Abstract
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 pre-university level, under the justification that it is implicit in mathematics and therefore does not need to be taught as an independent topic. This paper argues in the opposite direction, describing a one-week workshop done at the University of Minho, in Portugal, whose goal was to introduce to high-school students calculational principles and techniques of algorithmic problem solving supported by calculational logic. The workshop resorted to recreational problems to convey the principles and to software tools, the Alloy Analyzer and Netlogo, to animate models.

Abstract
Among many theories supported by SMT solvers, the theory of finite-precision bit-vector arithmetic is one of the most useful, for both hardware and software systems verification. This theory is also particularly useful for some specific domains such as cryptography, in which algorithms are naturally expressed in terms of bit-vectors. Cryptol is an example of a domain-specific language (DSL) and toolset for cryptography developed by Galois, Inc.; providing an SMT backend that relies on bit-vector decision procedures to certify the correctness of cryptographic specifications [3]. Most of these decision procedures use bit-blasting to reduce a bit-vector problem into pure propositional SAT. Unfortunately bit-blasting does not scale very well, especially in the presence of operators like multiplication or division. © 2012 Springer-Verlag.

Abstract
The subject of this paper is functional program transformation in the so-called point-free style. By this we mean first translating programs to a form consisting only of categorically-inspired combinators, algebraic data types defined as fixed points of functors, and implicit recursion through the use of type-parameterized recursion patterns. This form is appropriate for reasoning about programs equationally, but difficult to actually use in practice for programming. In this paper we present a collection of libraries and tools developed at Minho with the aim of supporting the automatic conversion of programs to point-free (embedded in Haskell), their manipulation and rule-driven simplification, and the (limited) automatic application of fusion for program transformation.

Abstract
This paper explores sonic ideas concerning the time-analysis of functional programs defined by instantiating typical recursion patterns such as folds, unfolds. and hylomorphisms. The concepts in this paper are illustrated through a rich set of examples in the Haskell programming language. We concentrate on unfolds and folds (also known as anamorphisms and catamorphisms respectively) of recursively defined types, as well as the more general hylomorphism pattern. For the latter, we use as case-studies two famous sorting algorithms, mergesort and quicksort. Even though time analysis is not compositional, we argue that splitting functions to expose the explicit construction of the recursion tree and its later consumption helps with this analysis.

Abstract
Functional programs are particularly well suited to formal manipulation by equational reasoning. In particular, it is straightforward to use calculational methods for program transformation. Well-known transformation techniques, like tupling or the introduction of accumulating parameters, can be implemented using calculation through the use of the fusion (or promotion) strategy. In this paper we revisit this transformation method, but, unlike most of the previous work on this subject, we adhere to a pure point-free calculus that emphasizes the advantages of equational reasoning. We focus on the accumulation strategy initially proposed by Bird, where the transformed programs are seen as higher-order folds calculated systematically from a specification. The machinery of the calculus is expanded with higher-order point-free operators that simplify the calculations. A substantial number of examples (both classic and new) are fully developed, and we introduce several shortcut optimization rules that capture typical transformation patterns.

Abstract
Records are a composite data type available in most programming and specification languages, but they are not natively supported by Alloy. As a consequence, users often find themselves having to simulate records in ad hoc ways, a strategy that is error prone and often encumbers the analysis procedures. This paper proposes a conservative extension to the Alloy language to support record signatures. Uniqueness and completeness is imposed on the atoms of such signatures, while still supporting Alloy’s flexible signature hierarchy. The Analyzer has been extended to internally expand such record signatures as partial knowledge for the solving procedure. Evaluation shows that the proposed approach is more efficient than commonly used idioms. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.