# Representability and Program Construction within Fork Algebras

@article{Frias1998RepresentabilityAP, title={Representability and Program Construction within Fork Algebras}, author={Marcelo Fabian Frias and Gabriel Baum and Armando Martin Haeberer}, journal={Log. J. IGPL}, year={1998}, volume={6}, pages={227-257} }

The representation theorem for fork algebras was always misunderstood regarding its applications in program construction. Its application was always described as “the portability of properties of the problem domain into the abstract calculus of fork algebras”. In this paper we show that the results provided by the representation theorem are by far more important. We show that not only the heuristic power coming from concrete binary relations is captured inside the abstract calculus, but also…

## 8 Citations

### A calculus for program construction based on fork algebras, design strategies and generic algorithms

- Computer Science, Mathematics
- 2001

A methodology for program construction based on the first-order theory of fork algebras, which will describe program design strategies, for instance case analysis, trivialization, divide-and-conquer and others, and derive parametric algorithms.

### Fork Algebras in Algebra, Logic and Computer Science

- Mathematics, Computer ScienceFundam. Informaticae
- 1997

This paper study fork algebras from the points of view of their algebraic and logical properties and applications, which will prove to be essential for the definition of a wide-spectrum calculus for program construction.

### The Allegory of E-Relations in Constructive Type Theory

- MathematicsRelMiCS
- 2000

The goal of this paper is allowing us to import relational calculus inside type theory, and take advantage of the wealth of results and methods for program construction and veriication that are well established in relational formalisms.

### Heterogeneous) Structured Specifications in Logics Without Interpolation

- Computer Science
- 2018

A calculus for structured specifications whose completeness proof does not require any form of interpolation is presented, and this calculus is extended to a complete calculus for heterogeneous structured specifications.

### Fork Algebras: Past, Present and Future

- Mathematics
- 2004

Fork algebras have interesting connections with Computing, Algebra and Logic. This paper presents a survey of ideas and results about fork algebras, with special emphasis on current developments and…

### Fork algebras como herramienta de razonamiento entre especificaciones heterogéneas

- Mathematics
- 2007

Las logicas han sido usadas como sistemas formales para especificar sistemas de software. Mas aun, las especificaciones logicas, por ser formales, contribuyen en la aplicacion de metodos tecnicas…

### Refinement and Development of Programs from Relational Specifications

- Computer ScienceElectron. Notes Theor. Comput. Sci.
- 2001

### ESTADO DEL ARTE EN LAS IMPLEMENTACIONES PARALELAS DE DIVIDE Y VENCERÁS

- 2006

Divide y Venceras, es una tecnica de diseno de algoritmos ampliamente utilizada en la solucion de problemas. Su implementacion en paralelo resulta natural. En este trabajo se realiza una revision…

## References

SHOWING 1-10 OF 33 REFERENCES

### From Specifications to Programs: A Fork-Algebraic Approach to Bridge the Gap

- Computer ScienceMFCS
- 1996

This work focuses on the construction of programs whose specifications involve universal quantifiers, and a new algebraic operation — relational implication — is introduced, shown to have deep significance in the relational statement of first-order expressions involvinguniversal quantifiers.

### Categories, Relations and Dynamic Programming

- Computer ScienceMath. Struct. Comput. Sci.
- 1994

This paper shows how many problems that may be solved by dynamic programming are instances of the same abstract specification, phrased using the calculus of relations offered by topos theory, and formalises the principle of optimality as a distributivity condition.

### On the Smooth Calculation of Relational Recursive Expressions out of First-Order Non-Constructive Specifications Involving Quantifiers

- Computer ScienceFormal Methods in Programming and Their Applications
- 1993

An extended abstract algebra of relations is devised for tackling the classic issue of lack of expressiveness of abstract relational algebras first stated by Tarski and later formally treated by Maddux, Nemeti, etc.

### Semantic Optimization of Queries in Deductive Object-Oriented Database

- Computer ScienceADBIS
- 1995

A new application of fork algebras is presented, namely, as a framework suitable for derivation by calculation of new strategies for optimization of queries in deductive object-oriented database.

### A finitary relational algebra for classical first-order logic

- Mathematics
- 1991

A simple extension of Tarski’s calculus of binary relations is shown to have the expressive power of first-order logic. In contrast with Cylindric and Polyadic algebras, this extension introduces…

### Relations and Graphs

- MathematicsEATCS Monographs on Theoretical Computer Science
- 1993

It is shown that results proved in such a way hold true in every relation algebra, hence also in those constructed by the procedure of (7.5.14).

### A Formalization Of Set Theory Without Variables

- Mathematics
- 1987

The formalism $\mathcal L$of predicate logic The formalism $\mathcal L^+$, a definitional extension of $\mathcal L$ The formalism $\mathcal L^+$ without variables and the problem of its equipollence…

### An introduction to the theory of lists

- Computer Science
- 1987

In these lectures a notation and a calculus for specifying and manipulating computable functions over lists are introduced, used to derive efficient solutions for a number of problems, including problems in text processing.

### On the Calculus of Relations

- PhilosophyJ. Symb. Log.
- 1941

The logical theory which is called the calculus of (binary) relations, and which will constitute the subject of this paper, has had a strange and rather capricious line of historical development.…

### Fork Algebras are Representable

- Bulletin of the Section of Logic, University of Lódź, (24)2
- 1995