Parse trees

While deriving 7+4-5, one could produce the Parse Tree shown on the right.

You can read off the productions from the tree. For any internal (i.e., non-leaf) tree node, its children give the right hand side (RHS) of a production having the node itself as the LHS.

The leaves of the tree, read from left to right, is called the yield of the tree. We call the tree a derivation of its yield from its root. The tree on the right is a derivation of 7+4-5 from list.

Ambiguity

An ambiguous grammar is one in which there are two or more parse trees yielding the same final string. We wish to avoid such grammars.

The grammar above is not ambiguous. For example 1+2+3 can be parsed only one way; the arithmetic must be done left to right. Note that I am not giving a rule of arithmetic, just of this grammar. If you reduced 2+3 to list you would be stuck since it is impossible to further reduce 1+list (said another way it is not possible to derive 1+list from the start symbol).