Haskell Type System Analysis

Types systems of programming languages are becoming more and more sophisticated and, in some cases, they are based on concepts from Logic, Type Theory and Category Theory. Haskell is a language with a modern type system and it is often singled out as an example using such theories. This work presents a small formalization of the Haskell type system and an analysis based on the mentioned theories, including its relation with the Intuitionist Propositional Second Order Logic and its logical characteristics, if there is a category in its type system and how monads are just monoids in the category of Haskell's endofunctors

Partial type constructors: Or, making ad hoc datatypes less ad hoc

This work is licensed under a Creative Commons Attribution 4.0 International License.Functional programming languages assume that type constructors are total. Yet functional programmers know better: counterexamples range from container types that make limiting assumptions about their contents (e.g., requiring computable equality or ordering functions) to type families with defining equations only over certain choices of arguments. We present a language design and formal theory of partial type constructors, capturing the domains of type constructors using qualified types. Our design is both simple and expressive: we support partial datatypes as first-class citizens (including as instances of parametric abstractions, such as the Haskell Functor and Monad classes), and show a simple type elaboration algorithm that avoids placing undue annotation burden on programmers. We show that our type system rejects ill-defined types and can be compiled to a semantic model based on System F. Finally, we have conducted an experimental analysis of a body of Haskell code, using a proof-of-concept implementation of our system; while there are cases where our system requires additional annotations, these cases are rarely encountered in practical Haskell code

Liquidate your assets: reasoning about resource usage in liquid Haskell

Liquid Haskell is an extension to the type system of Haskell that supports formal reasoning about program correctness by encoding logical properties as refinement types. In this article, we show how Liquid Haskell can also be used to reason about program efficiency in the same setting. We use the system’s existing verification machinery to ensure that the results of our cost analysis are valid, together with custom invariants for particular program contexts to ensure that the results of our analysis are precise. To illustrate our approach, we analyse the efficiency of a wide range of popular data structures and algorithms, and in doing so, explore various notions of resource usage. Our experience is that reasoning about efficiency in Liquid Haskell is often just as simple as reasoning about correctness, and that the two can naturally be combined

Functional Baby Talk: Analysis of Code Fragments from Novice Haskell Programmers

What kinds of mistakes are made by novice Haskell developers, as they learn about functional programming? Is it possible to analyze these errors in order to improve the pedagogy of Haskell? In 2016, we delivered a massive open online course which featured an interactive code evaluation environment. We captured and analyzed 161K interactions from learners. We report typical novice developer behavior; for instance, the mean time spent on an interactive tutorial is around eight minutes. Although our environment was restricted, we gain some understanding of Haskell novice errors. Parenthesis mismatches, lexical scoping errors and do block misunderstandings are common. Finally, we make recommendations about how such beginner code evaluation environments might be enhanced

Linear Haskell: practical linearity in a higher-order polymorphic language

Linear type systems have a long and storied history, but not a clear path forward to integrate with existing languages such as OCaml or Haskell. In this paper, we study a linear type system designed with two crucial properties in mind: backwards-compatibility and code reuse across linear and non-linear users of a library. Only then can the benefits of linear types permeate conventional functional programming. Rather than bifurcate types into linear and non-linear counterparts, we instead attach linearity to function arrows. Linear functions can receive inputs from linearly-bound values, but can also operate over unrestricted, regular values. To demonstrate the efficacy of our linear type system - both how easy it can be integrated in an existing language implementation and how streamlined it makes it to write programs with linear types - we implemented our type system in GHC, the leading Haskell compiler, and demonstrate two kinds of applications of linear types: mutable data with pure interfaces; and enforcing protocols in I/O-performing functions

Aspect-Oriented Programming with Type Classes

We consider the problem of adding aspects to a strongly typed language which supports type classes. We show that type classes as supported by the Glasgow Haskell Compiler can model an AOP style of programming via a simple syntax-directed transformation scheme where AOP programming idioms are mapped to type classes. The drawback of this approach is that we cannot easily advise functions in programs which carry type annotations. We sketch a more principled approach which is free of such problems by combining ideas from intentional type analysis with advanced overloading resolution strategies. Our results show that type-directed static weaving is closely related to type class resolution -- the process of typing and translating type class programs

Static Application-Level Race Detection in STM Haskell using Contracts

Writing concurrent programs is a hard task, even when using high-level synchronization primitives such as transactional memories together with a functional language with well-controlled side-effects such as Haskell, because the interferences generated by the processes to each other can occur at different levels and in a very subtle way. The problem occurs when a thread leaves or exposes the shared data in an inconsistent state with respect to the application logic or the real meaning of the data. In this paper, we propose to associate contracts to transactions and we define a program transformation that makes it possible to extend static contract checking in the context of STM Haskell. As a result, we are able to check statically that each transaction of a STM Haskell program handles the shared data in a such way that a given consistency property, expressed in the form of a user-defined boolean function, is preserved. This ensures that bad interference will not occur during the execution of the concurrent program.Comment: In Proceedings PLACES 2013, arXiv:1312.2218. [email protected]; [email protected]