Semantic subtyping for declarative data scripting language by calling a prover

An efficient, logical and expressive type system supports the combination of refinement types and type membership expressions, as well as a top type that encompasses all valid values as members. Various embodiments verify the validity of subtyping relationships by translating to first-order logic, and invoking a general-purpose theorem prover with the first-order logic as input. In contrast to treating formulas as types, types are translated into formulas of standard first-order logic. Moreover, to represent data structures of the programming language as first-order logic, universal and existential quantifiers of first-order logic, and function symbols in terms, are exploited. Data intensive applications can be generated, verified, and deployed with greater speed and scale.