Languages don't need built-in conditionals! Bah!

booldef.rkt

(define True (λ () (λ (a b) (a))))
(define False (λ () (λ (a b) (b))))

boolhelper.rkt

(define-syntax-rule (displayln str)
  (display (format
            (string-append str "~n"))))

(define (show-bool b)
  (b (λ () (displayln "True"))
     (λ () (displayln "False"))))

(show-bool (True))
; "True"

(show-bool (False))
; "False"

boolif.rkt

(define-syntax-rule (if/g condition then else)
  (let ((then-f (λ () then))
        (else-f (λ () else)))
    (condition then-f else-f)))

(if/g (True)
      (displayln "Condition was true")
      (displayln "Condition was false"))

; "Condition was true"

(if/g (False)
      (displayln "Condition was true")
      (displayln "Condition was false"))

; "Condition was false

boolops.rkt

(define (and/g p q)
  (p
   (q (λ () True)
      (λ () False))
   (q (λ () False)
      (λ () False))))

(define (or/g p q)
  (p
   (q (λ () True)
      (λ () True))
   (q (λ () True)
      (λ () False))))

(define (not/g b)
  (b False
     True))

boolopsshort.rkt

(define (and/s p q)
  (p (λ() q)
     (λ() p)))

(define (or/s p q)
  (p (λ () p)
     (λ () q)))

(define (not/s b)
  (b False
     True))

(show-bool (and/s (True) (False)))
(show-bool (and/s (False) (True)))
(show-bool (and/s (True) (True)))
(show-bool (or/s (False) (True)))
(show-bool (or/s (True) (False)))
(show-bool (or/s (False) (False)))
(show-bool (not/s (and/s (False) (True))))