Related papers: The nature of loops in programming
A general theory of programs, programming and programming languages built up from a few concepts of elementary set theory. Derives, as theorems, properties treated as axioms by classic approaches to programming. Covers sequential and…
Tiwari proved that termination of linear programs (loops with linear loop conditions and updates) over the reals is decidable through Jordan forms and eigenvectors computation. Braverman proved that it is also decidable over the integers.…
We introduce a variation on Barthe et al.'s higher-order logic in which formulas are interpreted as predicates over open rather than closed objects. This way, concepts which have an intrinsically functional nature, like continuity,…
One of my recent papers transforms an NP-Complete problem into the question of whether or not a feasible real solution exists to some Linear Program. The unique feature of this Linear Program is that though there is no explicit bound on the…
Computation is commonly defined as the execution of abstract algorithms over symbolic representations, with physical systems treated as substrates that realise predefined operations. While effective for engineered machines, this separation…
Users of program analyses expect that results change predictably in response to changes in their programs, but many analyses fail to provide such robustness. This paper introduces a theoretical framework that provides a unified language to…
Logic programming is a flexible programming paradigm due to the use of predicates without a fixed data flow. To extend logic languages with the compact notation of functional programming, there are various proposals to map evaluable…
Let $\cF$ be a family of finite loops closed under subloops and factor loops. Then every loop in $\cF$ has the strong Lagrange property if and only if every simple loop in $\cF$ has the weak Lagrange property. We exhibit several such…
There are often multiple ways to implement the same requirement in source code. Different implementation choices can result in code snippets that are similar, and have been defined in multiple ways: code clones, examples, simions and…
Linear optics (LO) prohibits certain transformations. In this paper, we study the conditions for a computation to be possible in LO. We find that there are finitely many polynomials such that each of these polynomials evaluates to the same…
Plausible reasoning concerns situations whose inherent lack of precision is not quantified; that is, there are no degrees or levels of precision, and hence no use of numbers like probabilities. A hopefully comprehensive set of principles…
In Programming by Example, a system attempts to infer a program from input and output examples, generally by searching for a composition of certain base functions. Performing a naive brute force search is infeasible for even mildly involved…
Applying dynamic logics to program verifications is a challenge, because their axiomatic rules for regular expressions can be difficult to be adapted to different program models. We present a novel dynamic logic, called DLp, which supports…
Understanding student difficulties in programming is a complex challenge due to the wide range of topics and the abundant varieties of misconceptions and errors. This paper presents the design and development of a fine-grained taxonomy that…
Many potentially non-terminating functions cannot be directly defined in a logic of total functions, such as HOL. A well-known solution to this is to define non-terminating functions using a clock that forces termination at a certain depth…
There are a lot of different programming paradigms. Since all Turing-complete programming languages are formally equivalent (they have the same ability to express any computable problem), the existence of so many different paradigms may…
We present an algebraic view on logic programming, related to proof theory and more specifically linear logic and geometry of interaction. Within this construction, a characterization of logspace (deterministic and non-deterministic)…
Many proofs in discrete mathematics and theoretical computer science are based on the probabilistic method. To prove the existence of a good object, we pick a random object and show that it is bad with low probability. This method is…
Humans can observe a single, imperfect demonstration and immediately generalize to very different problem settings. Robots, in contrast, often require hundreds of examples and still struggle to generalize beyond the training conditions. We…
Loop scopes have been shown to be a helpful tool in creating sound loop invariant rules which do not require program transformation of the loop body. Here we extend this idea from while-loops to for-loops and also present sound loop…