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Simple Equational Specifications of Rational Arithmetic

Abstract : We exhibit an initial specification of the rational numbers equipped with addition, subtraction, multiplication, greatest integer function, and absolute value. Our specification uses only the sort of rational numbers. It uses one hidden function; that function is unary. But it does not use an error constant, or extra (hidden) sorts, or conditional equations. All of our work is elementary and self-contained.
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Lawrence S. Moss. Simple Equational Specifications of Rational Arithmetic. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2001, 4 (2), pp.291-300. ⟨hal-00958963⟩

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