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Tilde immediately followed by a newline ignores the newline and any following non-newline whitespace[1] characters. With a :, the newline is ignored, but any following whitespace[1] is left in place. With an @, the newline is left in place, but any following whitespace[1] is ignored. For example:
(defun type-clash-error (fn nargs argnum right-type wrong-type)
(format *error-output*
"~&~S requires its ~:[~:R~;~*~]~
argument to be of type ~S,~%but it was called ~
with an argument of type ~S.~%"
fn (eql nargs 1) argnum right-type wrong-type))
(type-clash-error 'aref nil 2 'integer 'vector) prints:
AREF requires its second argument to be of type INTEGER,
but it was called with an argument of type VECTOR.
NIL
(type-clash-error 'car 1 1 'list 'short-float) prints:
CAR requires its argument to be of type LIST,
but it was called with an argument of type SHORT-FLOAT.
NIL
Note that in this example newlines appear in the output only as specified by the ~& and ~% directives; the actual newline characters in the control string are suppressed because each is preceded by a tilde.