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;; Ask ryli13 if confused about this file.
;; Define and dump a protocol to demonstrate knowledge of factoring 8616460799 = 89681 x 96079

;; Making sure code works
!(def and (lambda (x y) (if x (if y t nil) nil)))
!(def a 89681)
!(def b 96079)
!(def comm_a_real (hide #0x8239548349 a))
!(def comm_b_real (hide #0x3895383045 b))
(let ((open_a (open comm_a_real))
    (open_b (open comm_b_real)))
    (and (and (and (< 1 open_a) (< open_a 8616460799))
            (and (< 1 open_b) (< open_b 8616460799)))
        (eq 8616460799 (* open_a open_b))
    )
)

;; Defining the actual protocol
!(defprotocol factors_found (comm_a comm_b)
    (cons
        ;; claim definition
        (cons (cons 
                ;; expression
                ;; needs to be a quoted syntax tree
                (list 'let 
                    (
                        list (list 'open_a (list 'open comm_a))
                        (list 'open_b (list 'open comm_b))
                        (list 'and (list 'lambda (list 'x 'y) (list 'if 'x (list 'if 'y t nil) nil)))
                    )
                    (list 'and 
                        (list 'and 
                            (list 'and
                                (list '< 1 'open_a)
                                (list '< 'open_a 8616460799))
                            (list 'and
                                (list '< 1 'open_b)
                                (list '< 'open_b 8616460799))) 
                        (list 'eq 8616460799 (list '* 'open_a 'open_b))
                    )
                )
                ;; environment 
                (empty-env)
            )
            ;; expected output
            t )
        ;; post-verification predicate
        nil)
:description "proof that one knows two non-one factors that multiply to 8616460799")

!(dump-expr factors_found "factors-8616460799")

(eval (list 'eq (list 'open 'comm_a) 89681) (let ((comm_a comm_a_real)) (current-env)))

(eval 
    (emit 
    (list 'let 
        (
            list (list 'open_a (list 'open comm_a_real))
            (list 'open_b (list 'open comm_b_real))
            (list 'and (list 'lambda (list 'x 'y) (list 'if 'x (list 'if 'y t nil) nil)))
        )
        (list 'and 
            (list 'and 
                (list 'and
                    (list '< 1 'open_a)
                    (list '< 'open_a 8616460799))
                (list 'and
                    (list '< 1 'open_b)
                    (list '< 'open_b 8616460799))) 
            (list 'eq 8616460799 (list '* 'open_a 'open_b))
        )
    )
) (empty-env))