From type/IO/Path

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method basename(IO::Path:D:)

Returns the basename part of the path object, which is the name of the filesystem object itself that is referenced by the path.

"docs/README.pod".IO.basename.say; # OUTPUT: «README.pod␤» 
"/tmp/".IO.basename.say;           # OUTPUT: «tmp␤»

Note that in IO::Spec::Win32 semantics, the basename of a Windows share is \, not the name of the share itself:

IO::Path::Win32.new('//server/share').basename.say; # OUTPUT: «\␤»

From type/IO/Spec/Win32

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method basename(Str:D $path --> Str:D)

Takes a path as a string and returns a possibly-empty portion after the last slash or backslash:

IO::Spec::Win32.basename("foo/bar/") .raku.say; # OUTPUT: «""␤» 
IO::Spec::Win32.basename("foo/bar\\").raku.say; # OUTPUT: «""␤» 
IO::Spec::Win32.basename("foo/bar/.").raku.say; # OUTPUT: «"."␤» 
IO::Spec::Win32.basename("foo/bar")  .raku.say; # OUTPUT: «"bar"␤»

From type/IO/Spec/Unix

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method basename(Str:D $path --> Str:D)

Takes a path as a string and returns a possibly-empty portion after the last slash:

IO::Spec::Unix.basename("foo/bar/") .raku.say; # OUTPUT: «""␤» 
IO::Spec::Unix.basename("foo/bar/.").raku.say; # OUTPUT: «"."␤» 
IO::Spec::Unix.basename("foo/bar")  .raku.say; # OUTPUT: «"bar"␤»