A three-year study collected information bearing on the question of whether studying mathematics improves programming skills. An analysis of the data revealed significant differences in the programming effectiveness of two populations of students: (1) those who studied discrete mathematics through examples focused on reasoning about software and (2) those who studied the same mathematical topics illustrated with more traditional examples. Functional programming played a central role in the study because it provides a straightforward framework for the presentation of concepts such as predicate logic and proof by induction. Such topics can be covered in depth, staying almost entirely within the context of reasoning about software. The intricate complexities in logic that mutable variables carry with them need not arise, early on, to confuse novices struggling to understand new ideas. In addition, because functional languages provide useful and compact ways to express mathematical concepts, and because the choice of notation in mathematics courses is often at the discretion of the instructor (in contrast to the notational restrictions often fiercely guarded by the faculty in programming courses), discrete mathematics courses, as they are found in most computer science programs, provide an easy opportunity to enhance the education of students by exposing them to functional programming concepts.

In a functional program, a simple random number generator may generate a lazy list of random numbers. This is fine when the random numbers are consumed sequentially at a single point in the program. However, things are more complicated in a program where random numbers are used at many locations, such as in a large simulation. The programmer should not need to worry about providing separate generators with a unique seed at each point where random numbers are used. At the same time, the programmer should not need to coordinate the use of a single stream of random numbers in many parts of the program, which can be particularly difficult with lazy evaluation or parallel processing.We discuss several techniques for distributing random numbers to various parts of a program, and some methods of allowing different program components to evaluate random numbers locally. We then propose a new approach in which a random number sequence can be split at a random point to produce a pair of random number sequences that can be used independently at different points in the computation.The approach can also be used in distributed procedural programs, where it is desirable to avoid dealing with a single source of random numbers. The approach has the added advantage of producing repeatable results, as might be needed in debugging, for example.

Design and quality are fundamental themes in engineering education. Functional programming builds software from small components, a central element of good design, and facilitates reasoning about correctness, an important aspect of quality. Software engineering courses that employ functional programming provide a platform for educating students in the design of quality software. This pearl describes experiments in the use of ACL2, a purely functional subset of Common Lisp with an embedded mechanical logic, to focus on design and correctness in software engineering courses. Students find the courses challenging and interesting. A few acquire enough skill to use an automated theorem prover on the job without additional training. Many students, but not quite a majority, find enough success to suggest that additional experience would make them effective users of mechanized logic in commercial software development. Nearly all gain a new perspective on what it means for software to be correct and acquire a good understanding of functional programming.

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Teaching undergraduates to develop software in a formal framework such as ACL2 poses two immediate challenges. First, students typically do not know applicative programming and are often unfamiliar with ACL2's syntax. Second, for motivational reasons, students prefer to work on projects that involve designing interactive, graphical applications.In this paper, we present DRACULA, a pedagogic programming environment that partially solves these problems. The environment adds a subset of Applicative Common Lisp to DRSCHEME, an integrated programming environment for Scheme. DRACULA thus inherits DRSCHEME's pedagogic capabilities, especially its treatment of syntax and run-time errors. Further, DRACULA also comes with a library for programming interactive, graphical games. The library interface forces students to think of a graphical user interface in terms of state-transition functions, enabling them later to prove theorems about their games in ACL2. DRACULA provides a graphical front-end to the ACL2 theorem prover for this purpose. In short, DRACULA allows the formulation of student projects that represent an important intermediate point between data structure exercises in theorem proving and industrial applications.