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prover.A.scm
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prover.A.scm
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(load "prover-load-j-bob.scm")
(jbob.step (prelude)
'(car (cons 'ham '(cheese)))
'())
(jbob.step (prelude)
'(car (cons 'ham '(cheese)))
'((() (car/cons 'ham '(cheese)))))
(jbob.step (prelude)
'(equal 'flapjack (atom (cons a b)))
'(((2) (atom/cons a b))
(() (equal 'flapjack 'nil))))
(jbob.step (prelude)
'(atom (cdr (cons (car (cons p q)) '())))
'(((1 1 1) (car/cons p q))
((1) (cdr/cons p '()))
(() (atom '()))))
(jbob.step (prelude)
'(if a c c)
'())
(jbob.step (prelude)
'(if a c c)
'((() (if-same a c))))
(jbob.step (prelude)
'(if a c c)
'((() (if-same a c))
(() (if-same
(if (equal a 't)
(if (equal 'nil 'nil)
a
b)
(equal 'or (cons 'black '(coffee))))
c))
;;((Q E 2) (cons 'black '(coffee)))
))
(jbob.step (prelude)
'(if a c c)
'((() (if-same a c))
(() (if-same
(if (equal a 't)
(if (equal 'nil 'nil)
a
b)
(equal 'or (cons 'black '(coffee))))
c))
((Q E 2) (cons 'black '(coffee)))))
(jbob.step (prelude)
'(if a c c)
'((() (if-same a c))
(() (if-same
(if (equal a 't)
(if (equal 'nil 'nil)
a
b)
(equal 'or
(cons 'black '(coffee))))
c))
((Q E 2) (cons 'black '(coffee)))
((Q A Q) (equal-same 'nil))))
(jbob.step (prelude)
'(if a c c)
'((() (if-same a c))
(() (if-same
(if (equal a 't)
(if (equal 'nil 'nil)
a
b)
(equal 'or
(cons 'black '(coffee))))
c))
((Q E 2) (cons 'black '(coffee)))
((Q A Q) (equal-same 'nil))
((Q A 2) (if-true a b))))
(jbob.step (prelude)
'(if a c c)
'((() (if-same a c))
(() (if-same
(if (equal a 't)
(if (equal 'nil 'nil)
a
b)
(equal 'or
(cons 'black '(coffee))))
c))
((Q E 2) (cons 'black '(coffee)))
((Q A Q) (equal-same 'nil))
((Q A) (if-true a b))))
(jbob.prove (prelude)
'())
(jbob.prove (prelude)
'(((defun pair (x y)
(cons x (cons y '())))
nil)))
(jbob.prove (prelude)
'(((defun pair (x y)
(cons x (cons y '())))
nil)
((defun first-of (x)
(car x))
nil)
((defun second-of (x)
(car (cdr x)))
nil)))
(jbob.prove (prelude)
'(((defun pair (x y)
(cons x (cons y '())))
nil)
((defun first-of (x)
(car x))
nil)
((defun second-of (x)
(car (cdr x)))
nil)
((dethm first-of-pair (a b)
(equal (first-of (pair a b))
a))
nil
((1 1) (pair a b))
;; ((1) (first-of (cons a (cons b '()))))
)))
(jbob.prove (prelude)
'(((defun pair (x y)
(cons x (cons y '())))
nil)
((defun first-of (x)
(car x))
nil)
((defun second-of (x)
(car (cdr x)))
nil)
((dethm first-of-pair (a b)
(equal (first-of (pair a b))
a))
nil
((1 1) (pair a b))
((1) (first-of (cons a (cons b '()))))
)))
(jbob.prove (prelude)
'(((defun pair (x y)
(cons x (cons y '())))
nil)
((defun first-of (x)
(car x))
nil)
((defun second-of (x)
(car (cdr x)))
nil)
((dethm first-of-pair (a b)
(equal (first-of (pair a b))
a))
nil
((1 1) (pair a b))
((1) (first-of (cons a (cons b '()))))
((1) (car/cons a (cons b '())))
)))
(jbob.prove (prelude)
'(((defun pair (x y)
(cons x (cons y '())))
nil)
((defun first-of (x)
(car x))
nil)
((defun second-of (x)
(car (cdr x)))
nil)
((dethm first-of-pair (a b)
(equal (first-of (pair a b))
a))
nil
((1 1) (pair a b))
((1) (first-of (cons a (cons b '()))))
((1) (car/cons a (cons b '())))
(() (equal-same a))
)))
(defun prelude+first-of-pair ()
(J-Bob/define (prelude)
'(((defun pair (x y)
(cons x (cons y '())))
nil)
((defun first-of (x)
(car x))
nil)
((defun second-of (x)
(car (cdr x)))
nil)
((dethm first-of-pair (a b)
(equal (first-of (pair a b))
a))
nil
((1 1) (pair a b))
((1) (first-of (cons a (cons b '()))))
((1) (car/cons a (cons b '())))
(() (equal-same a))))))
(jbob.prove (prelude)
'(((dethm first-of-pair (a b)
(equal (first-of (pair a b))
a))
nil)))
(jbob.prove (prelude+first-of-pair)
'(((dethm second-of-pair (a b)
(equal (second-of (pair a b))
b))
nil)))
(jbob.prove (prelude+first-of-pair)
'(
((dethm second-of-pair (a b)
(equal (second-of (pair a b))
b))
nil)
((defun in-pair? (xs)
(if (equal (first-of xs) '?)
't
(equal (second-of xs) '?)))
nil)
((dethm in-first-of-pair (b)
(equal (in-pair? (pair '? b))
't))
nil)
((dethm in-second-of-pair (a)
(equal (in-pair? (pair a '?))
't))
nil)
))
(jbob.prove (prelude)
'(((defun list? (x)
(if (atom x)
(equal x '())
(list? (cdr x))))
nil)))
(jbob.prove (prelude)
'(((defun list? (x)
(if (atom x)
(equal x '())
(list? (cdr x))))
(size x)
((Q) (natp/size x))
(() (if-true (if (atom x)
't
(< (size (cdr x)) (size x)))
'nil))
((E) (size/cdr x))
(() (if-same (atom x) 't)))))
(defun defun.remb ()
(J-Bob/define (defun.memb?)
'()))
(jbob.prove (prelude)
'(
((defun memb? (xs)
(if (atom xs)
'nil
(if (equal (car xs) '?)
't
(memb? (cdr xs)))))
(size xs))
((defun remb (xs)
(if (atom xs)
'()
(if (equal (car xs) '?)
(remb (cdr xs))
(cons (car xs)
(remb (cdr xs))))))
(size xs))))
(jbob.prove (prelude)
'(
((defun memb? (xs)
(if (atom xs)
'nil
(if (equal (car xs) '?)
't
(memb? (cdr xs)))))
(size xs)
((A E E) (size/cdr xs))
((A E) (if-same (equal (car xs) '?) 't))
((Q) (natp/size xs))
((A) (if-same (atom xs) 't))
(() (if-true 't 'nil)))
((defun remb (xs)
(if (atom xs)
'()
(if (equal (car xs) '?)
(remb (cdr xs))
(cons (car xs)
(remb (cdr xs))))))
(size xs)
((A E) (size/cdr xs))
((A) (if-same (atom xs) 't))
((Q) (natp/size xs))
(() (if-true 't 'nil)))))