We introduce irregular constructible sheaves, which are $\mathbb{C}$-constructible with coefficients in a finite version of Novikov ring $\Lambda$ and special gradings. show that the bounded derived category cohomologically complexes is equivalent to holonomic $\mathcal{D}$-modules by modification D'Agnolo--Kashiwara's Riemann--Hilbert correspondence. The equipped perverse t-structure, straight...