Abstract
Functional programmers have an established tradition of using traversals as a design pattern to work with recursive data structures. The technique is so prolific that a whole host of libraries have been designed to help in the task of automatically providing traversals by analysing the generic structure of data types. More recently, lenses have entered the functional scene and have proved themselves to be a simple and versatile mechanism for working with product types. They make it easy to focus on the salient parts of a data structure in a composable and reusable manner. This paper uses the combination of lenses and traversals to give rise to a library with unprecedented expressivity and flexibility for querying and modifying complex data structures. Furthermore, since lenses and traversals are based on the generic shape of data, this information is used to generate code that is as efficient as hand-optimised versions. The technique leverages the structure of data to produce generic abstractions that are then eliminated by the standard workhorses of modern functional compilers: inlining and specialisation.
Highlights
Traversals are a ubiquitous way of querying and manipulating data
Implementing param poses a number of new challenges: Locating parameters The traversal must distinguish between values that correspond to the queried type parameter, and values that were monomorphically defined
(gl) generic-lens The library which we describe in this paper. geniplate-0.7.6 [Augustsson 2018] A library which provides a similar interface to the uniplate library below but uses Template Haskell in order to generate traversals. uniplate-1.6.12 [Mitchell and Runciman 2007] A library which provides an interface for traversing data
Summary
Traversals are a ubiquitous way of querying and manipulating data They provide a reliable interface for working with data types in a structured and predictable manner. 2003], treats this problem by performing run-time type tests to decide which part of the tree to traverse. In this paper we present generic-lens, a Haskell library that provides a suite of traversals that is both faster and richer than SYB. To have a taste of the generic-lens library, consider a data type of weighted trees. The generic-lens library provides a traversal for this data type called param which takes a type-level integer as an argument. This allows a traversal to specify which parameter it wants to focus on.
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