Idris (programming language)

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Idris
ParadigmFunctional
Designed byEdwin Brady
Stable release
1.3.1[1] / October 23, 2018; 8 months ago (2018-10-23)
OSCross-platform
LicenseBSD-3
Filename extensions.idr, .lidr
Websiteidris-lang.org
Influenced by
Agda, Clean,[2] Coq,[3] Epigram, Haskell,[3] ML,[3] Rust[2]

Idris is a purely functional programming language with dependent types, optional lazy evaluation, and features such as a totality checker. Idris may be used as a proof assistant, but it is designed to be a general-purpose programming language similar to Haskell.

The Idris type system is similar to Agda, and proofs are similar to Coq, including tactics. Compared to Agda and Coq, Idris prioritizes management of side effects and support for embedded domain-specific languages. Idris compiles to C (relying on a custom copying garbage collector using Cheney's algorithm) and JavaScript (both browser- and Node.js-based). There are third-party code generators for other platforms, including JVM, CIL, and LLVM.[4]

Idris is named after a singing dragon from the 1970s UK children's television program Ivor the Engine.[5]

Features[edit]

Idris combines a number of features from relatively mainstream functional programming languages with features borrowed from proof assistants.

Functional programming[edit]

The syntax of Idris shows many similarities with that of Haskell. A hello world program in Idris might look like this:

module Main

main : IO ()
main = putStrLn "Hello, World!"

The only differences between this program and its Haskell equivalent are the single colon (instead of two) in the signature of the main function and the omission of the word "where" in the module declaration.

Inductive and parametric data types[edit]

Idris supports inductively-defined data types and parametric polymorphism. Such types can be defined both in traditional "Haskell98" syntax:

data Tree a = Node (Tree a) (Tree a) | Leaf a

or in the more general GADT syntax:

data Tree : Type -> Type where
    Node : Tree a -> Tree a -> Tree a
    Leaf : a -> Tree a

Dependent types[edit]

With dependent types, it is possible for values to appear in the types; in effect, any value-level computation can be performed during typechecking. The following defines a type of lists of statically known length, traditionally called 'vectors':

data Vect : Nat -> Type -> Type where
  Nil  : Vect 0 a
  (::) : (x : a) -> (xs : Vect n a) -> Vect (n + 1) a

This type can be used as follows:

total
append : Vect n a -> Vect m a -> Vect (n + m) a
append Nil       ys = ys
append (x :: xs) ys = x :: append xs ys

The functions append a vector of m elements of type a to a vector of n elements of type a. Since the precise types of the input vectors depend on a value, it is possible to be certain at compile-time that the resulting vector will have exactly (n + m) elements of type a. The word "total" invokes the totality checker which will report an error if the function doesn't cover all possible cases or cannot be (automatically) proven not to enter an infinite loop.

Another common example is pairwise addition of two vectors that are parameterized over their length:

total
pairAdd : Num a => Vect n a -> Vect n a -> Vect n a
pairAdd Nil       Nil       = Nil
pairAdd (x :: xs) (y :: ys) = x + y :: pairAdd xs ys

Num a signifies that the type a belongs to the type class Num. Note that this function still typechecks successfully as total, even though there is no case matching Nil in one vector and a number in the other. Since both vectors are ensured by the type system to have exactly the same length, we can be sure at compile time that this case will not occur. Hence it does not need to be mentioned for the function to be total.

Proof assistant features[edit]

Dependent types are powerful enough to encode most properties of programs, and an Idris program can prove invariants at compile-time. This makes Idris into a proof assistant.

There are two standard ways of interacting with proof assistants: by writing a series of tactic invocations (Coq style), or by interactively elaborating a proof term (Epigram/Agda style). Idris supports both modes of interaction, although the set of available tactics is not yet as useful as that of Coq.

Code generation[edit]

Because Idris contains a proof assistant, Idris programs can be written to pass proofs around. If treated naïvely, such proofs remain around at runtime. Idris aims to avoid this pitfall by aggressively erasing unused terms,[6] with promising[vague] results.[7]

By default, Idris generates native code through C. The other officially supported backend generates JavaScript.

See also[edit]

References[edit]

  1. ^ "Idris 1.3.1 released". Retrieved 2018-10-23.
  2. ^ a b ""Uniqueness Types"". Retrieved 2018-11-20.
  3. ^ a b c "Idris, a language with dependent types". Retrieved 2014-10-26.
  4. ^ "Code Generation Targets — Idris 1.1.1 documentation". docs.idris-lang.org.
  5. ^ "Frequently Asked Questions". Retrieved 2015-07-19.
  6. ^ "Erasure By Usage Analysis — Idris 1.1.1 documentation". idris.readthedocs.org.
  7. ^ "Benchmark results". ziman.functor.sk.

External links[edit]