1. [adj]  refined or imposing in manner or appearance; befitting a royal court; "a courtly gentleman"
2. [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 ball"; "the requirement was only formal and often ignored"; "a formal education"
3. [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"
4. [adj]  logically deductive; "formal proof"
5. [adj]  characteristic of or befitting a person in authority; "formal duties"; "an official banquet"
6. [adj]  (fine arts) represented in simplified or symbolic form

1. \For"mal\ (f[^o]r"mal), n. [L. formic + alcohol.] (Chem.)
   See {Methylal}.
   
   

2. \Form"al\ (f[^o]rm"al), a. [L. formalis: cf. F. formel.]
   1. Belonging to the form, shape, frame, external appearance,
      or organization of a thing.
   
   2. Belonging to the constitution of a thing, as distinguished
      from the matter composing it; having the power of making a
      thing what it is; constituent; essential; pertaining to or
      depending on the forms, so called, of the human intellect.
   
            Of [the sounds represented by] letters, the material
            part is breath and voice; the formal is constituted
            by the motion and figure of the organs of speech.
                                                  --Holder.
   
   3. Done in due form, or with solemnity; according to regular
      method; not incidental, sudden or irregular; express; as,
      he gave his formal consent.
   
            His obscure funeral . . . No noble rite nor formal
            ostentation.                          --Shak.
   
   4. Devoted to, or done in accordance with, forms or rules;
      punctilious; regular; orderly; methodical; of a prescribed
      form; exact; prim; stiff; ceremonious; as, a man formal in
      his dress, his gait, his conversation.
   
            A cold-looking, formal garden, cut into angles and
            rhomboids.                            --W. Irwing.
   
            She took off the formal cap that confined her hair.
                                                  --Hawthorne.
   
   5. Having the form or appearance without the substance or
      essence; external; as, formal duty; formal worship; formal
      courtesy, etc.
   
   6. Dependent in form; conventional.
   
            Still in constraint your suffering sex remains, Or
            bound in formal or in real chains.    --Pope.
   
   7. Sound; normal. [Obs.]
   
            To make of him a formal man again.    --Shak.
   
   {Formal cause}. See under {Cause}.
   
   Syn: Precise; punctilious; stiff; starched; affected; ritual;
        ceremonial; external; outward.
   
   Usage: {Formal}, {Ceremonious}. When applied to things, these
          words usually denote a mere accordance with the rules
          of form or ceremony; as, to make a formal call; to
          take a ceremonious leave. When applied to a person or
          his manners, they are used in a bad sense; a person
          being called formal who shapes himself too much by
          some pattern or set form, and ceremonious when he lays
          too much stress on the conventional laws of social
          intercourse. Formal manners render a man stiff or
          ridiculous; a ceremonious carriage puts a stop to the
          ease and freedom of social intercourse.
   
   

1. FORmula MAnipulation Language.

An early fortran extension for symbolic mathematics.

["FORMAL, A Formula Manipulation Language", C.K. Mesztenyi, Computer Note CN-1, CS Dept, U Maryland (Jan 1971)].

2. A data manipulation language for nonprogrammers from ibm lasc.

["FORMAL: A Forms-Oriented and Visual-Directed Application System", N.C. Shu, IEEE Computer 18(8):38-49 (1985)].