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module m1 {
def id(x: Int): Double = x;
def cube(x: Int): Double = x * x * x;
def reciprocal(x: Int): Double = 1.0/x;
def sumInts(a: Int, b: Int): Double =
if (a > b) 0
else a + sumInts(a + 1, b);
def sumCubes(a: Int, b: Int): Double =
if (a > b) 0
else cube(a) + sumCubes(a + 1, b);
def sumReciprocals(a: Int, b: Int): Double =
if (a > b) 0
else 1.0/a + sumReciprocals(a, b);
}
module m2 {
def id(x: Int): Double = x;
def cube(x: Int): Double = x * x * x;
def reciprocal(x: Int): Double = 1.0/x;
def sum(f: Int => Double, a: Int, b: Int): Double =
if (a > b) 0
else f(a) + sum(f, a + 1, b);
def sumInts(a: Int, b: Int): Double = sum(id, a, b);
def sumCubes(a: Int, b: Int): Double = sum(cube, a, b);
def sumReciprocals(a: Int, b: Int): Double = sum(reciprocal, a, b);
}
module m3 {
def sum(f: Int => Double, a: Int, b: Int): Double =
if (a > b) 0
else f(a) + sum(f, a + 1, b);
def sumInts(a: Int, b: Int): Double = sum((x => x), a, b);
def sumCubes(a: Int, b: Int): Double = sum((x => x * x * x), a, b);
def sumReciprocals(a: Int, b: Int): Double = sum((x => 1.0/x), a, b);
}
module m4 {
def sum(f: Int => Double) = {
def sumF(a: Int, b: Int): Double =
if (a > b) 0
else f(a) + sumF(a + 1, b);
sumF
}
def sumInts = sum(x => x);
def sumCubes = sum(x => x * x * x);
def sumReciprocals = sum(x => 1.0/x);
sumCubes(1, 10) + sumReciprocals(10, 20);
}
module m5 {
def sum(f: Int => Double): (Int, Int) => Double = (a, b) =>
if (a > b) 0
else f(a) + sum(f)(a + 1, b);
def sumInts = sum(x => x);
def sumCubes = sum(x => x * x * x);
def sumReciprocals = sum(x => 1.0/x);
sumCubes(1, 10) + sumReciprocals(10, 20);
}
module m6 {
def sum(f: Int => Double)(a: Int, b: Int): Double =
if (a > b) 0
else f(a) + sum(f)(a + 1, b);
def sumInts = sum(x => x);
def sumCubes = sum(x => x * x * x);
def sumReciprocals = sum(x => 1.0/x);
sumCubes(1, 10) + sumReciprocals(10, 20);
}
module m7 {
def sum(f: Int => Double)(a: Int, b: Int): Double = {
def iter(a: Int, result: Double): Double =
if (a > b) result
else iter(a + 1, f(a) + result);
iter(a, 0);
}
def sumInts = sum(x => x);
def sumCubes = sum(x => x * x * x);
def sumReciprocals = sum(x => 1.0/x);
sumCubes(1, 10) + sumReciprocals(10, 20);
}
module m8 {
def product(f: Int => Double)(a: Int, step: Int, b: Int): Double =
if (a > b) 1
else f(a) * product(f)(a + step, step, b);
val pi = 8 * product(x => x * x)(4, 2, 40) / product(x => x * x)(3, 2, 40);
}
module m9 {
def accumulate[t](combiner: (t, t) => t, nullValue: t, f: Int => t, next: Int => Int)
(a: Int, b: Int): t =
if (a > b) nullValue
else combiner(f(a), accumulate(combiner, nullValue, f, next)(next(a), b));
def inc(x: Int) = x + 1;
def sum(f: Int => Double) =
accumulate((x: Double, y: Double) => x + y, 0, f, inc);
def product(f: Int => Double) =
accumulate((x: Double, y: Double) => x * y, 1, f, inc);
}
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