Idris (programming language)

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Idris
Paradigm Functional
Designed by Edwin Brady
Stable release
1.0[1] / April 1, 2017; 2 months ago (2017-04-01)
OS Cross-platform
License BSD-3
Filename extensions .idr, .lidr
Website idris-lang.org
Influenced by
Agda, Coq,[2] Epigram, Haskell,[2] ML,[2] Rust

Idris is a general-purpose purely functional programming language with dependent types, strict or optional lazy evaluation and features such as a totality checker.

Even before its possible usage for interactive theorem-proving, the focus of Idris is on general-purpose programming, like the purely functional Haskell, and with sufficient performance. The type system of Idris is similar to the one used by Agda and theorem-proving in it is similar to Coq, including tactics. In comparison, Idris has a priority on easy management of side-effects and support for implementing embedded domain specific languages.

As of May 2017, Idris compiles to C (relying on a custom copying garbage collector using Cheney's algorithm) and JavaScript (both browser- and Node.js-based). There is also a number of third-party code generators for other platforms, including Java, JVM, CIL, OCaml, and a partial LLVM backend.[3]

The name Idris goes back to the character of the singing dragon in the 1970s UK kids' program Ivor the Engine.[4]

Features[edit]

Idris combines a number of features from relatively mainstream functional programming languages with features borrowed from proof assistants, in effect blurring the boundary between the two kinds of software.

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]

Like most modern functional programming languages, Idris supports a notion of inductively-defined data type 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 appends 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 to not 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 naively, such proofs remain around at runtime. Idris aims to avoid this pitfall by aggressively erasing unused terms,[5] with promising results.[6]

By default, Idris generates native code by going through C. Other backends are available for generating JavaScript and Java.

See also[edit]

References[edit]

External links[edit]