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

Volker Braun, Jens Knoop, Dirk Koschützki
1998 Lecture Notes in Computer Science  
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

David Janin
2016 Zenodo  
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)

Amir Shaikhha, Lionel Parreaux, Michael Wagner
2019 European Conference on Object-Oriented Programming  
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]

James Koppel
2021 arXiv   pre-print
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)

Andrey Mokhov
2017 SIGPLAN notices  
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]

Makoto Hamana
2009 Lecture Notes in Computer Science  
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  
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

Alfredo Bautista, M. C. Cañadas, Bárbara M. Brizuela, Analúcia D. Schliemann
2015 Journal of Education and Training Studies  
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]

Henk Doornbos, Roland Backhouse
1995 Lecture Notes in Computer Science  
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  
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

Vanessa R. Pitts Bannister
2014 International Journal of Education in Mathematics Science and Technology  
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

Welf Löwe, Jonas Lundberg
2003 Electronical Notes in Theoretical Computer Science  
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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