$LR(1)$ Parsers

In order to introduce lookahead as early as possible into the parser construction, we define the following:

An $LR(1)$ item is an $LR(0)$ item plus some lookahead symbols.

Thus an $LR(1)$ item looks like: $[A\, \rightarrow\,\alpha_1 \alpha_2 \ldots \alpha_i {}_{\triangle} \alpha_{i+1} \ldots \alpha_n,\; a]$

This means that:

• we have just recognised $\alpha_1 \alpha_2 \ldots \alpha_i$, and
• should we go on to recognise $\alpha_{i+1} \ldots \alpha_n$ (or something which corresponds to them), then we can reduce by the rule $A\, \rightarrow\, \alpha_1 \ldots \alpha_n$,
• with the understanding that, when we do, the next symbol on the input will be `a'.

[Note: Given that the next input symbol will be following $A$ in the current sentential form, we know that the lookahead symbol `a' must be in $FOLLOW(A)$.]