Re-apply: Cache types in the constraint system expression type map.

I've been unable to reproduce the issue that hit on the builder, and
still expect this change to be NFC, so trying it out again. If it
fails, I'll revert again and try another shot at reproducing.

Original commit message:

We create new expressions that have the type on the expression
set. Make sure we capture these types in the constraint system type
map so that we can refer to types uniformally by consulting the map.

NFC.

(cherry picked from commit 57d5d97)

Author: rudkx