Lisp programmers have long used macros to extend their language. Indeed, their success has inspired macro notations for a variety of other languages, such as C and Java. There is, however, a paucity of effective pedagogic examples of macro use. This paper presents a short, non-trivial example that implements a construct not already found in mainstream languages. Furthermore, it motivates the need for tail-calls, as opposed to mere tail-recursion, and illustrates how support for tail-call optimization is crucial to support a natural style of macro-based language extension.

We formalize and prove the folklore theorem that the static delimited-control operators shift and reset can be simulated in terms of the dynamic delimited-control operators control and prompt. The proof is based on small-step operational semantics.

Every lazy functional programmer knows about the following approach to enumerating the positive rationals: generate a two-dimensional matrix (an infinite list of infinite lists), then traverse its finite diagonals (an infinite list of finite lists).

A huge discrepancy between theory and practice exists in one popular application area of functional programming – spreadsheets. Although spreadsheets are the most frequently used (functional) programs, they fall short of the quality level that is expected of functional programs, which is evidenced by the fact that existing spreadsheets contain many errors, some of which have serious impacts. We have developed a template specification language that allows the definition of spreadsheet templates that describe possible spreadsheet evolutions. This language is based on a table calculus that formally captures the process of creating and modifying spreadsheets. We have developed a type system for this calculus that can prevent type, reference, and omission errors from occurring in spreadsheets. On the basis of the table calculus we have developed Gencel, a system for generating reliable spreadsheets. We have implemented a prototype version of Gencel as an extension of Excel.

The Theory of Contexts is a type-theoretic axiomatization aiming to give a metalogical account of the fundamental notions of variable and context as they appear in Higher Order Abstract Syntax. In this paper, we prove that this theory is consistent by building a model based on functor categories. By means of a suitable notion of forcing, we prove that this model validates Classical Higher Order Logic, the Theory of Contexts, and also (parametrised) structural induction and recursion principles over contexts. Our approach, which we present in full detail, should also be useful for reasoning on other models based on functor categories. Moreover, the construction could also be adopted, and possibly generalized, for validating other theories of names and binders.