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Round brackets or parentheses are used in APL expressions to control the order of execution. They are also used in function/operator headers to indicate Namelists. A right parenthesis is also used to introduce a System Command.
Square brackets have three distinct meanings in Dyalog APL. They are used to select sub-arrays from an n-dimensional array and to indicate an axis along which a function (operand) is to apply. See Bracket Indexing and Bracket Axis Operator. A right bracket is also used to introduce a User Command.
Curly brackets have three distinct meanings in Dyalog APL. They are used to indicate shy results and optional left arguments in defined functions. They are also used to enclose the definition of a dfn and a dop. See Model Syntax and Dfns & Dops.