package coq-htt

Hoare Type Theory (HTT) is a verification system for reasoning about sequential heap-manipulating programs based on separation logic.

HTT incorporates Hoare-style specifications via preconditions and postconditions into types. A Hoare type ST P (fun x : A => Q) denotes computations with a precondition P and postcondition Q, returning a value x of type A. Hoare types are a dependently typed version of monads, as used in the programming language Haskell. Monads hygienically combine the language features for pure functional programming, with those for imperative programming, such as state or exceptions. In this sense, HTT establishes a formal connection between (functional programming variant of) Separation logic and monads, in the style of Curry-Howard isomorphism. Every effectful command in HTT has a type which corresponds to the appropriate non-structural inference rule in Separation logic, and vice versa, every non-structural inference rule corresponds to a command in HTT that has that rule as the type. The type for monadic bind is the Hoare-style rule for sequential composition, and the type for monadic unit combines the Hoare-style rule for the idle program and the Hoare-style rule for variable assignment (adapted for functional variables). In implementation terms, the above means that HTT implements Separation logic as a shallow embedding in Coq.