CS314 Fall 2007
Asignment 8

Imagine that in a programming language, arrays have their bounds as 
part of their type; that is, [1:10]int is the not the same type as [0:9]int.


	/* type definitions */
	type vector [1:10] int;
        type matrix [1:10] vector;
        type mm [1:10,1:10] int;
        type zz [1:10] vector;
	type yy [0:9] vector;
	type ss 1..10;
	type tt 5..7
	type integ int
	type s struct {int a1; ss t};
	type z struct {ss t1, ss t2};
	type w struct {int v, int u}
	type q struct {integ a2; ss a3};

	/* variable declarations */
        mm c,d;
        zz a,b;
	yy e,f
        vector v1,v2;
        matrix m1, m2;
	ss t1,t2;
	tt t3,t4;
	int t5;
	integ t6;
	s c1;
	z c3;
	w c4;
	q c2;
	

a. If we use structural equivalence for comparing types, group these
variables into sets where each set of variables has the same type:
{c,d,a,b,e,f,v1,v2,m1,m2,t1,t2,t3,t4,t5,t6,c1,c2,c3,c4}.

b. Show the groupings of the variables which would occur if we used
name equivalence: {c,d,a,b,e,f,v1,v2,m1,m2,t1,t2,t3,t4,t5,t6,c1,c2,c3,c4}.

c. Assume that the following statements are legal in some programming
language.  For each statement, tell if it could be type checked at
compile-time or run-time; briefly give a reason for your answer.
(Note: the general rule is coercion can occur if there is no loss of
precision in the implicit conversion.)

	/* assignment statements */
	m1[t1] = m2[t2];
	t2 = t4;
	t5 = t3;
	c1.a1 = c4.v;
	c1.a1 = m1[t5,t5+1];
	c4.v = c3.t1;
	t3 = t1;
	t5 = v1[2];