arliss_obsidian/fp/Language/Infix Operators.md

Infix operators are symbols that alias binary (2-argument) [[Functions|functions]].

They're defined like so:
```haskell
infixl <precedence> <fn> as <operator>
-- or
infixr -- ..
```

e.g.
```haskell
eq :: Int -> Int -> Boolean
eq = -- ...

add :: Int -> Int -> Int
add = -- ...

infixl 1 add as +
infixl 1 eq as ==

(1 + 2) == 3
-- same as
eq (add 1 2) 3
```

## Associativity
Operators are either left or right associative (`infixl` or `infixr`).

When multiple infix operators with the same precedence are chained, associativity tells the language how to group them, e.g. `&&` is right-associative, while `*` is left associative.

e.g.
```haskell

a && b && c
-- interpreted as 
(a && (b && c))

a * b * c
-- interpreted as
((a * b) * c)
```

## Precedence
The precedence of operators is an int from 1-9 used as a tie-break, for example in

```haskell
a + b == c
```

this behaves how you'd expect; this is equivalent to

```haskell
((a + b) == c)
```

as the precedence of `+` (6) is higher than `==`'s (4), the grouping is first done around `a + b`.

## Common Operators
|Operator|Associativity|Precedence|Aliases|
|--|--|--|--|
|`$`||||

## Directionality
Most commonly used operators have flipped variants, e.g.
- function composition has `g <<< f` or `f >>> g`
- function application has `f $ a` or `a # f`
- [[Functor|map]] has `f <$> a` or `a <#> f`
- [[Bind|bind]] has `f =<< m` or `m >>= f`

In general, right-to-left operators tend to be easier to refactor into & out of because they closely mirror the expressions they replace:

```haskell
map (add 1) maybeNum
-- into
add 1 <$> maybeNum

foo (bar a)
-- into
foo <<< bar
```

Left-to-right, on the other hand, can read better to humans and plays better with pipelines containing both [[Bind|bind `>>=`]] and [[Functor|map `<#>`]].

Consider an expression piping `Maybe String` to `split :: String -> Array String` then `Data.Array.NonEmpty.fromArray :: Array a -> Maybe (NonEmptyArray a)`, then `toLower` each element:

```haskell
String.toLower
  <$> (
    Array.NonEmpty.fromArray
    =<< String.split "."
    <$> mStr
  )
```

We need to wrap the right hand of the last `map` because the precedence of `=<<` is `1` (the lowest) and the precedence of `<$>` is `4`.

Written RTL, though, gives:
```haskell
mStr
  <#> String.split "."
  >>= Array.NonEmpty.fromArray
  <#> String.toLower
```

This works because `<#>`'s precedence (1) is the same as `>>=`. The lower precedence on flipped map means you'll often need more parentheses wrapping its arguments `(..) <#> (..) >>= (..)` as opposed to entire expressions `.. <$> (.. =<< ..)`.

Personally, I try to stick to RTL except for expressions including bind.