# Parsing/RPN to infix conversion

``````func p(pair, prec) {
pair[0] < prec ? "( #{pair[1]} )" : pair[1]
}

func rpm_to_infix(string) {
say "#{'='*17}\n#{string}"
var stack = []
string.each_word { |w|
if (w ~~ /\d/) {
stack << [9, Num(w)]
}
else {
var y = stack.pop
var x = stack.pop
given(w) {
when ('^')   { stack << [4, [p(x,5), w, p(y,4)].join(' ')] }
when (<* />) { stack << [3, [p(x,3), w, p(y,3)].join(' ')] }
when (<+ ->) { stack << [2, [p(x,2), w, p(y,2)].join(' ')] }
}
say stack
}
}
say '-'*17
stack.map{_[1]}
}

var tests = [
'3 4 2 * 1 5 - 2 3 ^ ^ / +',
'1 2 + 3 4 + ^ 5 6 + ^',
]

tests.each { say rpm_to_infix(_).join(' ') }
``````

#### Output:

``````=================
3 4 2 * 1 5 - 2 3 ^ ^ / +
[[9, 3], [3, "4 * 2"]]
[[9, 3], [3, "4 * 2"], [2, "1 - 5"]]
[[9, 3], [3, "4 * 2"], [2, "1 - 5"], [4, "2 ^ 3"]]
[[9, 3], [3, "4 * 2"], [4, "( 1 - 5 ) ^ 2 ^ 3"]]
[[9, 3], [3, "4 * 2 / ( 1 - 5 ) ^ 2 ^ 3"]]
[[2, "3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3"]]
-----------------
3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3
=================
1 2 + 3 4 + ^ 5 6 + ^
[[2, "1 + 2"]]
[[2, "1 + 2"], [2, "3 + 4"]]
[[4, "( 1 + 2 ) ^ ( 3 + 4 )"]]
[[4, "( 1 + 2 ) ^ ( 3 + 4 )"], [2, "5 + 6"]]
[[4, "( ( 1 + 2 ) ^ ( 3 + 4 ) ) ^ ( 5 + 6 )"]]
-----------------
( ( 1 + 2 ) ^ ( 3 + 4 ) ) ^ ( 5 + 6 )
``````