ParseTree

A parse tree, also called a parsetree, is a tree data structure that represents the syntactic structure of a sequence of tokens according to a formal grammar. The root is the start symbol, internal nodes are nonterminal symbols, and the leaves are terminal symbols or tokens. The tree encodes how the input can be derived step by step by applying the grammar’s productions.

In computing, a parse tree is produced by a parser during the syntax analysis phase. It provides a complete record of which productions were used to derive the input and is used to check that the input conforms to the grammar. The parse tree can serve as input to later stages such as semantic analysis, optimization, or code generation.

Parse trees are distinct from abstract syntax trees (ASTs). A parse tree preserves all details of the grammar, including punctuation and intermediate nonterminals, whereas an AST abstracts away much of this structure to focus on the program’s essential semantics. For grammars that are ambiguous, a given input may yield more than one parse tree, producing a set of parse trees known as a parse forest.

Constructing a parse tree depends on the parsing strategy, such as top-down parsers (LL) or bottom-up parsers (LR, LALR). The produced tree’s size is proportional to the input length, and its correctness depends on the grammar being applicable to the input.

Applications include compilers, interpreters, language tooling, static analysis, and data transformation. For example, in an expression grammar, the parse tree for an input like a + b * c reflects the precedence encoded by the grammar, guiding subsequent evaluation or translation.