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Consider the dependent sum of the above, but realigned strictly over A along phi.
The above actually accounts for all realignment situations, but it is much cleaner because the only strict isomorphisms the users has to type in are canonical isos with the unit type. This reduction simplifies implementation considerably, and makes the connective much easier to use than the traditional realignment.
To me, this connective is the basis of a modernized take on type refinements. If we add this, there is an immense amount of stuff that we could experimentally be doing...
The text was updated successfully, but these errors were encountered:
I have discovered a much more implementable version of Orton-Pitts strictification/realignment.
phi
-modal type, i.e.A : {phi} type
phi
-connected types indexed inA
, i.e.x : {phi} A |- B(x) type \ phi
. This requires Add judgmental notion of "strictly phi-connected type" #182A
alongphi
.The above actually accounts for all realignment situations, but it is much cleaner because the only strict isomorphisms the users has to type in are canonical isos with the unit type. This reduction simplifies implementation considerably, and makes the connective much easier to use than the traditional realignment.
To me, this connective is the basis of a modernized take on type refinements. If we add this, there is an immense amount of stuff that we could experimentally be doing...
The text was updated successfully, but these errors were encountered: