Examples
The following rules describe a formal language L over the alphabet Σ = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, +, = }:
- Every nonempty string that does not contain "+" or "=" and does not start with "0" is in L.
- The string "0" is in L.
- A string containing "=" is in L if and only if there is exactly one "=", and it separates two valid strings of L.
- A string containing "+" but not "=" is in L if and only if every "+" in the string separates two valid strings of L.
- No string is in L other than those implied by the previous rules.
Under these rules, the string "23+4=555" is in L, but the string "=234=+" is not. This formal language expresses natural numbers, well-formed addition statements, and well-formed addition equalities, but it expresses only what they look like (their syntax), not what they mean (semantics). For instance, nowhere in these rules is there any indication that "0" means the number zero, or that "+" means addition.
Read more about this topic: Formal Language
Famous quotes containing the word examples:
“There are many examples of women that have excelled in learning, and even in war, but this is no reason we should bring ‘em all up to Latin and Greek or else military discipline, instead of needle-work and housewifry.”
—Bernard Mandeville (1670–1733)
“Histories are more full of examples of the fidelity of dogs than of friends.”
—Alexander Pope (1688–1744)
“In the examples that I here bring in of what I have [read], heard, done or said, I have refrained from daring to alter even the smallest and most indifferent circumstances. My conscience falsifies not an iota; for my knowledge I cannot answer.”
—Michel de Montaigne (1533–1592)