Induction is bottom-up.
Recursion is top-down.
In parsing, YACC is bottom-up, PEG[1] is top-down.
YACC is LR(k), PEG is recursive-descent.
YACC is context-free, PEG can depend on context.
LR(k) is theoretical, PEG is practical.
Semi-colons exist in PL[2]s because of YACC. PEG doesn't require semi-colons in PLs.
Possible rewording: top-down is operational, whereas bottom-up is declarative[3].
Top-down implies the use of a Stack[4]. Bottom-up does not.
[Use of a Stack defies parallelism.]
"Context free" means that time[5] has been removed, there is no f(t).[6]
[1] PEG means Parsing Expression Grammar, see https://bford.info/packrat/. PEG is like REGEXPs on steroids.
[2] PL means Programming Language.
[3] Question to self: Is this a correct characterization?
[4] A stack of breadcrumbs - to "remember" where you were.
[5] Time is also known as History. History is also known as State.
[6] Lack of f(t) has been decried by Ilya Prigogene (Nobel laureate, "Order Out of Chaos") and Grace Hopper.