A concrete syntax tree or parse tree or parsing tree
is an ordered, rooted tree

Tree (data structure)

In computer science, a tree is a widely-used data structure that emulates a hierarchical tree structure with a set of linked nodes.Mathematically, it is an ordered directed tree, more specifically an arborescence: an acyclic connected graph where each node has zero or more children nodes and at...

 that represents the syntactic

Syntax

In linguistics, syntax is the study of the principles and rules for constructing phrases and sentences in natural languages....

 structure of a string

String (computer science)

In formal languages, which are used in mathematical logic and theoretical computer science, a string is a finite sequence of symbols that are chosen from a set or alphabet....

 according to some formal grammar

Formal grammar

A formal grammar is a set of formation rules for strings in a formal language. The rules describe how to form strings from the language's alphabet that are valid according to the language's syntax...

. In a parse tree, the interior nodes are labeled by non-terminals of the grammar, while the leaf nodes are labeled by terminals of the grammar. Parse trees may be generated for sentence

Sentence (linguistics)

In the field of linguistics, a sentence is an expression in natural language, and often defined to indicate a grammatical unit consisting of one or more words that generally bear minimal syntactic relation to the words that precede or follow it...

s in natural language

Natural language

In the philosophy of language, a natural language is any language which arises in an unpremeditated fashion as the result of the innate facility for language possessed by the human intellect. A natural language is typically used for communication, and may be spoken, signed, or written...

s (see natural language processing

Natural language processing

Natural language processing is a field of computer science and linguistics concerned with the interactions between computers and human languages; it began as a branch of artificial intelligence....

), as well as during processing

Compiler

A compiler is a computer program that transforms source code written in a programming language into another computer language...

 of computer languages, such as programming language

Programming language

A programming language is an artificial language designed to communicate instructions to a machine, particularly a computer. Programming languages can be used to create programs that control the behavior of a machine and/or to express algorithms precisely....

s.