Examples of ALWAYS, NEVER, and THEREIS clauses

;; Make sure I is always less than 11 (two ways).
;; The FOR construct terminates these loops.
 (loop for i from 0 to 10
       always (< i 11))
=>  T
 (loop for i from 0 to 10
       never (> i 11))
=>  T

;; If I exceeds 10 return I; otherwise, return NIL.
;; The THEREIS construct terminates this loop.
 (loop for i from 0
       thereis (when (> i 10) i) )
=>  11

;;; The FINALLY clause is not evaluated in these examples.
 (loop for i from 0 to 10
       always (< i 9)
       finally (print "you won't see this"))
=>  NIL
 (loop never t
       finally (print "you won't see this"))
=>  NIL
 (loop thereis "Here is my value"
       finally (print "you won't see this"))
=>  "Here is my value"

;; The FOR construct terminates this loop, so the FINALLY clause 
;; is evaluated.
 (loop for i from 1 to 10
       thereis (> i 11)
       finally (prin1 'got-here))
 |>  GOT-HERE
=>  NIL

;; If this code could be used to find a counterexample to Fermat's
;; last theorem, it would still not return the value of the
;; counterexample because all of the THEREIS clauses in this example
;; only return T.  But if Fermat is right, that won't matter
;; because this won't terminate.

 (loop for z upfrom 2
       thereis
         (loop for n upfrom 3 below (log z 2)
               thereis
                 (loop for x below z
                       thereis
                         (loop for y below z
                               thereis (= (+ (expt x n) (expt y n))
                                          (expt z n))))))

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