A Tutorial on the Universality and Expressiveness of Fold

In functional programming, fold is a standard operator that encapsulates a simple pattern of recursion for processing lists. This article is a tutorial on two key aspects of the fold operator for lists. First of all, we emphasize the use of the universal property of fold both as a proof principle that avoids the need for inductive proofs, and as a definition principle that guides the transformation of recursive functions into definitions using fold. Secondly, we show that even though the pattern of recursion encapsulated by fold is simple, in a language with tuples and functions as first-class values the fold operator has greater expressive power than might first be expected.

Monadic Parsing in Haskell

This paper is a tutorial on defining recursive descent parsers in Haskell. In the spirit of one-stop shopping, the paper combines material from three areas into a single source. The three areas are functional parsers, the use of monads to structure functional programs, and the use of special syntax for monadic programs in Haskell. More specifically, the paper shows how to define monadic parsers using do notation in Haskell. The paper is targeted at the level of a good undergraduate student who is familiar with Haskell, and has completed a grammars and parsing course. Some knowledge of functional parsers would be useful, but no experience with monads is assumed.

Proof Methods for Corecursive Programs

Recursion is a well-known and powerful programming technique, with a wide variety of applications. The dual technique of corecursion is less well-known, but is increasingly proving to be just as useful. This article is a tutorial on the four main methods for proving properties of corecursive programs: fixpoint induction, the approximation (or take) lemma, coinduction, and fusion.

'On Affinity Measures for Artificial Immune System Movie Recommenders'

Abstract. We combine Artificial Immune Systems (AIS) technology with Collaborative Filtering (CF) and use it to build a movie recommendation system. We already know that Artificial Immune Systems work well as movie recommenders from previous work by Cayzer and Aickelin ([3], [4], [5]). Here our aim is to investigate the effect of different affinity measure algorithms for the AIS. Two different affinity measures, Kendall's Tau and Weighted Kappa, are used to calculate the correlation coefficients for the movie recommender. We compare the results with those published previously and show that that Weighted Kappa is more suitable than others for movie problems. We also show that AIS are generally robust movie recommenders and that, as long as a suitable affinity measure is chosen, results are good.

'On Affinity Measures for Artificial Immune System Movie Recommenders'

Abstract. We combine Artificial Immune Systems (AIS) technology with Collaborative Filtering (CF) and use it to build a movie recommendation system. We already know that Artificial Immune Systems work well as movie recommenders from previous work by Cayzer and Aickelin ([3], [4], [5]). Here our aim is to investigate the effect of different affinity measure algorithms for the AIS. Two different affinity measures, Kendall's Tau and Weighted Kappa, are used to calculate the correlation coefficients for the movie recommender. We compare the results with those published previously and show that that Weighted Kappa is more suitable than others for movie problems. We also show that AIS are generally robust movie recommenders and that, as long as a suitable affinity measure is chosen, results are good.

On the suboptimality of the p-version interior penalty discontinuous Galerkin method

We address the question of the rates of convergence of the p-version interior penalty discontinuous Galerkin method (p-IPDG) for second order elliptic problems with non-homogeneous Dirichlet boundary conditions. It is known that the p-IPDG method admits slightly suboptimal a-priori bounds with respect to the polynomial degree (in the Hilbertian Sobolev space setting). An example for which the suboptimal rate of convergence with respect to the polynomial degree is both proven theoretically and validated in practice through numerical experiments is presented. Moreover, the performance of p- IPDG on the related problem of p-approximation of corner singularities is assessed both theoretically and numerically, witnessing an almost doubling of the convergence rate of the p-IPDG method.