<> (-- ?x) () -- ( N: little-endian natural numbers ) -- ( NOTE: this file requires a patched modal which increases some of the limits ) -- ( otherwise you'll get a Segmentation Fault ) -- ( constants ) <> zero ((0 ())) <> one ((1 ())) <> two ((0 (1 ()))) <> three ((1 (1 ()))) <> four ((0 (0 (1 ())))) <> eight ((0 (0 (0 (1 ()))))) <> ten ((0 (1 (0 (1 ()))))) <> sixteen ((0 (0 (0 (0 (1 ())))))) -- reverse ()-terminated list <> (reverse ?x) (reverse1 () ?x) <> (reverse1 ?a ()) (?a) <> (reverse1 ?a (?h ?t)) (reverse1 (?h ?a) ?t) -- ( to natural number ) <> ((nat ?*)) ((nat1 (?*))) <> ((nat1 ?x)) ((sum f (N one) g reverse ?x)) <> (g ()) (()) <> (g (?h ?t)) (((binary ?h) g ?t)) <> (f (N ?u) ()) (()) <> (f (N ?u) (?h ?t)) (((mul (N ?h) (N ?u)) f (mul (N ?u) (N ten)) ?t)) -- ( to integer ) <> ((nat-base (N ?b) ?*)) ((sum f' (N ?b) (N one) g' reverse (?*))) <> (g' ()) (()) <> (g' (?h ?t)) (((binary ?h) g' ?t)) <> (f' (N ?b) (N ?u) ()) (()) <> (f' (N ?b) (N ?u) (?h ?t)) (((mul (N ?h) (N ?u)) f' (N ?b) (mul (N ?u) (N ?b)) ?t)) -- ( comparison operartions ) <> ((cmp (N ?x) (N ?y))) ((cmpc #eq ?x ?y)) <> ((cmpc ?e () ())) (?e) <> ((cmpc ?e (1 ?x) ())) (#gt) <> ((cmpc ?e (0 ?x) ())) ((cmpc ?e ?x ())) <> ((cmpc ?e () (1 ?y))) (#lt) <> ((cmpc ?e () (0 ?y))) ((cmpc ?e () ?y)) <> ((cmpc ?e (0 ?x) (0 ?y))) ((cmpc ?e ?x ?y)) <> ((cmpc ?e (1 ?x) (0 ?y))) ((cmpc #gt ?x ?y)) <> ((cmpc ?e (0 ?x) (1 ?y))) ((cmpc #lt ?x ?y)) <> ((cmpc ?e (1 ?x) (1 ?y))) ((cmpc ?e ?x ?y)) -- ( addition ) <> ((add (N ?x) (N ?y))) (add/e force (addc 0 ?x ?y)) <> ((addc 0 () ())) (()) <> ((addc 1 () ())) ((1 ())) <> ((addc 0 ?x ())) (?x) <> ((addc 0 () ?y)) (?y) <> ((addc 1 ?x ())) ((addc 1 ?x (0 ()))) <> ((addc 1 () ?y)) ((addc 1 (0 ()) ?y)) <> ((addc 0 (0 ?x) (0 ?y))) ((0 (addc 0 ?x ?y))) <> ((addc 0 (0 ?x) (1 ?y))) ((1 (addc 0 ?x ?y))) <> ((addc 0 (1 ?x) (0 ?y))) ((1 (addc 0 ?x ?y))) <> ((addc 0 (1 ?x) (1 ?y))) ((0 (addc 1 ?x ?y))) <> ((addc 1 (0 ?x) (0 ?y))) ((1 (addc 0 ?x ?y))) <> ((addc 1 (0 ?x) (1 ?y))) ((0 (addc 1 ?x ?y))) <> ((addc 1 (1 ?x) (0 ?y))) ((0 (addc 1 ?x ?y))) <> ((addc 1 (1 ?x) (1 ?y))) ((1 (addc 1 ?x ?y))) <> (add/e force/r ?x) ((N ?x)) -- ( summation ) <> ((sum ())) ((N (0 ()))) <> ((sum (?a ()))) (?a) <> ((sum (?a (?b ?c)))) ((sum ((add ?a ?b) ?c))) -- ( multiplication ) <> ((mul (N ?x) (N ?y))) (mul/e (mulc () ?x ?y)) <> ((mulc ?t () ?y)) ((sum ?t)) <> ((mulc ?t (0 ?x) ?y)) ((mulc ?t ?x (0 ?y))) <> ((mulc ?t (1 ?x) ?y)) ((mulc ((N ?y) ?t) ?x (0 ?y))) <> (mul/e (N ?x)) ((N ?x)) -- ( subtraction ) <> ((sub (N ?x) (N ?y))) ((sub1 0 ?x ?y ())) <> ((sub1 ?c (?b ?x) (?b ?y) ?s)) ((sub1 ?c ?x ?y (?c ?s))) <> ((sub1 0 (1 ?x) (0 ?y) ?s)) ((sub1 0 ?x ?y (1 ?s))) <> ((sub1 1 (1 ?x) (0 ?y) ?s)) ((sub1 0 ?x ?y (0 ?s))) <> ((sub1 0 (0 ?x) (1 ?y) ?s)) ((sub1 1 ?x ?y (1 ?s))) <> ((sub1 1 (0 ?x) (1 ?y) ?s)) ((sub1 1 ?x ?y (0 ?s))) <> ((sub1 0 () () ?s)) ((sub/u ?s)) <> ((sub1 1 () ?y ?s)) (#err) <> ((sub1 ?c ?x () ?s)) ((sub1 ?c ?x (0 ()) ?s)) <> ((sub1 ?c () ?y ?s)) ((sub1 ?c (0 ()) ?y ?s)) <> ((sub/u (1 ?t))) ((sub/v (1 ?t) ())) <> ((sub/u (0 ()))) ((N (0 ()))) <> ((sub/u (0 ?t))) ((sub/u ?t)) <> ((sub/v () ?s)) ((N ?s)) <> ((sub/v (?h ?t) ?s)) ((sub/v ?t (?h ?s))) <> ((dec (N (1 ())))) ((N (0 ()))) <> ((dec (N (0 ())))) (#err) <> ((dec (N (0 ?t)))) (dec/e (dec1 (0 ?t))) <> ((dec (N (1 ?t)))) ((N (0 ?t))) <> ((dec1 (0 ?t))) ((1 (dec1 ?t))) <> ((dec1 (1 ()))) (dec/r ()) <> ((dec1 (1 ?t))) (dec/r (0 ?t)) <> ((?h dec/r ?t)) (dec/r (?h ?t)) <> (dec/e dec/r ?x) ((N ?x)) -- ( inc ) <> ((inc (N ?x))) (inc/e force (inc1 ?x)) <> ((inc1 ())) ((1 ())) <> ((inc1 (0 ?t))) ((1 ?t)) <> ((inc1 (1 ?t))) ((0 (inc1 ?t))) <> (inc/e force/r ?x) ((N ?x)) -- ( left shift; lshift x b means x< ((lshift (N ?x) (N ?k))) (lshift/e force/r (lshift1 ?x (N ?k))) <> ((lshift1 ?x (N (0 ())))) (?x) <> ((lshift1 ?x (N (1 ())))) ((0 ?x)) <> ((lshift1 ?x (N (0 (?a ?b))))) ((lshift1 (0 ?x) (dec (N (0 (?a ?b)))))) <> ((lshift1 ?x (N (1 (?a ?b))))) ((lshift1 (0 ?x) (N (0 (?a ?b))))) <> (lshift/e force/r ?x) ((N ?x)) <> ((rshift1 (N (?a ())))) ((N (0 ()))) <> ((rshift1 (N (?a (?b ?c))))) ((N (?b ?c))) -- ( divmod, i.e. quotient and remainder ) -- ( x is the dividend, or what's left of it ) -- ( y is the divisor ) -- ( s is the number of bits to shift, so far ) -- ( o is the next valuet o add to the quotient ) -- ( m is the next multiple of y to work with ) -- ( d is the quotient, so far ) <> ((divmod (N ?x) (N ?y))) (divmod/p (divmod1 ?x ?y (cmp (N ?x) (N ?y)))) <> ((divmod1 ?x ?y #lt)) (((N zero) (N ?x))) <> ((divmod1 ?x ?y #eq)) (((N one) (N zero))) <> ((divmod1 ?x ?y #gt)) ((divmod2 (N ?x) (N ?y) (N zero) (N ?y))) <> ((divmod2 (N ?x) (N ?y) (N ?s) (N ?m))) ((divmod3 (N ?x) (N ?y) (N ?s) (N ?m) (cmp (N ?x) (N (0 ?m))))) <> ((divmod3 (N ?x) (N ?y) (N ?s) (N ?m) #gt)) ((divmod2 (N ?x) (N ?y) (inc (N ?s)) (N (0 ?m)))) <> ((divmod3 (N ?x) (N ?y) (N ?s) (N ?m) #eq)) ((divmod4 (N ?x) (N ?y) (inc (N ?s)) (N (0 ?m)) (N zero))) <> ((divmod3 (N ?x) (N ?y) (N ?s) (N ?m) #lt)) ((divmod4 (N ?x) (N ?y) (N ?s) (N ?m) (N zero))) <> ((divmod4 (N ?x) (N ?y) (N (0 ())) (N ?m) (N ?d))) (((add (N ?d) (N one)) (sub (N ?x) (N ?y)))) <> ((divmod4 (N ?x) (N ?y) (N ?s) (N ?m) (N ?d))) ((divmod5 (sub (N ?x) (N ?m)) (N ?y) (dec (N ?s)) (rshift1 (N ?m)) (add (N ?d) (lshift (N one) (N ?s))))) <> ((divmod5 (N (0 ())) (N ?y) (N ?s) (N ?m) (N ?d))) (((N ?d) (N (0 ())))) <> ((divmod5 (N ?x) (N ?y) (N ?s) (N ?m) (N ?d))) ((divmod6 (N ?x) (N ?y) (N ?s) (N ?m) (N ?d) (cmp (N ?x) (N ?m)))) <> ((divmod6 (N ?x) (N ?y) (N (0 ())) (N ?m) (N ?d) #lt)) (((N ?d) (N ?x))) <> ((divmod6 (N ?x) (N ?y) (N ?s) (N ?m) (N ?d) #lt)) ((divmod5 (N ?x) (N ?y) (dec (N ?s)) (rshift1 (N ?m)) (N ?d))) <> ((divmod6 (N ?x) (N ?y) (N ?s) (N ?m) (N ?d) #eq)) ((divmod4 (N ?x) (N ?y) (N ?s) (N ?m) (N ?d))) <> ((divmod6 (N ?x) (N ?y) (N ?s) (N ?m) (N ?d) #gt)) ((divmod4 (N ?x) (N ?y) (N ?s) (N ?m) (N ?d))) <> (divmod/p ((N ?q) (N ?r))) (divmod/e (force ?q force ?r)) <> (divmod/e (force/r ?q force/r ?r)) (((N ?q) (N ?r))) -- ( floor divison ) <> ((div (N ?x) (N ?y))) ((div1 (divmod (N ?x) (N ?y)))) <> ((div1 (?q ?r))) (?q) -- ( remainder ) <> ((mod (N ?x) (N ?y))) ((mod1 (divmod (N ?x) (N ?y)))) <> ((mod1 (?q ?r))) (?r) -- ( expontentiation ) <> ((pow (N ?x) ())) ((N one)) <> ((pow (N ?x) (N (0 ())))) ((pow (N ?x) ())) <> ((pow (N ?x) (N (1 ())))) ((N ?x)) <> ((pow (N ?x) (N (0 ?k)))) ((pow (mul (N ?x) (N ?x)) (N ?k))) <> ((pow (N ?x) (N (1 ?k)))) ((mul (N ?x) (pow (mul (N ?x) (N ?x)) (N ?k)))) -- ( greatest common denominator ) <> ((gcd ?a ?b)) ((gcd1 ?a ?b (cmp ?b (N (0 ()))))) <> ((gcd1 ?a ?b #eq)) (?a) <> ((gcd1 ?a ?b #gt)) ((gcd ?b (mod ?a ?b))) <> ((gcd1 ?a ?b #lt)) ((gcd ?b (mod ?a ?b))) -- ( least common multiple ) <> ((lcm ?a ?b)) ((mul ?a (div ?b (gcd ?a ?b)))) -- ( decimal digit to binary ) <> ((binary 0)) ((0 ())) <> ((binary 1)) ((1 ())) <> ((binary 2)) ((0 (1 ()))) <> ((binary 3)) ((1 (1 ()))) <> ((binary 4)) ((0 (0 (1 ())))) <> ((binary 5)) ((1 (0 (1 ())))) <> ((binary 6)) ((0 (1 (1 ())))) <> ((binary 7)) ((1 (1 (1 ())))) <> ((binary 8)) ((0 (0 (0 (1 ()))))) <> ((binary 9)) ((1 (0 (0 (1 ()))))) <> ((binary a)) ((0 (1 (0 (1 ()))))) <> ((binary b)) ((1 (1 (0 (1 ()))))) <> ((binary c)) ((0 (0 (1 (1 ()))))) <> ((binary d)) ((1 (0 (1 (1 ()))))) <> ((binary e)) ((0 (1 (1 (1 ()))))) <> ((binary f)) ((1 (1 (1 (1 ()))))) <> ((binary g)) ((0 (0 (0 (0 (1 ())))))) <> ((binary h)) ((1 (0 (0 (0 (1 ())))))) <> ((binary i)) ((0 (1 (0 (0 (1 ())))))) <> ((binary j)) ((1 (1 (0 (0 (1 ())))))) <> ((binary k)) ((0 (0 (1 (0 (1 ())))))) <> ((binary l)) ((1 (0 (1 (0 (1 ())))))) <> ((binary m)) ((0 (1 (1 (0 (1 ())))))) <> ((binary n)) ((1 (1 (1 (0 (1 ())))))) <> ((binary o)) ((0 (0 (0 (1 (1 ())))))) <> ((binary p)) ((1 (0 (0 (1 (1 ())))))) <> ((binary q)) ((0 (1 (0 (1 (1 ())))))) <> ((binary r)) ((1 (1 (0 (1 (1 ())))))) <> ((binary s)) ((0 (0 (1 (1 (1 ())))))) <> ((binary t)) ((1 (0 (1 (1 (1 ())))))) <> ((binary u)) ((0 (1 (1 (1 (1 ())))))) <> ((binary v)) ((1 (1 (1 (1 (1 ())))))) <> ((binary w)) ((0 (0 (0 (0 (0 (1 ()))))))) <> ((binary x)) ((1 (0 (0 (0 (0 (1 ()))))))) <> ((binary y)) ((0 (1 (0 (0 (0 (1 ()))))))) <> ((binary z)) ((1 (1 (0 (0 (0 (1 ()))))))) -- ( binary to digits ) <> ((decimal ())) (0) <> ((decimal (0 ()))) (0) <> ((decimal (1 ()))) (1) <> ((decimal (0 (1 ())))) (2) <> ((decimal (1 (1 ())))) (3) <> ((decimal (0 (0 (1 ()))))) (4) <> ((decimal (1 (0 (1 ()))))) (5) <> ((decimal (0 (1 (1 ()))))) (6) <> ((decimal (1 (1 (1 ()))))) (7) <> ((decimal (0 (0 (0 (1 ())))))) (8) <> ((decimal (1 (0 (0 (1 ())))))) (9) -- ( Z: signed integers ) <> ((nat>int + (N ?x))) ((Z (+ ?x))) <> ((nat>int - (N ?x))) ((Z (- ?x))) <> ((nat>pos (N ?x))) ((Z (+ ?x))) <> ((nat>neg (N ?x))) ((Z (- ?x))) <> ((negate (Z (+ ?x)))) ((Z (- ?x))) <> ((negate (Z (+ ?x)))) ((Z (- ?x))) <> ((cmp (Z (?s (0 ()))) (Z (?s (0 ()))))) (#eq) <> ((cmp (Z (+ ?x)) (Z (+ ?y)))) ((cmp (N ?x) (N ?y))) <> ((cmp (Z (+ ?x)) (Z (?s ?y)))) (#gt) <> ((cmp (Z (- ?x)) (Z (- ?y)))) ((cmp (N ?y) (N ?x))) <> ((cmp (Z (- ?x)) (Z (?s ?y)))) (#lt) <> ((add (Z (+ ?x)) (Z (+ ?y)))) ((nat>pos (add (N ?x) (N ?y)))) <> ((add (Z (- ?x)) (Z (- ?y)))) ((nat>neg (add (N ?x) (N ?y)))) <> ((add (Z (+ ?x)) (Z (- ?y)))) ((zadd ?x ?y (cmp (N ?x) (N ?y)))) <> ((add (Z (- ?x)) (Z (+ ?y)))) ((zadd ?y ?x (cmp (N ?y) (N ?x)))) <> ((zadd ?p ?n #gt)) ((nat>pos (sub (N ?p) (N ?n)))) <> ((zadd ?p ?n #eq)) ((Z (+ (0 ())))) <> ((zadd ?p ?n #lt)) ((nat>neg (sub (N ?n) (N ?p)))) <> ((mul (Z (?s ?x)) (Z (?s ?y)))) ((nat>pos (mul (N ?x) (N ?y)))) <> ((mul (Z (?s ?x)) (Z (?t ?y)))) ((nat>neg (mul (N ?x) (N ?y)))) <> ((sub (Z (+ ?x)) (Z (+ ?y)))) ((add (Z (+ ?x)) (Z (- ?y)))) <> ((sub (Z (+ ?x)) (Z (- ?y)))) ((add (Z (+ ?x)) (Z (+ ?y)))) <> ((sub (Z (- ?x)) (Z (+ ?y)))) ((add (Z (- ?x)) (Z (- ?y)))) <> ((sub (Z (- ?x)) (Z (- ?y)))) ((add (Z (- ?x)) (Z (+ ?y)))) -- ( n/d = q, n%d = r ) -- ( n = d * q + r ) -- ( ---------------- ) -- ( 9 = 2 * 4 + 1 ) -- ( -9 = 2 * -4 - 1 ) -- ( 9 = -2 * -4 + 1 ) -- ( -9 = -2 * 4 - 1 ) <> ((divmod (Z (+ ?x)) (Z (+ ?y)))) ((zdm + + (divmod (N ?x) (N ?y)))) <> ((divmod (Z (- ?x)) (Z (+ ?y)))) ((zdm - - (divmod (N ?x) (N ?y)))) <> ((divmod (Z (+ ?x)) (Z (- ?y)))) ((zdm - + (divmod (N ?x) (N ?y)))) <> ((divmod (Z (- ?x)) (Z (- ?y)))) ((zdm + - (divmod (N ?x) (N ?y)))) <> ((zdm ?s ?t ((N ?q) (N ?r)))) (((Z (?s ?q)) (Z (?t ?r)))) <> ((div (Z (?s ?x)) (Z (?s ?y)))) ((nat>pos (div (N ?x) (N ?y)))) <> ((div (Z (?s ?x)) (Z (?t ?y)))) ((nat>neg (div (N ?x) (N ?y)))) <> ((mod (Z (+ ?x)) (Z (?s ?y)))) ((nat>pos (div (N ?x) (N ?y)))) <> ((mod (Z (- ?x)) (Z (?s ?y)))) ((nat>neg (div (N ?x) (N ?y)))) <> ((pow (Z (+ ?x)) (N ?k))) ((nat>pos (pow (N ?x) (N ?k)))) <> ((pow (Z (- ?x)) (N (0 ?k)))) ((nat>pos (pow (N ?x) (N (0 ?k))))) <> ((pow (Z (- ?x)) (N (1 ?k)))) ((nat>neg (pow (N ?x) (N (1 ?k))))) -- ( to integer ) <> ((int ?*)) ((int1 (?*))) <> ((int1 (- ?t))) ((int2 - (nat1 ?t))) <> ((int1 (?h ?t))) ((int2 + (nat1 (?h ?t)))) <> ((int2 ?s (N ?x))) ((Z (?s ?x))) -- ( Q: rational numbers ) -- ( ensure n and d are coprime by dividing both by their gcd ) <> ((ratify ?s (N (0 ())) (N ?d))) ((Q (+ zero one))) <> ((ratify ?s (N ?n) (N ?d))) ((ratify1 ?s (N ?n) (N ?d) (gcd (N ?n) (N ?d)))) <> ((ratify1 ?s (N ?n) (N ?d) (N ?g))) ((ratify2 ?s (div (N ?n) (N ?g)) (div (N ?d) (N ?g)))) <> ((ratify2 ?s (N ?n) (N ?d))) ((Q (?s ?n ?d))) -- ( convert N to Q ) <> ((nat>rat + (N ?x))) ((Q (+ ?x one))) <> ((nat>rat - (N ?x))) ((Q (- ?x one))) -- ( convert Z to Q ) <> ((int>rat (Z (+ ?x)))) ((Q (+ ?x one))) <> ((int>rat (Z (- ?x)))) ((Q (- ?x one))) <> ((negate (Q (+ ?n ?d)))) ((Q (- ?n ?d))) <> ((negate (Q (- ?n ?d)))) ((Q (+ ?n ?d))) <> ((cmp (Q (?s (0 ()) (1 ()))) (Q (?s (0 ()) (1 ()))))) (#eq) <> ((cmp (Q (+ ?x ?d)) (Q (+ ?y ?e)))) ((cmp (mul (N ?x) (N ?e)) (mul (N ?y) (N ?d)))) <> ((cmp (Q (+ ?x ?d)) (Q (?s ?y ?e)))) (#gt) <> ((cmp (Q (- ?x ?d)) (Q (- ?y ?e)))) ((cmp (mul (N ?y) (N ?d)) (mul (N ?x) (N ?e)))) <> ((cmp (Q (- ?x ?d)) (Q (?s ?y ?e)))) (#lt) <> ((add (Q (?s ?x ?d)) (Q (?t ?y ?e)))) ((qadd1 ?s ?t (mul (N ?x) (N ?e)) (mul (N ?y) (N ?d)) (mul (N ?d) (N ?e)))) <> ((qadd1 ?s ?t (N ?x) (N ?y) (N ?d))) ((qadd2 (add (Z (?s ?x)) (Z (?t ?y))) (N ?d))) <> ((qadd2 (Z (?s ?n)) (N ?d))) ((ratify ?s (N ?n) (N ?d))) <> ((sub (Q (?s ?x ?d)) (Q (?t ?y ?e)))) ((qsub1 ?s ?t (mul (N ?x) (N ?e)) (mul (N ?y) (N ?d)) (mul (N ?d) (N ?e)))) <> ((qsub1 ?s ?t (N ?x) (N ?y) (N ?d))) ((qsub2 (sub (Z (?s ?x)) (Z (?t ?y))) (N ?d))) <> ((qsub2 (Z (?s ?n)) (N ?d))) ((ratify ?s (N ?n) (N ?d))) <> ((mul (Q (?s ?x ?d)) (Q (?t ?y ?e)))) ((qmul1 (mul (Z (?s ?x)) (Z (?t ?y))) (mul (N ?d) (N ?e)))) <> ((qmul1 (Z (?s ?n)) (N ?d))) ((ratify ?s (N ?n) (N ?d))) <> ((div (Q (?s ?x ?d)) (Q (?t ?y ?e)))) ((mul (Q (?s ?x ?d)) (Q (?t ?e ?y)))) <> ((pow (Q (?s ?x ?d)) (N ?k))) ((qpow (pow (Z (?s ?x)) (N ?k)) (pow (N ?d) (N ?k)))) <> ((qpow (Z (?s ?n)) (N ?d))) ((ratify ?s (N ?n) (N ?d))) -- ( to rational number ) <> ((rat ?*)) ((rat1 (?*))) <> ((rat1 (- ?t))) ((rat2 - ?t ())) <> ((rat1 (?h ?t))) ((rat2 + (?h ?t) ())) <> ((rat2 ?s (/ ?t) ?a)) ((rat3 ?s (nat1 reverse ?a) (nat1 ?t))) <> ((rat2 ?s (?h ?t) ?a)) ((rat2 ?s ?t (?h ?a))) <> ((rat3 ?s (N ?n) (N ?d))) ((Q (?s ?n ?d))) -- ( render as a list of characters ) <> ((tostr (N (0 ())))) ((0 ())) <> ((tostr (N ?x))) ((tostr1 (N ?x) ())) <> ((tostr1 (N (0 ())) ?a)) (?a) <> ((tostr1 (N (?h ?t)) ?a)) ((tostr2 (divmod (N (?h ?t)) (N ten)) ?a)) <> ((tostr2 ((N ?q) (N ?r)) ?a)) ((tostr1 (N ?q) ((decimal ?r) ?a))) <> ((tostr (Z (+ ?x)))) ((tostr (N ?x))) <> ((tostr (Z (- ?x)))) ((concat (- ()) (tostr (N ?x)))) -- ( concatenate lists ) <> ((concat (?h ?t) ?r)) ((?h (concat ?t ?r))) <> ((concat () ?r)) (?r) -- ( to string ) <> ((str (N ?x))) (emit force (tostr (N ?x))) <> ((str (Z (+ ?x)))) ((str (N ?x))) <> ((str (Z (- ?x)))) (emit force (- (tostr (N ?x)))) <> ((str (Q (?s ?n ?d)))) ((qstr ?s (force (tostr (N ?n))) (force (tostr (N ?d))))) <> ((qstr + (force/r ?l) (force/r ?m))) (emit force (concat ?l (/ ?m))) <> ((qstr - (force/r ?l) (force/r ?m))) (emit force (concat (- ?l) (/ ?m))) -- ( force a list to evaluate to digits/letters ) <> ((?h force/r ?t)) (force/r (?h ?t)) <> (force ()) (force/r ()) <> (force (- ?t)) ((- force ?t)) <> (force (/ ?t)) ((/ force ?t)) <> (force (0 ?t)) ((0 force ?t)) <> (force (1 ?t)) ((1 force ?t)) <> (force (2 ?t)) ((2 force ?t)) <> (force (3 ?t)) ((3 force ?t)) <> (force (4 ?t)) ((4 force ?t)) <> (force (5 ?t)) ((5 force ?t)) <> (force (6 ?t)) ((6 force ?t)) <> (force (7 ?t)) ((7 force ?t)) <> (force (8 ?t)) ((8 force ?t)) <> (force (9 ?t)) ((9 force ?t)) <> (force (a ?t)) ((a force ?t)) <> (force (b ?t)) ((b force ?t)) <> (force (c ?t)) ((c force ?t)) <> (force (d ?t)) ((d force ?t)) <> (force (e ?t)) ((e force ?t)) <> (force (f ?t)) ((f force ?t)) <> (force (o ?t)) ((o force ?t)) <> (force (x ?t)) ((x force ?t)) -- ( emit ) <> (emit force/r ?^) ((S ?^)) -- ( to binary string ) <> ((bstr (N ?x))) ((bstr1 force ?x ())) <> ((bstr1 force/r () ?a)) (emit force/r (0 (b ?a))) <> ((bstr1 force/r (?h ?t) ?a)) ((bstr1 force/r ?t (?h ?a))) -- ( to octal string ) <> ((ostr (N ?x))) ((ostr1 () ?x)) <> ((ostr1 ?s (?a (?b (?c ?t))))) ((ostr1 ((hdigit ?a ?b ?c 0) ?s) ?t)) <> ((ostr1 ?s (?a (?b ?t)))) ((ostr1 ((hdigit ?a ?b 0 0) ?s) ?t)) <> ((ostr1 ?s (?a ?t))) ((ostr1 ((hdigit ?a 0 0 0) ?s) ?t)) <> ((ostr1 ?s ())) (emit force (0 (o ?s))) -- ( to hex string ) <> ((hstr (N ?x))) ((hstr1 () ?x)) <> ((hstr1 ?s (?a (?b (?c (?d ?t)))))) ((hstr1 ((hdigit ?a ?b ?c ?d) ?s) ?t)) <> ((hstr1 ?s (?a (?b (?c ?t))))) ((hstr1 ((hdigit ?a ?b ?c 0) ?s) ?t)) <> ((hstr1 ?s (?a (?b ?t)))) ((hstr1 ((hdigit ?a ?b 0 0) ?s) ?t)) <> ((hstr1 ?s (?a ?t))) ((hstr1 ((hdigit ?a 0 0 0) ?s) ?t)) <> ((hstr1 ?s ())) (emit force (0 (x ?s))) <> ((hdigit 0 0 0 0)) (0) <> ((hdigit 1 0 0 0)) (1) <> ((hdigit 0 1 0 0)) (2) <> ((hdigit 1 1 0 0)) (3) <> ((hdigit 0 0 1 0)) (4) <> ((hdigit 1 0 1 0)) (5) <> ((hdigit 0 1 1 0)) (6) <> ((hdigit 1 1 1 0)) (7) <> ((hdigit 0 0 0 1)) (8) <> ((hdigit 1 0 0 1)) (9) <> ((hdigit 0 1 0 1)) (a) <> ((hdigit 1 1 0 1)) (b) <> ((hdigit 0 0 1 1)) (c) <> ((hdigit 1 0 1 1)) (d) <> ((hdigit 0 1 1 1)) (e) <> ((hdigit 1 1 1 1)) (f) -- approximate decimal expansion of rational <> ((approx (Q (?s ?n ?d)) (N ?k))) (emit force (astr ?s (N ?k) (div (mul (pow (N ten) (N ?k)) (N ?n)) (N ?d)))) <> ((astr - (N ?k) (N ?x))) ((- (astr1 (N ?k) (N ?x) ()))) <> ((astr + (N ?k) (N ?x))) ((astr1 (N ?k) (N ?x) ())) <> ((astr1 (N (0 ())) (N ?x) ?a)) ((concat (tostr (N ?x)) (. ?a))) <> ((astr1 (N ?k) (N (0 ())) ?a)) ((astr1 (dec (N ?k)) (N (0 ())) (0 ?a))) <> ((astr1 (N ?k) (N ?x) ?a)) ((astr2 (N ?k) (divmod (N ?x) (N ten)) ?a)) <> ((astr2 (N ?k) ((N ?q) (N ?r)) ?a)) ((astr1 (dec (N ?k)) (N ?q) ((decimal ?r) ?a))) -- ( first 16 convergents of the continued fraction. the 14th term provides more precision than 64-bit floating point ) <> (pi/cf) (((nat 3) ((nat 7) ((nat 15) ((nat 1) ((nat 292) ((nat 1) ((nat 1) ((nat 1) ((nat 2) ((nat 1) ((nat 3) ((nat 1) ((nat 14) ((nat 2) ((nat 1) ((nat 1) ()))))))))))))))))) <> ((pi/rat (N ?k))) ((pi/rat1 (N ?k) pi/cf)) <> ((pi/rat1 (N (0 ())) ((N ?h) ?t))) ((Q (+ ?h one))) <> ((pi/rat1 (N ?k) ())) (#err) <> ((pi/rat1 (N ?k) ((N ?h) ?t))) ((add (Q (+ ?h one)) (div (Q (+ one one)) (pi/rat1 (dec (N ?k)) ?t)))) <> ((pi/rat-x (N ?k))) ((pi/finish (pi/approx (N ?k) (N one) (N three)))) <> ((pi/approx (N (0 ())) (N ?n) (N ?d))) ((ratify + (N ?n) (inc (N ?d)))) <> ((pi/approx (N ?k) (N ?n) (N ?d))) ((div (Q (+ ?n one)) (add (Q (+ ?d one)) (pi/approx (dec (N ?k)) (add (N ?n) (N ?d)) (add (N ?d) (N two)))))) <> ((pi/finish (Q ?q))) ((div (Q (+ four one)) (add (Q (+ one one)) (Q ?q)))) <> (print (S ?:)) (?:) -- ( print (str (mul (add (rat 3/4) (rat 19/21)) (rat 135/136))) ) print (str (pi/rat (nat 0))) print (S \n) print (str (pi/rat (nat 1))) print (S \n) print (str (pi/rat (nat 2))) print (S \n) print (str (pi/rat (nat 3))) print (S \n) print (str (pi/rat (nat 4))) print (S \n) print (str (pi/rat (nat 5))) print (S \n) print (str (pi/rat (nat 6))) print (S \n) print (str (pi/rat (nat 7))) print (S \n) print (str (pi/rat (nat 8))) print (S \n) print (str (pi/rat (nat 9))) print (S \n) print (str (pi/rat (nat 10))) print (S \n) print (str (pi/rat (nat 11))) print (S \n) print (str (pi/rat (nat 12))) print (S \n) print (str (pi/rat (nat 13))) print (S \n) print (str (pi/rat (nat 14))) print (S \n)