-- -- -- Number -- -- -- -- Natural Numbers -- nat := matcher | o as () with | 0 -> [()] | _ -> [] | s \$ as nat with | \$tgt -> match compare tgt 0 as ordering with | greater -> [tgt - 1] | _ -> [] | #\$n as () with | \$tgt -> if tgt = n then [()] else [] | \$ as (something) with | \$tgt -> [tgt] nats := [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100] ++ map (+ 100) nats nats0 := 0 :: nats odds := 1 :: map (+ 2) odds evens := 2 :: map (+ 2) evens fibs := [1, 1] ++ map2 (+) fibs (tail fibs) isPrime := \match as integer with | ?(< 2) -> False | \$n -> n = findFactor n primes := 2 :: filter isPrime (drop 2 nats) divisor n d := 0 = n % d findFactor := memoizedLambda n -> match takeWhile (<= floor (sqrt (itof n))) primes as list integer with | _ ++ (?1#(divisor n %1) & \$x) :: _ -> x | _ -> n primeFactorization := \match as integer with | #1 -> [] | ?(< 0) & \$n -> (-1) :: primeFactorization (neg n) | \$n -> let p := findFactor n in p :: primeFactorization (quotient n p) pF := primeFactorization isEven n := 0 = modulo n 2 isOdd n := 1 = modulo n 2 fact n := foldl (*) 1 [1..n] perm n r := foldl (*) 1 [(n - (r - 1))..n] comb n r := perm n r / fact r nAdic n x := if x = 0 then [] else let q := quotient x n r := x % n in nAdic n q ++ [r] -- -- Integers -- mod m := matcher | #\$n as () with | \$tgt -> if modulo tgt m = modulo n m then [()] else [] | \$ as (something) with | \$tgt -> [tgt] -- -- Floats -- exp2 x y := exp (log x * y) -- -- Decimal Fractions -- rtodHelper m n := let q := quotient (m * 10) n r := m * 10 % n in (q, r) :: rtodHelper r n rtod x := let m := numerator x n := denominator x q := quotient m n r := m % n in (q, map fst (rtodHelper r n)) rtod' x := let m := numerator x n := denominator x q := quotient m n r := m % n (s, c) := findCycle (rtodHelper r n) in (q, map fst s, map fst c) showDecimal c x := match 2#(%1, take c %2) (rtod x) as (integer, list integer) with | (\$q, \$sc) -> foldl S.append (S.append (show q) ".") (map show sc) showDecimal' x := match rtod' x as (integer, list integer, list integer) with | (\$q, \$s, \$c) -> foldl S.append "" (S.append (show q) "." :: map show s ++ " " :: map show c ++ [" ..."]) -- -- Continued Fraction -- regularContinuedFraction n xs := n + foldr (\a r -> 1 / (a + r)) 0 xs continuedFraction n xs ys := match (xs, ys) as (list integer, list integer) with | (\$x :: \$xs, \$y :: \$ys) -> n + y / continuedFraction x xs ys | ([], []) -> n regularContinuedFractionOfSqrtHelper m a b := let n := floor (f.+ (rtof a) (f.* (rtof b) (sqrt (rtof m)))) x := m - power n 2 in if x = 0 then [(a, b, n)] else let y := power (n - a) 2 - b * b * m in (a, b, n) :: regularContinuedFractionOfSqrtHelper m ((a - n) / y) (neg (b / y)) regularContinuedFractionOfSqrt m := let n := floor (sqrt (rtof m)) x := m - power n 2 in if x = 0 then (n, []) else ( n , map 3#%3 (regularContinuedFractionOfSqrtHelper m (n / x) (1 / x)) ) regularContinuedFractionOfSqrt' m := let n := floor (sqrt (rtof m)) x := m - power n 2 in if x = 0 then (n, [], []) else let (s, c) := findCycle (regularContinuedFractionOfSqrtHelper m (n / x) (1 / x)) in (n, map 3#%3 s, map 3#%3 c)