scholarly journals Nominal Sets over Algebraic Atoms

2014 ◽  
pp. 429-445 ◽  
Author(s):  
Joanna Ochremiak
Keyword(s):  
Nominal Sets

scholarly journals Fast Computations on Ordered Nominal Sets

2018 ◽  
pp. 493-512
Author(s):  
David Venhoek ◽  
Joshua Moerman ◽  
Jurriaan Rot
Keyword(s):  
Nominal Sets

Nominal Sets

2009 ◽  
Author(s):  
Andrew M. Pitts
Keyword(s):  
Nominal Sets

scholarly journals Structural recursion with locally scoped names

2011 ◽  
Vol 21 (3) ◽  
pp. 235-286 ◽  
Author(s):  
ANDREW M. PITTS
Keyword(s):  
Programming Languages ◽  
Simple Interpretation ◽  
Nominal System ◽  
Structural Recursion ◽  
Recursive Definitions ◽  
Nominal Sets

AbstractThis paper introduces a new recursion principle for inductively defined data modulo α-equivalence of bound names that makes use of Odersky-style local names when recursing over bound names. It is formulated in simply typed λ-calculus extended with names that can be restricted to a lexical scope, tested for equality, explicitly swapped and abstracted. The new recursion principle is motivated by the nominal sets notion of ‘α-structural recursion’, whose use of names and associated freshness side-conditions in recursive definitions formalizes common practice with binders. The new calculus has a simple interpretation in nominal sets equipped with name-restriction operations. It is shown to adequately represent α-structural recursion while avoiding the need to verify freshness side-conditions in definitions and computations. The paper is a revised and expanded version of Pitts (Nominal System T. In Proceedings of the 37th ACM SIGACT-SIGPLAN Symposium on Principles of Programming Languages, POPL 2010 (Madrid, Spain). ACM Press, pp. 159–170, 2010).

Free functor from the category of G-nominal sets to that of 01-G-nominal sets

2017 ◽  
Vol 22 (11) ◽  
pp. 3637-3648
Author(s):  
Khadijeh Keshvardoost ◽  
Mojgan Mahmoudi
Keyword(s):  
Nominal Sets

scholarly journals The nominal/FM Yoneda Lemma

2020 ◽  
Vol 30 (9) ◽  
pp. 1011-1024
Author(s):  
R. L. Crole
Keyword(s):  
Finite Support ◽  
Natural Transformations ◽  
Equivariant Functions ◽  
Yoneda Lemma ◽  
Nominal Sets

AbstractThis paper explores versions of the Yoneda Lemma in settings founded upon FM sets. In particular, we explore the lemma for three base categories: the category of nominal sets and equivariant functions; the category of nominal sets and all finitely supported functions, introduced in this paper; and the category of FM sets and finitely supported functions. We make this exploration in ordinary, enriched and internal settings. We also show that the finite support of Yoneda natural transformations is a theorem for free.

scholarly journals Binding Operators for Nominal Sets

2016 ◽  
Vol 325 ◽  
pp. 3-27
Author(s):  
Arthur Azevedo de Amorim
Keyword(s):  
Nominal Sets

scholarly journals Automata theory in nominal sets

2014 ◽  
Vol 10 (3) ◽  
Author(s):  
Mikołaj Bojańczyk ◽  
Bartek Klin ◽  
Sławomir Lasota
Keyword(s):  
Automata Theory ◽  
Nominal Sets

scholarly journals A design criterion for symmetric model discrimination based on flexible nominal sets

2020 ◽  
Vol 62 (4) ◽  
pp. 1090-1104
Author(s):  
Radoslav Harman ◽  
Werner G. Müller
Keyword(s):  
Design Criterion ◽  
Model Discrimination ◽  
Symmetric Model ◽  
Nominal Sets

scholarly journals Stone duality for first-order logic: a nominal approach to logic and topology

10.29007/tp3z ◽  
2018 ◽  
Author(s):  
Murdoch J. Gabbay
Keyword(s):  
Order Logic ◽  
Boolean Algebras ◽  
First Order Logic ◽  
Specific Class ◽  
Stone Duality ◽  
First Order ◽  
And Topology ◽  
Universal Quantification ◽  
Stone Spaces ◽  
Nominal Sets

What are variables, and what is universal quantification over a variable?Nominal sets are a notion of `sets with names', and using equational axioms in nominal algebra these names can be given substitution and quantification actions.So we can axiomatise first-order logic as a nominal logical theory.We can then seek a nominal sets representation theorem in which predicates are interpreted as sets; logical conjunction is interpreted as sets intersection; negation as complement.Now what about substitution; what is it for substitution to act on a predicate-interpreted-as-a-set, in which case universal quantification becomes an infinite sets intersection?Given answers to these questions, we can seek notions of topology.What is the general notion of topological space of which our sets representation of predicates makes predicates into `open sets'; and what specific class of topological spaces corresponds to the image of nominal algebras for first-order logic?The classic Stone duality answers these questions for Boolean algebras, representing them as Stone spaces.Nominal algebra lets us extend Boolean algebras to `FOL-algebras', and nominal sets let us correspondingly extend Stone spaces to `∀-Stone spaces'.These extensions reveal a wealth of structure, and we obtain an attractive and self-contained account of logic and topology in which variables directly populate the denotation, and open predicates are interpreted as sets rather than functions from valuations to sets.

Sign in / Sign up

Export Citation Format

Share Document