Flow

Flow provides operators for writing more understandable Haskell. It is an alternative to some common idioms like ($) for function application and (.) for function composition.

Flow is designed to be imported unqualified. It does not export anything that conflicts with the base package.

>>> import Flow

Rationale

I think that Haskell can be hard to read. It has two operators for applying functions. Both are not really necessary and only serve to reduce parentheses. But they make code hard to read. People who do not already know Haskell have no chance of guessing what foo $ bar or baz & qux mean.

Those that do know Haskell are forced to read lines forwards and backwards at the same time, thanks to function composition. Even something simple, like finding the minimum element, bounces around: f = head . sort.

I think we can do better. By using directional operators, we can allow readers to move their eye in only one direction, be that left-to-right or right-to-left. And by using idioms common in other programming languages, we can allow people who aren't familiar with Haskell to guess at the meaning.

So instead of ($), I propose (<|). It is a pipe, which anyone who has touched a Unix system should be familiar with. And it points in the direction it sends arguments along. Similarly, replace (&) with (|>). And for composition, (<.) replaces (.). I would have preferred <<, but its counterpart >> is taken by Haskell's syntax. So-called "backwards" composition is normally expressed with (>>>), which Flow provides as (.>).

Function application

(|>) :: a -> (a -> b) -> b infixl 0

Left-associative apply operator. Read as "apply forward" or "pipe into". Use this to create long chains of computation that suggest which direction things move in.

>>> 3 |> succ |> recip |> negate
-0.25

Or use it anywhere you would use (&).

\ x -> (x |> f) == f x

\ x -> (x |> f |> g) == g (f x)

(<|) :: (a -> b) -> a -> b infixr 0

Right-associative apply operator. Read as "apply backward" or "pipe from". Use this to create long chains of computation that suggest which direction things move in. You may prefer this operator over (|>) for IO actions since it puts the last function first.

>>> print <| negate <| recip <| succ <| 3
-0.25

Or use it anywhere you would use ($).

Note that (<|) and (|>) have the same precedence, so they cannot be used together.

>>> -- This doesn't work!
>>> -- print <| 3 |> succ |> recip |> negate

\ x -> (f <| x) == f x

\ x -> (g <| f <| x) == g (f x)

apply :: a -> (a -> b) -> b

Function application. This function usually isn't necessary, but it can be more readable than some alternatives when used with higher-order functions like map.

>>> map (apply 2) [succ, recip, negate]
[3.0,0.5,-2.0]

In general you should prefer using an explicit lambda or operator section.

>>> map (\ f -> 2 |> f) [succ, recip, negate]
[3.0,0.5,-2.0]
>>> map (2 |>) [succ, recip, negate]
[3.0,0.5,-2.0]
>>> map (<| 2) [succ, recip, negate]
[3.0,0.5,-2.0]

\ x -> apply x f == f x

Function composition

(.>) :: (a -> b) -> (b -> c) -> a -> c infixl 9

Left-associative compose operator. Read as "compose forward" or "and then". Use this to create long chains of computation that suggest which direction things move in.

>>> let f = succ .> recip .> negate
>>> f 3
-0.25

Or use it anywhere you would use (>>>).

\ x -> (f .> g) x == g (f x)

\ x -> (f .> g .> h) x == h (g (f x))

(<.) :: (b -> c) -> (a -> b) -> a -> c infixr 9

Right-associative compose operator. Read as "compose backward" or "but first". Use this to create long chains of computation that suggest which direction things move in. You may prefer this operator over (.>) for IO actions since it puts the last function first.

>>> let f = print <. negate <. recip <. succ
>>> f 3
-0.25

Or use it anywhere you would use (.).

Note that (<.) and (.>) have the same precedence, so they cannot be used together.

>>> -- This doesn't work!
>>> -- print <. succ .> recip .> negate

\ x -> (g <. f) x == g (f x)

\ x -> (h <. g <. f) x == h (g (f x))

compose :: (a -> b) -> (b -> c) -> a -> c

Function composition. This function usually isn't necessary, but it can be more readable than some alternatives when used with higher-order functions like map.

>>> let fs = map (compose succ) [recip, negate]
>>> map (apply 3) fs
[0.25,-4.0]

In general you should prefer using an explicit lambda or operator section.

>>> map (\ f -> f 3) (map (\ f -> succ .> f) [recip, negate])
[0.25,-4.0]
>>> map (\ f -> f 3) (map (succ .>) [recip, negate])
[0.25,-4.0]
>>> map (\ f -> f 3) (map (<. succ) [recip, negate])
[0.25,-4.0]

\ x -> compose f g x == g (f x)

Strict function application

(!>) :: a -> (a -> b) -> b infixl 0

Left-associative apply' operator. Read as "strict apply forward" or "strict pipe info". Use this to create long chains of computation that suggest which direction things move in.

>>> 3 !> succ !> recip !> negate
-0.25

The difference between this and (|>) is that this evaluates its argument before passing it to the function.

>>> undefined |> const True
True
>>> undefined !> const True
*** Exception: Prelude.undefined
...

\ x -> (x !> f) == seq x (f x)

\ x -> (x !> f !> g) == let y = seq x (f x) in seq y (g y)

(<!) :: (a -> b) -> a -> b infixr 0

Right-associative apply' operator. Read as "strict apply backward" or "strict pipe from". Use this to create long chains of computation that suggest which direction things move in. You may prefer this operator over (!>) for IO actions since it puts the last function first.

>>> print <! negate <! recip <! succ <! 3
-0.25

The difference between this and (<|) is that this evaluates its argument before passing it to the function.

>>> const True <| undefined
True
>>> const True <! undefined
*** Exception: Prelude.undefined
...

Note that (<!) and (!>) have the same precedence, so they cannot be used together.

>>> -- This doesn't work!
>>> -- print <! 3 !> succ !> recip !> negate

\ x -> (f <! x) == seq x (f x)

\ x -> (g <! f <! x) == let y = seq x (f x) in seq y (g y)

apply' :: a -> (a -> b) -> b

Strict function application. This function usually isn't necessary, but it can be more readable than some alternatives when used with higher-order functions like map.

>>> map (apply' 2) [succ, recip, negate]
[3.0,0.5,-2.0]

The different between this and apply is that this evaluates its argument before passing it to the function.

>>> apply undefined (const True)
True
>>> apply' undefined (const True)
*** Exception: Prelude.undefined
...

In general you should prefer using an explicit lambda or operator section.

>>> map (\ f -> 2 !> f) [succ, recip, negate]
[3.0,0.5,-2.0]
>>> map (2 !>) [succ, recip, negate]
[3.0,0.5,-2.0]
>>> map (<! 2) [succ, recip, negate]
[3.0,0.5,-2.0]

\ x -> apply' x f == seq x (f x)