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UC Berkeley – CS164 Midterm 2
Fall 2002
Midterm 2
1. [20 points] Consider the language that consist of possibly empty lists of the identifier x
enclosed by parentheses and separated by commas. The language includes { () (x) (x,x)
(x,x,x) } etc.
(a) Write a short grammar suitable for use with your LALR parser generator, including augments, so that you accept only these sentences. The sentence () should produce an AST that looks like (ExpList). The sentence (x,x,x) should look like (ExpList x x x).
(b) Stephen claims this language can be recognized by a DFA with 5 states. Is he right? If so, draw the DFA. If not, explain why this cannot be.
2. [8 points] In assignment 3 you made extensive use of the program (defun aug(&rest r)(if (null (cdr r)) (car r) r))
(a) What program calls aug?
(b) When is it called?
(c) What does r get bound to?
(d) What does (aug ’(1 2 3)) return?
3. [16 points] Henry considers implementing the following modifications to the Tiger programming language. For each proposed modification, identify the component(s) of the
compiler that Henry will need to change. Select from the lexical analyzer (L), parser (P), type-
checker (T), or interpreter (I). It is possible that no change is necessary at all (N). Sometimes
more than one may be appropriate or possible. Unless it is utterly clear to you that there is only
one possible answer that we are after, we recommend that you write your answer here and also explain on the reverse of this page why you said so.
- Forbid the type definition let type foo= {}
- Make the expression () identical to VOID.
- Make the expression () identical to nil.
- Allow arithmetic on Boolean results like (1>0)+(2<3).
- Make the statement (a<b<c) mean the same as (a<b) & (b<c).
- Introduce a type Boolean with two values true and false, such that comparisons result in one of these values rather than 1 or 0.
- Allow a recursive x.next:=x given that x is of type z= { val=int, next=z }.
- Addition of a procedure shell() that takes no argument and opens up an interactive shell window, returning an integer “return code” when the shell command is done. 4. [10 points] Lee is building an implementation of Tiger (not necessarily built on top of Lisp).
Lee needs to consider storage management, and needs your answers to the following questions in
complete English sentences.
- At what point in a Tiger computation would a garbage collection likely be started? Hint: you ordinarily do a garbage collection when you need more memory but don’t seem to have enough free. Even bigger hint: What kinds of statements in Tiger allocate heap space?
- What kinds of statements in Tiger allocate space on a stack?
- What kinds of statements in Tiger de-allocate space?
- If you wish to provide explicit heap memory management, what changes would you have to make to Tiger?
- Any discussion of garbage collection refers to the roots needed to start the operation. In a Tiger implementation using garbage collection, what are the roots? 5. [9 points]
a. How does the Tiger interpreter discussed in class deal with logical “and” and “or” expressions such as A&B|C?
b. Typechecking comparison (such as >) is more elaborate in Tiger than typechecking addition +. Explain why.
c. What do you know about the type of x give than the expression if x=nil then 1 else 2 passes a semantic check?
6. [6 points] Explain in complete English sentences what steps are necessary in the Tiger
interpreter to interpret a Tiger expression “call” such as F(3,a).
3+4*(("big"<"little")>0)-9)
8. [4 points] What is the amortized cost (that is, the cost per reclaimed cell) of a 2-space copying garbage collector process in which, at time t a garbage collection is begun, there are R live nodes
and a total of H cells in the heap.
a. Explain any additional symbols you introduce using complete English sentences.
b. What happens if R = H /2?
9. [11 points] In the Leopard programming language, a language similar in some respects to
Tiger, the following program is legal. let function q(a,b)= let in a:=3;b:=7 end type ar=array of int var m:=ar [6] of 0 var i:= in q(i, m[i+2]); for i:=0 to 5 do print(chr(m[i]+ ord("0"))) end
a. If Leopard has call-by-reference parameter passing, what are the six values in the array m when they are printed?
b. If Leopard has call-by-name parameter passing, what are the six values in the array m?
c. If Leopard has the same parameter passing as Tiger, what are the six values in the array m?
d. Why did we not write print(m[i])?
e. What prevents this program from being legal Tiger?
