HANDBOOK / GENTLE PRIMER /

Describing Syntax

We have discussed rules of the form

that could be interpreted as a decomposition scheme describing how a task A can be solved: Select a suitable rule for A, and solve the subtasks B1, B2, ... , Bn. Given the interpretation this could also be read as: A proof of A can be obtained from proofs of B1 , B2 , ... , Bn.

The same kind of rules can also be used to describe formal languages by recursive definitions. In the definition of Algol 60 the following notation (known as Backus-Naur-Formalism, BNF) was used:

which states that a member of a syntactic class < A > can be composed from members of syntactic classes < B1 >, < B2 >, ..., < Bn >.