Write a clearly legible T to the left of each of the following that is true, and a clearly legible F to the left of each that is false.

1. All compilers translate to machine language.
2. All programming language implementations are compilers.
3. A simple value is a value that has no visible internal structure.
4. A complex value is one that has characteristics that change over time.
5. Integers are typically considered simple values.
6. A token can only have one associated lexeme.
7. A variable name is typically a single lexeme in a program.
8. Backus-Naur Form is a notation for giving precise definitions of syntax.
9. Pattern matching can be used to bind names by solving simple equations.

An implementation of a programming language is not an adequate definition of the language. Why not? What would be the consequences of using an implementation as a definition?

What is an important advantage of the linked representation of sequences over the sequential representation?

What is an important advantage of the sequential representation of sequences over the linked representation?

Show that the following BNF grammar is ambiguous. The start symbol is <S>.

    <S> ::= <S> a
         |  a <S>
         |  a
  

Show a parse tree for string aacacab according to the following grammar, where the start symbol is <S>.

    <S> ::= <F> a <S>
         |  b
    <F> ::= a <F>
         |  c
  

Write a BNF grammar for sequences of left and right parentheses that are balanced. A sequence of parentheses is balanced if parentheses match and are well nested. For example, (()(())) is balanced, but )( and ())()( are not balanced.

What is a solution for x and y to pattern match equation (x+1)::y = [3,4,5,6]?