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Alloy meets the algebra of programming : a case study
Oliveira, José Nuno Fonseca; Ferreira, Miguel A.Relational algebra offers to software engineering the same degree of conciseness and calculational power as linear algebra in other engineering disciplines. Binary relations play the role of matrices with similar emphasis on multiplication and transposition. This matches with Alloy’s lemma “everything is a relation” and with the relational basis of the Algebra of Programming (AoP). Altogether, it provides a sim...
Weighted automata as coalgebras in categories of matrices
Oliveira, José Nuno FonsecaThe evolution from non-deterministic to weighted automata represents a shift from qual- itative to quantitative methods in computer science. The trend calls for a language able to reconcile quantitative reasoning with formal logic and set theory, which have for so many years supported qualitative reasoning. Such a lingua franca should be typed, poly- morphic, diagrammatic, calculational and easy to blend with c...
Typing linear algebra : a biproduct-oriented approach
Macedo, Hugo Daniel; Oliveira, José Nuno FonsecaInterested in formalizing the generation of fast running code for linear algebra applications, the authors show how an index-free, calculational approach to matrix algebra can be developed by regarding matrices as morphisms of a category with biproducts. This shifts the traditional view of matrices as indexed structures to a type-level perspective analogous to that of the pointfree algebra of programming. The d...
Calculating fault propagation in functional programs
Murta, Daniel R.; Oliveira, José Nuno FonsecaTechn. Report TR-HASLab:01:2013 ; The production of safety critical software is bound to a number of safety and certification standards in which estimating the risk of failure plays a central role. Yet risk estimation seems to live outside most programmers’ core practice, involving simulation techniques and worst case analysis performed a posteriori. In this paper we propose that risk be constructively handled...
Programming from Galois connections
Mu, Shin-Cheng; Oliveira, José Nuno FonsecaProblem statements often resort to superlatives such as in eg. “. . . the smallest such number”, “. . . the best approximation”, “. . . the longest such list” which lead to specifications made of two parts: one defining a broad class of solutions (the easy part) and the other requesting the optimal such solution (the hard part). This paper introduces a binary relational combinator which mirrors this linguistic ...
Programming from Galois connections
Mu, Shin-Cheng; Oliveira, José Nuno FonsecaProblem statements often resort to superlatives such as in e.g. “...the smallest such number", “...the best approximation", “...the longest such list" which lead to specifications made of two parts: one defining a broad class of solutions (the easy part) and the other requesting one particular such solution, optimal in some sense (the hard part). This article introduces a binary relational combinator which mirr...
Towards a linear algebra of programming
Oliveira, José Nuno FonsecaThe Algebra of Programming (AoP) is a discipline for programming from specifications using relation algebra. Specification vagueness and nondeterminism are captured by relations. (Final) implemen- tations are functions. Probabilistic functions are half way between relations and functions: they express the propensity, or like- lihood of ambiguous, multiple outputs. This paper puts forward a basis for a Linear Al...
Typed linear algebra for weighted (probabilistic) automata
Oliveira, José Nuno FonsecaThere is a need for a language able to reconcile the recent upsurge of interest in quantitative methods in the software sciences with logic and set theory that have been used for so many years in capturing the qualitative aspects of the same body of knowledge. Such a lingua franca should be typed, polymorphic, diagrammatic, calculational and easy to blend with traditional notation. This paper puts forward typed...
Functions as types or the "Hoare logic" of functional dependencies
Oliveira, José Nuno FonsecaInspired by the trend on unifying theories of programming, this paper shows how the algebraic treatment of standard data dependency theory equips relational data with functional types and an associated type system which is useful for type checking database operations and for query optimization. Such a typed approach to database programming is then shown to be of the same family as other programming logics such ...
Logic training through algorithmic problem solving
Ferreira, João Fernando; Mendes, Alexandra; Cunha, Alcino; Baquero, Carlos; Silva, Paulo; Barbosa, L. S.; Oliveira, José Nuno FonsecaAvailable for individual study only. ; Although much of mathematics is algorithmic in nature, the skills needed to formulate and solve algorithmic problems do not form an integral part of mathematics education. In particular, logic, which is central to algorithm development, is rarely taught explicitly at preuniversity level, under the justification that it is implicit in mathematics and therefore does not nee...
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