Results 1  10
of
11
On functors expressible in the polymorphic typed lambda calculus
 Logical Foundations of Functional Programming
, 1990
"... This is a preprint of a paper that has been submitted to Information and Computation. ..."
Abstract

Cited by 16 (1 self)
 Add to MetaCart
This is a preprint of a paper that has been submitted to Information and Computation.
Recursive Types in Kleisli Categories
 Preprint 2004. MFPS Tutorial, April 2007 Classical Domain Theory 75/75
, 1992
"... We show that an enriched version of Freyd's principle of versality holds in the Kleisli category of a commutative strong monad with fixedpoint object. This gives a general categorical setting in which it is possible to model recursive types involving the usual datatype constructors. ..."
Abstract

Cited by 8 (2 self)
 Add to MetaCart
We show that an enriched version of Freyd's principle of versality holds in the Kleisli category of a commutative strong monad with fixedpoint object. This gives a general categorical setting in which it is possible to model recursive types involving the usual datatype constructors.
Homological algebra of semimodules and semicontramodules
, 2007
"... Abstract. We develop the basic constructions of homological algebra in the (appropriately defined) unbounded derived categories of modules over algebras over coalgebras over noncommutative rings (which we call semialgebras over corings). We define doublesided derived functors SemiTor and SemiExt of ..."
Abstract

Cited by 7 (3 self)
 Add to MetaCart
Abstract. We develop the basic constructions of homological algebra in the (appropriately defined) unbounded derived categories of modules over algebras over coalgebras over noncommutative rings (which we call semialgebras over corings). We define doublesided derived functors SemiTor and SemiExt of the functors of semitensor product and semihomomorphisms, and construct an equivalence between the exotic derived categories of semimodules and semicontramodules. Certain (co)flatness and/or (co)projectivity conditions have to be imposed on the coring and semialgebra to make the module categories abelian. Besides, we mostly have to assume that the basic ring has a finite homological dimension (no such assumptions about the coring and semialgebra are made). In the final sections we construct model category structures on the categories of complexes of semi(contra)modules, and develop nonhomogeneous Koszul duality theory for semialgebras. Our motivating
Logical Construction of Final Coalgebras
, 2003
"... We prove that every finitary polynomial endofunctor of a category C has a final coalgebra, provided that C is locally Cartesian closed, it has finite coproducts and is an extensive category, it has a natural number object. ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
We prove that every finitary polynomial endofunctor of a category C has a final coalgebra, provided that C is locally Cartesian closed, it has finite coproducts and is an extensive category, it has a natural number object.
Note on the construction of free monoids
, 802
"... We construct free monoids in a monoidal category (C, ⊗, I) with finite limits and countable colimits, in which tensoring on either side preserves reflexive coequalizers and colimits of countable chains. ..."
Abstract
 Add to MetaCart
We construct free monoids in a monoidal category (C, ⊗, I) with finite limits and countable colimits, in which tensoring on either side preserves reflexive coequalizers and colimits of countable chains.
From grammars and automata to algebras and coalgebras
, 2013
"... Abstract. The increasing application of notions and results from category theory, especially from algebra and coalgebra, has revealed that any formal software or hardware model is constructor or destructorbased, a whitebox or a blackbox model. A highlystructured system may involve both construct ..."
Abstract
 Add to MetaCart
Abstract. The increasing application of notions and results from category theory, especially from algebra and coalgebra, has revealed that any formal software or hardware model is constructor or destructorbased, a whitebox or a blackbox model. A highlystructured system may involve both constructor and destructorbased components. The two model classes and the respective ways of developing them and reasoning about them are dual to each other. Roughly said, algebras generalize the modeling with contextfree grammars, word languages and structural induction, while coalgebras generalize the modeling with automata, Kripke structures, streams, process trees and all other state or objectoriented formalisms. We summarize the basic concepts of co/algebra and illustrate them at a couple of signatures including those used in language or compiler construction like regular expressions or acceptors. 1
Abstract CMCS’03 Preliminary Version Logical Construction of Final Coalgebras
"... We prove that every finitary polynomial endofunctor of a category C has a final coalgebra, provided that C is locally Cartesian closed, it has finite coproducts and ..."
Abstract
 Add to MetaCart
We prove that every finitary polynomial endofunctor of a category C has a final coalgebra, provided that C is locally Cartesian closed, it has finite coproducts and
A Category Theoretic View of Nondeterministic Recursive Program Schemes
"... Deterministic recursive program schemes (RPS’s) have a clear category theoretic semantics presented by Ghani et al. and by Milius and Moss. Here we extend it to nondeterministic RPS’s. We provide a category theoretic notion of guardedness and of solutions. Our main result is a description of the can ..."
Abstract
 Add to MetaCart
Deterministic recursive program schemes (RPS’s) have a clear category theoretic semantics presented by Ghani et al. and by Milius and Moss. Here we extend it to nondeterministic RPS’s. We provide a category theoretic notion of guardedness and of solutions. Our main result is a description of the canonical greatest solution for every guarded nondeterministic RPS, thereby giving a category theoretic semantics for nondeterministic RPS’s. We show how our notions and results are connected to classical work.
This is a preprint of a paper that has been submitted to Information and Computation. On Functors Expressible in the Polymorphic Typed Lambda Calculus
, 1991
"... Given a model of the polymorphic typed lambda calculus based upon a Cartesian closed category K, there will be functors from K to K whose action on objects can be expressed by type expressions and whose action on morphisms can be expressed by ordinary expressions. We show that if T is such a functor ..."
Abstract
 Add to MetaCart
Given a model of the polymorphic typed lambda calculus based upon a Cartesian closed category K, there will be functors from K to K whose action on objects can be expressed by type expressions and whose action on morphisms can be expressed by ordinary expressions. We show that if T is such a functor then there is a weak initial Talgebra and if, in addition, K possesses equalizers of all subsets of its morphism sets, then there is an initial Talgebra. These results are used to establish the impossibility of certain models, including those in which types denote sets and S → S ′ denotes the set of all functions from S to S ′.