Bruno C. d. S. Oliveira

Type classes as objects and implicits

Type classes were originally developed in Haskell as a disciplined alternative to ad-hoc polymorphism. Type classes have been shown to provide a type-safe solution to important challenges in software engineering and programming languages such as, for example, retroactive extension of programs. They are also recognized as a good mechanism for concept-based generic programming and, more recently, have evolved into a mechanism for type-level computation. This paper presents a lightweight approach to type classes in object-oriented (OO) languages with generics using the CONCEPT pattern and implicits (a type-directed implicit parameter passing mechanism). This paper also shows how Scalas type system conspires with implicits to enable, and even surpass, many common extensions of the Haskell type class system, making Scala ideally suited for generic programming in the large.

“Scrap your boilerplate” reloaded

The paper “Scrap your boilerplate” (SYB) introduces a combinator library for generic programming that offers generic traversals and queries. Classically, support for generic programming consists of two essential ingredients: a way to write (type-)overloaded functions, and independently, a way to access the structure of data types. SYB seems to lack the second. As a consequence, it is difficult to compare with other approaches such as PolyP or Generic Haskell. In this paper we reveal the structural view that SYB builds upon. This allows us to define the combinators as generic functions in the classical sense. We explain the SYB approach in this changed setting from ground up, and use the understanding gained to relate it to other generic programming approaches. Furthermore, we show that the SYB view is applicable to a very large class of data types, including generalized algebraic data types.

The essence of the iterator pattern

The ITERATOR pattern gives a clean interface for element-by-element access to a collection. Imperative iterations using the pattern have two simultaneous aspects: mapping and accumulating. Various existing functional iterations model one or other of these, but not both simultaneously. We argue that McBride and Patersons idioms, and in particular the corresponding traverse operator, do exactly this, and therefore capture the essence of the ITERATOR pattern. We present some axioms for traversal, and illustrate with a simple example, the repmin problem.

Modular Visitor Components

The expression families problem can be defined as the problem of achieving reusability and composability across the components involved in a family of related datatypes and corresponding operations over those datatypes. Like the traditional expression problem , adding new components (either variants or operations) should be possible while preserving modular and static type-safety . Moreover, different combinations of components should have different type identities and the subtyping relationships between components should be preserved. By generalizing previous work exploring the connection between type-theoretic encodings of datatypes and visitors, we propose two solutions for this problem in Scala using modular visitor components . These components can be grouped into features that can be easily composed in a feature-oriented programming style to obtain customized datatypes and operations.

Extensibility for the masses: practical extensibility with object algebras

This paper presents a new solution to the expression problem (EP) that works in OO languages with simple generics (including Java or C#). A key novelty of this solution is that advanced typing features, including F-bounded quantification, wildcards and variance annotations, are not needed. The solution is based on object algebras, which are an abstraction closely related to algebraic datatypes and Church encodings. Object algebras also have much in common with the traditional forms of the Visitor pattern, but without many of its drawbacks: they are extensible, remove the need for accept methods, and do not compromise encapsulation. We show applications of object algebras that go beyond toy examples usually presented in solutions for the expression problem. In the paper we develop an increasingly more complex set of features for a mini-imperative language, and we discuss a real-world application of object algebras in an implementation of remote batches. We believe that object algebras bring extensibility to the masses: object algebras work in mainstream OO languages, and they significantly reduce the conceptual overhead by using only features that are used by everyday programmers.

TypeCase: a design pattern for type-indexed functions

A type-indexed function is a function that is defined for each member of some family of types. Haskells type class mechanism provides collections of open type-indexed functions, in which the indexing family can be extended by defining a new type class instance but the collection of functions is fixed. The purpose of this paper is to present TypeCase: a design pattern that allows the definition of closed type-indexed functions, in which the index family is fixed but the collection of functions is extensible. It is inspired by Cheney and Hinzes work on lightweight approaches to generic programming. We generalise their techniques as a design pattern. Furthermore, we show that type-indexed functions with type-indexed types, and consequently generic functions with generic types, can also be encoded in a lightweight manner, thereby overcoming one of the main limitations of the lightweight approaches.

The visitor pattern as a reusable, generic, type-safe component

The VISITOR design pattern shows how to separate the structure of an object hierarchy from the behaviour of traversals over that hierarchy. The pattern is very flexible; this very flexibility makes it difficult to capture the pattern as anything more formal than prose, pictures and prototypes. We show how to capture the essence of the VISITOR pattern as a reusable software library, by using advanced type system features appearing in modern object-oriented languages such as Scala. We preserve type-safety statically and modularly: no reflection or similar mechanisms are used and modules can be independently compiled. The library is generic, in two senses: not only is it parametrised by both the return type and the shape of the object hierarchy, but also it allows a number of implementation choices (internal versus external control, imperative versus functional behaviour, orthogonal aspects such as tracing and memoisation) to be specified by parameters rather than fixed in early design decisions. Finally, we propose a generalised datatype-like notation,on top of our visitor library: this provides a convenient functional decomposition style in object-oriented languages.

EffectiveAdvice: disciplined advice with explicit effects

Advice is a mechanism, widely used in aspect-oriented languages, that allows one program component to augment or modify the behavior of other components. When advice and other components are composed together they become tightly coupled, sharing both control and data flows. However this creates important problems: modular reasoning about a component becomes very difficult; and two tightly coupled components may interfere with each others control and data flows. This paper presents EffectiveAdvice, a disciplined model of advice, inspired by Aldrichs Open Modules, that has full support for effects. With EffectiveAdvice, equivalence of advice, as well as base components, can be checked by equational reasoning. The paper describes EffectiveAdvice as a Haskell library in which advice is modeled by mixin inheritance and effects are modeled by monads. Interference patterns previously identified in the literature are expressed as combinators. Parametricity, together with the combinators, is used to prove two harmless advice theorems. The result is an effective semantic model of advice that supports effects, and allows these effects to be separated with strong non-interference guarantees, or merged as needed.

Partition-based regression verification

Regression verification (RV) seeks to guarantee the absence of regression errors in a changed program version. This paper presents Partition-based Regression Verification (PRV): an approach to RV based on the gradual exploration of differential input partitions. A differential input partition is a subset of the common input space of two program versions that serves as a unit of verification. Instead of proving the absence of regression for the complete input space at once, PRV verifies differential partitions in a gradual manner. If the exploration is interrupted, PRV retains partial verification guarantees at least for the explored differential partitions. This is crucial in practice as verifying the complete input space can be prohibitively expensive. Experiments show that PRV provides a useful alternative to state-of-the-art regression test generation techniques. During the exploration, PRV generates test cases which can expose different behaviour across two program versions. However, while test cases are generally single points in the common input space, PRV can verify entire partitions and moreover give feedback that allows programmers to relate a behavioral difference to those syntactic changes that contribute to this difference.

Meta-theory à la carte

Formalizing meta-theory, or proofs about programming languages, in a proof assistant has many well-known benefits. Unfortunately, the considerable effort involved in mechanizing proofs has prevented it from becoming standard practice. This cost can be amortized by reusing as much of existing mechanized formalizations as possible when building a new language or extending an existing one. One important challenge in achieving reuse is that the inductive definitions and proofs used in these formalizations are closed to extension. This forces language designers to cut and paste existing definitions and proofs in an ad-hoc manner and to expend considerable effort to patch up the results. The key contribution of this paper is the development of an induction technique for extensible Church encodings using a novel reinterpretation of the universal property of folds. These encodings provide the foundation for a framework, formalized in Coq, which uses type classes to automate the composition of proofs from modular components. This framework enables a more structured approach to the reuse of meta-theory formalizations through the composition of modular inductive definitions and proofs. Several interesting language features, including binders and general recursion, illustrate the capabilities of our framework. We reuse these features to build fully mechanized definitions and proofs for a number of languages, including a version of mini-ML. Bounded induction enables proofs of properties for non-inductive semantic functions, and mediating type classes enable proof adaptation for more feature-rich languages.