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Algebraic Definition of Programming Languages
 Twente Workshop on Language Technology, TWL 16
, 1999
"... This paper provides an algebraic definition of programming languages. It presents a methodology for the construction of syntax and semantics of a programming language as similar algebras specified by the same specification rules. Then we show that syntax and semantics algebras of a programming langu ..."
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Cited by 3 (2 self)
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This paper provides an algebraic definition of programming languages. It presents a methodology for the construction of syntax and semantics of a programming language as similar algebras specified by the same specification rules. Then we show that syntax and semantics algebras of a programming
AN ALGEBRAIC DEFINITION OF (∞, N)CATEGORIES
"... Abstract. In this paper we define a sequence of monads T(∞,n)(n ∈ N) on the category ∞Gr of ∞graphs. We conjecture that algebras for T(∞,0), which are defined in a purely algebraic setting, are models of∞groupoids. More generally, we conjecture that T(∞,n)algebras are models for (∞, n)categori ..."
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Abstract. In this paper we define a sequence of monads T(∞,n)(n ∈ N) on the category ∞Gr of ∞graphs. We conjecture that algebras for T(∞,0), which are defined in a purely algebraic setting, are models of∞groupoids. More generally, we conjecture that T(∞,n)algebras are models for (∞, n
Concrete Relation Algebra Definition
, 2012
"... A concrete relation R between two sets A and B is a subset of the Cartesian product A ×B, where A ×B = {(a,b) ∶ a ∈ A,b ∈ B} [3] [1] Example Let A = {1,2,3,4} and let R be a relation defined on A such that R = {(a,b) ∣ a < b}, then the relation can be visualized as set given by: R = {(1,2), (1, ..."
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A concrete relation R between two sets A and B is a subset of the Cartesian product A ×B, where A ×B = {(a,b) ∶ a ∈ A,b ∈ B} [3] [1] Example Let A = {1,2,3,4} and let R be a relation defined on A such that R = {(a,b) ∣ a < b}, then the relation can be visualized as set given by: R = {(1,2), (1,3), (1,4), (2,3), (2,4), (3,4)}. R can also be visualized as a graph, a table or a boolean matrix as shown in the figures below: 1 23 4 oo R 1 2 3 4 1 x x x 2 x x
Algebraic laws for nondeterminism and concurrency
 Journal of the ACM
, 1985
"... Abstract. Since a nondeterministic and concurrent program may, in general, communicate repeatedly with its environment, its meaning cannot be presented naturally as an input/output function (as is often done in the denotational approach to semantics). In this paper, an alternative is put forth. Firs ..."
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Cited by 608 (13 self)
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. First, a definition is given of what it is for two programs or program parts to be equivalent for all observers; then two program parts are said to be observation congruent iff they are, in all program contexts, equivalent. The behavior of a program part, that is, its meaning, is defined to be its
ALGEBRAIC DEFINITION OF HOLONOMY ON POISSON MANIFOLD
, 706
"... Abstract. We give an algebraic construction of connection on the symplectic leaves of Poisson manifold, introduced in [6]. This construction is suitable for the definition of the linearized holonomy on a regular symplectic foliation. 1. ..."
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Abstract. We give an algebraic construction of connection on the symplectic leaves of Poisson manifold, introduced in [6]. This construction is suitable for the definition of the linearized holonomy on a regular symplectic foliation. 1.
ALGEBRAIC DEFINITION OF HOLONOMY ON POISSON MANIFOLD
, 706
"... Abstract. We give an algebraic construction of connection on the symplectic leaves of Poisson manifold, introduced in [6]. This construction is suitable for the definition of the linearized holonomy on a regular symplectic foliation. 1. ..."
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Abstract. We give an algebraic construction of connection on the symplectic leaves of Poisson manifold, introduced in [6]. This construction is suitable for the definition of the linearized holonomy on a regular symplectic foliation. 1.
Algebraic Definition of weak (∞, n)Categories
 Camell Kachour 83 Boulevard du Temple, 93390, ClichysousBois, France Phone: 0033143512807 Email:camell.kachour@gmail.com
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Universal coalgebra: a theory of systems
, 2000
"... In the semantics of programming, nite data types such as finite lists, have traditionally been modelled by initial algebras. Later final coalgebras were used in order to deal with in finite data types. Coalgebras, which are the dual of algebras, turned out to be suited, moreover, as models for certa ..."
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Cited by 408 (42 self)
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the notion of coalgebra homomorphism, the definition of bisimulation on coalgebras can be shown to be formally dual to that of congruence on algebras. Thus, the three basic notions of universal algebra: algebra, homomorphism of algebras, and congruence, turn out to correspond to coalgebra, homomorphism
EXERCISES IN THE BIRATIONAL GEOMETRY OF ALGEBRAIC VARIETIES
, 2008
"... The book [KM98] gave an introduction to the birational geometry of algebraic varieties, as the subject stood in 1998. The developments of the last decade made the more advanced parts of Chapters 6 and 7 less important and the detailed treatment of surface singularities in Chapter 4 less necessary. H ..."
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Cited by 322 (1 self)
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The book [KM98] gave an introduction to the birational geometry of algebraic varieties, as the subject stood in 1998. The developments of the last decade made the more advanced parts of Chapters 6 and 7 less important and the detailed treatment of surface singularities in Chapter 4 less necessary
Results 1  10
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