Note: this problem is taken from the Programming Languages subject at Barcelona School of Informatics. Design a parser to describe heterogeneous lists of numbers. The following example shows the elements of the language:

  L1 = []
  L2 = [1,2,3]
  L3 = L1#L2
  L4 = [[[1,2],3],4]
  L5 = lreduce + L4
  L6 = lmap - 1 L4
  print L5
  L7 = lfilter > 2 L4

Make the grammar so that the parser generator builds the following AST for the previous example:

  list
   \__=
   |   \__L1
   |   \__[
   \__=
   |   \__L2
   |   \__[
   |       \__1
   |       \__2
   |       \__3
   \__=
   |   \__L3
   |   \__#
   |       \__L1
   |       \__L2
   \__=
   |   \__L4
   |   \__[
   |       \__[
   |       |   \__[
   |       |   |   \__1
   |       |   |   \__2
   |       |   \__3
   |       \__4
   \__=
   |   \__L5
   |   \__lreduce
   |             \__+
   |             \__L4
   \__=
   |   \__L6
   |   \__lmap
   |          \__-
   |          |   \__1
   |          \__L4
   \__print
   |       \__L5
   \__=
       \__L7
       \__lfilter
                 \__>
                 |   \__2
                 \__L4

Remarks:

• An identifier is a non-empty sequence of alphanumeric characters, not starting by a digit.
• A number is a non-empty sequence of digits.
• An identifier cannot appear alone in an expression. Thus, “L1=L2” is not a valid expression.
• A list literal, i.e., an expression of the form [ ... ] cannot contain list identifiers nor operations. Just numbers and other list literals.
• The operator # cannot appear more than once in an expression. Thus “L4 = L1#L2#L3” is not a valid expression. Furthermore, it can only be applied to identifiers, and not arbitrary expressions.
• The print instruction can only be applied to an identifier, and not an arbitrary expression.
• lmap, lfilter, and lreduce can only receive an identifier as last parameter.
• The operators available for lreduce and lmap are +, -, and *.
• The relational operators available for lfilter are >, <, ==, and !=.