For questions 1--7, please read pages 17--26 (the book sections on
environments and on operational semantics of expressions).

1.  What is $\xi$?

2.  What is $\phi$?

3.  What is $\rho$?

<!-- NEXT YEAR: CQ's on what rho{x->7}(x) meant
                and what rho{x->7}{x->0} meant -->


4.  In operational semantics, what kind of a thing does $e$ stand for?

5.  In operational semantics, what kind of a thing does $v$ stand for?

6.  Examine the evaluation rules for all the syntactic forms of
    Impcore, and list all the forms to which more than one rule can apply.
    ("Syntactic form" is in the index *twice*; you will probably find
    both pages helpful.) 

    *Example answer*: more than one rule applies to the VAR(x) form.

7.  Pick three of the syntactic forms from the previous question.  For each one, explain
    briefly in your own words *why* that form has more than one evaluation
    rule.

    *Example answer*: there are two rules for the VAR form because a name can
    be either a formal parameter or a global variable.

For question 8, please skim section 1.5, and carefully read section 1.5.2 
on pages 43--53.

8.  Pick one of the syntactic forms from the previous question.  Find
    the place in the interpreter where the form is implemented, and
    answer the following two questions:

    (a) How does the interpreter decide which rule applies?  Identify
        both the math and the code involved in the decision.

    (b) If neither rule applies, how does the interpreter know, and
        what does it do?

    *Example answer*: The VAR(x) form is evaluated in chunk 45a at the
    top of page 45.  It decides which rule applies by checking the
    math $x \in \mathop{dom} \rho$---the code is `isvalbound(e->u.var,
    formals)`.  If\ the answer is yes, rule FormalVar applies.  If the
    answer is no, the only possible rule is GlobalVar. 

    If\ neither rule applies, it is because $x \notin \mathop{dom} \rho$ and
    also $x \notin \mathop{dom} \xi$.  In that case, no rule's conditions are
    satisfied.  The interpreter knows by checking
    `isvalbound(e->u.var, formals)` and then if that fails, checking
    `isvalbound(e->u.var, globals)`.  If both conditions fail, no rule
    applies, and the interpreter triggers a run-time error (by calling
    `runerror`). 

For questions 9 and 10, please read section 1.1.5 (page 15) on the
difference between primitive functions and predefined functions, and
please study the rules for function application on pages 24 to 26.

9.  Function `<=` is *predefined*.  When evaluating `(<= 0 n)`, what
    rule of the operational semantics is used at the root of the derivation?

10. Function `<` is *primitive*.  When evaluating `(< n 10)`, what
    rule of the operational semantics is used at the root of the derivation?