Cartesian cubical delta

The interval retains only $0,1$, and variables; cofibrations admit arbitrary equations $r=s$. Composition is split into coercion and homogeneous composition:

$\mathrm{\Gamma },i:\mathbb{I}⊢A\mathsf{type}$$\mathrm{\Gamma }⊢r:\mathbb{I}$$\mathrm{\Gamma }⊢s:\mathbb{I}$$\mathrm{\Gamma }⊢a:A[r/i]$

$\mathrm{\Gamma }⊢{\mathsf{coe}}_{i.A}^{r\to s}(a):A[s/i]$

$\mathrm{\Gamma }⊢A\mathsf{type}$$\mathrm{\Gamma }⊢r:\mathbb{I}$$\mathrm{\Gamma }⊢s:\mathbb{I}$$\mathrm{\Gamma }⊢\phi \mathsf{cof}$$\mathrm{\Gamma },i:\mathbb{I},\phi ⊢u:A$$\mathrm{\Gamma }⊢a:A$$\mathrm{\Gamma },\phi ⊢u[r/i]\equiv a:A$

$\mathrm{\Gamma }⊢{\mathsf{hcom}}_A^{r\to s}[\phi \mapsto i.u](a):A$