In a pure functional language like Clean the values of the functional variables are constants; variables of functional programs do not change in time. Hence it seems that temporality has no meaning in functional programs. However, in certain cases (e.g. in interactive or distributed programs, or in ones that use IO) we would like to consider a series of values computed from each other as differ...

We analyze the geometry behind the problem of non-negative matrix factorization (NMF) and devise yet another NMF algorithm. In contrast to the vast majority of algorithms discussed in the literature, our approach does not involve any form of constrained gradient descent or alternating least squares procedures but is of purely geometric nature. In other words, it does not require advanced mathem...

We propose a very simple modification of Kreisel’s modified realizability in order to computationally realize Markov’s Principle in the context of Heyting Arithmetic. Intuitively, realizers correspond to arbitrary strategies in Hintikka-Tarski games, while in Kreisel’s realizability they can only represent winning strategies. Our definition, however, does not employ directly game semantical con...

We characterize properly purely infinite Steinberg algebras \(A_K({\mathcal {G}})\) for strongly effective, ample Hausdorff groupoids \({\mathcal {G}}\). As an application, we show that the notions of pure infiniteness and proper are equivalent Kumjian–Pask algebra \(\mathrm {KP}_K(\Lambda )\) in case \(\Lambda \) is a aperiodic k-graph. In particular, unital cases, give simple graph-theoretic ...