Multi-parameter Type Classes Research Articles

Multiparty Session Type-safe Web Development with Static Linearity

Modern web applications can now offer desktop-like experiences from within the browser, thanks to technologies such as WebSockets, which enable low-latency duplex communication between the browser and the server. While these advances are great for the user experience, they represent a new responsibility for web developers who now need to manage and verify the correctness of more complex and potentially stateful interactions in their application. In this paper, we present a technique for developing interactive web applications that are statically guaranteed to communicate following a given protocol. First, the global interaction protocol is described in the Scribble protocol language -- based on multiparty session types. Scribble protocols are checked for well-formedness, and then each role is projected to a Finite State Machine representing the structure of communication from the perspective of the role. We use source code generation and a novel type-level encoding of FSMs using multi-parameter type classes to leverage the type system of the target language and guarantee only programs that communicate following the protocol will type check. Our work targets PureScript -- a functional language that compiles to JavaScript -- which crucially has an expressive enough type system to provide static linearity guarantees. We demonstrate the effectiveness of our approach through a web-based Battleship game where communication is performed through WebSocket connections.

Embedding a full linear Lambda calculus in Haskell

We present an encoding of full linear lambda calculus in Haskell using higher order abstract syntax. By making use of promoted data kinds, multi-parameter type classes and functional dependencies, the encoding allows Haskell to do both linear type checking and linear type inference.

Depending on types

Is Haskell a dependently typed programming language? Should it be? GHC's many type-system features, such as Generalized Algebraic Datatypes (GADTs), datatype promotion, multiparameter type classes, and type families, give programmers the ability to encode domain-specific invariants in their types. Clever Haskell programmers have used these features to enhance the reasoning capabilities of static type checking. But really, how far have we come? Could we do more? In this talk, I will discuss dependently typed programming in Haskell, through examples, analysis and comparisons with modern full-spectrum dependently typed languages, such as Coq, Agda and Idris. What sorts of dependently typed programming can be done in Haskell now? What could GHC learn from these languages? Conversely, what lessons can GHC offer in return?

Terminating constraint set satisfiability and simplification algorithms for context-dependent overloading

Abstract Algorithms for constraint set satisfiability and simplification of Haskell type class constraints are used during type inference in order to allow the inference of more accurate types and to detect ambiguity. Unfortunately, both constraint set satisfiability and simplification are in general undecidable, and the use of these algorithms may cause non-termination of type inference. This paper presents algorithms for these problems that terminate on any given input, based on the use of a criterion that is tested on each recursive step. The use of this criterion eliminates the need of imposing syntactic conditions on Haskell type class and instance declarations in order to guarantee termination of type inference in the presence of multi-parameter type classes, and allows program compilation without the need of compiler flags for lifting such restrictions. Undecidability of the problems implies the existence of instances for which the algorithm incorrectly reports unsatisfiability, but we are not aware of any practical example where this occurs.

Ambiguity and context-dependent overloading

Abstract This paper discusses ambiguity in the context of languages that support context-dependent overloading, such as Haskell. A type system for a Haskell-like programming language that supports context-dependent overloading and follow the Hindley-Milner approach of providing context-free type instantiation, allows distinct derivations of the same type for ambiguous expressions. Such expressions are usually rejected by the type inference algorithm, which is thus not complete with respect to the type system. Also, Haskell’s open world approach considers a definition of ambiguity that does not conform to the existence of two or more distinct type system derivations for the same type. The article presents an alternative approach, where the standard definition of ambiguity is followed. A type system is presented that allows only context-dependent type instantiation, enabling only one type to be derivable for each expression in a given typing context: the type of an expression can be instantiated only if required by the program context where the expression occurs. We define a notion of greatest instance type for each occurrence of an expression, which is used in the definition of a standard dictionary-passing semantics for core Haskell based on type system derivations, for which coherence is trivial. Type soundness is obtained as a result of disallowing all ambiguous expressions and all expressions involving unsatisfiability in the use of overloaded names. Following the standard definition of ambiguity, satisfiability is tested—i.e., “the world is closed” —if only if overloading is (or should have been) resolved, that is, if and only if there exist unreachable variables in the constraints on types of expressions. Nowadays, satisfiability is tested in Haskell, in the presence of multi-parameter type classes, only upon the presence of functional dependencies or an alternative mechanism that specifies conditions for closing the world, and that may happen when there exist or not unreachable type variables in constraints. The satisfiability trigger condition is then given automatically, by the existence of unreachable variables in constraints, and does not need to be specified by programmers, using an extra mechanism.

A generic deriving mechanism for Haskell

Haskell's deriving mechanism supports the automatic generation of instances for a number of functions. The Haskell 98 Report only specifies how to generate instances for the Eq, Ord, Enum, Bounded, Show , and Read classes. The description of how to generate instances is largely informal. The generation of instances imposes restrictions on the shape of datatypes, depending on the particular class to derive. As a consequence, the portability of instances across different compilers is not guaranteed. We propose a new approach to Haskell's deriving mechanism, which allows users to specify how to derive arbitrary class instances using standard datatype-generic programming techniques. Generic functions, including the methods from six standard Haskell 98 derivable classes, can be specified entirely within Haskell 98 plus multi-parameter type classes, making them lightweight and portable. We can also express Functor, Typeable , and many other derivable classes with our technique. We implemented our deriving mechanism together with many new derivable classes in the Utrecht Haskell Compiler.

A theory of overloading

We present a novel approach to allow for overloading of identifiers in the spirit of type classes. Our approach relies on a combination of the HM(X) type system framework with Constraint Handling Rules (CHRs). CHRs are a declarative language for writing incremental constraint solvers, that provide our scheme with a form of programmable type language. CHRs allow us to precisely describe the relationships among overloaded identifiers. Under some sufficient conditions on the CHRs we achieve decidable type inference and the semantic meaning of programs is unambiguous. Our approach provides a common formal basis for many type class extensions such as multiparameter type classes and functional dependencies.

Type-checking multi-parameter type classes

Type classes are a novel combination of parametric polymorphism and constrained types. Although most implementations restrict type classes to be single-parameter, the generalization to multi-parameter type classes has gained increasing attention. A problem with multi-parameter type classes is the increased possibilities they introduce for ambiguity in inferred types, impacting their usefulness in many practical situations. A new type-checking strategy, domain-driven unifying resolution, is identified as an approach to solve these problems. Domain-driven unifying resolution is simple, efficient, and practically useful. However, even with severe restrictions on instance definitions, it is not possible to guarantee that type-checking with unifying resolution terminates. This is in contrast with the naive generalization of single parameter resolution strategies. Domain-driven unifying resolution is guaranteed to terminate if the type class constraints are satisfiable; however satisfiability is undecidable even with severe restrictions on instance definitions. These results shed some light on ambiguity problems with multi-parameter type classes.