Modules and Namespaces

An Idris program consists of a collection of modules. Each module includes an optional module declaration giving the name of the module, a list of import statements giving the other modules which are to be imported, and a collection of declarations and definitions of types, interfaces and functions. For example, the listing below gives a module which defines a binary tree type BTree (in a file BTree.idr):

module BTree

public export
data BTree a = Leaf
             | Node (BTree a) a (BTree a)

export
insert : Ord a => a -> BTree a -> BTree a
insert x Leaf = Node Leaf x Leaf
insert x (Node l v r) = if (x < v) then (Node (insert x l) v r)
                                   else (Node l v (insert x r))

export
toList : BTree a -> List a
toList Leaf = []
toList (Node l v r) = BTree.toList l ++ (v :: BTree.toList r)

export
toTree : Ord a => List a -> BTree a
toTree [] = Leaf
toTree (x :: xs) = insert x (toTree xs)

The modifiers export and public export say which names are visible from other namespaces. These are explained further below.

Then, this gives a main program (in a file bmain.idr) which uses the BTree module to sort a list:

module Main

import BTree

main : IO ()
main = do let t = toTree [1,8,2,7,9,3]
          print (BTree.toList t)

The same names can be defined in multiple modules: names are qualified with the name of the module. The names defined in the BTree module are, in full:

  • BTree.BTree
  • BTree.Leaf
  • BTree.Node
  • BTree.insert
  • BTree.toList
  • BTree.toTree

If names are otherwise unambiguous, there is no need to give the fully qualified name. Names can be disambiguated either by giving an explicit qualification, using the with keyword, or according to their type.

The with keyword in expressions comes in two variants:

  • with BTree.insert (insert x empty) for one name
  • with [BTree.insert, BTree.empty] (insert x empty) for multiple names

This is particularly useful with do notation, where it can often improve error messages: with MyModule.(>>=) do ...

There is no formal link between the module name and its filename, although it is generally advisable to use the same name for each. An import statement refers to a filename, using dots to separate directories. For example, import foo.bar would import the file foo/bar.idr, which would conventionally have the module declaration module foo.bar. The only requirement for module names is that the main module, with the main function, must be called Main — although its filename need not be Main.idr.

Export Modifiers

Idris allows for fine-grained control over the visibility of a namespace’s contents. By default, all names defined in a namespace are kept private. This aids in specification of a minimal interface and for internal details to be left hidden. Idris allows for functions, types, and interfaces to be marked as: private, export, or public export. Their general meaning is as follows:

  • private meaning that it is not exported at all. This is the default.
  • export meaning that its top level type is exported.
  • public export meaning that the entire definition is exported.

A further restriction in modifying the visibility is that definitions must not refer to anything within a lower level of visibility. For example, public export definitions cannot use private or export names, and export types cannot use private names. This is to prevent private names leaking into a module’s interface.

Meaning for Functions

  • export the type is exported
  • public export the type and definition are exported, and the definition can be used after it is imported. In other words, the definition itself is considered part of the module’s interface. The long name public export is intended to make you think twice about doing this.

Note

Type synonyms in Idris are created by writing a function. When setting the visibility for a module, it is usually a good idea to public export all type synonyms if they are to be used outside the module. Otherwise, Idris won’t know what the synonym is a synonym for.

Since public export means that a function’s definition is exported, this effectively makes the function definition part of the module’s API. Therefore, it’s generally a good idea to avoid using public export for functions unless you really mean to export the full definition.

Note

For beginners: If the function needs to be accessed only at runtime, use export. However, if it’s also meant to be used at compile time (e.g. to prove a theorem), use public export. For example, consider the function plus : Nat -> Nat -> Nat discussed previously, and the following theorem: thm : plus Z m = m. In order to prove it, the type checker needs to reduce plus Z m to m (and hence obtain thm : m = m). To achieve this, it will need access to the definition of plus, which includes the equation plus Z m = m. Therefore, in this case, plus has to be marked as public export.

Meaning for Data Types

For data types, the meanings are:

  • export the type constructor is exported
  • public export the type constructor and data constructors are exported

Meaning for Interfaces

For interfaces, the meanings are:

  • export the interface name is exported
  • public export the interface name, method names and default definitions are exported

Propagating Inner Module API’s

Additionally, a module can re-export a module it has imported, by using the public modifier on an import. For example:

module A

import B
import public C

The module A will export the name a, as well as any public or abstract names in module C, but will not re-export anything from module B.

Renaming imports

Sometimes it is convenient to be able to access the names in another module via a different namespace (typically, a shorter one). For this, you can use import…as. For example:

module A

import Data.List as L

This module A has access to the exported names from module Data.List, but can also explicitly access them via the module name L. import...as can also be combined with import public to create a module which exports a larger API from other sub-modules:

module Books

import public Books.Hardback as Books
import public Books.Comic as Books

Here, any module which imports Books will have access to the exported interfaces of Books.Hardback and Books.Comic both under the namespace Books.

Explicit Namespaces

Defining a module also defines a namespace implicitly. However, namespaces can also be given explicitly. This is most useful if you wish to overload names within the same module:

module Foo

namespace X
  export
  test : Int -> Int
  test x = x * 2

namespace Y
  export
  test : String -> String
  test x = x ++ x

This (admittedly contrived) module defines two functions with fully qualified names Foo.X.test and Foo.Y.test, which can be disambiguated by their types:

*Foo> test 3
6 : Int
*Foo> test "foo"
"foofoo" : String

The export rules, public export and export, are per namespace, not per file, so the two test definitions above need the export flag to be visible outside their own namespaces.

Parameterised blocks

Groups of functions can be parameterised over a number of arguments using a parameters declaration, for example:

parameters (x : Nat, y : Nat)
  addAll : Nat -> Nat
  addAll z = x + y + z

The effect of a parameters block is to add the declared parameters to every function, type and data constructor within the block. Specifically, adding the parameters to the front of the argument list. Outside the block, the parameters must be given explicitly. The addAll function, when called from the REPL, will thus have the following type signature.

*params> :t addAll
addAll : Nat -> Nat -> Nat -> Nat

and the following definition.

addAll : (x : Nat) -> (y : Nat) -> (z : Nat) -> Nat
addAll x y z = x + y + z

Parameters blocks can be nested, and can also include data declarations, in which case the parameters are added explicitly to all type and data constructors. They may also be dependent types with implicit arguments:

parameters (y : Nat, xs : Vect x a)
  data Vects : Type -> Type where
    MkVects : Vect y a -> Vects a

  append : Vects a -> Vect (x + y) a
  append (MkVects ys) = xs ++ ys

To use Vects or append outside the block, we must also give the xs and y arguments. Here, we can use placeholders for the values which can be inferred by the type checker:

Main> show (append _ _ (MkVects _ [1,2,3] [4,5,6]))
"[1, 2, 3, 4, 5, 6]"