We present a system called Adelfa that provides mechanized support for reasoning about specifications developed in the Edinburgh Logical Framework or LF. Underlying is new logic named L_LF. Typing judgements LF are represented by atomic formulas L_LF and quantification permitted over contexts terms appear such formulas. Contexts, which constitute type assignments to uniquely variables modelled ...

We propose a new decision procedure for dependency quantified Boolean formulas (DQBFs) that uses interpolation-based definition extraction to compute Skolem functions in counter-example guided inductive synthesis (CEGIS) loop. In each iteration, family of candidate is tested correctness using SAT solver, which either determines model has been found, or returns an assignment the universal variab...

We define and implement an interprocedural analysis for automatically checking safety of recursive programs with an unbounded state space. The main idea is to infer modular universally quantified inductive invariants in the form of procedure summaries that are sufficient to prove the safety property. We assume that the effect of the atomic commands of the program can be modeled via effectively ...

Verification problems of programs written in various paradigms (such as imperative, logic, concurrent, functional, and objectoriented ones) can be reduced to problems of solving Horn clause constraints on predicate variables that represent unknown inductive invariants. This paper presents a novel Horn constraint solving method based on inductive theorem proving: the method reduces Horn constrai...

This theory defines a type constructor representing the free Boolean algebra over a set of generators. Values of type (α)formula represent propositional formulas with uninterpreted variables from type α, ordered by implication. In addition to all the standard Boolean algebra operations, the library also provides a function for building homomorphisms to any other Boolean algebra type. 1 Free Boo...

We describe a sequent calculus μLJ with primitives for inductive and co-inductive datatypes and equip it with reduction rules allowing a sound translation of Gödel’s system T. We introduce the notion of a μ-closed category, relying on a uniform interpretation of open μLJ formulas as strong functors. We show that any μ-closed category is a sound model for μLJ . We then turn to the construction o...

We propose a “formula slicing” method for finding inductive invariants. It is based on the observation that many loops in the program affect only a small part of the memory, and many invariants which were valid before a loop are still valid after. Given a precondition of the loop, obtained from the preceding program fragment, we weaken it until it becomes inductive. The weakening procedure is g...

We propose a new approach to delineating logics of programs, based directly on inductive definition of program semantics. The ingredients are elementary and well-known, but their fusion yields a simple yet powerful approach, surprisingly overlooked for decades. The denotational semantics of a regular program can be construed as a relation, easily definable by structural induction on programs. I...