PartialFunctions

This is a small Julia package that makes partial function application as simple as possible

Usage

To apply an argument x to a function f, use the $ binary operator like so

julia> f $ x
f(x, ...)

To apply multiple arguments, wrap them in a Tuple, like you would a normal function call

julia> f $ (x, y, z)
f(x, y, z, ...)

julia> f = println $ (("This is", "a Tuple"),)
println(("This is", "a Tuple"), ...)

julia> f(", and this is an additional argument")
("This is", "a Tuple"), and this is an additional argument

You can add keyword arguments by passing a NamedTuple

julia> sort_by_length = sort $ (;by = length)
sort(...; by = length, ...)

julia> sort_by_length([[1,2,3], [1,2]])
2-element Vector{Vector{Int64}}:
 [1, 2]
 [1, 2, 3]

You can pass arguments and keyword arguments at the same time

julia> a = [[1,2,3], [1,2]];

julia> sort_a_by_length = sort $ (a, (;by = length))
sort([[1, 2, 3], [1, 2]], ...; by = length, ...)

julia> sort_a_by_length()
2-element Vector{Vector{Int64}}:
 [1, 2]
 [1, 2, 3]

You can also pass a tuple of arguments to this form, or pass the args first then the keyword args second to reduce the number of parentheses. Care must be taken here to avoid unintended results.

# These are equivalent
sort $ a $ (;by = length)
sort $ (a, (;by = length))
sort $ ((a,), (;by = length))

The following are incorrect, or will yield unintended results

julia> a = [[1,2,3], [1,2]];

julia> sort $ (a, by = length)
sort(..., a = [[1,2,3], [1,2]], by = length)

In this first case, a is parsed as a part of the NamedTuple and is thus treated as a keyword argument instead of a positional argument

julia> sort $ (a; by = length)
sort(length, ... )

In the second case, the argument to julia $ is simply a block of two expressions, the result of which is the function length.

Examples

julia> using PartialFunctions

julia> a(x) = x^2
a (generic function with 1 method)

julia> f = map $ a
map(a, ...)

julia> f([1,2,3])
3-element Vector{Int64}:
 1
 4
 9

julia> simonsays = println $ "Simon says: "
println("Simon says: ", ...)

julia> simonsays("Partial function application is cool!")
Simon says: Partial function application is cool!

Reversed functions

PartialFunctions exports the flip function, which creates a ReversedFunction object. This is a function which takes its arguments in reverse order.

The Reverse Pipe

PartialFunctions also exports the <|, or "reverse pipe" operator, which can be used to apply the arguments succeeding it to the function preceding it. This operator has low precedence, making it useful when chaining function calls if one wants to avoid a lot of parentheses

Here's an extremely contrived example to add a bunch of numbers together

julia> (+) $ 2 $ 3 $ 5 $ 10 <| 12
32

Unlike the normal pipe (|>), it can also be used with tuples of arguments

julia> (+) <| (1, 2)...
3

Passing an empty tuple calls the preceding function with zero arguments

julia> a = isequal $ (1, 2)
isequal(1, 2, ...)

julia> isequal $ (1, 2) <| ()   # equivalent to a() or isequal(1, 2)
false

The @$ Macro

@$ allows users to create general partial functions by replacing the currently unknown arguments with _. For example, we can implement matrix multiplication as:

julia> matmul(A, X, B) = A * X .+ B
matmul (generic function with 1 method)

julia> A = randn(2, 2); B = rand(2, 2); X = randn(2, 2);

julia> pf = @$ matmul(_, X, _)
matmul(_, X, _)

julia> pf(A, B) ≈ matmul(A, X, B)
true