A sound gradual type system ensures that untyped components of a program can never break the guarantees of statically typed components. This assurance relies on runtime checks, which in turn impose performance overhead in proportion to the frequency and nature of interaction between typed and untyped components. The literature on gradual typing lacks rigorous descriptions of methods for measuring the performance of gradual type systems. This gap has consequences for the implementors of gradual type systems and developers who use such systems. Without systematic evaluation of mixed-typed programs, implementors cannot precisely determine how improvements to a gradual type system affect performance. Developers cannot predict whether adding types to part of a program will significantly degrade (or improve) its performance. This paper presents the first method for evaluating the performance of sound gradual type systems. The method quantifies both the absolute performance of a gradual type system and the relative performance of two implementations of the same gradual type system. To validate the method, the paper reports on its application to 20 programs and 3 implementations of Typed Racket.

Enumerations represented as bijections between the natural numbers and elements of some given type have recently garnered interest in property-based testing because of their efficiency and flexibility. There are, however, many ways of defining these bijections, some of which are better than others. This paper offers a new property of enumeration combinators called fairness that identifies enumeration combinators that are better suited to property-based testing. Intuitively, the result of a fair combinator indexes into its argument enumerations equally when constructing its result. For example, extracting the nth element from our enumeration of three-tuples indexes about $\sqrt[3]{𝑛}$ elements into each of its components instead of, say, indexing $\sqrt[2]{𝑛}$ into one and $\sqrt[4]{𝑛}$ into the other two, as you would if a three-tuple were built out of nested pairs. Similarly, extracting the nth element from our enumeration of a three-way union returns an element that is $\frac{𝑛}{3}$ into one of the argument enumerators. The paper presents a semantics of enumeration combinators, a theory of fairness, proofs establishing fairness of our new combinators and that some combinations of fair combinators are not fair. We also report on an evaluation of fairness for the purpose of finding bugs in programming-language models. We show that fair enumeration combinators have complementary strengths to an existing, well-tuned ad hoc random generator (better on short time scales and worse on long time scales) and that using unfair combinators is worse across the board.

Contracts feel misunderstood, especially those with a higher-order soul. While software engineers appreciate contracts as tools for articulating the interface between components, functional programmers desperately search for their types and meaning, completely forgetting about their pragmatics.

This gem presents a novel analysis of contract systems. Applied to the higher-order kind, this analysis reveals their large and clearly unappreciated software engineering potential. Three sample applications illustrate where this kind of exploration may lead.