This article is the second part of a two articles series about a calculus with higher-order polymorphic functions, recursive types with arrow and product type constructors and set-theoretic type connectives (union, intersection, and negation). In the first part, presented in a companion paper, we defined and studied the syntax, semantics, and evaluation of the explicitly-typed version of the calculus, in which type instantiation is driven by explicit instantiation annotations. In this second part we present a local type inference system that allows the programmer to omit explicit instantiation annotations, and a type reconstruction system that allows the programmer to omit explicit type annotations. The work presented in the two articles provides the theoretical foundations and technical machinery needed to design and implement higher-order polymorphic functional languages for semi-structured data.