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Lisp and other S-expression-based languages do not differentiate statements from expressions, and parentheses are enough to control the scoping of all statements within the language. As in curly bracket languages, whitespace is mostly ignored by the reader (i.e., the read function). Whitespace is used to separate tokens. [5]
In mathematics, brackets of various typographical forms, such as parentheses ( ), square brackets [ ], braces { } and angle brackets , are frequently used in mathematical notation. Generally, such bracketing denotes some form of grouping: in evaluating an expression containing a bracketed sub-expression, the operators in the sub-expression take ...
In computer science, an operator-precedence parser is a bottom-up parser that interprets an operator-precedence grammar.For example, most calculators use operator-precedence parsers to convert from the human-readable infix notation relying on order of operations to a format that is optimized for evaluation such as Reverse Polish notation (RPN).
The whitespace-separated notation used in Lisp (and this article) is typical. Line breaks (newline characters) usually qualify as separators. This is a simple context-free grammar for a tiny subset of English written as an S-expression (Gazdar/Melish, Natural Language Processing in Lisp), where S=sentence, NP=Noun Phrase, VP=Verb Phrase, V=Verb:
Reverse Polish notation is parenthesis-free, which usually leads to fewer button presses needed to perform an operation. By the use of a stack, one can enter formulas without the need to rearrange operands. Hewlett-Packard's calculators are well-known examples among calculators which use RPN.
The enclosed text becomes a string literal, which Python usually ignores (except when it is the first statement in the body of a module, class or function; see docstring). Elixir. The above trick used in Python also works in Elixir, but the compiler will throw a warning if it spots this.
For example, in the expression 3(x+y) the parentheses are symbols of grouping, but in the expression (3, 5) the parentheses may indicate an open interval. The most common symbols of grouping are the parentheses and the square brackets, and the latter are usually used to avoid too many repeated parentheses.
Order of operations, uses multiple types of brackets; Set, uses braces "{}" Interval, uses square brackets and parentheses; Matrix, uses square brackets and parentheses; Inner product space, uses parentheses and chevrons