Editing Polish notation (section)

{{Short description|Mathematics notation with operators preceding operands}}
{{About|a prefix notation in mathematics and computer sciences|the similarly named logic|Łukasiewicz logic}}
{{Use dmy dates|date=May 2019|cs1-dates=y}}
{{Use list-defined references|date=July 2022}}
{{Operator notation sidebar |logo=[[File:Prefix-dia.svg|125px]]}}

'''Polish notation''' ('''PN'''), also known as '''normal Polish notation''' ('''NPN'''),<ref name="Jorke_1989"/> '''Łukasiewicz notation''', '''Warsaw notation''', '''Polish prefix notation''', '''Eastern Notation''' or simply '''prefix notation''', is a mathematical notation in which [[Operation (mathematics)|operators]] ''precede'' their [[operand]]s, in contrast to the more common [[infix notation]], in which operators are placed ''between'' operands, as well as [[reverse Polish notation]] (RPN), in which operators ''follow'' their operands. It does not need any parentheses as long as each operator has a fixed [[arity|number of operands]]. The description "Polish" refers to the [[nationality]] of [[logician]] [[Jan Łukasiewicz]],<ref name="Łukasiewicz_1929"/>{{rp|page=24}}<ref name="Łukasiewicz_1957"/>{{rp|page=78}}<ref name="Kennedy_1982"/> who invented Polish notation in 1924.<ref name="Łukasiewicz_1931"/>{{rp|page=367, Footnote 3}}<ref name="Łukasiewicz_1970"/>{{rp|page=180, Footnote 3}}

The term ''Polish notation'' is sometimes taken (as the opposite of ''infix notation'') to also include reverse Polish notation.<ref name="Main_2006"/>

When Polish notation is used as a syntax for mathematical expressions by [[programming language]] [[Interpreter (computing)|interpreter]]s, it is readily parsed into [[abstract syntax tree]]s and can, in fact, define a [[Bijection|one-to-one representation]] for the same. Because of this, [[Lisp (programming language)|Lisp]] ([[#Implementations|see below]]) and related programming languages define their entire syntax in prefix notation (and others use postfix notation).