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Initial Algebra and Final Coalgebra Semantics for Concurrency
, 1994
"... The aim of this paper is to relate initial algebra semantics and final coalgebra semantics. It is shown how these two approaches to the semantics of programming languages are each others dual, and some conditions are given under which they coincide. More precisely, it is shown how to derive initial ..."
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Cited by 55 (9 self)
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The aim of this paper is to relate initial algebra semantics and final coalgebra semantics. It is shown how these two approaches to the semantics of programming languages are each others dual, and some conditions are given under which they coincide. More precisely, it is shown how to derive initial semantics from final semantics, using the initiality and finality to ensure their equality. Moreover, many facts about congruences (on algebras) and (generalized) bisimulations (on coalgebras) are shown to be dual as well.
Closed categories generated by commutative monads
 J. Austral. Math. Soc
, 1971
"... The notion of commutative monad was denned by the author in [4]. The ..."
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Cited by 15 (4 self)
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The notion of commutative monad was denned by the author in [4]. The
*Autonomous Categories: Once More Around The Track
 AND CHU CONSTRUCTIONS: COUSINS? 149
, 1999
"... . This represents a new and more comprehensive approach to the  autonomous categories constructed in the monograph [Barr, 1979]. The main tool in the new approach is the Chu construction. The main conclusion is that the category of separated extensional Chu objects for certain kinds of equationa ..."
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Cited by 6 (1 self)
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. This represents a new and more comprehensive approach to the  autonomous categories constructed in the monograph [Barr, 1979]. The main tool in the new approach is the Chu construction. The main conclusion is that the category of separated extensional Chu objects for certain kinds of equational categories is equivalent to two usually distinct subcategories of the categories of uniform algebras of those categories. 1. Introduction The monograph [Barr, 1979] was devoted to the investigation of autonomous categories. Most of the book was devoted to the discovery of autonomous categories as full subcategories of seven different categories of uniform or topological algebras over concrete categories that were either equational or reflective subcategories of equational categories. The base categories were: 1. vector spaces over a discrete field; 2. vector spaces over the real or complex numbers; 3. modules over a ring with a dualizing module; 4. abelian groups; 5. modules ove...
MONAD COMPOSITIONS I: GENERAL CONSTRUCTIONS AND RECURSIVE DISTRIBUTIVE LAWS
"... ABSTRACT. New techniques for constructing a distributive law of a monad over another are studied using submonads, quotient monads, product monads, recursivelydefined distributive laws, and linear equations. Sequel papers will consider distributive laws in closed categories and will construct monad ..."
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Cited by 2 (0 self)
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ABSTRACT. New techniques for constructing a distributive law of a monad over another are studied using submonads, quotient monads, product monads, recursivelydefined distributive laws, and linear equations. Sequel papers will consider distributive laws in closed categories and will construct monad approximations for compositions which fail to be a monad. 1.
Instances of computational effects: an algebraic perspective
"... Abstract—We investigate the connections between computational effects, algebraic theories, and monads on functor categories. We develop a syntactic framework with variable binding that allows us to describe equations between programs while taking into account the idea that there may be different ins ..."
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Cited by 1 (1 self)
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Abstract—We investigate the connections between computational effects, algebraic theories, and monads on functor categories. We develop a syntactic framework with variable binding that allows us to describe equations between programs while taking into account the idea that there may be different instances of a particular computational effect. We use our framework to give a general account of several notions of computation that had previously been analyzed in terms of monads on presheaf categories: the analysis of local store by Plotkin and Power; the analysis of restriction by Pitts; and the analysis of the pi calculus by Stark. I.
Universal Properties of Impure Programming Languages
"... We investigate impure, callbyvalue programming languages. Our first language only has variables and letbinding. Its equational theory is a variant of Lambek’s theory of multicategories that omits the commutativity axiom. We demonstrate that type constructions for impure languages — products, sums ..."
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We investigate impure, callbyvalue programming languages. Our first language only has variables and letbinding. Its equational theory is a variant of Lambek’s theory of multicategories that omits the commutativity axiom. We demonstrate that type constructions for impure languages — products, sums and functions — can be characterized by universal properties in the setting of ‘premulticategories’, multicategories where the commutativity law may fail. This leads us to new, universal characterizations of two earlier equational theories of impure programming languages: the premonoidal categories of Power and Robinson, and the monadbased models of Moggi. Our analysis thus puts these earlier abstract ideas on a canonical foundation, bringing them to a new, syntactic level. F.3.2 [Semantics of Pro
Contents
"... Abstract. An unpublished result by the first author states that there exists a Hopf algebra H such that for any Möbius category C (in the sense of Leroux) there exists a canonical algebra morphism from the dual H ∗ of H to the incidence algebra of C. Moreover, the Möbius inversion principle in incid ..."
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Abstract. An unpublished result by the first author states that there exists a Hopf algebra H such that for any Möbius category C (in the sense of Leroux) there exists a canonical algebra morphism from the dual H ∗ of H to the incidence algebra of C. Moreover, the Möbius inversion principle in incidence algebras follows from a ‘master’ inversion result in H ∗. The underlying module of H was originally defined as the free module on the set of iso classes of Möbius intervals, i.e. Möbius categories with initial and terminal objects. Here we consider a category of Möbius intervals and construct the Hopf algebra via the objective approach applied to a monoidal extensive category of combinatorial objects, with the values in appropriate rings being abstracted from combinatorial functors on the objects. The explicit consideration of a category of Möbius
1 INTRODUCTION 1 Guarded and Banded Semigroups
"... The variety of guarded semigroups consists of all (S, ·, ) where (S, ·) is a semigroup ..."
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The variety of guarded semigroups consists of all (S, ·, ) where (S, ·) is a semigroup