Some 10 years ago, Harper illustrated the powerful method of proof-directed debugging for developing programs with an article in this journal. Unfortunately, his example uses both higher-order functions and continuation-passing style, which is too difficult for students in an introductory programming course. In this pearl, we present a first-order version of Harper's example and demonstrate that it is easy to transform the final version into an efficient state machine. Our new version convinces students that the approach is useful, even essential, in developing both correct and efficient programs.

There's no maths involved. You solve the puzzle with reasoning and logic. Advice on how to play Sudoku, The Independent Newspaper

Polytypic programming is a way of defining type-indexed operations, such as map, fold and zip, based on type information. Run-time polytypic programming allows that type information to be dynamically computed – this support is essential in modern programming languages that support separate compilation, first-class type abstraction, or polymorphic recursion. However, in previous work we defined run-time polytypic programming with a type-passing semantics. Although it is natural to define polytypic programs as operating over first-class types, such a semantics suffers from a number of drawbacks. This paper describes how to recast that work in a type-erasure semantics, where terms represent type information in a safe manner. The resulting language is simple and easy to implement – we present a prototype implementation of the necessary machinery as a small Haskell library.

XML data are described by types involving regular expressions. This raises the question of what language feature is convenient for manipulating such data. Previously, we have given an answer to this question by proposing regular expression pattern matching. However, since this construct is derived from ML pattern matching, it does not have an iteration functionality in itself, which makes it cumbersome to process data typed by Kleene stars. In this paper, we propose a novel programming feature regular expression filters. This construct extends the previous proposal by permitting pattern clauses to be closed under arbitrary regular expression operators. This yields many convenient programming idioms such as non-uniform processing of sequences and almost-copying of trees. We further develop a type inference mechanism that obtains (1) types for pattern variables that are locally precise with respect to the type of input values and (2) a type for the result of the whole filter expression that is also locally precise with respect to the types of the body expressions. We discuss how our construct is useful in the practice of XML processing and, in particular, how our type inference is crucial for avoiding changes of programs when types of data to be processed evolve frequently.

We investigate a technique from the literature, called the phantom-types technique, that uses parametric polymorphism, type constraints, and unification of polymorphic types to model a subtyping hierarchy. Hindley-Milner type systems, such as the one found in Standard ML, can be used to enforce the subtyping relation, at least for first-order values. We show that this technique can be used to encode any finite subtyping hierarchy (including hierarchies arising from multiple interface inheritance). We formally demonstrate the suitability of the phantom-types technique for capturing first-order subtyping by exhibiting a type-preserving translation from a simple calculus with bounded polymorphism to a calculus embodying the type system of SML.

Existing approaches to object encapsulation either rely on ad hoc syntactic restrictions or require the use of specialised type systems. Syntactic restrictions are difficult to scale and to prove correct, while specialised type systems require extensive changes to programming languages. We demonstrate that confinement can be enforced cheaply in Featherweight Generic Java, with no essential change to the underlying language or type system. This result demonstrates that polymorphic type parameters can simultaneously act as ownership parameters and should facilitate the adoption of confinement and ownership type systems in general-purpose programming languages.