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