# Demonic operators and monotype factors

@article{Backhouse1993DemonicOA, title={Demonic operators and monotype factors}, author={Roland Carl Backhouse and Jaap van der Woude}, journal={Mathematical Structures in Computer Science}, year={1993}, volume={3}, pages={417 - 433} }

This paper tackles the problem of constructing a compact, point-free proof of the associativity of demonic composition of binary relations and its distributivity through demonic choice. In order to achieve this goal, a definition of demonic composition is proposed in which angelic composition is restricted by means of a so-called ‘monotype factor’. Monotype factors are characterised by a Galois connection similar to the Galois connection between composition and factorisation of binary relations…

## 71 Citations

### Demonic orders and quasi-totality in Dedekind categories (Algebra, Logic and Geometry in Informatics)

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This paper presents a proof of the associativity of demonic composition of relations in Dedekind categories and shows that the demonic composition is monotonic with respect to two demonic orderings…

### How to generalise demonic composition

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Demonic composition is defined on the set of binary relations over the non-empty set X , $$Rel_X$$ R e l X , and is a variant of standard or “angelic” composition. It arises naturally in the setting…

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### The algebra of non-deterministic programs: demonic operators, orders and axioms

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The angelic and demonic cases are motivated via an analysis of the behaviour of non-deterministic programs, with the angelic associated with partial correctness and demonic with total correctness, both cases emerging from a richer algebraic model ofnon-d deterministic programs incorporating both aspects.

### Demonic I/O of Compound Diagrams Monotype/Residual Style

- MathematicsISCIS
- 2003

It is shown how the notion of relational diagram, introduced by Schmidt, can be used to give a single demonic definition for a wide range of programming constructs by using monotypes and residuals.

### Demonic Fixed Points

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The expression of the greatest fixed point with respect to the demonic ordering (demonic inclusion) of the semantic function is given and it is proved that this greatest fixed coincides with the least fixed point of the usual ordering of the same function.

### Domain and range for angelic and demonic compositions

- MathematicsJ. Log. Algebraic Methods Program.
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### Demonic semantics: using monotypes and residuals

- Computer ScienceInt. J. Math. Math. Sci.
- 2004

It is shown how the notion of relational flow diagram (essentially a matrix whose entries are relations on the set of states of the program), introduced by Schmidt, can be used to give a single demonic definition for a wide range of programming constructs.

### Demonic Semantics and Fixed Points

- Mathematics2009 International Conference on Computing, Engineering and Information
- 2009

We deal with a relational model for the demonic semantics of programs. The demonic semantics of a while loop is given as a fixed point of a function involving the demonic operators. This motivates us…

### From operational to denotational demonic semantics of nondeterministic while loops

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- 2006

In this paper, we show that the operational semantics of a nondeterministic while loop give in previous paper is equal to the denotational one, which is given as the greatest fixed point of the…

## References

SHOWING 1-10 OF 53 REFERENCES

### Non-Commutative Residuated Lattices

- Mathematics
- 1939

In the theory of non-commutative rings certain distinguished subrings, one-sided and two-sided ideals, play the important roles. Ideals combine under crosscut, union and multiplication and hence are…

### A Category of Galois Connections

- MathematicsCategory Theory and Computer Science
- 1987

One of the categories—the one which is the most closely related to the closed and open elements of the Galois connections—is Cartesian-closed.

### A Relational Model of Demonic Nondeterministic Programs

- Computer ScienceInt. J. Found. Comput. Sci.
- 1991

A self-contained account of a calculus of relations from basic operations through the treatment of recursive relation equations, developed in the framework of set theory, which may be regarded as a systematic generalization of the functional style.

### Galois Connections and Pair Algebras

- MathematicsCanadian Journal of Mathematics
- 1969

Unless further restricted, P, Q, and R denote arbitrary partially ordered sets whose order relations are all written “≦” . An isotone mapping ϕ: P → Q is said to be residuated if there is an isotone…

### Calois Connections and Computer Science Applications

- Computer Science, MathematicsCTCS
- 1985

The proof of correctness of an implementation follows simply from the construction of a Galois insertion, and further applications of Galois connections theory to computing-related problems are planned.

### Galois Connections

- Mathematics

The paper is the Mizar encoding of the chapter 0 section 3 of [9] In the paper the following concept are defined: Galois connections, Heyting algebras, and Boolean algebras. the notation and…

### Foundations of Compositional Program Refinement - Safety Properties

- Computer ScienceREX Workshop
- 1989

This paper develops a foundation for refinement of parallel programs that may synchronously communicate and/or share variables; programs rendered as 1st order transition systems and shows that they yield assertional methods for refinement that resemble the methods used in Z. Manna and A. Pnueli's temporal logic proof system.

### Relational Algebraic Semantics of Deterministic and Nondeterministic Programs

- Computer ScienceTheor. Comput. Sci.
- 1986

### Factor Graphs, Failure Functions and BI-Trees

- Computer Science, MathematicsICALP
- 1977

The Knuth, Morris, Pratt pattern-matching algorithm, its extensions and Weiner's substring identifier algorithm are all shown to correspond to finding the factor graph of some regular language.