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Reduce

Reduce is a powerful way to process a collection of data into a new form.
<exp> as $<name> ireduce (<init>; <block>)
e.g.
.[] as $item ireduce (0; . + $item)
On the LHS we are configuring the collection of items that will be reduced <exp> as well as what each element will be called $<name>. Note that the array has been splatted into its individual elements.
On the RHS there is <init>, the starting value of the accumulator and <block>, the expression that will update the accumulator for each element in the collection. Note that within the block expression, . will evaluate to the current value of the accumulator.

yq vs jq syntax

Reduce syntax in yq is a little different from jq - as yq (currently) isn't as sophisticated as jq and its only supports infix notation (e.g. a + b, where the operator is in the middle of the two parameters) - where as jq uses a mix of infix notation with prefix notation (e.g. reduce a b is like writing + a b).
To that end, the reduce operator is called ireduce for backwards compatibility if a jq like prefix version of reduce is ever added.

Sum numbers

Given a sample.yml file of:
- 10
- 2
- 5
- 3
then
yq '.[] as $item ireduce (0; . + $item)' sample.yml
will output
20

Merge all yaml files together

Given a sample.yml file of:
a: cat
And another sample another.yml file of:
b: dog
then
yq eval-all '. as $item ireduce ({}; . * $item )' sample.yml another.yml
will output
a: cat
b: dog

Convert an array to an object

Given a sample.yml file of:
- name: Cathy
has: apples
- name: Bob
has: bananas
then
yq '.[] as $item ireduce ({}; .[$item | .name] = ($item | .has) )' sample.yml
will output
Cathy: apples
Bob: bananas