Extending monads with pattern matching

Sequencing of effectful computations can be neatly captured using monads and elegantly written using do notation. In practice such monads often allow additional ways of composing computations, which have to be written explicitly using combinators. We identify joinads, an abstract notion of computation that is stronger than monads and captures many such ad-hoc extensions. In particular, joinads are monads with three additional operations: one of type m a → m b → m (a, b) captures various forms of parallel composition, one of type m a → m a → m a that is inspired by choice and one of type m a → m (m a) that captures aliasing of computations. Algebraically, the first two operations form a near-semiring with commutative multiplication. We introduce docase notation that can be viewed as a monadic version of case. Joinad laws imply various syntactic equivalences of programs written using docase that are analogous to equiva-lences about case. Examples of joinads that benefit from the nota-tion include speculative parallelism, waiting for a combination of user interface events, but also encoding of validation rules using the intersection of parsers

Type-Directed Language Extension for Effectful Computations

ABSTRACT Computation types such as functors, applicative functors and monads have become common abstractions for modeling effectful computations in functional programming languages. They are often used together with special language extensions intended to simplify the syntax of monadic expressions. We can simplify it even more by employing types rather than just mechanical syntactic transformation. In this paper we present scala-workflow, a macro-based extension to the Scala programming language that offers uniform syntax for structuring effectful computations expressed as abstract interfaces with a stackable set of combinators. Unlike similar syntactic extensions, such as F#'s computation expressions, Haskell's do-notation and Scala's own for-expressions, scala-workflow allows users to transparently blend pure and effectful functions in a bounded context, as they are separated during macro expansion based on the types of subexpressions

Relational Algebra by Way of Adjunctions

Bulk types such as sets, bags, and lists are monads, and therefore support a notation for database queries based on comprehensions. This fact is the basis of much work on database query languages. The monadic structure easily explains most of standard relational algebra—specifically, selections and projections—allowing for an elegant mathematical foundation for those aspects of database query language design. Most, but not all: monads do not immediately offer an explanation of relational join or grouping, and hence important foundations for those crucial aspects of relational algebra are missing. The best they can offer is cartesian product followed by selection. Adjunctions come to the rescue: like any monad, bulk types also arise from certain adjunctions; we show that by paying due attention to other important adjunctions, we can elegantly explain the rest of standard relational algebra. In particular, graded monads provide a mathematical foundation for indexing and grouping, which leads directly to an efficient implementation, even of joins

Query Flattening and the Nested Data Parallelism Paradigm

This work is based on the observation that languages for two seemingly distant domains are closely related. Orthogonal query languages based on comprehension syntax admit various forms of query nesting to construct nested query results and express complex predicates. Languages for nested data parallelism allow to nest parallel iterators and thereby admit the parallel evaluation of computations that are themselves parallel. Both kinds of languages center around the application of side-effect-free functions to each element of a collection. The motivation for this work is the seamless integration of relational database queries with programming languages. In frameworks for language-integrated database queries, a host language's native collection-programming API is used to express queries. To mediate between native collection programming and relational queries, we define an expressive, orthogonal query calculus that supports nesting and order. The challenge of query flattening is to translate this calculus to bundles of efficient relational queries restricted to flat, unordered multisets. Prior approaches to query flattening either support only query languages that lack in expressiveness or employ a complex, monolithic translation that is hard to comprehend and generates inefficient code that is hard to optimize. To improve on those approaches, we draw on the similarity to nested data parallelism. Blelloch's flattening transformation is a static program transformation that translates nested data parallelism to flat data parallel programs over flat arrays. Based on the flattening transformation, we describe a pipeline of small, comprehensible lowering steps that translates our nested query calculus to a bundle of relational queries. The pipeline is based on a number of well-defined intermediate languages. Our translation adopts the key concepts of the flattening transformation but is designed with specifics of relational query processing in mind. Based on this translation, we revisit all aspects of query flattening. Our translation is fully compositional and can translate any term of the input language. Like prior work, the translation by itself produces inefficient code due to compositionality that is not fit for execution without optimization. In contrast to prior work, we show that query optimization is orthogonal to flattening and can be performed before flattening. We employ well-known work on logical query optimization for nested query languages and demonstrate that this body of work integrates well with our approach. Furthermore, we describe an improved encoding of ordered and nested collections in terms of flat, unordered multisets. Our approach emits idiomatic relational queries in which the effort required to maintain the non-relational semantics of the source language (order and nesting) is minimized. A set of experiments provides evidence that our approach to query flattening can handle complex, list-based queries with nested results and nested intermediate data well. We apply our approach to a number of flat and nested benchmark queries and compare their runtime with hand-written SQL queries. In these experiments, our SQL code generated from a list-based nested query language usually performs as well as hand-written queries

Bringing back monad comprehensions

This paper is about a Glasgow Haskell Compiler (GHC) extension that generalises Haskell’s list comprehension notation to monads. The monad comprehension notation implemented by the extension supports generator and filter clauses, as was the case in the Haskell 1.4 standard. In addition, the extension generalises the recently proposed parallel and SQL-like list comprehension notations to monads. The aforementioned generalisations are formally defined in this paper. The extension will be available in GHC 7.2. This paper gives several instructive examples that we hope will facilitate wide adoption of the extension by the Haskell community. We also argue why the do notation is not always a good fit for monadic libraries and embedded domain-specific languages, especially for those that are based on collection monads. Should the question of how to integrate the extension into the Haskell standard arise, the paper proposes a solution to the problem that led to the removal of the monad comprehension notation from the language standard

ICT, search behavior and market outcomes

Information and Communication Technologies (ICT) help to reduce transaction costs in several ways. The study of this phenomenon and the resulting economic consequences are the underlying common theme in the four subsequent chapters of my dissertation. Each of them is a self-contained paper that contributes to the field of Industrial Organization. In particular, I contribute to the study of two important phenomena that arose as a consequence of the ICT-enabled reduction in transaction costs, which modern societies have seen over the last two decades: electronic commerce (E-Commerce, in what follows) and (commons based) “peer production