(10 points) Consider a fictitious programming language containing only two numerical types integer and real), in which arbitrarily long (possibly empty) 1-dimensional arrays of numbers are declared, instantiated, and initialized in a single statement, two of which are given below: integer [] numbers = { 1, 5, 7, 9, 10 }; reall) reals = { 2.0, 3.35, 1.24, 54.145, -4.9 }; Write an EBNF grammar with as its start symbol that can generate all and only the syntactically correct array declarations of this form. Instead of creating rules to generate the set of all possible identifiers (variable names), integer constants, and floating point constants, your grammar must refer to the non-terminals , , and , which can be assumed to be already defined elsewhere. (To think about: Why does it make sense for these non-terminals to be defined in another grammar, or in a distinct part of the grammar?) For full credit, you MUST use EBNF extensions WHENEVER possible to minimize the number of productions in your grammar (10 points) Consider a fictitious programming language containing only two numerical types integer and real), in which arbitrarily long (possibly empty) 1-dimensional arrays of numbers are declared, instantiated, and initialized in a single statement, two of which are given below: integer [] numbers = { 1, 5, 7, 9, 10 }; reall) reals = { 2.0, 3.35, 1.24, 54.145, -4.9 }; Write an EBNF grammar with as its start symbol that can generate all and only the syntactically correct array declarations of this form. Instead of creating rules to generate the set of all possible identifiers (variable names), integer constants, and floating point constants, your grammar must refer to the non-terminals , , and , which can be assumed to be already defined elsewhere. (To think about: Why does it make sense for these non-terminals to be defined in another grammar, or in a distinct part of the grammar?) For full credit, you MUST use EBNF extensions WHENEVER possible to minimize the number of productions in your grammar