Grammar for Arithmetic Expressions

Question

I was assigned a task for creating a parser for Arithmetic Expressions (with parenthesis and unary operators). So I just wanna know if this grammar correct or not and is it in LL(1) form and having real problems constructing the parse table for this

S -> TS'

S' -> +TS' | -TS' | epsilon

T -> UT'

T' -> *UT' | /UT' | epsilon

U -> VX

X -> ^U | epsilon

V -> (W) | -W | W | epsilon

W -> S | number

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Precedence (high to low)

(), unary –

^

*, /

+, -

Associativity for binary operators

^ = right

+, -, *, / = left

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Answer 1

Is it in LL(1) form?

To tell if the grammar is LL(1) or not, you need to expand the production rules out. If you can generate any sequence of productions which results in the left-hand-side appearing as the first thing on the right-hand-side, the grammar is not LL(1).

For example, consider this rule:

X --> X | x | epsilon

This clearly can't be part of an LL(1) grammar, since it's left-recursive if you apply the leftmost production. But what about this?

X --> Y | x
Y --> X + X

This isn't an LL(1) grammar either, but it's more subtle: first you have to apply X --> Y, then apply Y --> X + X to see that you now have X --> X + X, which is left-recursive.

Answer 2

You seem to be missing anything for unary plus operator. Try this instead...

V -> (W) | -W | +W | epsilon