COMP 105 fault graph for type unifiers

The graph below shows the results of testing type unifiers.
Read the nodes as follows:

• The number or numbers in each node identify a submission or set of submissions. Numbers are chosen to keep students anonymous; you should have received your number by email.
• Each node shows how many tests were passed by submissions in that node. The graph includes only meaningful tests. A test is meaningful if it distinguishes a unique set of outcomes, and if its results are not implied by a combination of other tests. Most outcomes have a set of equivalent tests which produce identical outcomes; we use the smallest such test.
• The bars at the bottom of each node show exactly which tests were passed. A vertical bar represents a pass; a dot represents failure or a catastrophic error.

• If node A points to node B, than node B passed strictly more tests than node A; node B is strictly better. The edge from A to B shows the smallest test case that A fails and B passes.
• If there is a single node at the top, which all the others point to, it contains the submissions that passed all tests.
• If two nodes are not connected by any path, then the submissions in those nodes have distinct, independent bugs.
• If there is a node not at the top which contains more than one submission, it means that as far as we could discover by testing, these submissions have identical faults.

If the graph is blurry or pixelated, click on it to get Scalable Vector Graphics, then zoom.

1. Types 'a and 'a can be unified, but your unifier failed with the message Cannot unify 'a and 'a.
2a. Unifying int and 'a raised an exception other than TypeError, which is the only exception that 'unify' may raise.
3a. Unifying 'a and ('a) raised an exception other than TypeError, which is the only exception that 'unify' may raise.
3b. Types 'a and ('a) are not unifiable, but instead of raising the 'TypeError' exception, your 'unify' function returned a substitution.
4a. Unifying 'a and ('b 'a) raised an exception other than TypeError, which is the only exception that 'unify' may raise.
4b. Types 'a and ('b 'a) are not unifiable, but instead of raising the 'TypeError' exception, your 'unify' function returned a substitution.
5. Types ((int)) and ((int)) can be unified, but your unifier failed with the message Cannot unify int and int.
6a. Types (list 'a) and (tuple 'b) are not unifiable, but instead of raising the 'TypeError' exception, your 'unify' function returned a substitution.
7a. Unifying (list 'a) and (list 'a 'b) raised an exception other than TypeError, which is the only exception that 'unify' may raise.
8a. Unifying (((list)) (('a 'b))) and ('c 'b) raised an exception other than TypeError, which is the only exception that 'unify' may raise.
8b. Types (((list)) (('a 'b))) and ('c 'b) are not unifiable, but instead of raising the 'TypeError' exception, your 'unify' function returned a substitution.
9. Types (list ('b 'a)) and (list ('a 'b)) can be unified, but your unifier failed with the message Cannot unify 'a 'b and 'b 'a.
9a. Given input types tau1 = (list ('b 'a)) and tau2 = (list ('a 'b)), your 'unify(tau1, tau2)' function returned a substitution theta that is not a unifier. The two types theta tau1 and theta tau2 should be equal, but theta tau1 = (list ('b 'a)), and theta tau2 = (list ('a 'b)) are different.
10a. Types (tuple 'a 'a) and (tuple int bool) are not unifiable, but instead of raising the 'TypeError' exception, your 'unify' function returned a substitution.
11a. Unifying ((ref) (('a 'a array 'b))) and (('b) ('b)) raised an exception other than TypeError, which is the only exception that 'unify' may raise.
11b. Types ((ref) (('a 'a array 'b))) and (('b) ('b)) are not unifiable, but instead of raising the 'TypeError' exception, your 'unify' function returned a substitution.
12a. Unifying (((list)) ((bool list) (array) bool)) and ('a ((bool list) 'b 'a)) raised an exception other than TypeError, which is the only exception that 'unify' may raise.
12b. Types (((list)) ((bool list) (array) bool)) and ('a ((bool list) 'b 'a)) are not unifiable, but instead of raising the 'TypeError' exception, your 'unify' function returned a substitution.
13. Types ('a (('b 'c 'c array) ('d 'd ref bool 'd))) and ('c (('b 'd 'c array) ('d 'b ref bool 'a))) can be unified, but your unifier failed.
13a. Given input types tau1 = ('a (('b 'c 'c array) ('d 'd ref bool 'd))) and tau2 = ('c (('b 'd 'c array) ('d 'b ref bool 'a))), your 'unify(tau1, tau2)' function returned a substitution theta that is not a unifier.