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Indexed Containers
"... Abstract. The search for an expressive calculus of datatypes in which canonical algorithms can be easily written and proven correct has proved to be an enduring challenge to the theoretical computer science community. Approaches such as polynomial types, strictly positive types and inductive types h ..."
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Abstract. The search for an expressive calculus of datatypes in which canonical algorithms can be easily written and proven correct has proved to be an enduring challenge to the theoretical computer science community. Approaches such as polynomial types, strictly positive types and inductive types have all met with some success but they tend not to cover important examples such as types with variable binding, types with constraints, nested types, dependent types etc. In order to compute with such types, we generalise from the traditional treatment of types as free standing entities to families of types which have some form of indexing. The hallmark of such indexed types is that one must usually compute not with an individual type in the family, but rather with the whole family simultaneously. We implement this simple idea by generalising our previous work on containers to what we call indexed containers and show that they cover a number of sophisticated datatypes and, indeed, other computationally interesting structures such as the refinement calculus and interaction structures. Finally, and rather surprisingly, the extra structure inherent in indexed containers simplifies the theory of containers and thereby allows for a much richer and more expressive calculus. 1
A Syntactical Approach to Weak ωGroupoids
"... Abstract—When moving to a Type Theory without proof irrelevance the notion of a setoid has to be generalized to the notion of a weak ωgroupoid. As a first step in this direction we study the formalisation of weak ωgroupoids in Type Theory. This is motivated by Voevodsky’s proposal of univalent typ ..."
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Abstract—When moving to a Type Theory without proof irrelevance the notion of a setoid has to be generalized to the notion of a weak ωgroupoid. As a first step in this direction we study the formalisation of weak ωgroupoids in Type Theory. This is motivated by Voevodsky’s proposal of univalent type theory which is incompatible with proofirrelevance and the results by Lumsdaine and Garner/van de Berg showing that the standard eliminator for equality gives rise to a weak ωgroupoid.
Preface
, 2011
"... CALCO brings together researchers and practitioners to exchange new results related to foundational aspects and both traditional and emerging uses of algebras and coalgebras in computer science. This is a highlevel, biannual conference formed by joining the forces and ..."
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CALCO brings together researchers and practitioners to exchange new results related to foundational aspects and both traditional and emerging uses of algebras and coalgebras in computer science. This is a highlevel, biannual conference formed by joining the forces and