Ambiguity in definition of identities
alexarice opened this issue · comments
the identity on a zero cell can be defined in two possible ways
let id = coh (x : *) : x -> x
let id2 = comp (x : *) : x -> x
@jamievicary seemed to believe that each term should either be a comp or a coh. Is it possible that the second term should not be accepted?
Right, the second term should not be accepted. The boundary of the pasting diagram (x : *) should be the empty context so that the second one is not well typed. This should be pretty easy to fix.
I could take a look tomorrow if you want
The arXiv version of the catt paper states that the boundary of (x : *) is (x : *) and not the empty context. This seems to agree with the definition of boundary on globular sums
I think we only define the boundary for k >= 0, in which case this is correct. But in the case you point out, we should actually be calculating the -1-boundary (1 less than the dimension of the pasting diagram), in which case empty is the correct answer. I just pushed a fix.