.. _sect-namespaces: ********************** 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``): .. code-block:: idris 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: .. code-block:: idris 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 Meaning for fixity declarations ------------------------------- The modifiers differ slightly when applied to fixities. Un-labelled fixities are exported rather than be private. There is no difference between `public export` and `export`. In summary: - ``private`` means the fixity declaration is only visible within the file. - ``public export`` and ``export`` are the same and the fixity is exported. The access modifier could also be eluded for the same effect. 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: .. code-block:: idris 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. Explicit namespaces inside functions ------------------------------------ Explicit namespaces can be defined inside ``where``-blocks of functions. Unlike other definitions (e.g. ``data`` or ``record``), such namespace definitions are understood as belonging to the scope of the function definition itself. For example, the following code should typecheck. .. code-block:: idris withNSInside : Nat withNSInside = g where namespace X export g : Nat g = 5 useNSFromOutside : Nat useNSFromOutside = X.g Notice that if a function that contains namespace definition has parameters, then definitions inside this namespace will have these parameters too. This is done because such definitions have access to values of the parameters. These parameters must be passed explicitly when accessing namespaced definitions from outside the function where they are declared, and must not be passed when accessed from the inside. This behaviour is similar to parameterised blocks described below. Look at the following example. .. code-block:: idris withNSInside' : String -> Nat withNSInside' str = String.length g where namespace Y export g : String g = str ++ "a" useNSFromOutside' : String useNSFromOutside' = Y.g "x" -- value is "xa" Parameterised blocks ==================== Groups of functions can be parameterised over a number of arguments using a ``parameters`` declaration, for example: .. code-block:: idris 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. .. code-block:: idris 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: .. code-block:: idris 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]"