mirror of
https://github.com/idris-lang/Idris2.git
synced 2024-12-30 07:02:24 +03:00
768 lines
24 KiB
ReStructuredText
768 lines
24 KiB
ReStructuredText
.. _sect-interfaces:
|
||
|
||
**********
|
||
Interfaces
|
||
**********
|
||
|
||
We often want to define functions which work across several different
|
||
data types. For example, we would like arithmetic operators to work on
|
||
``Int``, ``Integer`` and ``Double`` at the very least. We would like
|
||
``==`` to work on the majority of data types. We would like to be able
|
||
to display different types in a uniform way.
|
||
|
||
To achieve this, we use *interfaces*, which are similar to type classes in
|
||
Haskell or traits in Rust. To define an interface, we provide a collection of
|
||
overloadable functions. A simple example is the ``Show``
|
||
interface, which is defined in the prelude and provides an interface for
|
||
converting values to ``String``:
|
||
|
||
.. code-block:: idris
|
||
|
||
interface Show a where
|
||
show : a -> String
|
||
|
||
This generates a function of the following type (which we call a
|
||
*method* of the ``Show`` interface):
|
||
|
||
.. code-block:: idris
|
||
|
||
show : Show a => a -> String
|
||
|
||
We can read this as: “under the constraint that ``a`` has an implementation
|
||
of ``Show``, take an input ``a`` and return a ``String``.” An implementation
|
||
of an interface is defined by giving definitions of the methods of the interface.
|
||
For example, the ``Show`` implementation for ``Nat`` could be defined as:
|
||
|
||
.. code-block:: idris
|
||
|
||
Show Nat where
|
||
show Z = "Z"
|
||
show (S k) = "s" ++ show k
|
||
|
||
::
|
||
|
||
Main> show (S (S (S Z)))
|
||
"sssZ" : String
|
||
|
||
Only one implementation of an interface can be given for a type — implementations may
|
||
not overlap. Implementation declarations can themselves have constraints.
|
||
To help with resolution, the arguments of an implementation must be
|
||
constructors (either data or type constructors) or variables
|
||
(i.e. you cannot give an implementation for a function). For
|
||
example, to define a ``Show`` implementation for vectors, we need to know
|
||
that there is a ``Show`` implementation for the element type, because we are
|
||
going to use it to convert each element to a ``String``:
|
||
|
||
.. code-block:: idris
|
||
|
||
Show a => Show (Vect n a) where
|
||
show xs = "[" ++ show' xs ++ "]" where
|
||
show' : forall n . Vect n a -> String
|
||
show' Nil = ""
|
||
show' (x :: Nil) = show x
|
||
show' (x :: xs) = show x ++ ", " ++ show' xs
|
||
|
||
Note that we need the explicit ``forall n .`` in the ``show'`` function
|
||
because otherwise the ``n`` is already in scope, and fixed to the value of
|
||
the top level ``n``.
|
||
|
||
Default Definitions
|
||
===================
|
||
|
||
The Prelude defines an ``Eq`` interface which provides methods for
|
||
comparing values for equality or inequality, with implementations for all of
|
||
the built-in types:
|
||
|
||
.. code-block:: idris
|
||
|
||
interface Eq a where
|
||
(==) : a -> a -> Bool
|
||
(/=) : a -> a -> Bool
|
||
|
||
To declare an implementation for a type, we have to give definitions of all
|
||
of the methods. For example, for an implementation of ``Eq`` for ``Nat``:
|
||
|
||
.. code-block:: idris
|
||
|
||
Eq Nat where
|
||
Z == Z = True
|
||
(S x) == (S y) = x == y
|
||
Z == (S y) = False
|
||
(S x) == Z = False
|
||
|
||
x /= y = not (x == y)
|
||
|
||
It is hard to imagine many cases where the ``/=`` method will be
|
||
anything other than the negation of the result of applying the ``==``
|
||
method. It is therefore convenient to give a default definition for
|
||
each method in the interface declaration, in terms of the other method:
|
||
|
||
.. code-block:: idris
|
||
|
||
interface Eq a where
|
||
(==) : a -> a -> Bool
|
||
(/=) : a -> a -> Bool
|
||
|
||
x /= y = not (x == y)
|
||
x == y = not (x /= y)
|
||
|
||
A minimal complete implementation of ``Eq`` requires either
|
||
``==`` or ``/=`` to be defined, but does not require both. If a method
|
||
definition is missing, and there is a default definition for it, then
|
||
the default is used instead.
|
||
|
||
Extending Interfaces
|
||
====================
|
||
|
||
Interfaces can also be extended. A logical next step from an equality
|
||
relation ``Eq`` is to define an ordering relation ``Ord``. We can
|
||
define an ``Ord`` interface which inherits methods from ``Eq`` as well as
|
||
defining some of its own:
|
||
|
||
.. code-block:: idris
|
||
|
||
data Ordering = LT | EQ | GT
|
||
|
||
.. code-block:: idris
|
||
|
||
interface Eq a => Ord a where
|
||
compare : a -> a -> Ordering
|
||
|
||
(<) : a -> a -> Bool
|
||
(>) : a -> a -> Bool
|
||
(<=) : a -> a -> Bool
|
||
(>=) : a -> a -> Bool
|
||
max : a -> a -> a
|
||
min : a -> a -> a
|
||
|
||
The ``Ord`` interface allows us to compare two values and determine their
|
||
ordering. Only the ``compare`` method is required; every other method
|
||
has a default definition. Using this we can write functions such as
|
||
``sort``, a function which sorts a list into increasing order,
|
||
provided that the element type of the list is in the ``Ord`` interface. We
|
||
give the constraints on the type variables left of the fat arrow
|
||
``=>``, and the function type to the right of the fat arrow:
|
||
|
||
.. code-block:: idris
|
||
|
||
sort : Ord a => List a -> List a
|
||
|
||
Functions, interfaces and implementations can have multiple
|
||
constraints. Multiple constraints are written in brackets in a comma
|
||
separated list, for example:
|
||
|
||
.. code-block:: idris
|
||
|
||
sortAndShow : (Ord a, Show a) => List a -> String
|
||
sortAndShow xs = show (sort xs)
|
||
|
||
Constraints are, like types, first class objects in the language. You can
|
||
see this at the REPL:
|
||
|
||
::
|
||
|
||
Main> :t Ord
|
||
Prelude.Ord : Type -> Type
|
||
|
||
So, ``(Ord a, Show a)`` is an ordinary pair of ``Types``, with two constraints
|
||
as the first and second element of the pair.
|
||
|
||
Note: Interfaces and ``mutual`` blocks
|
||
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||
|
||
Idris is strictly "define before use", except in ``mutual`` blocks.
|
||
In a ``mutual`` block, Idris elaborates in two passes: types on the first
|
||
pass and definitions on the second. When the mutual block contains an
|
||
interface declaration, it elaborates the interface header but none of the
|
||
method types on the first pass, and elaborates the method types and any
|
||
default definitions on the second pass.
|
||
|
||
Quantities for Parameters
|
||
=========================
|
||
|
||
By default parameters that are not explicitly ascribed a type in an ``interface``
|
||
declaration are assigned the quantity ``0``. This means that the parameter is not
|
||
available to use at runtime in the methods' definitions.
|
||
|
||
For instance, ``Show a`` gives rise to a ``0``-quantified type variable ``a`` in
|
||
the type of the ``show`` method:
|
||
|
||
::
|
||
|
||
Main> :set showimplicits
|
||
Main> :t show
|
||
Prelude.show : {0 a : Type} -> Show a => a -> String
|
||
|
||
However some use cases require that some of the parameters are available at runtime.
|
||
We may for instance want to declare an interface for ``Storable`` types. The constraint
|
||
``Storable a size`` means that we can store values of type ``a`` in a ``Buffer`` in
|
||
exactly ``size`` bytes.
|
||
|
||
If the user provides a method to read a value for such a type ``a`` at a given offset,
|
||
then we can read the ``k`` th element stored in the buffer by computing the appropriate
|
||
offset from ``k`` and ``size``. This is demonstrated by providing a default implementation
|
||
for the method ``peekElementOff`` implemented in terms of ``peekByteOff`` and the parameter
|
||
``size``.
|
||
|
||
.. code-block:: idris
|
||
|
||
data ForeignPtr : Type -> Type where
|
||
MkFP : Buffer -> ForeignPtr a
|
||
|
||
interface Storable (0 a : Type) (size : Nat) | a where
|
||
peekByteOff : HasIO io => ForeignPtr a -> Int -> io a
|
||
|
||
peekElemOff : HasIO io => ForeignPtr a -> Int -> io a
|
||
peekElemOff fp k = peekByteOff fp (k * cast size)
|
||
|
||
|
||
Note that ``a`` is explicitly marked as runtime irrelevant so that it is erased by the
|
||
compiler. Equivalently we could have written ``interface Storable a (size : Nat)``.
|
||
The meaning of ``| a`` is explained in :ref:`DeterminingParameters`.
|
||
|
||
|
||
Functors and Applicatives
|
||
=========================
|
||
|
||
So far, we have seen single parameter interfaces, where the parameter
|
||
is of type ``Type``. In general, there can be any number of parameters
|
||
(even zero), and the parameters can have *any* type. If the type
|
||
of the parameter is not ``Type``, we need to give an explicit type
|
||
declaration. For example, the ``Functor`` interface is defined in the
|
||
prelude:
|
||
|
||
.. code-block:: idris
|
||
|
||
interface Functor (0 f : Type -> Type) where
|
||
map : (m : a -> b) -> f a -> f b
|
||
|
||
|
||
A functor allows a function to be applied across a structure, for
|
||
example to apply a function to every element in a ``List``:
|
||
|
||
.. code-block:: idris
|
||
|
||
Functor List where
|
||
map f [] = []
|
||
map f (x::xs) = f x :: map f xs
|
||
|
||
::
|
||
|
||
Idris> map (*2) [1..10]
|
||
[2, 4, 6, 8, 10, 12, 14, 16, 18, 20] : List Integer
|
||
|
||
Having defined ``Functor``, we can define ``Applicative`` which
|
||
abstracts the notion of function application:
|
||
|
||
.. code-block:: idris
|
||
|
||
infixl 2 <*>
|
||
|
||
interface Functor f => Applicative (0 f : Type -> Type) where
|
||
pure : a -> f a
|
||
(<*>) : f (a -> b) -> f a -> f b
|
||
|
||
.. _monadsdo:
|
||
|
||
Monads and ``do``-notation
|
||
==========================
|
||
|
||
The ``Monad`` interface allows us to encapsulate binding and computation,
|
||
and is the basis of ``do``-notation introduced in Section
|
||
:ref:`sect-do`. It extends ``Applicative`` as defined above, and is
|
||
defined as follows:
|
||
|
||
.. code-block:: idris
|
||
|
||
interface Applicative m => Monad (m : Type -> Type) where
|
||
(>>=) : m a -> (a -> m b) -> m b
|
||
|
||
There is also a non-binding sequencing operator, defined for ``Monad`` as:
|
||
|
||
.. code-block:: idris
|
||
|
||
v >> e = v >>= \_ => e
|
||
|
||
Inside a ``do`` block, the following syntactic transformations are
|
||
applied:
|
||
|
||
- ``x <- v; e`` becomes ``v >>= (\x => e)``
|
||
|
||
- ``v; e`` becomes ``v >> e``
|
||
|
||
- ``let x = v; e`` becomes ``let x = v in e``
|
||
|
||
``IO`` has an implementation of ``Monad``, defined using primitive functions.
|
||
We can also define an implementation for ``Maybe``, as follows:
|
||
|
||
.. code-block:: idris
|
||
|
||
Monad Maybe where
|
||
Nothing >>= k = Nothing
|
||
(Just x) >>= k = k x
|
||
|
||
Using this we can, for example, define a function which adds two
|
||
``Maybe Int``, using the monad to encapsulate the error handling:
|
||
|
||
.. code-block:: idris
|
||
|
||
m_add : Maybe Int -> Maybe Int -> Maybe Int
|
||
m_add x y = do x' <- x -- Extract value from x
|
||
y' <- y -- Extract value from y
|
||
pure (x' + y') -- Add them
|
||
|
||
This function will extract the values from ``x`` and ``y``, if they are both
|
||
available, or return ``Nothing`` if one or both are not ("fail fast"). Managing
|
||
the ``Nothing`` cases is achieved by the ``>>=`` operator, hidden by the ``do``
|
||
notation.
|
||
|
||
::
|
||
|
||
Main> m_add (Just 82) (Just 22)
|
||
Just 94
|
||
Main> m_add (Just 82) Nothing
|
||
Nothing
|
||
|
||
The translation of ``do`` notation is entirely syntactic, so there is no
|
||
need for the ``(>>=)`` and ``(>>)`` operators to be the operator defined in the
|
||
``Monad`` interface. Idris will, in general, try to disambiguate which
|
||
operators you mean by type, but you can explicitly choose with qualified do
|
||
notation, for example:
|
||
|
||
.. code-block:: idris
|
||
|
||
m_add : Maybe Int -> Maybe Int -> Maybe Int
|
||
m_add x y = Prelude.do
|
||
x' <- x -- Extract value from x
|
||
y' <- y -- Extract value from y
|
||
pure (x' + y') -- Add them
|
||
|
||
The ``Prelude.do`` means that Idris will use the ``(>>=)`` and ``(>>)``
|
||
operators defined in the ``Prelude``.
|
||
|
||
Pattern Matching Bind
|
||
~~~~~~~~~~~~~~~~~~~~~
|
||
|
||
Sometimes we want to pattern match immediately on the result of a function
|
||
in ``do`` notation. For example, let's say we have a function ``readNumber``
|
||
which reads a number from the console, returning a value of the form
|
||
``Just x`` if the number is valid, or ``Nothing`` otherwise:
|
||
|
||
.. code-block:: idris
|
||
|
||
import Data.String
|
||
|
||
readNumber : IO (Maybe Nat)
|
||
readNumber = do
|
||
input <- getLine
|
||
if all isDigit (unpack input)
|
||
then pure (Just (stringToNatOrZ input))
|
||
else pure Nothing
|
||
|
||
If we then use it to write a function to read two numbers, returning
|
||
``Nothing`` if neither are valid, then we would like to pattern match
|
||
on the result of ``readNumber``:
|
||
|
||
.. code-block:: idris
|
||
|
||
readNumbers : IO (Maybe (Nat, Nat))
|
||
readNumbers =
|
||
do x <- readNumber
|
||
case x of
|
||
Nothing => pure Nothing
|
||
Just x_ok => do y <- readNumber
|
||
case y of
|
||
Nothing => pure Nothing
|
||
Just y_ok => pure (Just (x_ok, y_ok))
|
||
|
||
If there's a lot of error handling, this could get deeply nested very quickly!
|
||
So instead, we can combine the bind and the pattern match in one line. For example,
|
||
we could try pattern matching on values of the form ``Just x_ok``:
|
||
|
||
.. code-block:: idris
|
||
|
||
readNumbers : IO (Maybe (Nat, Nat))
|
||
readNumbers
|
||
= do Just x_ok <- readNumber
|
||
Just y_ok <- readNumber
|
||
pure (Just (x_ok, y_ok))
|
||
|
||
There is still a problem, however, because we've now omitted the case for
|
||
``Nothing`` so ``readNumbers`` is no longer total! We can add the ``Nothing``
|
||
case back as follows:
|
||
|
||
.. code-block:: idris
|
||
|
||
readNumbers : IO (Maybe (Nat, Nat))
|
||
readNumbers
|
||
= do Just x_ok <- readNumber
|
||
| Nothing => pure Nothing
|
||
Just y_ok <- readNumber
|
||
| Nothing => pure Nothing
|
||
pure (Just (x_ok, y_ok))
|
||
|
||
The effect of this version of ``readNumbers`` is identical to the first (in
|
||
fact, it is syntactic sugar for it and directly translated back into that form).
|
||
The first part of each statement (``Just x_ok <-`` and ``Just y_ok <-``) gives
|
||
the preferred binding - if this matches, execution will continue with the rest
|
||
of the ``do`` block. The second part gives the alternative bindings, of which
|
||
there may be more than one.
|
||
|
||
``!``-notation
|
||
~~~~~~~~~~~~~~
|
||
|
||
In many cases, using ``do``-notation can make programs unnecessarily
|
||
verbose, particularly in cases such as ``m_add`` above where the value
|
||
bound is used once, immediately. In these cases, we can use a
|
||
shorthand version, as follows:
|
||
|
||
.. code-block:: idris
|
||
|
||
m_add : Maybe Int -> Maybe Int -> Maybe Int
|
||
m_add x y = pure (!x + !y)
|
||
|
||
The notation ``!expr`` means that the expression ``expr`` should be
|
||
evaluated and then implicitly bound. Conceptually, we can think of
|
||
``!`` as being a prefix function with the following type:
|
||
|
||
.. code-block:: idris
|
||
|
||
(!) : m a -> a
|
||
|
||
Note, however, that it is not really a function, merely syntax! In
|
||
practice, a subexpression ``!expr`` will lift ``expr`` as high as
|
||
possible within its current scope, bind it to a fresh name ``x``, and
|
||
replace ``!expr`` with ``x``. Expressions are lifted depth first, left
|
||
to right. In practice, ``!``-notation allows us to program in a more
|
||
direct style, while still giving a notational clue as to which
|
||
expressions are monadic.
|
||
|
||
For example, the expression:
|
||
|
||
.. code-block:: idris
|
||
|
||
let y = 94 in f !(g !(print y) !x)
|
||
|
||
is lifted to:
|
||
|
||
.. code-block:: idris
|
||
|
||
let y = 94 in do y' <- print y
|
||
x' <- x
|
||
g' <- g y' x'
|
||
f g'
|
||
|
||
Monad comprehensions
|
||
~~~~~~~~~~~~~~~~~~~~
|
||
|
||
The list comprehension notation we saw in Section
|
||
:ref:`sect-more-expr` is more general, and applies to anything which
|
||
has an implementation of both ``Monad`` and ``Alternative``:
|
||
|
||
.. code-block:: idris
|
||
|
||
interface Applicative f => Alternative (0 f : Type -> Type) where
|
||
empty : f a
|
||
(<|>) : f a -> f a -> f a
|
||
|
||
In general, a comprehension takes the form ``[ exp | qual1, qual2, …,
|
||
qualn ]`` where ``quali`` can be one of:
|
||
|
||
- A generator ``x <- e``
|
||
|
||
- A *guard*, which is an expression of type ``Bool``
|
||
|
||
- A let binding ``let x = e``
|
||
|
||
To translate a comprehension ``[exp | qual1, qual2, …, qualn]``, first
|
||
any qualifier ``qual`` which is a *guard* is translated to ``guard
|
||
qual``, using the following function:
|
||
|
||
.. code-block:: idris
|
||
|
||
guard : Alternative f => Bool -> f ()
|
||
|
||
Then the comprehension is converted to ``do`` notation:
|
||
|
||
.. code-block:: idris
|
||
|
||
do { qual1; qual2; ...; qualn; pure exp; }
|
||
|
||
Using monad comprehensions, an alternative definition for ``m_add``
|
||
would be:
|
||
|
||
.. code-block:: idris
|
||
|
||
m_add : Maybe Int -> Maybe Int -> Maybe Int
|
||
m_add x y = [ x' + y' | x' <- x, y' <- y ]
|
||
|
||
Interfaces and IO
|
||
=================
|
||
|
||
In general, ``IO`` operations in the libraries aren't written using ``IO``
|
||
directly, but rather via the ``HasIO`` interface:
|
||
|
||
.. code-block:: idris
|
||
|
||
interface Monad io => HasIO io where
|
||
liftIO : (1 _ : IO a) -> io a
|
||
|
||
``HasIO`` explains, via ``liftIO``, how to convert a primitive ``IO`` operation
|
||
to an operation in some underlying type, as long as that type has a ``Monad``
|
||
implementation. These interface allows a programmer to define some more
|
||
expressive notion of interactive program, while still giving direct access to
|
||
``IO`` primitives.
|
||
|
||
Idiom brackets
|
||
==============
|
||
|
||
While ``do`` notation gives an alternative meaning to sequencing,
|
||
idioms give an alternative meaning to *application*. The notation and
|
||
larger example in this section is inspired by Conor McBride and Ross
|
||
Paterson’s paper “Applicative Programming with Effects” [#ConorRoss]_.
|
||
|
||
First, let us revisit ``m_add`` above. All it is really doing is
|
||
applying an operator to two values extracted from ``Maybe Int``. We
|
||
could abstract out the application:
|
||
|
||
.. code-block:: idris
|
||
|
||
m_app : Maybe (a -> b) -> Maybe a -> Maybe b
|
||
m_app (Just f) (Just a) = Just (f a)
|
||
m_app _ _ = Nothing
|
||
|
||
Using this, we can write an alternative ``m_add`` which uses this
|
||
alternative notion of function application, with explicit calls to
|
||
``m_app``:
|
||
|
||
.. code-block:: idris
|
||
|
||
m_add' : Maybe Int -> Maybe Int -> Maybe Int
|
||
m_add' x y = m_app (m_app (Just (+)) x) y
|
||
|
||
Rather than having to insert ``m_app`` everywhere there is an
|
||
application, we can use idiom brackets to do the job for us.
|
||
To do this, we can give ``Maybe`` an implementation of ``Applicative``
|
||
as follows, where ``<*>`` is defined in the same way as ``m_app``
|
||
above (this is defined in the Idris library):
|
||
|
||
.. code-block:: idris
|
||
|
||
Applicative Maybe where
|
||
pure = Just
|
||
|
||
(Just f) <*> (Just a) = Just (f a)
|
||
_ <*> _ = Nothing
|
||
|
||
Using ``<*>`` we can use this implementation as follows, where a function
|
||
application ``[| f a1 …an |]`` is translated into ``pure f <*> a1 <*>
|
||
… <*> an``:
|
||
|
||
.. code-block:: idris
|
||
|
||
m_add' : Maybe Int -> Maybe Int -> Maybe Int
|
||
m_add' x y = [| x + y |]
|
||
|
||
An error-handling interpreter
|
||
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||
|
||
Idiom notation is commonly useful when defining evaluators. McBride
|
||
and Paterson describe such an evaluator [#ConorRoss]_, for a language similar
|
||
to the following:
|
||
|
||
.. code-block:: idris
|
||
|
||
data Expr = Var String -- variables
|
||
| Val Int -- values
|
||
| Add Expr Expr -- addition
|
||
|
||
Evaluation will take place relative to a context mapping variables
|
||
(represented as ``String``\s) to ``Int`` values, and can possibly fail.
|
||
We define a data type ``Eval`` to wrap an evaluator:
|
||
|
||
.. code-block:: idris
|
||
|
||
data Eval : Type -> Type where
|
||
MkEval : (List (String, Int) -> Maybe a) -> Eval a
|
||
|
||
Wrapping the evaluator in a data type means we will be able to provide
|
||
implementations of interfaces for it later. We begin by defining a function to
|
||
retrieve values from the context during evaluation:
|
||
|
||
.. code-block:: idris
|
||
|
||
fetch : String -> Eval Int
|
||
fetch x = MkEval (\e => fetchVal e) where
|
||
fetchVal : List (String, Int) -> Maybe Int
|
||
fetchVal [] = Nothing
|
||
fetchVal ((v, val) :: xs) = if (x == v)
|
||
then (Just val)
|
||
else (fetchVal xs)
|
||
|
||
When defining an evaluator for the language, we will be applying functions in
|
||
the context of an ``Eval``, so it is natural to give ``Eval`` an implementation
|
||
of ``Applicative``. Before ``Eval`` can have an implementation of
|
||
``Applicative`` it is necessary for ``Eval`` to have an implementation of
|
||
``Functor``:
|
||
|
||
.. code-block:: idris
|
||
|
||
Functor Eval where
|
||
map f (MkEval g) = MkEval (\e => map f (g e))
|
||
|
||
Applicative Eval where
|
||
pure x = MkEval (\e => Just x)
|
||
|
||
(<*>) (MkEval f) (MkEval g) = MkEval (\x => app (f x) (g x)) where
|
||
app : Maybe (a -> b) -> Maybe a -> Maybe b
|
||
app (Just fx) (Just gx) = Just (fx gx)
|
||
app _ _ = Nothing
|
||
|
||
Evaluating an expression can now make use of the idiomatic application
|
||
to handle errors:
|
||
|
||
.. code-block:: idris
|
||
|
||
eval : Expr -> Eval Int
|
||
eval (Var x) = fetch x
|
||
eval (Val x) = [| x |]
|
||
eval (Add x y) = [| eval x + eval y |]
|
||
|
||
runEval : List (String, Int) -> Expr -> Maybe Int
|
||
runEval env e = case eval e of
|
||
MkEval envFn => envFn env
|
||
|
||
For example:
|
||
|
||
::
|
||
|
||
InterpE> runEval [("x", 10), ("y",84)] (Add (Var "x") (Var "y"))
|
||
Just 94
|
||
InterpE> runEval [("x", 10), ("y",84)] (Add (Var "x") (Var "z"))
|
||
Nothing
|
||
|
||
Named Implementations
|
||
=====================
|
||
|
||
It can be desirable to have multiple implementations of an interface for the
|
||
same type, for example to provide alternative methods for sorting or printing
|
||
values. To achieve this, implementations can be *named* as follows:
|
||
|
||
.. code-block:: idris
|
||
|
||
[myord] Ord Nat where
|
||
compare Z (S n) = GT
|
||
compare (S n) Z = LT
|
||
compare Z Z = EQ
|
||
compare (S x) (S y) = compare @{myord} x y
|
||
|
||
This declares an implementation as normal, but with an explicit name,
|
||
``myord``. The syntax ``compare @{myord}`` gives an explicit implementation to
|
||
``compare``, otherwise it would use the default implementation for ``Nat``. We
|
||
can use this, for example, to sort a list of ``Nat`` in reverse.
|
||
Given the following list:
|
||
|
||
.. code-block:: idris
|
||
|
||
testList : List Nat
|
||
testList = [3,4,1]
|
||
|
||
We can sort it using the default ``Ord`` implementation, by using the ``sort``
|
||
function available with ``import Data.List``, then we can try with the named
|
||
implementation ``myord`` as follows, at the Idris prompt:
|
||
|
||
::
|
||
|
||
Main> show (sort testList)
|
||
"[1, 3, 4]"
|
||
Main> show (sort @{myord} testList)
|
||
"[4, 3, 1]"
|
||
|
||
Sometimes, we also need access to a named parent implementation. For example,
|
||
the prelude defines the following ``Semigroup`` interface:
|
||
|
||
.. code-block:: idris
|
||
|
||
interface Semigroup ty where
|
||
(<+>) : ty -> ty -> ty
|
||
|
||
Then it defines ``Monoid``, which extends ``Semigroup`` with a “neutral”
|
||
value:
|
||
|
||
.. code-block:: idris
|
||
|
||
interface Semigroup ty => Monoid ty where
|
||
neutral : ty
|
||
|
||
We can define two different implementations of ``Semigroup`` and
|
||
``Monoid`` for ``Nat``, one based on addition and one on multiplication:
|
||
|
||
.. code-block:: idris
|
||
|
||
[PlusNatSemi] Semigroup Nat where
|
||
(<+>) x y = x + y
|
||
|
||
[MultNatSemi] Semigroup Nat where
|
||
(<+>) x y = x * y
|
||
|
||
The neutral value for addition is ``0``, but the neutral value for multiplication
|
||
is ``1``. It's important, therefore, that when we define implementations
|
||
of ``Monoid`` they extend the correct ``Semigroup`` implementation. We can
|
||
do this with a ``using`` clause in the implementation as follows:
|
||
|
||
.. code-block:: idris
|
||
|
||
[PlusNatMonoid] Monoid Nat using PlusNatSemi where
|
||
neutral = 0
|
||
|
||
[MultNatMonoid] Monoid Nat using MultNatSemi where
|
||
neutral = 1
|
||
|
||
The ``using PlusNatSemi`` clause indicates that ``PlusNatMonoid`` should
|
||
extend ``PlusNatSemi`` specifically.
|
||
|
||
.. _InterfaceConstructors:
|
||
|
||
Interface Constructors
|
||
======================
|
||
|
||
Interfaces, just like records, can be declared with a user-defined constructor.
|
||
|
||
.. code-block:: idris
|
||
|
||
interface A a where
|
||
getA : a
|
||
|
||
interface A t => B t where
|
||
constructor MkB
|
||
|
||
getB : t
|
||
|
||
Then ``MkB : A t => t -> B t``.
|
||
|
||
.. _DeterminingParameters:
|
||
|
||
Determining Parameters
|
||
======================
|
||
|
||
When an interface has more than one parameter, it can help resolution if the
|
||
parameters used to find an implementation are restricted. For example:
|
||
|
||
.. code-block:: idris
|
||
|
||
interface Monad m => MonadState s (0 m : Type -> Type) | m where
|
||
get : m s
|
||
put : s -> m ()
|
||
|
||
In this interface, only ``m`` needs to be known to find an implementation of
|
||
this interface, and ``s`` can then be determined from the implementation. This
|
||
is declared with the ``| m`` after the interface declaration. We call ``m`` a
|
||
*determining parameter* of the ``MonadState`` interface, because it is the
|
||
parameter used to find an implementation. This is similar to the concept of
|
||
*functional dependencies* `in Haskell <https://wiki.haskell.org/Functional_dependencies>`_.
|
||
|
||
.. [#ConorRoss] Conor McBride and Ross Paterson. 2008. Applicative programming
|
||
with effects. J. Funct. Program. 18, 1 (January 2008),
|
||
1-13. DOI=10.1017/S0956796807006326
|
||
https://dx.doi.org/10.1017/S0956796807006326
|