# Reductions

In Tomo, reductions are a way to express the idea of folding or reducing a
collection of values down to a single value. Reductions use a parenthesized
infix operator followed by a colon, followed by a collection:

```tomo
nums := [10, 20, 30]
sum := (+: nums)
>> sum
= 60 : Int?
```

Reductions return an optional value which will be a null value if the thing
being iterated over has no values. In such cases, the reduction is undefined.
As with all optionals, you can use either the postfix `!` operator to perform
a runtime check and error if there's a null value, or you can use `or` to
provide a fallback value:

```tomo
nums := [:Int]
sum := (+: nums)

>> sum
= none : Int?

>> sum or 0
= 0

>> nums = [10, 20]
>> (+: nums)!
= 30
```

Reductions can be used as an alternative to generic functions like `sum()`,
`product()`, `any()`, and `all()` in Python, or higher-order functions like
`foldl` and `foldr` in functional programming:

```tomo
# Sum:
>> (+: [10, 20, 30])!
= 60

# Product:
>> (*: [2, 3, 4])!
= 24

# Any:
>> (or: [no, yes, no])!
= yes

# All:
>> (and: [no, yes, no])!
= no
```

## Minimum and Maximum

Reductions are _especially_ useful for finding the minimum or maximum values in
a collection using the `_min_` and `_max_` infix operators.

```tomo
# Get the maximum value:
>> (_max_: [10, 30, 20])!
= 30

# Get the minimum value:
>> (_min_: [10, 30, 20])!
= 10
```

The `_min_` and `_max_` operators also support field and method call suffixes,
which makes it very easy to compute the argmin/argmax (or keyed
minimum/maximum) of a collection. This is when you want to get the minimum or
maximum value _according to some feature_.

```tomo
# Get the longest text:
>> (_max_.length: ["z", "aaaaa", "mmm"])!
= "aaaaa"

# Get the number with the biggest absolute value:
>> (_max_:abs(): [1, -2, 3, -4])!
= -4
```

## Comprehensions

Reductions work not only with iterable values (arrays, sets, integers, etc.),
but also with comprehensions. You can use comprehensions to perform reductions
while filtering out values or while applying a transformation:

```tomo
# Sum the lengths of these texts:
>> (+: t.length for t in ["a", "bc", "def"])!
= 6

# Sum the primes between 1-100:
>> (+: i for i in 100 if i:is_prime())!
= 1060
```
