Quotients in Simple Type Theory
نویسنده
چکیده
We introduce a syntax for quotient types in a predicate logic over a simply type theory. To illustrate its usefulness we construct in purely type theoretic terms (a) the free abelian group on a commutative monoid H, as quotient of H H; a special instance is the construction of Z from N; (b) the quotient poset of a preorder, (c) the abelian quotient of an arbitrary group, and (d) tensor products and sums of abelian groups. The syntax we use comes from a categorical analysis, in which quotients are described as certain adjunctions. This gives us introduction and elimination rules as transposes, and the associated ()-and ()-conversions. A brief discussion of this matter is included.
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