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Cool: A control-flow generator for system analysis
[chapter]
1998
Lecture Notes in Computer Science
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It uniformly supports the automatic generation 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, ...
doi:10.1007/bfb0026442
fatcat:nnuxqtmp45hrpgoiksmasbyieq
A Robust Algebraic Framework For High-Level Music Programming
2016
Zenodo
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In this paper, we present a new 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. ...
doi:10.5281/zenodo.1289575
fatcat:sreircw63fdh7lwxlglv7ialom
Finally, a Polymorphic Linear Algebra Language (Pearl)
2019
European Conference on Object-Oriented Programming
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This design enables us to change the behaviour 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 ...
doi:10.4230/lipics.ecoop.2019.25
dblp:conf/ecoop/ShaikhhaP19
fatcat:uw35z2shozcs3lghnngzenfrwe
Version Space Algebras are Acyclic Tree Automata
[article]
2021
arXiv
pre-print
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Version space 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. ...
arXiv:2107.12568v1
fatcat:7mhjl7lnufckpfhtkwlyrztvgi
Algebraic graphs with class (functional pearl)
2017
SIGPLAN notices
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The flexibility 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. ...
doi:10.1145/3156695.3122956
fatcat:w33jwwrf5rb4fac6p27urqjjmi
Initial Algebra Semantics for Cyclic Sharing Structures
[chapter]
2009
Lecture Notes in Computer Science
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In the case 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. ...
doi:10.1007/978-3-642-02273-9_11
fatcat:ktvhen52arccxbxt7ytyspjjyq
Page 4774 of Mathematical Reviews Vol. , Issue 90H
[page]
1990
Mathematical Reviews
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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
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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
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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
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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
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Results suggest that the features 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. ...
doi:10.11114/jets.v3i2.676
fatcat:xtbabfbtabbtbcqkh3hm2zklie
Induction and recursion on datatypes
[chapter]
1995
Lecture Notes in Computer Science
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Handling Intervals with Relation 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. ...
doi:10.1007/3-540-60117-1_14
fatcat:namzjvik6vapne363qzzvaqdlu
Page 1574 of Mathematical Reviews Vol. , Issue 91C
[page]
1991
Mathematical Reviews
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representation category of (so-called) ribbon Hopf algebras. ...
This provides the machinery and correspondence for the construction of invariants via representations of quantum groups. ...
Flexible Conceptions of Perspectives and Representations: An Examination of Pre-Service Mathematics Teachers' Knowledge
2014
International Journal of Education in Mathematics Science and Technology
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link them across problems, or (3) 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 ...
doi:10.18404/ijemst.23592
fatcat:l5cqfft5qvgq7d4qptbrbzlroq
A Low-Level Analysis Library for Architecture Recovery
2003
Electronical Notes in Theoretical Computer Science
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We discuss low-level 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 ...
doi:10.1016/s1571-0661(04)80736-9
fatcat:a6waws66ezdtrmzhyph5pik2mm
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