A Complete Calculus of Monotone and Antitone Higher-Order Functions

Thomas Icard; Lawrence Moss

doi:10.29007/3n54

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A Complete Calculus of Monotone and Antitone Higher-Order Functions

5 pages•Published: July 28, 2014

Thomas Icard and Larry Moss

Abstract

This 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

Links:	https://easychair.org/publications/paper/cNV
	https://doi.org/10.29007/3n54

BibTeX entry

@inproceedings{TACL2013:Complete_Calculus_of_Monotone,
  author    = {Thomas Icard and Lawrence Moss},
  title     = {A Complete Calculus of Monotone and Antitone Higher-Order Functions},
  booktitle = {TACL 2013. Sixth International Conference on Topology, Algebra and Categories in Logic},
  editor    = {Nikolaos Galatos and Alexander Kurz and Constantine Tsinakis},
  series    = {EPiC Series in Computing},
  volume    = {25},
  pages     = {96--100},
  year      = {2014},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {https://easychair.org/publications/paper/cNV},
  doi       = {10.29007/3n54}}

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