rigorous mathematical foundation -an*algebra**of**graphs*-that allows us to apply equational reasoning for proving the correctness*of**graph*transformation algorithms. ... Last but not least, I'm very grateful to Victor Khomenko for his contribution to the*algebra**of*parameterised*graphs*that forms the mathematical foundation*of*this work. ...##
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Initial Algebra Semantics for Cyclic Sharing Structures
[chapter]

2009
*
Lecture Notes in Computer Science
*

In the case

doi:10.1007/978-3-642-02273-9_11
fatcat:ktvhen52arccxbxt7ytyspjjyq
*of**graphs*or "tree-like" structurestrees involving cycles and sharing -however, it is not clear what kind*of*inductive structures exists and how we can faithfully assign a term*representation*... Terms are a concise*representation**of*tree structures. ... The basis for this work, which was motivated by a question*of*Zhenjiang Hu, was done while the author visited IPL, University*of*Tokyo during April 2007 -March 2008. ...##
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Page 4774 of Mathematical Reviews Vol. , Issue 90H
[page]

1990
*
Mathematical Reviews
*

Mal’tsev [

*Algebraic*systems (Russian), “Nauka”, Moscow, 1970; MR 44 #142], the authors*construct*an*algebraic*system T(A)/F which is defined uniquely up to an isomorphism. ... We show that this canonical*representation*can be computed from any*representation*by a rational function. ...##
###
Page 3597 of Mathematical Reviews Vol. , Issue 90F
[page]

1990
*
Mathematical Reviews
*

We also give a

*representational*description*of*our own*construction*using the notion*of*a prime event structure.” ... We discuss the problem*of**representation**of*parametric*programs*in the form*of*ordinary logic*programs*.” 68Q_ Theory*of*computing 90f:68108 90f:68105 68Q55 03B40 Coquand, Thierry (4-CAMB-C); Gunter, Carl ...##
###
Page 3939 of Mathematical Reviews Vol. , Issue 2000f
[page]

2000
*
Mathematical Reviews
*

Summary: “The main result

*of*this paper is a non-Buchberger al- gorithm for*constructing*initial ideals and Grébner bases*of*toric ideals, based on the connections between toric ideals and integer*programming*... The main results are as follows: a complete characterization*of**graphs*(*of*the aforementioned type) whose edge*algebras*are defined by quadratic binomial ideals, a complete characterization*of**graphs*whose ...##
###
Page 5136 of Mathematical Reviews Vol. , Issue 97H
[page]

1997
*
Mathematical Reviews
*

The new and old

*algebraic**constructions*coexist within a pushout cube. ... The two formulations are entirely equivalent in the world*of**algebraic**graph*rewriting. ...##
###
Examining How Teachers Use Graphs to Teach Mathematics during a Professional Development Program

2015
*
Journal of Education and Training Studies
*

Results suggest that the features

doi:10.11114/jets.v3i2.676
fatcat:xtbabfbtabbtbcqkh3hm2zklie
*of*the PD*program*had a positive effect on teachers' classroom practices regarding the use*of**graphs*. ... We analyzed all lessons where teachers used*graphs*in class at the start and end*of*the*program*, finding that teachers' use*of**graphs*was qualitatively more sophisticated in the end lessons. ... The ideas expressed herein are those*of*the authors and do not necessarily reflect the ideas*of*the funding agency. ...##
###
Induction and recursion on datatypes
[chapter]

1995
*
Lecture Notes in Computer Science
*

Handling Intervals with Relation

doi:10.1007/3-540-60117-1_14
fatcat:namzjvik6vapne363qzzvaqdlu
*Algebra*Robin Hirsch Given a*representation**of*a relation*algebra*we*construct*relation*algebras**of*pairs and*of*intervals. ... We introduced subgraph and quotient*graph**constructions*. The key parts*of*the well-definedness proofs*of*these*constructions*were presented in two fashions. ... Here, in contrast, an*algebra**of*formal languages and relations is used to derive*graph*algorithms. ...##
###
Page 1574 of Mathematical Reviews Vol. , Issue 91C
[page]

1991
*
Mathematical Reviews
*

*representation*category

*of*(so-called) ribbon Hopf

*algebras*. ... This provides the machinery and correspondence for the

*construction*

*of*invariants via

*representations*

*of*quantum groups. ...

##
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Flexible Conceptions of Perspectives and Representations: An Examination of Pre-Service Mathematics Teachers' Knowledge

2014
*
International Journal of Education in Mathematics Science and Technology
*

link them across problems, or (3)

doi:10.18404/ijemst.23592
fatcat:l5cqfft5qvgq7d4qptbrbzlroq
*constructs**of*one perspective and did not operate within*algebraic*and graphical*representations*. ... Specifically, teachers demonstrated: (1)*constructs**of*both perspectives and operated within*algebraic*and graphical*representations*, (2)*constructs**of*both perspectives, but not transitional enough to ... With respect to constrained conceptions, prospective teachers demonstrated*constructs**of*object perspective, but failed to incorporate*constructs**of*process perspective and facets*of*the*algebraic**representations*...##
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A Low-Level Analysis Library for Architecture Recovery

2003
*
Electronical Notes in Theoretical Computer Science
*

We discuss low-level

doi:10.1016/s1571-0661(04)80736-9
fatcat:a6waws66ezdtrmzhyph5pik2mm
*program*analyses that are reusable in many high-level analyses for architecture recovery. ... They include both*program*structure analyses known from compiler front-ends and data-flow analyses. In general, high-level analyses use the low-level results only partially. ... General Approach We use a meta*programming*front-end for the AST*construction*and the approach*of*[28] to*construct*an SSA*representation**of*the system with the optimizations*of*[2] to reduce its size ...
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