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The monadic secondorder logic of graphs I. Recognizable sets of Finite Graphs
 Information and Computation
, 1990
"... The notion of a recognizable sef offinite graphs is introduced. Every set of finite graphs, that is definable in monadic secondorder logic is recognizable, but not vice versa. The monadic secondorder theory of a contextfree set of graphs is decidable. 0 19W Academic Press. Inc. This paper begins ..."
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Cited by 301 (17 self)
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an investigation of the monadic secondorder logic of graphs and of sets of graphs, using techniques from universal algebra, and the theory of formal languages. (By a graph, we mean a finite directed hyperedgelabelled hypergraph, equipped with a sequence of distinguished vertices.) A survey of this research can
Modules over relative monads For Syntax and semantics
 UNDER CONSIDERATION FOR PUBLICATION IN MATH. STRUCT. IN COMP. SCIENCE
, 2012
"... We give an algebraic characterization of the syntax and semantics of a class of functional programming languages. We introduce a notion of 2–signature: such a signature specifies not only the terms of a language, but also reduction rules on those terms. To any 2–signature S we associate a ..."
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Cited by 4 (2 self)
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We give an algebraic characterization of the syntax and semantics of a class of functional programming languages. We introduce a notion of 2–signature: such a signature specifies not only the terms of a language, but also reduction rules on those terms. To any 2–signature S we associate a
Modules over Monads and Linearity
"... Replace this file with prentcsmacro.sty for your meeting, or with entcsmacro.sty for your meeting. Both can be ..."
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Cited by 9 (2 self)
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Replace this file with prentcsmacro.sty for your meeting, or with entcsmacro.sty for your meeting. Both can be
QF FUNCTORS AND (CO)MONADS
"... Abstract. One reason for the universal interest in Frobenius algebras is that their characterisation can be formulated in arbitrary categories: a functor K: A → B between categories is Frobenius if there exists a functor G: B → A which is at the same time a right and left adjoint of K; a monad F on ..."
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Cited by 3 (1 self)
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on A is a Frobenius monad provided the forgetful functor AF → A is a Frobenius functor, where AF denotes the category of Fmodules. With these notions, an algebra A over a field k is a Frobenius algebra if and only if A ⊗k − is a Frobenius monad on the category of kvector spaces. The purpose
MONADS AND COMONADS ON MODULE CATEGORIES
"... known in module theory that any Abimodule B is an Aring if and only if the functor − ⊗A B: MA → MA is a monad (or triple). Similarly, an Abimodule C is an Acoring provided the functor − ⊗A C: MA → MA is a comonad (or cotriple). The related categories of modules (or algebras) of − ⊗A B and comodu ..."
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Cited by 24 (13 self)
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known in module theory that any Abimodule B is an Aring if and only if the functor − ⊗A B: MA → MA is a monad (or triple). Similarly, an Abimodule C is an Acoring provided the functor − ⊗A C: MA → MA is a comonad (or cotriple). The related categories of modules (or algebras) of − ⊗A B
MONADS OF EFFECTIVE DESCENT TYPE AND COMONADICITY
"... Abstract. We show, for an arbitrary adjunction F ⊣ U: B→Awith B Cauchy complete, that the functor F is comonadic if and only if the monad T on A induced by the adjunction is of effective descent type, meaning that the free Talgebra functor F T: A→A T is comonadic. This result is applied to several ..."
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Cited by 17 (6 self)
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situations: In Section 4 to give a sufficient condition for an exponential functor on a cartesian closed category to be monadic, in Sections 5 and 6 to settle the question of the comonadicity of those functors whose domain is Set, orSet⋆, or the category of modules over a semisimple ring, in Section 7
MODULES OVER MONADS, MONADIC SYNTAX AND THE CATEGORY OF UNTYPED LAMBDACALCULI
"... Abstract. We define a notion of module over a monad and use it to propose a new definition (or semantics) for abstract syntax (with binding constructions). Using our notion of module, we build a category of exponential monads, which can be understood as the category of lambdacalculi, and prove that ..."
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Abstract. We define a notion of module over a monad and use it to propose a new definition (or semantics) for abstract syntax (with binding constructions). Using our notion of module, we build a category of exponential monads, which can be understood as the category of lambdacalculi, and prove
MODULES OVER MONADS AND THE STRUCTURE OF UNTYPED LAMBDACALCULI
, 2006
"... Abstract. Using the natural notion of module over a monad, we give a oneline definition of an untyped lambdacalculus. Our untyped lambdacalculi form naturally a category and we prove that this category has an initial object (the pure untyped lambdacalculus). Our definitions and results are formal ..."
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Abstract. Using the natural notion of module over a monad, we give a oneline definition of an untyped lambdacalculus. Our untyped lambdacalculi form naturally a category and we prove that this category has an initial object (the pure untyped lambdacalculus). Our definitions and results
Monadic Fold, Monadic Build, Monadic Short Cut Fusion
"... Short cut fusion improves the efficiency of modularly constructed programs by eliminating intermediate data structures produced by one program component and immediately consumed by another. We define a combinator which expresses uniform production of data structures in monadic contexts, and is the n ..."
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Cited by 1 (0 self)
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, and is the natural counterpart to the wellknown monadic fold which consumes them. Like the monadic fold, our new combinator quantifies over monadic algebras rather than standard ones. Together with the monadic fold, it gives rise to a new short cut fusion rule for eliminating intermediate data structures in monadic
Partially ordered monads for monadic topologies, rough sets and Kleene algebras
, 2006
"... In this paper we will show that partially ordered monads contain sufficient structure for modelling monadic topologies, rough sets and Kleene algebras. Convergence represented by extension structures over partially ordered monads includes notions of regularity and compactness. A compactification the ..."
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In this paper we will show that partially ordered monads contain sufficient structure for modelling monadic topologies, rough sets and Kleene algebras. Convergence represented by extension structures over partially ordered monads includes notions of regularity and compactness. A compactification
Results 1  10
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