nLab language

Idea

A formal language is a collection of words over an alphabet, i.e. strings of symbols from the alphabet, according to certain rules.

Related concepts

• object language

• metalanguage

• syntax, theory

• mathematical linguistics

• linguistics

mathematical statements

• theory

• judgement, assertion

• hypothesis, consequence

• axiom

• assignment

• definition (inductive, coinductive)

• lemma

• proposition/type (propositions as types)

• theorem

• proof/program (proofs as programs)

• example, counterexample

• conjecture, folklore

• exercise

• analogy

• tautology

• paradox

References

• Joachim Lambek (with Michael Barr), Programs, Grammars, Arguments, lecture notes (2007) [pdf, pdf]

See also:

• Wikipedia, Formal language