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Epigram (programming language)

Epigram is a functional programming language with dependent types, and the integrated development environment (IDE) usually packaged with the language. Epigram's type system is strong enough to express program specifications. The goal is to support a smooth transition from ordinary programming to integrated programs and proofs whose correctness can be checked and certified by the compiler. Epigram exploits the Curry–Howard correspondence, also termed the propositions as types principle, and is based on intuitionistic type theory. The Epigram prototype was implemented by Conor McBride based on joint work with James McKinna. Its development is continued by the Epigram group in Nottingham, Durham, St Andrews, and Royal Holloway, University of London in the United Kingdom (UK). The current experimental implementation of the Epigram system is freely available together with a user manual, a tutorial and some background material. The system has been used under Linux, Windows, and macOS. It is currently unmaintained, and version 2, which was intended to implement Observational Type Theory, was never officially released but exists in GitHub. Epigram uses a two-dimensional, natural deduction style syntax, with versions in LaTeX and ASCII. Here are some examples from The Epigram Tutorial: The following declaration defines the natural numbers: The declaration says that Nat is a type with kind * (i.e., it is a simple type) and two constructors: zero and suc. The constructor suc takes a single Nat argument and returns a Nat. This is equivalent to the Haskell declaration "data Nat = Zero | Suc Nat". In LaTeX, the code is displayed as: The horizontal-line notation can be read as "assuming (what is on the top) is true, we can infer that (what is on the bottom) is true." For example, "assuming n is of type Nat, then suc n is of type Nat." If nothing is on the top, then the bottom statement is always true: "zero is of type Nat (in all cases)." And in ASCII: And in ASCII: Epigram is essentially a typed lambda calculus with generalized algebraic data type extensions, except for two extensions.

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Related concepts (11)
Dependent type
In computer science and logic, a dependent type is a type whose definition depends on a value. It is an overlapping feature of type theory and type systems. In intuitionistic type theory, dependent types are used to encode logic's quantifiers like "for all" and "there exists". In functional programming languages like Agda, ATS, Coq, F*, Epigram, and Idris, dependent types help reduce bugs by enabling the programmer to assign types that further restrain the set of possible implementations.
Haskell
Haskell (ˈhæskəl) is a general-purpose, statically-typed, purely functional programming language with type inference and lazy evaluation. Designed for teaching, research, and industrial applications, Haskell has pioneered a number of programming language features such as type classes, which enable 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).
Agda (programming language)
Agda is a dependently typed functional programming language originally developed by Ulf Norell at Chalmers University of Technology with implementation described in his PhD thesis. The original Agda system was developed at Chalmers by Catarina Coquand in 1999. The current version, originally known as Agda 2, is a full rewrite, which should be considered a new language that shares a name and tradition. Agda is also a proof assistant based on the propositions-as-types paradigm, but unlike Coq, has no separate tactics language, and proofs are written in a functional programming style.
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