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README
IfCxt
This package introduces the function:
ifCxt :: IfCxt cxt => proxy cxt > (cxt => a) > a > a
This function acts like an if
statement where the proxy cxt
parameter is the condition.
If the type checker can satisfy the cxt
constraint, then the second argument cxt => a
is returned;
otherwise, the third argument a
is returned.
Before seeing more details about how ifCxt
is implemented,
let's look at three examples of how to use it.
Example 1: show every type
The cxtShow
function below is polymorphic over the type a
.
If a
is an instance of Show
, then cxtShow a
evaluates to show a
;
but if a
is not an instance of Show
, cxtShow a
evaluates to <<unshowable>>
.
cxtShow :: forall a. IfCxt (Show a) => a > String
cxtShow a = ifCxt (Proxy::Proxy (Show a))
(show a)
"<<unshowable>>"
In ghci:
ghci> cxtShow (1 :: Int)
"1"
ghci> cxtShow (id :: a > a)
"<<unshowable>>"
Example 2: make your code asymptotically efficient
The nub
function removes duplicate elements from lists.
It can be defined as:
nub :: Eq a => [a] > [a]
nub [] = []
nub (x:xs) = x : nub (filter (x/=) xs)
This function takes time O(n^{2).}
But if we also have an Ord
constraint, we can define a much more efficient version that takes time O(n log n):
nubOrd :: Ord a => [a] > [a]
nubOrd = go . sort
where
go (x1:x2:xs)
 x1==x2 = go (x2:xs)
 otherwise = x1 : go (x2:xs)
go [x] = [x]
go [] = []
Now, we can use the ifCxt
function to define a version of nub
that will automatically select the most efficient implementation for whatever type we happen to run it on:
cxtNub :: forall a. (Eq a, IfCxt (Ord a)) => [a] > [a]
cxtNub = ifCxt (Proxy::Proxy (Ord a)) nubOrd nub
Example 3: make your code numerically stable
The simplest way to sum a list of numbers is:
sumSimple :: Num a => [a] > a
sumSimple = foldl' (+) 0
This method has numerical stability issues on floating point representations. Kahan summation is a more accurate technique shown below:
sumKahan :: Num a => [a] > a
sumKahan = snd . foldl' go (0,0)
where
go (c,t) i = ((t't)y,t')
where
y = ic
t' = t+y
Because Kahan summation does a lot more work than simple summation, we would prefer not to run it on nonfloating point types.
The sumCxt
function below accomplishes this:
cxtSum :: forall a. (Num a, IfCxt (Floating a)) => [a] > a
cxtSum = ifCxt (Proxy::Proxy (Floating a)) sumKahan sumSimple
Notice that the ifCxt
function is conditioning on the Floating a
constraint,
which isn't actually used by the sumKahan
function.
How it works
The magic of the technique is in the IfCxt
class:
class IfCxt (cxt :: Constraint) where
ifCxt :: proxy cxt > (cxt => a) > a > a
(Notice that making a constraint an instance of a class requires theConstraintKinds
extension,
and the higher order (cxt => a)
parameter requires the RankNTypes
extension.)
There is a "global" instance defined as:
instance {# OVERLAPPABLE #} IfCxt cxt where ifCxt _ t f = f
What this says is that if no more specific instance is available, then the "global" ifCxt
function will be used, which always returns the f
(false) parameter.
Then for every instance of every other class, we need to define an overlapping IfCxt
instance that always returns the t
(true) parameter.
For example, for Show Int
, we define:
instance {# OVERLAPS #} IfCxt (Show Int) where ifCxt _ t f = t
This is a lot of boilerplate, so the template haskell function mkIfCxtInstances
can be used to define these instances automatically.
Unfortunately, due to a bug in template haskell we cannot enumerate all the classes currently in scope.
So you must manually call mkIfCxtInstances
on each class you want ifCxt
to work with.