Download PDFOpen PDF in browserA Complete Calculus of Monotone and Antitone Higher-Order Functions5 pages•Published: July 28, 2014AbstractThis paper adds monotonicity and antitonicity information to the typed lambda calculus, thereby providing a foundation for the Monotonicity Calculus first developed by van Benthem and others. We establish properties of the type system, propose a syntax, semantics, and proof calculus, and prove completeness for the calculus with respect to hierarchies of monotone and antitone functions over base preorders.Keyphrases: monotone and antitone functions, monotonicity calculus, typed lambda calculus In: Nikolaos Galatos, Alexander Kurz and Constantine Tsinakis (editors). TACL 2013. Sixth International Conference on Topology, Algebra and Categories in Logic, vol 25, pages 96-100.
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