Soundness proofs of program logics such as Hoare logics and type systems are often made easier by decorating the operational semantics with information that is useful in the proof. However, modifying the operational semantics to carry around such information can make it more difficult to show that the operational semantics corresponds to what actually occurs on a real machine. In this work we present a program logic framework targeting operational semantics in Curry-style - that is, operational semantics without proof decorations such as separation algebras, share models, and step indexes. Although we target Curry-style operational semantics, our framework permits local reasoning via the frame rule and retains expressive assertions in the program logic. Soundness of the program logic is derived mechanically from simple properties of primitive commands and expressions. We demonstrate our framework by deriving a separation logic for the model of a core imperative programming language with external function calls. We also apply our framework in a more realistic setting in the soundness proof of a separation logic for CompCert's Cminor. Our proofs are machine-checked in Coq.