Etymology
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formal (adj.)

late 14c., "pertaining to form or arrangement;" also, in philosophy and theology, "pertaining to the form or essence of a thing," from Old French formal, formel "formal, constituent" (13c.) and directly from Latin formalis, from forma "a form, figure, shape" (see form (n.)). From early 15c. as "in due or proper form, according to recognized form," As a noun, c. 1600 (plural) "things that are formal;" as a short way to say formal dance, recorded by 1906 among U.S. college students.

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Definitions of formal
1
formal (adj.)
being in accord with established forms and conventions and requirements (as e.g. of formal dress);
pay one's formal respects
formal dress
a formal education
a formal ball
the requirement was only formal and often ignored
formal (adj.)
characteristic of or befitting a person in authority;
formal duties
formal (adj.)
(of spoken and written language) adhering to traditional standards of correctness and without casual, contracted, and colloquial forms;
the paper was written in formal English
formal (adj.)
represented in simplified or symbolic form;
Synonyms: conventional / schematic
formal (adj.)
logically deductive;
formal proof
formal (adj.)
refined or imposing in manner or appearance; befitting a royal court;
Synonyms: courtly / stately
2
formal (n.)
a lavish dance requiring formal attire;
Synonyms: ball
formal (n.)
a gown for evening wear;
Synonyms: dinner dress / dinner gown / evening gown
From wordnet.princeton.edu