function collatz(n) # unproven: always terminates
    k = 0
    while n > 1
        n = isodd(n) ? 3n+1 : n>>1
        k += 1
    end
    return k
end

collatz(89)

for i = 2:2:20
    α = collatz(i)
    println("$i = $α")
end

@time for i = 1:1e6 collatz(18) end

@code_native collatz(123)

@code_llvm collatz(123)

f(a::Any, b) = "fallback"
f(a::Number, b::Number) = "a and b are both numbers"
f(a::Number, b) = "a is a number"
f(a, b::Number) = "b is a number"
f(a::Integer, b::Integer) = "a and b are both integers"

f(1.5, 2)

print(typeof(1.5), ", ", typeof(2))

f(1, "bar")

f(1, 2)

f("foo", [1,2])

f{T<:Number}(a::T, b::T) = "a and b are both $(T)s"

methods(f)

f(big(1.5), big(2.5))

f("foo", "bar") #<== still doesn't apply to non-numbers

immutable Interval{T<:Real} <: Number
  lo::T
  hi::T
end

(a::Real)..(b::Real) = Interval(a,b)

Base.show(io::IO, iv::Interval) = print(io, "($(iv.lo))..($(iv.hi))")

(1..2) + 3 # tries but fails to find a way to reconcile two Numbers

1..2

typeof(ans)

sizeof(1..2) # two 64-bit/8-byte ints

(1//2)..(2//3)

a::Interval + b::Interval = (a.lo + b.lo)..(a.hi + b.hi)
a::Interval - b::Interval = (a.lo - b.hi)..(a.hi - b.lo)

(2..3) + (-1..1)

(2..3) + (1.0..3.14159)  # autoconverts

@code_native (2..3) + (-1..1)

methods(round) # click through...

round(123.321)

round(123.321, 2)

round(123.321, -1)

round(123.321, 1, 2)

for i = 1:10 println(round(123.321, i, 2)) end

Pkg.installed()

using RDatasets
iris = dataset("datasets", "iris")

typeof(iris)

by(iris, :Species, df -> DataFrame(mean_length = mean(df[:PetalLength])))

using GLM
lm1 = fit(LinearModel, SepalLength ~ SepalWidth + PetalLength, iris)

a ~ b + c