<!DOCTYPE
HTML PUBLIC "-//IETF//DTD HTML 2.0//EN"><!--Converted with
LaTeX2HTML 96.1-beta (Jan 15, 1996) by Nikos Drakos (nikos@cbl.leeds.ac.uk),
CBLU, University of Leeds -->Homework 1
- Write a grammar using the BNF meta-language for
four-function calculator 'programs' using the calculator pictured below.
Each 'program' consists of pressing the ON button, followed by any number
of calculations followed by pressing the OFF button. Your grammar should
only include meaningful programs that produce useful results (any sequence
of button pushes is allowed, but not all these sequences produce
meaningful results). In particular, notice that parentheses must be
matched for a result to be produced. Use the normal notion of
parenthesized infix expressions to guide your grammar. The +/- button
changes the sign of the previous operand. The following sequences are
valid programs:
·
ON 1 ´ ( 2 + 3 ) = 5 .1 1 1 1 1 ¸ 7 . 1 2 3 4 5 +/- + 1 2 3
4 . 5 6 7 8 = ( 3 2 - 5 6 +/- ) - ( 8 9 +/- 2 4 ) = OFF
·
ON OFF
·
ON 1 2 3 4 5 6 = OFF
·
ON ( ( ( 3 + 2 ) ´ ( 4 +/- - 5 ) ) ¸ 2 2
) + 1 5 = OFF
- Draw the syntax tree for the last example above to
demonstrate that your grammar works.
- Rewrite your BNF grammar in EBNF form aiming to
remove as much recursion as possible from the BNF form.
- Redraw your EBNF grammar in syntax diagram form.
|
|
OFF
|
ON
|
|
|
7
|
8
|
9
|
(
|
+
|
|
4
|
5
|
6
|
)
|
-
|
|
1
|
2
|
3
|
|
´
|
|
0
|
.
|
+/-
|
=
|
¸
|
Assignment due: Friday, February 9th., in class.