What is the definition of "parse/parse out"?

What is the underlying theme amongst the four definitions I've listed below? What is the distinction between the four definitions?

parse
verb https://dictionary.cambridge.org/help/codes.html

LANGUAGE specialized

definition 1: to https://dictionary.cambridge.org/dictionary/english/separate a https://dictionary.cambridge.org/dictionary/english/sentence into https://dictionary.cambridge.org/dictionary/english/grammatical https://dictionary.cambridge.org/dictionary/english/part, such as https://dictionary.cambridge.org/dictionary/english/subject, https://dictionary.cambridge.org/dictionary/english/verb, etc.:

example: These https://dictionary.cambridge.org/dictionary/english/day, https://dictionary.cambridge.org/dictionary/english/children aren't https://dictionary.cambridge.org/dictionary/english/taught how to parse a https://dictionary.cambridge.org/dictionary/english/sentence.

COMPUTING specialized
definition 2: to https://dictionary.cambridge.org/dictionary/english/examine https://dictionary.cambridge.org/dictionary/english/computer https://dictionary.cambridge.org/dictionary/english/data and https://dictionary.cambridge.org/dictionary/english/change it into a https://dictionary.cambridge.org/dictionary/english/form that can be https://dictionary.cambridge.org/dictionary/english/easily https://dictionary.cambridge.org/dictionary/english/read or https://dictionary.cambridge.org/dictionary/english/understood :

example: Before https://dictionary.cambridge.org/dictionary/english/version 3.0, a https://dictionary.cambridge.org/dictionary/english/stream was https://dictionary.cambridge.org/dictionary/english/converted to a https://dictionary.cambridge.org/dictionary/english/string before being parsed.

definition 3: to https://dictionary.cambridge.org/dictionary/english/examine or https://dictionary.cambridge.org/dictionary/english/think about something https://dictionary.cambridge.org/dictionary/english/carefully in https://dictionary.cambridge.org/dictionary/english/order to https://dictionary.cambridge.org/dictionary/english/understand it:

example: We parse every https://dictionary.cambridge.org/dictionary/english/moment for https://dictionary.cambridge.org/dictionary/english/clue to why he took his https://dictionary.cambridge.org/dictionary/english/life.

Example 2: The https://dictionary.cambridge.org/dictionary/english/economist parses the https://dictionary.cambridge.org/dictionary/english/role of https://dictionary.cambridge.org/dictionary/english/emotion, https://dictionary.cambridge.org/dictionary/english/cognition, and https://dictionary.cambridge.org/dictionary/english/perception in the https://dictionary.cambridge.org/dictionary/english/understanding of https://dictionary.cambridge.org/dictionary/english/business https://dictionary.cambridge.org/dictionary/english/risk.
to https://dictionary.cambridge.org/dictionary/english/understand something:

Example 3: Some https://dictionary.cambridge.org/dictionary/english/people https://dictionary.cambridge.org/dictionary/english/know they're https://dictionary.cambridge.org/dictionary/english/gay from an early https://dictionary.cambridge.org/dictionary/english/age, but https://dictionary.cambridge.org/dictionary/english/others don't parse it until much https://dictionary.cambridge.org/dictionary/english/later.
For those https://dictionary.cambridge.org/dictionary/english/trying to parse what he https://dictionary.cambridge.org/dictionary/english/think about the https://dictionary.cambridge.org/dictionary/english/proposed https://dictionary.cambridge.org/dictionary/english/change, today's https://dictionary.cambridge.org/dictionary/english/hearing was hard going.