From parametricity to conservation laws, via Noether’s theorem

Reference. From parametricity to conservation laws, via Noether’s theorem

Robert Atkey · POPL · 2014 · parametricity · PDF · DOI · pldb

Cite

Cite as @atkey-2014-from (helia, typst) · \cite{atkey-2014-from} (LaTeX)

BibTeX

bibtex · 1 line

@inproceedings{atkey-2014-from, series={POPL ’14}, title={From parametricity to conservation laws, via Noether’s theorem}, url={http://dx.doi.org/10.1145/2535838.2535867}, DOI={10.1145/2535838.2535867}, booktitle={Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages}, publisher={ACM}, author={Atkey, Robert}, year={2014}, month=Jan, pages={491–502}, collection={POPL ’14} }

hayagriva YAML (typst)

yaml · 16 lines

atkey-2014-from:
  type: article
  title: From parametricity to conservation laws, via Noether’s theorem
  author: Atkey, Robert
  date: 2014-01
  page-range: 491-502
  url: http://dx.doi.org/10.1145/2535838.2535867
  serial-number:
    doi: 10.1145/2535838.2535867
  parent:
    type: proceedings
    title: Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
    publisher: ACM
    parent:
      type: proceedings
      title: POPL ’14

Download: atkey-2014-from.bib · atkey-2014-from.yml

Cited by (2)

The Road to General Intelligence swan-2022-theStudies in Computational Intelligence · 2022

DOI

Models for Polymorphism over Physical Dimension atkey-2015-modelsTLCA · 2015

We provide a categorical framework for models of a type theory that has special types for physical quantities. The types are indexed by the physical dimensions that they involve. Fibrations are used to organize this index structure in the models of the type theory. We develop some informative models of this type theory: firstly, a model based on group actions, which captures invariance under scaling, and secondly, a way of constructing new models using relational parametricity.

DOI

Cites 22 works (2 here)

With notes (2)

A relationally parametric model of dependent type theory atkey-2014-aPOPL · 2014

PDF · DOI · pldb

Homotopy Type Theory: Univalent Foundations of Mathematics hottbookarXiv · 2013

Web · arXiv

External (20)

Abstraction and invariance for algebraically indexed types (2013)
Proofs for Free: Parametricity for Dependent Types (2012)
Relational Parametricity for Higher Kinds (2012)
Type Inference for Units of Measure (tech report) (2011)
Emmy Noether's Wonderful Theorem (2011)
High-Level Methods for Quantum Computation and Information (2004)
Types and Programming Languages (2002)
Structure and Interpretation of Classical Mechanics (2001)
Calculus of Variations (2000)
Categories for the Working Mathematician (2nd ed.) (1998)
Relational parametricity and units of measure (1997)
Dimension types (1994)
Reflexive Graphs and Parametric Polymorphism (1994)
Relational Limits in General Polymorphism (1994)
Mathematical Methods of Classical Mechanics (1989)
Theorems for free! (1989)
Polymorphism is Set Theoretic, Constructively (1987)
Types, Abstraction and Parametric Polymorphism (1983)
Invariant variation problems (1971)
Mechanics (Landau & Lifschitz) (1967)