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The Knuth–Morris–Pratt (KMP) algorithm for string search is notoriously difficult to understand. Lost in a sea of index arithmetic, most explanations of KMP obscure its essence. This paper constructs KMP incrementally, using pictures to illustrate each step. The end result is easier to comprehend. Additionally, the derivation uses only elementary functional programming techniques.

Behavioral software contracts allow programmers to strengthen the obligations and promises that they express with conventional types. They lack expressive power, though, when it comes to invariants that hold across several function calls. Trace contracts narrow this expressiveness gap. A trace contract is a predicate over the sequence of values that flow through function calls and returns. This paper presents a principled design, an implementation, and an evaluation of trace contracts.

Software contracts empower programmers to describe functional properties of components. When it comes to constraining effects, though, the literature offers only one-off solutions for various effects. It lacks a universal principle. This paper presents the design of an effectful contract system in the context of effect handlers. A key metatheorem shows that contracts cannot unduly interfere with a program's execution. An implementation of this design, along with an evaluation of its generality, demonstrates that the theory can guide practice.

Sound migratory typing envisions a safe and smooth refactoring of untyped code bases to typed ones. However, the cost of enforcing safety with run-time checks is often prohibitively high, thus performance regressions are a likely occurrence. Additional types can often recover performance, but choosing the right components to type is difficult because of the exponential size of the migratory typing lattice. In principal though, migration could be guided by off-the-shelf profiling tools. To examine this hypothesis, this paper follows the rational programmer method and reports on the results of an experiment on tens of thousands of performance-debugging scenarios via seventeen strategies for turning profiler output into an actionable next step. The most effective strategy is the use of deep types to eliminate the most costly boundaries between typed and untyped components; this strategy succeeds in more than 50% of scenarios if two performance degradations are tolerable along the way.

Equipping an existing programming language with a gradual type system requires two major steps. The first and most visible one in academia is to add a notation for types and a type checking apparatus. The second, highly practical one is to provide a type veneer for the large number of existing untyped libraries; doing so enables typed components to import pieces of functionality and get their uses type-checked, without any changes to the libraries. When programmers create such typed veneers for libraries, they make mistakes that persist and cause trouble. The question is whether the academically investigated run-time checks for gradual type systems assist programmers with debugging such mistakes. This paper provides a first, surprising answer to this question via a rational-programmer investigation: run-time checks alone are typically less helpful than the safety checks of the underlying language. Combining Natural run-time checks with blame, however, provides significantly superior debugging hints.