Prismatic cohomology and de Rham-Witt forms

For any prism $(A,d)$, we construct an analogue of Fontaine’s map $W_r(A\mathrm{/}d)\to A\mathrm{/}d\varphi (d)\cdots {\varphi }^{r-1}(d)$. Subsequently, we define a canonical map from de Rham-Witt forms to prismatic cohomology in the perfect case and prove that it is an isomorphism. Using this result, we obtain an explicit description of the prismatic cohomology for a $p$-completed polynomial algebra over $A\mathrm{/}d$.