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Programming with algebraic effects and handlers
The realizability approach to computable analysis and topology
In this dissertation, I explore aspects of computable analysis and topology in the framework of relative realizability. The computational models are partial combinatory algebras with subalgebras of…
An Effect System for Algebraic Effects and Handlers
An effect system for algebraic effects and handlers is presented, based on a domain-theoretic model with partial equivalence relations, which validates equational reasoning about effectful computations.
The HoTT library: a formalization of homotopy type theory in Coq
- A. Bauer, Jason Gross, P. Lumsdaine, Michael Shulman, Matthieu Sozeau, Bas Spitters
- 14 October 2016
We report on the development of the HoTT library, a formalization of homotopy type theory in the Coq proof assistant. It formalizes most of basic homotopy type theory, including univalence, higher…
Metric spaces in synthetic topology
Stone Duality for Skew Boolean Algebras with Intersections
We extend Stone duality between generalized Boolean algebras and Boolean spaces, which are the zero-dimensional locally-compact Hausdorff spaces, to a non-commutative setting. We first show that the…
Multibasic and Mixed Hypergeometric Gosper-Type Algorithms
The concept of greatest factorial factorization to the mixed hypergeometric case is generalized and provided as an algorithm for finding polynomial as well ashypergeometric solutions of recurrences in the mixed case.
Propositions as Types
It is shown that dependent type theory with the unit type, strong extensional equality types, strong dependent sums, and bracket types is the internal type theory of regular categories, in the same way that the usual dependenttype theory with dependent sums and products is theinternal type theories of locallyCartesian closed categories.
Comparing Functional Paradigms for Exact Real-Number Computation
It is shown that the type hierarchies coincide up to second-order types, and it is demonstrated that, in the extensional approach, parallel primitives are necessary for programming total first-order functions, but are not needed for second- order types and below.