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CS415 โ Written Assignment 6
This assignment asks you to prepare written answers to questions on code layout
and operational semantics. Each of the questions has a short answer. You may discuss
this assignment with other students and work on the problems together. However, your
write-up should be your own individual work.
Please print your name and email address on your homework!
We need this information so that we can give you credit for the assignment and so that
we can return it to you.
1. Consider the following piece of code:
fact(n : Int) : Int {
if n > 0 then n*fact(n-1) else 1 fi
Draw the tree of activation records for a call to fact(4).
2. Consider these six operational semantics rules:
so, E, S e 1 : Bool(f alse), S 1 so, E, S while e 1 loop e 2 pool : void, S 1 (4)
E(id) = lid S(lid) = v so, E, S ` id : v, S
so, E, S e 1 : Bool(true), S 1 so, E, S 1 e 2 : v, S 2 so, e, S 2 while e 1 loop e 2 pool : void, S 3 so, E, S while e 1 loop e 2 pool : void, S 3
so, E, S e : v, S 1 E(id) = lid S 2 = S 1 [v/lid] so, E, S id โ e : v, S 2
so, E, S e 1 : v 1 , S 1 lnew = newloc(S 1 ) so, E[lnew/id], S 1 [v 1 /lnew] e 2 : v 2 , S 2 so, E, S ` let id : T โ e 1 in e 2 : v 2 , S 2
so, E, S e 1 : Int(n 1 ), S 1 so, E, S 1 e 2 : Int(n 2 ), S 2
v =
Bool(true) if n 1 < n 2 Bool(f alse) if n 1 โฅ n 2
so, E, S ` e 1 < e 2 : v, S 2
Use these rules to construct a derivation for the following piece of code:
let x : Int <- 2 in
while 1 < x loop
x <- x - 1
pool
You may assume reasonable axioms, e.g. it is always true that so, E, S ` 2 โ 1 :
Int(1), S. Start your derivation using the let rule (3) as follows:
so, E, S ` 2 : Int(2), S
... so, E[lnew /x], S[Int(2)/lnew ] while 1 < x loop x โ x โ 1 pool : void, Sf inal^ (2) so, E, S let x : Int โ 2 in while 1 < x loop x โ x โ 1 pool : void, Sf inal^ (3)
Note that you only need to expand hypotheses that need to be proved (i.e. those
containing `).
3. Suppose we wanted to add arrays to COOL, using the following syntax:
let a:T[e 1 ] in e 2 Create an array a with size e 1 of T s, usable in e 2
a[e 1 ] <- e 2 Assign e 2 to element e 1 in a
a[e] Get element e of a
Write the operational semantics for these three syntactic constructs. You may
find it helpful to think of an array of type T [n] as an object with n attributes of
type T.
4. The operational semantics for COOLโs while expression show that result of
evaluating such an expression is always void.
However, we could have used the following alternative semantics:
- If the loop body executes at least once, the result of the while expression
is the result from the last iteration of the loop body.
- If the loop body never executes (i.e., the condition is false the first time it
is evaluated), then the result of the while expression is void.
For example, consider the following expression:
while (x < 10) loop x <- x+1 pool
