  We contribute XTT, a cubical reconstruction of Observational Type Theory
which extends Martin-L\"of's intensional type theory with a dependent equality
type that enjoys function extensionality and a judgmental version of the
unicity of identity types principle (UIP): any two elements of the same
equality type are judgmentally equal. Moreover, we conjecture that the typing
relation can be decided in a practical way. In this paper, we establish an
algebraic canonicity theorem using a novel cubical extension (independently
proposed by Awodey) of the logical families or categorical gluing argument
inspired by Coquand and Shulman: every closed element of boolean type is
derivably equal to either 'true' or 'false'.
