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Haskell

Haskell is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Haskell rather than just read about it. In short: Haskell () is a general-purpose, statically typed, purely functional programming language with type inference and lazy evaluation. Haskell pioneered several programming language features including type classes for type-safe operator overloading and monadic input/output (IO).

Haskell — main illustration
Haskell — illustration

Key takeaways

  • Haskell belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Haskell to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Haskell from memory before moving on to harder problems.

Reference excerpt

Haskell () is a general-purpose, statically typed, purely functional programming language with type inference and lazy evaluation. Haskell pioneered several programming language features including type classes for type-safe operator overloading and monadic input/output (IO). It is named after logician Haskell Curry. Haskell's main implementation is the Glasgow Haskell Compiler (GHC). Haskell's semantics are historically based on those of the Miranda programming language, which served to focus the efforts of the initial Haskell working group. The last formal specification of the language was made in July 2010, while the development of GHC continues to expand Haskell via language extensions. Haskell is used in academia and industry. As of May 2021, Haskell was the 28th most popular programming language by Google searches for tutorials, and made up less than 1% of active users on the GitHub source code repository.

History After the release of Miranda by Research Software Ltd. in 1985, interest in lazy functional languages grew. By 1987, more than a dozen non-strict, purely functional programming languages existed. Miranda was the most widely used, but it was proprietary software. At the conference on Functional Programming Languages and Computer Architecture (FPCA '87) in Portland, Oregon, there was a strong consensus that a committee be formed to define an open standard for such languages. The committee's purpose was to consolidate existing functional languages into a common one to serve as a basis for future research in functional-language design.

Haskell 1.0 to 1.4 Haskell was developed by a committee, attempting to bring together off-the-shelf solutions where possible. Type classes were first proposed by Philip Wadler and Stephen Blott to address the ad hoc handling of equality types and arithmetic overloading in languages at the time. In early versions of Haskell up until and including version 1.2, user interaction and input/output (IO) were handled by both streams-based and continuation-based mechanisms, which were widely considered unsatisfactory. In version 1.3, monadic IO was introduced, along with the generalisation of type classes to higher kinds (type constructors). Along with "do notation", which provides syntactic sugar for the Monad type class, this gave Haskell an effect system that maintained referential transparency and was convenient. Another notable change in early versions was the moving of the "sequential evaluation" operation seq (which creates a data dependency between values, and is used in lazy languages to avoid excessive memory consumption) from a type class to a standard function to make refactoring more practical. The first version of Haskell ("Haskell 1.0") was defined in 1990. The committee's efforts resulted in a series of language definitions (1.0, 1.1, 1.2, 1.3, and 1.4).

Haskell 98 In late 1997, the series culminated in Haskell 98, intended to specify a stable, minimal, portable version of the language and an accompanying standard library for teaching, and as a base for future extensions. The committee expressly welcomed creating extensions and variants of Haskell 98 via adding and incorporating experimental features. In February 1999, the Haskell 98 language standard was originally published as The Haskell 98 Report. In January 2003, a revised version was published as Haskell 98 Language and Libraries: The Revised Report. The language continues to evolve rapidly, with the Glasgow Haskell Compiler (GHC) implementation representing the current de facto standard.

Haskell 2010 In early 2006, the process of defining a successor to the Haskell 98 standard, informally named Haskell Prime, began. This was intended to be an ongoing incremental process to revise the language definition, producing a new revision up to once per year. The first revision, named Haskell 2010, was announced in November 2009 and published in July 2010. Haskell 2010 added several well-used and uncontroversial features previously enabled via compiler-specific flags.

Hierarchical module names. Module names are allowed to consist of dot-separated sequences of capitalized identifiers, rather than only one such identifier. This lets modules be named in a hierarchical manner (e.g., Data.List instead of List), although technically modules are still in a single monolithic namespace. This extension was specified in an addendum to Haskell 98 and was in practice universally used. The foreign function interface (FFI) allows bindings to other programming languages. Only bindings to C are specified in the Report, but the design allows for other language bindings. To support this, data type declarations were permitted to contain no constructors, enabling robust nonce types for foreign data that could not be constructed in Haskell. This extension was also previously specified in an Addendum to the Haskell 98 Report and widely used. So-called n+k patterns (definitions of the form fact (n+1) = (n+1) * fact n) were no longer allowed. This syntactic sugar had misleading semantics, in which the code looked like it used the (+) operator, but in fact desugared to code using (-) and (>=). The rules of type inference were relaxed to allow more programs to type check. Some syntax issues (changes in the formal grammar) were fixed: pattern guards were added, allowing pattern matching within guards; resolution of operator fixity was specified in a simpler way that reflected actual practice; an edge case in the interaction of the language's lexical syntax of operators and comments was addressed, and the interaction of do-notation and if-then-else was tweaked to eliminate unexpected syntax errors. The LANGUAGE pragma was specified. By 2010, dozens of extensions to the language were in wide use, and GHC (among other compilers) provided the LANGUAGE pragma to specify individual extensions with a list of identifiers. Haskell 2010 compilers are required to support the Haskell2010 extension and are encouraged to support several others, which correspond to extensions added in Haskell 2010.

Future standards The next formal specification had been planned for 2020. On 29 October 2021, with GHC version 9.2.1, the GHC2021 extension was released. While this is not a formal language spec, it combines several stable, widely used GHC extensions to Haskell 2010.

Features

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Haskell

Start with the simplest possible case. Write down what Haskell claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Haskell before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Haskell ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Haskell

In research
Haskell appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Haskell in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Haskell is common in secondary-school and first-year university syllabi. It links to neighbouring topics Academic programming languages, Compiled programming languages, Educational programming languages, so understanding it makes those chapters shorter.
In everyday life
Look for Haskell outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study Haskell in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Haskell means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Haskell out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Haskell in simple terms?

Haskell () is a general-purpose, statically typed, purely functional programming language with type inference and lazy evaluation. Haskell pioneered several programming language features including type classes for type-safe operator overloading and monadic input/output (IO).

Why does Haskell matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Haskell?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Haskell.

Tags

  • Academic programming languages
  • Compiled programming languages
  • Educational programming languages
  • Functional languages
  • Haskell programming language family
  • Literate programming
  • Pattern matching programming languages
  • Programming languages created in 1990
  • Statically typed programming languages

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