Derivations

If the LL(1) grammar has no empty derivations it is SLR(1) and if all symbols with empty derivations have non-empty derivations it is LALR(1).

Few full derivations of complex mathematical theorems from set theory have been formally verified, however, because such formal derivations are often much longer than the natural language proofs mathematicians commonly present.

Other derivations Many alternative derivations of the quadratic formula are in the literature.

Similarly, derivations in the limited systems may be longer than derivations in systems that include additional connectives.

A key property of deductive systems is that they are purely syntactic, so that derivations can be verified without considering any interpretation.

Alternate derivations of CGS units in electromagnetism Electromagnetic relationships to length, time and mass may be derived by several equally appealing methods.

Although directly based on the then-best available observational measurements, the definition was recast in terms of the then-best mathematical derivations from celestial mechanics and planetary ephemerides.

Analysis of several cases Below are three examples of increasing complexity, with derivations of the formulas governing velocity and acceleration.

A number of alternative derivations can be found in the literature.

As an example, consider the derivation of "A ⊃ (B ⊃ (A ∧ B)) true": This full derivation has no unsatisfied premises; however, sub-derivations are hypothetical.

Both the tall rectangle and circle control volumes have been used in derivations of the theorem.

Depending on the presence of empty derivations, a LL(1) grammar can be equal to a SLR(1) or a LALR(1) grammar.

Derivations and syntax trees A derivation of a string for a grammar is a sequence of grammar rule applications that transforms the start symbol into the string.

Derivations For a relatively short poem apparently dashed off quickly (and denied by its author for years), "Casey at the Bat" had a profound effect on American popular culture.

Derivations from the word vidi (to see) are vida (visual), vide (visually), and vido (vision).

Derivations Many idiomatic expressions, in their original use, were not figurative but had literal meaning.

Derivations that do not end in a string composed of terminal symbols only are possible, but don't contribute to L(G).

Einstein, "Fundamental Ideas and Methods of the Theory of Relativity", 1920 Following Einstein's original presentation of special relativity in 1905, many different sets of postulates have been proposed in various alternative derivations.

For a survey of such derivations, see Lucas and Hodgson, Spacetime and Electromagnetism, 1990 However, the most common set of postulates remains those employed by Einstein in his original paper.

Haxor and suxxor (suxorz) Haxor, and derivations thereof, is leet for "hacker", LeBlanc, 30; 32. and it is one of the most commonplace examples of the use of the -xor suffix.