A relation-algebraic approach to the “Hoare logic” of functional dependencies

Oliveira, José Nuno

doi:10.1016/j.jlap.2014.02.013

Cited by 11 publications

(12 citation statements)

References 22 publications

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“…Can f g be generalized to some R S and still retain metaphors' ability to equate objects of incompatible orders [38]? Facts (26), (27) and (33) point towards such a generalization. This relates to another direction for possible genericity: metaphorisms as given in this paper call for a division allegory [20] such as that of binary relations.…”

Section: Future Workmentioning

confidence: 96%

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Programming from metaphorisms

Oliveira¹

2018

Journal of Logical and Algebraic Methods in Programming

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This paper presents a study of the metaphorism pattern of relational specification, showing how it can be refined into recursive programs.Metaphorisms express input-output relationships which preserve relevant information while at the same time some intended optimization takes place. Text processing, sorting, representation changers, etc., are examples of metaphorisms.The kind of metaphorism refinement studied in this paper is a strategy known as change of virtual data structure. By framing metaphorisms in the class of (inductive) regular relations, sufficient conditions are given for such implementations to be calculated using relation algebra.The strategy is illustrated with examples including the derivation of the quicksort and mergesort algorithms, showing what they have in common and what makes them different from the very start of development.Keywords: Programming from specifications, Algebra of programming, Weakest precondition calculus. Politicians and diapers should be changed often and for the same reason.(attributed to Mark Twain) ContextThe witty quote by 19th century author Mark Twain that provided inspiration for the title of this paper embodies a metaphor which the reader will surely appreciate. But, what do metaphors of this kind have to do with computer programming?A synergy between metaphors in cognitive linguistics and some relational patterns common in the field of formal specification, termed metaphorisms, was suggested in our earlier conference paper [1], which the current paper extends by framing the approach into the study of the wider class of inductive regular

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Section: Future Workmentioning

confidence: 96%

“…Recall that tips = (|[singl , conc]|) K converts a tree into the sequence of its leaves. 27 Heights of trees are calculated by function…”

Section: Example: Minimum Height Treesmentioning

confidence: 99%

Programming from metaphorisms

Oliveira¹

2018

Journal of Logical and Algebraic Methods in Programming

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“…This somewhat redundant construction proves essential to the reasoning, as shown in [Oli11,Oli14a]. Expressed in set-theoretical notation, projection (2) is set-comprehension tptrAs, trBsq |t T u where trAs (resp.…”

Section: From Relations To Matricesmentioning

confidence: 99%

A linear algebra approach to OLAP

Macedo

Oliveira

2015

Form. Asp. Comput.

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Inspired by the relational algebra of data processing, this paper addresses the foundations of data analytical processing from a linear algebra perspective. The paper investigates, in particular, how aggregation operations such as cross tabulations and data cubes essential to quantitative analysis of data can be expressed solely in terms of matrix multiplication, transposition and the Khatri-Rao variant of the Kronecker product. The approach offers a basis for deriving an algebraic theory of data consolidation, handling the quantitative as well as qualitative sides of data science in a natural, elegant and typed way. It also shows potential for parallel analytical processing (OLAP), as the parallelization theory of such matrix operations is well acknowledged.

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“…As stated in the opening quote by José N. Oliveira, conciseness facilitates reasoning and the identification of patterns. Indeed, Oliveira's work in pointfree calculational techniques and algebraic methods in programming [2,3,4] is an excellent example of how conciseness leads to shorter documents and elegant theories. As Oliveira writes in [3]:…”

Section: Introductionmentioning

confidence: 99%