Practice Question

Duration: 4 min

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AI Summary

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This lecture demonstrates constructing a parse tree and a corresponding syntax tree for the arithmetic expression `2+3*4` using a context-free grammar with semantic translation rules. The instructor presents grammar rules defining how expressions (E), terms (T), and factors (F) are structured and how their semantic values (nptr) are computed using `mknnode`. The task is to apply these rules to the input string. The instructor systematically builds the parse tree from the root symbol 'E', expanding non-terminals until terminal symbols (identifiers) are reached. Subsequently, he translates this parse tree into a syntax tree by creating nodes for operators and operands, linking them according to the grammar's semantic actions. This process demonstrates how a compiler represents the structure of an expression for evaluation.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor introduces the problem statement: "Consider the grammar with the following translation rules and E as the start symbol." He lists production rules with semantic actions. The task is to "Construct the parse tree for the expression: 2+3*4". He begins drawing the parse tree on the whiteboard. He starts with the root 'E' and expands it using the rule `E -> E + T`. He then expands the left 'E' down to 'T', then 'F', and finally to 'id', labeling the leaf as `id(2)`. Moving to the right side of the addition, he expands 'T' using `T -> T * F`. He further expands the left 'T' to 'F' and then to `id(3)`, and the right 'F' to `id(4)`. By the end of this segment, the hierarchical structure of the parse tree is fully drawn, showing the precedence of multiplication over addition.

  2. 2:00 – 3:36 02:00-03:36

    The instructor transitions from the parse tree to constructing the syntax tree (semantic tree). He draws rectangular boxes to represent nodes. He starts at the bottom with the leaf nodes, drawing boxes for `id(2)`, `id(3)`, and `id(4)`. He then moves up to the multiplication operator. He draws a box containing `*` and connects it to the nodes for `3` and `4`, representing the rule `T -> T1 * F`. Next, he constructs the node for the addition operator `+`. He draws a box with `+` and connects its left child to the node for `2` and its right child to the previously created `*` node. This reflects the rule `E -> E1 + T`. He labels the final root node as `E.nptr`, completing the syntax tree which correctly represents the expression `2 + (3 * 4)`.

The lecture effectively demonstrates the bottom-up construction of a syntax tree from a parse tree. By starting with the grammar rules and the input expression, the instructor shows how non-terminals are expanded to terminals in the parse tree. Then, by applying the semantic actions associated with each production rule, he builds a tree of nodes where operators are internal nodes and operands are leaves. This visual progression clarifies how the abstract syntax tree captures the precedence and associativity of operators, ensuring that multiplication is evaluated before addition in the final structure.