Jq strange behavior of pipe involving variable on the left hand side

Contrary to what the examples in the Scoping section assume, . * 4 as $times_four | . is equivalent to . * ( 4 as $times_four | . ) and therefore squares its input.

You might expect

. * 4 as $times_four | .

to be equivalent to

( . * 4 ) as $times_four | .

And as you point out, some example even suggest this is the case. However, the first snippet is actually equivalent to the following:

. * ( 4 as $times_four | . )

And since … as $x produces its context^[1], that's the same as

. * ( . | . )

or

. * .

jq's operator precedence is inconsistent and/or quirky.

"def" | "abc" + "def" | length means
"def" | ( "abc" + "def" ) | length, but
"def" | "abc" + "def" as $x | length means
"def" | "abc" + ( "def" as $x | length ).

This behaviour suggests that that as isn't a binary operator of the form X as $Y as one might expect, but a ternary operator of the form X as $Y | Z.

And, in fact, this is how it's documented:

Variable / Symbolic Binding Operator: ... as $identifier | ...

This leads to surprises, especially since it binds a lot more tightly than expected. And it looks like whomever authored the examples in the Scoping section fell into the trap.

1. It might produce it multiple times e.g. .[] as $x.

Indeed, there seems to be a mistake in the manual. In section Scoping it is contrasting the (faulty) examples

... | .*3 as $times_three | [. + $times_three] | ...         # faulty!

and

... | (.*3 as $times_three | [. + $times_three]) | ...       # faulty!

While the overall statement stays valid, both examples are missing additional parentheses around .*3. Thus, it should actually read

... | (.*3) as $times_three | [. + $times_three] | ...

and

... | ((.*3) as $times_three | [. + $times_three]) | ...

respectively.

From the manual under section Variable / Symbolic Binding Operator:

The expression exp as $x | ... means: for each value of expression exp, run the rest of the pipeline with the entire original input, and with $x set to that value. Thus as functions as something of a foreach loop.

This means that a variable assignment takes the one expression left of as and assigns its evaluation to the defined variable right of as (and this happens as many times as exp produces an output). But, as everything in jq is a filter, the assignment itself also is, and as such it needs to have an output itself. If you look closely, the full title of that section

Variable / Symbolic Binding Operator: ... as $identifier | ...

also features a pipe symbol next to it, which indicates that it belongs to the assignment's structure. Try just running . as $x. You will get an error because the | ... part is missing. Thus, to simply keep the input context as is (apart from maybe duplicating it as many times as the expression left of as produced an output), a complete assignment would rather look like … as $x | ., or, if the input context is what you wanted to capture in the variable, . as $x | .

That said, let's clarify what happens with your examples by putting explicit parentheses around the assignments:

3 | . * 3 as $times_three | .
3 | . * (3 as $times_three | .)
3 | . * .                           # with $times_three set to 3
3 * 3                               # with $times_three set to 3
9                                   # with $times_three set to 3

3 | . * 4 as $times_four | .
3 | . * (4 as $times_four | .)
3 | . * .                           # with $times_four set to 4
3 * 3                               # with $times_four set to 4
9                                   # with $times_four set to 4

3 | (. * 3) as $times_three | .
3 | ((. * 3) as $times_three | .)
3 | ((3 * 3) as $times_three | .)
3 | (9 as $times_three | .)
3 | .                               # with $times_three set to 9
3                                   # with $times_three set to 9

3 | (. * 4) as $times_four | .
3 | ((. * 4) as $times_four | .)
3 | ((3 * 4) as $times_four | .)
3 | (12 as $times_four | .)
3 | .                               # with $times_four set to 12
3                                   # with $times_four set to 12