142 lines
4.0 KiB
Plaintext
142 lines
4.0 KiB
Plaintext
<> (-- ?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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-- ( 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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-- ( constants )
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<> (a) ((1 (1 nil)))
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<> (b) ((0 (1 nil)))
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<> (c) ((1 (1 (1 nil))))
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<> (d) (int 135)
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<> (e) (int 1913)
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-- ( <> (f) (int 4294967295) )
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-- ( cmp c c )
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-- ( add a b )
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-- ( sum (a (b (c nil))) )
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-- ( mul a c )
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-- ( add d e )
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-- ( lshift (int 3) (int 1) )
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