Logic Writing Style: the Incongruousness of the Word “Actually”

Here's the inline doc of “assoc” from GNU Emacs 24.3.1:

assoc is a built-in function in `C source code'.

(assoc KEY LIST)

Return non-nil if KEY is `equal' to the car of an element of LIST. The value is actually the first element of LIST whose car equals KEY.

note the word “actually”.

the word “actually” is often used for emphasis purposes. It means “in fact”. It came from “actual” + “ly”.

etymology of actually

early 15c., “in fact, in reality” (as opposed to in possibility), from actual + -ly (2). Meaning “actively, vigorously” is from mid-15c.; that of “at this time, at present” is from 1660s. As an intensive added to a statement and suggesting “as a matter of fact, really, in truth” it is attested from 1762.

[etymology of actually https://www.etymonline.com/word/actually]

when writing in a logical style, the use of “actually” is a oddity, incongruous, or redundant.