Log In Sign Up

Locally Nameless Permutation Types

by   Edsko de Vries, et al.

We define "Locally Nameless Permutation Types", which fuse permutation types as used in Nominal Isabelle with the locally nameless representation. We show that this combination is particularly useful when formalizing programming languages where bound names may become free during execution ("extrusion"), common in process calculi. It inherits the generic definition of permutations and support, and associated lemmas, from the Nominal approach, and the ability to stay close to pencil-and-paper proofs from the locally nameless approach. We explain how to use cofinite quantification in this setting, show why reasoning about renaming is more important here than in languages without extrusion, and provide results about infinite support, necessary when reasoning about countable choice.


page 1

page 2

page 3

page 4


On local presentability of T/A

We prove that if A is a locally λ-presentable category and T : A→A is a ...

A Type and Scope Safe Universe of Syntaxes with Binding: Their Semantics and Proofs

Almost every programming language's syntax includes a notion of binder a...

Two types of permutation polynomials with special forms

Let q be a power of a prime and F_q be a finite field with q elements. I...

GADTs, Functoriality, Parametricity: Pick Two

GADTs can be represented either as their Church encodings à la Atkey, or...

Removing Qualified Names in Modular Languages

Although the notion of qualified names is popular in module systems, it ...

An Algebraic System for Constructing Cryptographic Permutations over Finite Fields

In this paper we identify polynomial dynamical systems over finite field...

Regularization for Shuffled Data Problems via Exponential Family Priors on the Permutation Group

In the analysis of data sets consisting of (X, Y)-pairs, a tacit assumpt...