Updated examples
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Devine Lu Linvega
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0012004ee5
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77046e2645
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<> (add (s ?x) (s ?y)) (s (add ?x (s ?y)))
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<> (add (s ?x) (0)) (s ?x)
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<> (add (0) (s ?y)) (s ?y)
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<> (add (0) (0)) (0)
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<> (sub (s ?x) (s ?y)) (sub ?x ?y)
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<> (sub (s ?x) (0)) (s ?x)
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<> (sub (0) (s ?y)) (s ?y)
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<> (sub (0) (0)) (0)
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<> (mul (s ?x) (s ?y)) (add (s ?x) (mul (s ?x) (sub (s ?y) (s (0)))))
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<> (mul (s ?x) (s (0))) (s ?x)
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<> (mul (s (0)) (s ?y)) (s ?y)
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<> (mul (s ?x) (0)) (0)
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<> (mul (0) (s ?x)) (0)
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<> (?x + ?y) (add ?x ?y)
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<> (?x - ?y) (sub ?x ?y)
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<> (?x * ?y) (mul ?x ?y)
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<> (factorial (s (0))) ((s (0)))
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<> (factorial (s ?x)) (((s ?x) * factorial ((s ?x) - (s (0)))))
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factorial (s (s (s (s (s (0))))))
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<> (-- ?x) ()
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-- ( little endian binary integers )
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-- ( constants )
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<> zero ((0 nil))
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<> one ((1 nil))
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<> two ((0 (1 nil)))
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<> three ((1 (1 nil)))
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<> ten ((0 (1 (0 (1 nil)))))
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-- ( decimal digit to binary )
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<> (binary 0) ((0 nil))
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<> (binary 1) ((1 nil))
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<> (binary 2) ((0 (1 nil)))
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<> (binary 3) ((1 (1 nil)))
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<> (binary 4) ((0 (0 (1 nil))))
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<> (binary 5) ((1 (0 (1 nil))))
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<> (binary 6) ((0 (1 (1 nil))))
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<> (binary 7) ((1 (1 (1 nil))))
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<> (binary 8) ((0 (0 (0 (1 nil)))))
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<> (binary 9) ((1 (0 (0 (1 nil)))))
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-- ( binary to decimal digit )
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<> (decimal (0 nil)) (0)
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<> (decimal (1 nil)) (1)
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<> (decimal (0 (1 nil))) (2)
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<> (decimal (1 (1 nil))) (3)
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<> (decimal (0 (0 (1 nil)))) (4)
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<> (decimal (1 (0 (1 nil)))) (5)
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<> (decimal (0 (1 (1 nil)))) (6)
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<> (decimal (1 (1 (1 nil)))) (7)
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<> (decimal (0 (0 (0 (1 nil))))) (8)
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<> (decimal (1 (0 (0 (1 nil))))) (9)
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-- create nil-terminated list
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<> (nilify (?h)) ((?h nil))
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<> (nilify (?h ?t)) ((?h nilify ?t))
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-- reverse nil-terminated list
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<> (reverse ?x) (reverse' nil ?x)
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<> (reverse' ?a nil) (?a)
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<> (reverse' ?a (?h ?t)) (reverse' (?h ?a) ?t)
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-- ( normalize, remove trailing zeros )
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-- ( currently zero is (0 nil) though arguably it could be nil )
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-- ( that change would require auditing our rules )
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<> (normalize (?h ?t)) ((?h normalize' nil ?t))
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<> (normalize' ?s nil) (nil)
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<> (normalize' ?s (0 ?t)) (normalize' (0 ?s) ?t)
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<> (normalize' nil (1 ?t)) ((1 normalize' nil ?t))
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<> (normalize' (0 ?s) (1 ?t)) ((0 normalize' ?s (1 ?t)))
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-- ( to integer )
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<> ((int ?*)) ((sum f (one) g reverse nilify (?*)))
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<> (g nil) (nil)
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<> (g (?h ?t)) ((binary ?h g ?t))
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<> (f (?u) nil) (nil)
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<> (f (?u) (?h ?t)) (((mul ?h ?u) f ((mul ?u ten)) ?t))
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-- ( to string: TODO, need division for this one )
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-- ( comparison operartions )
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<> ((cmp ?x ?y)) ((cmpc #eq ?x ?y))
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<> ((cmpc ?e nil nil)) (?e)
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<> ((cmpc ?e (1 ?x) nil)) (#gt)
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<> ((cmpc ?e (0 ?x) nil)) ((cmpc ?e ?x nil))
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<> ((cmpc ?e nil (1 ?y))) (#lt)
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<> ((cmpc ?e nil (0 ?y))) ((cmpc ?e nil ?y))
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<> ((cmpc ?e (0 ?x) (0 ?y))) ((cmpc ?e ?x ?y))
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<> ((cmpc ?e (1 ?x) (0 ?y))) ((cmpc #gt ?x ?y))
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<> ((cmpc ?e (0 ?x) (1 ?y))) ((cmpc #lt ?x ?y))
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<> ((cmpc ?e (1 ?x) (1 ?y))) ((cmpc ?e ?x ?y))
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-- ( addition )
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<> ((add ?x ?y)) (addc 0 ?x ?y)
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<> (addc 0 nil nil) (nil)
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<> (addc 1 nil nil) ((1 nil))
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<> (addc ?c ?x nil) (addc ?c ?x (0 nil))
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<> (addc ?c nil ?y) (addc ?c (0 nil) ?y)
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<> (addc 0 (0 ?x) (0 ?y)) ((0 addc 0 ?x ?y))
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<> (addc 0 (0 ?x) (1 ?y)) ((1 addc 0 ?x ?y))
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<> (addc 0 (1 ?x) (0 ?y)) ((1 addc 0 ?x ?y))
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<> (addc 0 (1 ?x) (1 ?y)) ((0 addc 1 ?x ?y))
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<> (addc 1 (0 ?x) (0 ?y)) ((1 addc 0 ?x ?y))
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<> (addc 1 (0 ?x) (1 ?y)) ((0 addc 1 ?x ?y))
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<> (addc 1 (1 ?x) (0 ?y)) ((0 addc 1 ?x ?y))
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<> (addc 1 (1 ?x) (1 ?y)) ((1 addc 1 ?x ?y))
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-- ( summation )
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<> ((sum nil)) ((0 nil))
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<> ((sum (?a nil))) (?a)
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<> ((sum (?a (?b ?c)))) ((sum ((add ?a ?b) ?c)))
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-- ( multiplication )
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<> ((mul ?x ?y)) (mulc nil ?x ?y)
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<> (mulc ?t nil ?y) ((sum ?t))
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<> (mulc ?t (0 ?x) ?y) (mulc ?t ?x (0 ?y))
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<> (mulc ?t (1 ?x) ?y) (mulc (?y ?t) ?x (0 ?y))
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-- ( subtraction )
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<> ((sub ?x ?y)) (normalize subc 0 ?x ?y)
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<> (subc 0 nil nil) (nil)
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<> (subc 1 nil nil) (#err)
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<> (subc 0 ?x nil) (?x)
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<> (subc 1 ?x nil) (subc 1 ?x (0 nil))
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<> (subc ?c nil ?y) (subc ?c (0 nil) ?y)
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<> (subc 0 (0 ?x) (0 ?y)) ((0 subc 0 ?x ?y))
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<> (subc 0 (0 ?x) (1 ?y)) ((1 subc 1 ?x ?y))
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<> (subc 0 (1 ?x) (0 ?y)) ((1 subc 0 ?x ?y))
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<> (subc 0 (1 ?x) (1 ?y)) ((0 subc 0 ?x ?y))
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<> (subc 1 (0 ?x) (0 ?y)) ((1 subc 1 ?x ?y))
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<> (subc 1 (0 ?x) (1 ?y)) ((0 subc 1 ?x ?y))
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<> (subc 1 (1 ?x) (0 ?y)) ((0 subc 0 ?x ?y))
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<> (subc 1 (1 ?x) (1 ?y)) ((1 subc 1 ?x ?y))
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-- ( dec )
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<> (dec (0 nil)) (#err)
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<> (dec ?x) (normalize dec' ?x)
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<> (dec' (0 ?t)) ((1 dec' ?t))
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<> (dec' (1 ?t)) ((0 ?t))
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-- ( inc )
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<> ((inc nil)) ((1 nil))
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<> ((inc (0 ?t))) ((1 ?t))
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<> ((inc (1 ?t))) ((0 (inc ?t)))
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-- ( left shift; lshift x b means x<<b )
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<> ((lshift ?x (0 nil))) (?x)
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<> ((lshift ?x (1 nil))) ((0 ?x))
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<> ((lshift ?x (?h (?a ?b)))) ((lshift (0 ?x) dec (?h (?a ?b))))
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-- ( divmod, i.e. quotient and remainder )
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<> ((divmod ?x ?y)) ((divmod1 ?x ?y (cmp ?x ?y)))
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<> ((divmod1 ?x ?y #lt)) (zero)
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<> ((divmod1 ?x ?y #eq)) (one)
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<> ((divmod1 ?x ?y #gt)) ((divmod2 ?x ?y zero (0 ?y)))
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<> ((divmod2 ?x ?y ?s ?m)) ((divmod3 ?x ?y ?s ?m (cmp ?x ?m)))
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<> ((divmod3 ?x ?y ?s ?m #lt)) ((divmod4 ?x ?y ?s zero))
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<> ((divmod3 ?x ?y ?s ?m #eq)) ((divmod4 ?x ?y (inc ?s) zero))
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<> ((divmod3 ?x ?y ?s ?m #gt)) ((divmod2 ?x ?y (inc ?s) (0 ?m)))
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<> ((divmod4 ?x ?y (0 nil) ?d)) (((add ?d one) (sub ?x ?y)))
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<> ((divmod4 ?x ?y ?s ?d)) ((divmod5 (sub ?x (lshift ?y ?s)) ?y dec ?s (add ?d (lshift one ?s))))
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<> ((divmod5 (0 nil) ?y ?s ?d)) ((?d (0 nil)))
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<> ((divmod5 ?x ?y ?s ?d)) ((divmod6 ?x ?y ?s ?d (cmp ?x (lshift ?y ?s))))
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<> ((divmod6 ?x ?y (0 nil) ?d #lt)) ((?d ?x))
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<> ((divmod6 ?x ?y ?s ?d #lt)) ((divmod5 ?x ?y dec ?s ?d))
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<> ((divmod6 ?x ?y ?s ?d #eq)) ((divmod4 ?x ?y ?s ?d))
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<> ((divmod6 ?x ?y ?s ?d #gt)) ((divmod4 ?x ?y ?s ?d))
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-- ( floor divison )
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<> ((div ?x ?y)) ((div' (divmod ?x ?y)))
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<> ((div' (?q ?r))) (?q)
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-- ( remainder )
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<> ((mod ?x ?y)) ((mod' (divmod ?x ?y)))
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<> ((mod' (?q ?r))) (?r)
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(divmod (int 1234567) (int 1357))
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@ -1,9 +1,9 @@
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<> (read) (?~)
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<> (read ?~) (?~)
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<> (?: print ') (?:)
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<> (' ?x) (?x ')
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(Tell me three things: \n) print '
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' (You said: read
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then, you continued: read
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finaly, you concluded: read) print
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' (You said: read stdin
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then, you continued: read stdin
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finaly, you concluded: read stdin) print
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