Polymorphism and separation in hoare type theory

Abstract

In previous work we have proposed a Dependent Hoare Type Theory (HTT) as a framework for development and reasoning about higher-order functional programs with effects of state, aliasing and nontermination. The main feature of HTT is the type of Hoare triples {P }x:A{Q} specifying computations with precondition P and postcondition Q, that return a result of type A.Here we extend HTT with predicative type polymorphism. Type quantification is possible in both types and assertions, and we can also quantify over Hoare triples. We show that as a consequence it becomes possible to reason about disjointness of heaps in the assertion logic of HTT. We use this expressiveness to interpret the Hoare triples in the "small footprint" manner advocated by Separation Logic, whereby a precondition tightly describes the heap fragment required by the computation. We support stateful commands of allocation, lookup, strong update, deallocation, and pointer arithmetic.

Dijkstra monads forever: termination-sensitive specifications for interaction trees

“…The work we build on most directly is that found in the Dijkstra Monad literature. This line of research has its roots in Hoare Type Theory [Nanevski et al 2006], which presented a dependently typed functional programming language with mutable state and a novel Hoare type. A Hoare Type consists of some base type A, a precondition P on the state, and a postcondition Q on the state; it is inhabited by a computation producing an A that changes the state in a way that satisfies the postcondition given the precondition.…”

Separation logic for sequential programs (functional pearl)

“…Varming and Birkedal [2008] demonstrate the possibility to formalize higher-order Separation Logic as a shallow embedding in Isabelle/HOLCF. Nanevski et al [2008b] and Chlipala et al [2009] present the Ynot tool, which consists of an axiomatic embedding in Coq of Hoare Type Theory (HTT) [Nanevski et al 2006[Nanevski et al , 2008a. HTT is a presentation of higher-order Separation Logic with higher-order stores in the form of a type system for a dependently typed functional language.…”

A logical analysis of aliasing in imperative higher-order functions

“…We believe that content quantification can be generalised to allow compositional logical reasoning even with strong update. Nanevski et al (2006) study Hoare Type Theory (HTT), which combines dependent types and Hoare triples with anchors based on a monadic understanding of computation. The aim of HTT is to provide an effective general validation framework that unifies standard static checking techniques (in particular type inference and type checking) with logical verifications.…”