Parse tree

• It shows how the start symbol of a grammar derives a string in the language
• root is labeled by the start symbol
• leaf nodes are labeled by tokens
• Each internal node is labeled by a non terminal
• if A is a non-terminal labeling an internal node and x₁ , x₂ , .x_n are labels of the children of that node then A x₁ x₂ . x_n is a production

A parse tree may be viewed as a graphical representation for a derivation that filters out the choice regarding replacement order. Thus, a parse tree pictorially shows how the start symbol of a grammar derives a string in the language. Each interior node of a parse tree is labeled by some non-terminal A , and that the children of the node are labeled, from left to right, by the symbols in the right side of the production by which this A was replaced in the derivation. The root of the parse tree is labeled by the start symbol and the leaves by non-terminals or terminals and, read from left to right, they constitute a sentential form, called the yield or frontier of the tree. So, if A is a non-terminal labeling an internal node and x₁ , x₂ , .x_n are labels of children of that node then A x₁ x₂ . x_n is a production. We will consider an example in the next slide.