alonzo.rb

def λ
  $. += 1
  proc.curry
end

# Convert a Ruby integer to a Church numeral.
def church n
  n.times.reduce(λ { |_, x| x }) { |n| λ { |n, f, x| f[n[f][x]] }[n] }
end

# Undo the above for printing/verifying that this madness wasn't all for naught.
def unchurch p
  p[-> n { n + 1 }][0]
end

Common = λ{|f|λ{|x|f[λ{|_|x[x][_]}]}[λ{|x|f[λ{|_|x[x][_]}]}]}[λ{|f,a,b,c,i|λ{|n|
n[λ{|x|λ{|a,b|b}}][λ{|a,b|a}]}[i][c][λ{|_|λ{|m,n|n[λ{|n,f,x|f[n[f][x]]}][m]}[λ{|
f|λ{|x|f[λ{|_|x[x][_]}]}[λ{|x|f[λ{|_|x[x][_]}]}]}[λ{|f,n|λ{|n|n[λ{|x|λ{|a,b|b}}][
λ{|a,b|a}]}[n][λ{|a,b|a}][λ{|_|λ{|n|n[λ{|x|λ{|a,b|b}}][λ{|a,b|a}]}[λ{|n,f,x|n[λ{
|g,h|h[g[f]]}][λ{|_|x}][λ{|u|u}]}[n]][λ{|a,b|b}][f[λ{|n,f,x|n[λ{|g,h|h[g[f]]}][λ{
|_|x}][λ{|u|u}]}[λ{|n,f,x|n[λ{|g,h|h[g[f]]}][λ{|_|x}][λ{|u|u}]}[n]]]][_]}]}][λ{|
m,n|n[λ{|n,f,x|f[n[f][x]]}][m]}[a][b]][λ{|f,x|f[x]}][λ{|f,x|x}]][f[λ{|f|λ{|x|f[λ{
|_|x[x][_]}]}[λ{|x|f[λ{|_|x[x][_]}]}]}[λ{|f,n,m|λ{|n|n[λ{|x|λ{|a,b|b}}][λ{|a,b|a
}]}[λ{|m,n|n[λ{|n,f,x|n[λ{|g,h|h[g[f]]}][λ{|_|x}][λ{|u|u}]}][m]}[n][m]][n][λ{|_|
f[λ{|n,f,x|n[λ{|g,h|h[g[f]]}][λ{|_|x}][λ{|u|u}]}[n]][λ{|n,f,x|f[n[f][x]]}[m]][_]
}]}][a][λ{|f,x|x}]][λ{|f|λ{|x|f[λ{|_|x[x][_]}]}[λ{|x|f[λ{|_|x[x][_]}]}]}[λ{|f,n,
m|λ{|n|n[λ{|x|λ{|a,b|b}}][λ{|a,b|a}]}[λ{|m,n|n[λ{|n,f,x|n[λ{|g,h|h[g[f]]}][λ{|_|
x}][λ{|u|u}]}][m]}[n][m]][n][λ{|_|f[λ{|n,f,x|n[λ{|g,h|h[g[f]]}][λ{|_|x}][λ{|u|u}
]}[n]][λ{|n,f,x|f[n[f][x]]}[m]][_]}]}][b][λ{|f,x|x}]][c][λ{|n,f,x|n[λ{|g,h|h[g[f
]]}][λ{|_|x}][λ{|u|u}]}[i]]][_]}]}]

a = church 10
b = church 17
c = church  8 # bit width of calculations

puts "Common bits: #{unchurch Common[a, b, λ { |_, x| x }, c]}"
puts "Created #$. lambdas!"              # ^ Church zero