A Framework for Resource Dependent EDSLs in a Dependently Typed Language (Pearl)

Idris' Effects library demonstrates how to embed resource dependent algebraic effect handlers into a dependently typed host language, providing run-time and compile-time based reasoning on type-level resources. Building upon this work, Resources is a framework for realising Embedded Domain Specific Languages (EDSLs) with type systems that contain domain specific substructural properties. Differing from Effects, Resources allows a language’s substructural properties to be encoded within type-level resources that are associated with language variables. Such an association allows for multiple effect instances to be reasoned about autonomically and without explicit type-level declaration. Type-level predicates are used as proof that the language’s substructural properties hold. Several exemplar EDSLs are presented that illustrates our framework’s operation and how dependent types provide correctness-by-construction guarantees that substructural properties of written programs hold

A Semantic Framework to Debug Parallel Lazy Functional Languages

It is not easy to debug lazy functional programs. The reason is that laziness and higherorder complicates basic debugging strategies. Although there exist several debuggers for sequential lazy languages, dealing with parallel languages is much harder. In this case, it is important to implement debugging platforms for parallel extensions, but it is also important to provide theoretical foundations to simplify the task of understanding the debugging process. In this work, we deal with the debugging process in two parallel languages that extend the lazy language Haskell. In particular, we provide an operational semantics that allows us to reason about our parallel extension of the sequential debugger Hood. In addition, we show how we can use it to analyze the amount of speculative work done by the processes, so that it can be used to optimize their use of resources

Do Judge a Test by its Cover: Combining Combinatorial and Property-Based Testing

Property-based testing uses randomly generated inputs to validate high-level program specifications. It can be shockingly effective at finding bugs, but it often requires generating a very large number of inputs to do so. In this paper, we apply ideas from combinatorial testing, a powerful and widely studied testing methodology, to modify the distributions of our random generators so as to find bugs with fewer tests. The key concept is combinatorial coverage, which measures the degree to which a given set of tests exercises every possible choice of values for every small combination of input features. In its “classical” form, combinatorial coverage only applies to programs whose inputs have a very particular shape—essentially, a Cartesian product of finite sets. We generalize combinatorial coverage to the richer world of algebraic data types by formalizing a class of sparse test descriptions based on regular tree expressions. This new definition of coverage inspires a novel combinatorial thinning algorithm for improving the coverage of random test generators, requiring many fewer tests to catch bugs. We evaluate this algorithm on two case studies, a typed evaluator for System F terms and a Haskell compiler, showing significant improvements in both

Interleaving Data and Effects

The study of programming with and reasoning about inductive datatypes such as lists and trees has benefited from the simple categorical principle of initial algebras. In initial algebra semantics, each inductive datatype is represented by an initial f-algebra for an appropriate functor f. The initial algebra principle then supports the straightforward derivation of definitional principles and proof principles for these datatypes. This technique has been expanded to a whole methodology of structured functional programming, often called origami programming.In this article we show how to extend initial algebra semantics from pure inductive datatypes to inductive datatypes interleaved with computational effects. Inductive datatypes interleaved with effects arise naturally in many computational settings. For example, incrementally reading characters from a file generates a list of characters interleaved with input/output actions, and lazily constructed infinite values can be represented by pure data interleaved with the possibility of non-terminating computation. Straightforward application of initial algebra techniques to effectful datatypes leads either to unsound conclusions if we ignore the possibility of effects, or to unnecessarily complicated reasoning because the pure and effectful concerns must be considered simultaneously. We show how pure and effectful concerns can be separated using the abstraction of initial f-and-m-algebras, where the functor f describes the pure part of a datatype and the monad m describes the interleaved effects. Because initial f-and-m-algebras are the analogue for the effectful setting of initial f-algebras, they support the extension of the standard definitional and proof principles to the effectful setting. Initial f-and-m-algebras are originally due to Filinski and Støvring, who studied them in the category Cpo. They were subsequently generalised to arbitrary categories by Atkey, Ghani, Jacobs, and Johann in a FoSSaCS 2012 paper. In this article we aim to introduce the general concept of initial f-and-m-algebras to a general functional programming audience

No Unification Variable Left Behind: Fully Grounding Type Inference for the HDM System

The Hindley-Damas-Milner (HDM) system provides polymorphism, a key feature of functional programming languages such as Haskell and OCaml. It does so through a type inference algorithm, whose soundness and completeness have been well-studied and proven both manually (on paper) and mechanically (in a proof assistant). Earlier research has focused on the problem of inferring the type of a top-level expression. Yet, in practice, we also may wish to infer the type of subexpressions, either for the sake of elaboration into an explicitly-typed target language, or for reporting those types back to the programmer. One key difference between these two problems is the treatment of underconstrained types: in the former, unification variables that do not affect the overall type need not be instantiated. However, in the latter, instantiating all unification variables is essential, because unification variables are internal to the algorithm and should not leak into the output. We present an algorithm for the HDM system that explicitly tracks the scope of all unification variables. In addition to solving the subexpression type reconstruction problem described above, it can be used as a basis for elaboration algorithms, including those that implement elaboration-based features such as type classes. The algorithm implements input and output contexts, as well as the novel concept of full contexts, which significantly simplifies the state-passing of traditional algorithms. The algorithm has been formalised and proven sound and complete using the Coq proof assistant

Foundations of Information-Flow Control and Effects

In programming language research, information-flow control (IFC) is a technique for enforcing a variety of security aspects, such as confidentiality of data,on programs. This Licenciate thesis makes novel contributions to the theory and foundations of IFC in the following ways: Chapter A presents a new proof method for showing the usual desired property of noninterference; Chapter B shows how to securely extend the concurrent IFC language MAC with asynchronous exceptions; and, Chapter C presents a new and simpler language for IFC with effects based on an explicit separation of pure and effectful computations

Lightweight Computation Tree Tracing for Lazy Functional Languages

A computation tree of a program execution describes computations of functions and their dependencies. A computation tree describes how a program works and is at the heart of algorithmic debugging. To generate a computation tree, existing algorithmic debuggers either use a complex implementation or yield a less informative approximation. We present a method for lazy functional languages that requires only a simple tracing library to generate a detailed computation tree. With our algorithmic debugger a programmer can debug any Haskell program by only importing our library and annotating suspected functions

A shortcut fusion rule for circular program calculation

Circular programs are a powerful technique to express multiple traversal algorithms as a single traversal function in a lazy setting. In this paper, we present a shortcut deforestation technique to calculate circular programs. The technique we propose takes as input the composition of two functions, such that the first builds an intermediate structure and some additional context information which are then processed by the second one, to produce the final result. Our transformation into circular programs achieves intermediate structure deforestation and multiple traversal elimination. Furthermore, the calculated programs preserve the termination properties of the original ones