用Ruby的Lambda实现基本数值运算

ruby-lambda-expression.rb

ZERO = -> p { -> x { x } }
ONE = -> p { -> x { p[x] } }
TWO = -> p { -> x { p[p[x]] } }
THREE = -> p { -> x { p[p[p[x]]] } }
FOUR = -> p { -> x { p[p[p[p[x]]]] } }
FIVE = -> p { -> x { p[p[p[p[p[x]]]]] } }

def to_integer(n)
  n[-> x {x + 1}][0]
end


SUCC = -> n {
  -> p {
    -> x {
      p[n[p][x]]
    }
  }
}


ADD = -> n {
  -> m {
   n[SUCC][m]
  }
}

MULTI = -> n {
  -> m {
    n[ADD[m]][ZERO]
  }
}

PAIR = -> first {
  -> second {
    -> p {
      p[first][second]
    }
  }
}

LEFT = -> first {
  -> second {
    first
  }
}

RIGHT = -> first {
  -> second {
    second
  }
}

SLIDE = -> p {
  PAIR[p[RIGHT]][SUCC[p[RIGHT]]]
}

def to_pair(pair)
  "(#{to_integer(pair[LEFT])}, #{to_integer(pair[RIGHT])})"
end

PRED = -> n {
  n[SLIDE][PAIR[ZERO][ZERO]][LEFT]
}

SUBT = -> m {
  -> n {
    n[PRED][m]
  }
}


POWER = -> m {
  -> n {
    n[MULTI[m]][ONE]
  }
}

if __FILE__ == $0
  p to_integer(ADD[FOUR][FIVE])
  p to_integer(MULTI[FOUR][FIVE])
  p to_integer(MULTI[ONE][FIVE])

  p to_integer(PAIR[TWO][FIVE][LEFT])
  p to_integer(PAIR[TWO][FIVE][RIGHT])

  puts to_pair(PAIR[ONE][TWO])
  puts to_pair(SLIDE[PAIR[ONE][TWO]])
  puts to_pair(SLIDE[SLIDE[PAIR[ONE][TWO]]])

  p to_integer(PRED[FOUR])
  p to_integer(PRED[TWO])
  p to_integer(PRED[ONE])

  p to_integer(SUBT[FIVE][ONE])
  p to_integer(SUBT[FIVE][TWO])
  p to_integer(SUBT[THREE][TWO])

  p to_integer(POWER[FIVE][FIVE])
  p to_integer(POWER[FOUR][FOUR])
  p to_integer(POWER[FOUR][ONE])  
end