Simple example of Parslet.

expression.rb

require 'parslet'

class Expressions < Parslet::Parser
  rule(:operator)  { match("[+*/-]").as(:op) }
  rule(:operation) { operator >> space >> vector.as(:args) }
  rule(:space)     { match('\s').repeat(1) }
  rule(:numbers)   { space >> number }
  rule(:vector)    { (number >> numbers.repeat(1)).as(:vec) }
  rule(:number)    { match("[0-9]").repeat(1).as(:number) }
  rule(:expr)      { vector | number | operation }
  root :expr
end

def parse(str)
  c = Expressions.new
  c.parse(str)
rescue Parslet::ParseFailed => failure
  puts failure.cause.ascii_tree
end

parse("12")       # => {:number=>"12"@0}
parse("12 34 56") # => {:vec=>[{:number=>"12"@0}, {:number=>"34"@3}, {:number=>"56"@6}]}
parse("+ 1 2 3")  # => {:op=>"+"@0, :args=>{:vec=>[{:number=>"1"@2}, {:number=>"2"@4}, {:number=>"3"@6}]}}
parse("* 1 2 3")  # => {:op=>"*"@0, :args=>{:vec=>[{:number=>"1"@2}, {:number=>"2"@4}, {:number=>"3"@6}]}}

def expr_eval(tree)
  if tree[:number]
    tree[:number].to_i
  elsif tree[:vec]
    tree[:vec].map { |item| expr_eval(item) }
  elsif tree[:op]
    apply_op(tree[:op], expr_eval(tree[:args]))
  end
end

def apply_op(op, vec)
  vec.inject { |s, n| s.send(op, n) }
end

expr_eval(parse("12"))         # => 12
expr_eval(parse("12 34 56"))   # => [12, 34, 56]
expr_eval(parse("+ 12 34 56")) # => 102