too much stored in cache tables?

David Eisenbud has pointed out that in some respects M2 is not as close to a functional language as it could be:

i1 : M = ZZ^1 ++ ZZ^2

       3
o1 = ZZ

o1 : ZZ-module, free

i2 : N = ZZ^2 ++ ZZ^1

       3
o2 = ZZ

o2 : ZZ-module, free

i3 : M===N

o3 = true

i4 : M^[1]===N^[1]

o4 = false

i5 : M^[1]==N^[1]

o5 = false

i6 : M^[1]

o6 = | 0 1 0 |
     | 0 0 1 |

              2        3
o6 : Matrix ZZ  <--- ZZ

i7 : N^[1]

o7 = | 0 0 1 |

              1        3
o7 : Matrix ZZ  <--- ZZ

The issue is what information should enter into determining whether X===Y
in general. If we want to get as close as possible to a functional language, then for
any function f, we'd prefer X===Y to imply f X===f Y. The failure of that was what was
surprising for David, and the function "memoize" is built on that principle.

Should we audit everything in all cacheTables, and move items that affect behavior not related to timing of computations outside of them?

If adopted, it would mean, for example, that Hom(R^1,M)===M is false but Hom(R^1,M)==M is true.

No source files or tests are named. Start by reproducing the M2 examples involving M, N, ===, ==, and memoize, then inventory the referenced cacheTables and determine which stored values affect behavior beyond computation timing. Done requires an agreed rule for cache contents and a defined audit scope.