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.

Can foster carers help children resolve their emotional and behavioural difficulties?

Although foster care is generally seen as providing a positive experience for the children and young people for whom it caters, it is rarely conceived of as a place where the children are helped to address their emotional difficulties and modify their often difficult behaviour. Yet research evidence suggests that some foster carers are consistently less likely to have placements which break down, and that foster carers who show particular skills in parenting can make a difference to successful outcomes. The paper draws on a large longitudinal study of foster care to argue that it is possible to learn from what these foster carers do in order to develop these skills in others. A model of successful foster care. developed from the main statistical part of the study is first described. Two cases from the qualitative, case studies component of the research are then analysed to demonstrate a quality of responsive parenting. The model is further developed within the framework of the dynamic of attachment and interest sharing proposed by Heard and Lake, to show how this can be used as a basis for future approaches to working with foster placements.