• Corpus ID: 237490954

# Restriction in Program Algebra

@inproceedings{Jackson2021RestrictionIP,
title={Restriction in Program Algebra},
author={Marcel Jackson and Tim Stokes},
year={2021}
}
• Published 13 September 2021
• Mathematics
intersection, ∩: f ∩ g = {(x, y) ∈ X × Y | (x, y) ∈ f and (x, y) ∈ g} and difference, \: f\g = {(x, y) ∈ X × Y | (x, y) ∈ f and (x, y) 6∈ g}. Before we proceed further, we note that the surrounding literature contains a number of conflicting notations for the operations just introduced. In [2], the operation we have denoted ◦ is referred to in an equivalent form as “intersection”, with definition and notation f@g := g ◦ f . The notation for ⊔ in [2] is ⊲, however, the notation ⊲ is well…

## References

SHOWING 1-10 OF 30 REFERENCES
Comparison semigroups and algebras of transformations
We characterize algebras of transformations on a set under the operations of composition and the pointwise switching function defined as follows: (f,g)[h,k](x)=h(x) if f(x)=g(x), and k(x) otherwise.
The axiomatization of override and update
• Computer Science, Mathematics
J. Appl. Log.
• 2010
It is established that override and minus are functionally complete in the sense that any operation on general functions that corresponds to a valid coloring of a Venn diagram can be described using just these two operations.
Monoids with tests and the algebra of possibly non-halting programs
• Computer Science, Mathematics
J. Log. Algebraic Methods Program.
• 2015
By extending the notion of {\em if-then-else}, this work is able to give finite axiomatisations of the resulting algebras of (partial) functions, with {\em while-do} in the signature if the state space is assumed finite.
Modal restriction Semigroups: towards an Algebra of Functions
• Mathematics, Computer Science
Int. J. Algebra Comput.
• 2011
This work considers restriction semigroups for which the usual Boolean operations on domains are modeled, leading to algebraic models of partial maps incorporating all the domain-related and set-theoretic operations previously considered.
Difference-restriction algebras of partial functions: axiomatisations and representations
• Mathematics, Computer Science
ArXiv
• 2020
The correctness of a finite equational axiomatisation for the class of algebras representable by partial functions with the signature of relative complement and domain restriction is provided and proved.
Nearlattices with an Overriding Operation
A representation theorem (in terms of algebras of partial functions) for Boolean nearlattices with associative overriding is presented, and several results concerning associativity of the operation and the structure of function nearlATTices with overriding are presented.
Relation algebras and function semigroups
The concept of relation algebra unifies many familiar notions from algebra (especially those of systems having “natural” models as groups, Boolean algebras etc.). The fundamental theorem on relation
Skew lattices and binary operations on functions
• Computer Science, Mathematics
J. Appl. Log.
• 2013
It is shown the latter to be term equivalent to the variety of right-handed skew Boolean algebras, and both override and update operations are studied within the broader context of skew lattices with an eye towards achieving greater insight into their joint algebraic behavior.
Skew Boolean algebras and discriminator varieties
• Mathematics
• 1995
We investigate the class of skew Boolean algebras which are also meet semilattices under the natural skew lattice partial order. Such algebras, called hereskew Boolean ∩-algebras, are quite common.
Override and update
• Mathematics, Computer Science
ArXiv
• 2019
This work uses an unexpected connection with combinatorial geometry to provide a complete finite system of equational axioms for the first order theory of the override and update constructions on partial functions, resolving the main unsolved problem in the area.