# Rick van der Zwet
# StudentID: 0433373
# $Id: lecture3.txt 248 2007-10-04 19:37:40Z rick $

All quotes are based on the 7th edition of Concepts of programming
languages from Robert W. Sebesta, cause the 8th edition has not come in
yet

*** Chapter 3 Problem Set ***

24)
Q: Write an attribute grammar whose base BNF is that of Example 3.2 and
   whose type rules are the same as for the assignment statement examples
   of Section 3.4.5.

A:
Syntax Rule: <assign> -> <id> = <expr>
Semantic Rule: <expr>.expected_type <- <id>.actual_type

Syntax Rule: <id> -> A | B | C
Semantic Rule: <id>.actual_type <- look-up(<id>.string)

Syntax Rule: <expr> -> <id>[2] + <expr>[3]
Semantic Rule: <expr>.actual_type <- 
                    if (<id>[2].actual_type = int) and
                       (<expr[3].actual_type = int)
                       than int
                    else real
                    end if
                <expr>[3].expected_type <-
                    if (<id>[2].actual_type = int) and
                       (<expr>.expected_type = int)
                       than int
                    else real
                    end if
Predicate: <expr>.actual_type == <expr>.expected_type

Syntax Rule: <expr> -> <id>[2] * <expr>[3]
Semantic Rule: <expr>.actual_type <- 
                    if (<id>[2].actual_type = int) and
                       (<expr[3].actual_type = int)
                       than int
                    else real
                    end if
                <expr>[3].expected_type <-
                    if (<id>[2].actual_type = int) and
                       (<expr>.expected_type = int
                       than int
                    else real
                    end if
Predicate: <expr>.actual_type == <expr>.expected_type

Syntax Rule: <expr> -> ( <expr>[2] )
Semantic Rule: <expr>.actual_type <- <expr>[2].actual_type
               <expr>[2].expected_type <- <expr>.expected_type
Predicate: <expr>.actual_type == <expr>.expected_type

Syntax Rule: <expr> -> <id>
Semantic Rule: <expr>.actual_type <- <id>.actual_type
Predicate: <expr>.actual_type == <expr>.expected_type



25)
Q: Prove the following program is correct:
    {n > 0}
    count = n;
    sum = 0;
    while count <> 0 do
        sum = sum + count;
        count = count - 1;
    end
    {sum = 1 + 2 + ... + n}
A: (with some help from http://www.cs.unb.ca/profs/wdu/cs4613/a5ans.htm
   cause I was looking at the wrong I)
* First step is linear,
  {n > 0} count = n {Q}
  Q: {n > 0 AND count = n}
* Second as well
  {n > 0 AND count = n} sum = 0 {Q}
  Q: {n > 0 AND count = n AND sum = 0}

* Loop invariant vality checks:
A) P => I
B) {I and B} S {I}
C) {I and not(B)} => Q
D) Check is loops terminates
 * count is liniary decreased with 1 and starts with a number than 0.
   logically it will always becomes 0, which ends the loop