The observation that program structure follows data structure is a key lesson in introductory programming: good hints for possible program designs can be found by considering the structure of the data concerned. In particular, this lesson is a core message of the influential textbook “How to Design Programs” by Felleisen, Findler, Flatt, and Krishnamurthi. However, that book discusses using only the structure of input data for guiding program design, typically leading towards structurally recursive programs. We argue that novice programmers should also be taught to consider the structure of output data, leading them also towards structurally corecursive programs.

We show how to systematically derive an efficient regular expression (regex) matcher using a variety of program transformation techniques, but very little specialized formal language and automata theory. Starting from the standard specification of the set-theoretic semantics of regular expressions, we proceed via a continuation-based backtracking matcher, to a classical, table-driven state machine. All steps of the development are supported by self-contained (and machine-verified) equational correctness proofs.

Actors collaborate via message exchanges to reach a common goal. Experience has shown, however, that pure message-based communication is limiting and forces developers to use design patterns. The recently introduced dataspace actor model borrows ideas from the tuple space realm. It offers a tightly controlled, shared storage facility for groups of actors. In this model, actors assert facts that they wish to share and interests in such assertions. The dataspace notifies interested parties of changes to the set of assertions that they are interested in. Although it is straightforward to add the dataspace model to untyped languages, adding a typed interface is both necessary and challenging. Without restrictions on exchanged data, a faulty actor may propagate erroneous data through a malformed assertion, causing an otherwise well-behaved actor to crash—violating the key principle of failure isolation. A properly designed type system can prevent this scenario and rule out other kinds of uncooperative actors. This paper presents the first structural type system for the dataspace model of actors; it does not address the question of behavioral types for assertion-oriented protocols.

Consider two widely used definitions of equality. That of Leibniz: one value equals another if any predicate that holds of the first holds of the second. And that of Martin-Löf: the type identifying one value with another is occupied if the two values are identical. The former dates back several centuries, while the latter is widely used in proof systems such as Agda and Coq. Here we show that the two definitions are isomorphic: we can convert any proof of Leibniz equality to one of Martin-Löf identity and vice versa, and each conversion followed by the other is the identity. One direction of the isomorphism depends crucially on values of the type corresponding to Leibniz equality satisfying functional extensionality and Reynolds’ notion of parametricity. The existence of the conversions is widely known (meaning that if one can prove one equality then one can prove the other), but that the two conversions form an isomorphism (internally) in the presence of parametricity and functional extensionality is, we believe, new. Our result is a special case of a more general relation that holds between inductive families and their Church encodings. Our proofs are given inside type theory, rather than meta-theoretically. Our paper is a literate Agda script.