The Agda Universal Algebra Library, Part 1: Foundation
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by
William DeMeo
2021
Abstract
The Agda Universal Algebra Library (UALib) is a library of types and programs
(theorems and proofs) we developed to formalize the foundations of universal
algebra in dependent type theory using the Agda programming language and proof
assistant. The UALib includes a substantial collection of definitions,
theorems, and proofs from general algebra and equational logic, including many
examples that exhibit the power of inductive and dependent types for
representing and reasoning about relations, algebraic structures, and
equational theories. In this paper we describe several important aspects of the
logical foundations on which the library is built. We also discuss (though
sometimes only briefly) all of the types defined in the first 13 modules of the
library, with special attention given to those details that seem most
interesting or challenging from a type theory or mathematical foundations
perspective.
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