Automated Synthesis of Induction Axioms for Programs with Second-Order Recursion

Aderhold, Markus

doi:10.1007/978-3-642-14203-1_23

Cited by 3 publications

(6 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Another challenge is to derive all relevant induction schemes and auxiliary lemmas such that the automated verification of subgoals succeeds. Guided by our experiments with the POPLMARK challenge and other calculi, we will extend our proof strategies to derive relevant lemmas, incorporating techniques developed by others that proved successful [1,20,29].…”

Section: Automated Metatheorymentioning

confidence: 99%

See 1 more Smart Citation

Type systems for the masses: deriving soundness proofs and efficient checkers

Grewe

Erdweg

Wittmann

et al. 2015

2015 ACM International Symposium on New Ideas, New Paradigms, and Reflections on Programming and Software (Onward!)

View full text Add to dashboard Cite

The correct definition and implementation of non-trivial type systems is difficult and requires expert knowledge, which is not available to developers of domain-specific languages (DSLs) in practice. We propose Veritas, a workbench that simplifies the development of sound type systems. Veritas provides a single, high-level specification language for type systems, from which it automatically tries to derive soundness proofs and efficient and correct type-checking algorithms. For verification, Veritas combines off-the-shelf automated first-order theorem provers with automated proof strategies specific to type systems. For deriving efficient type checkers, Veritas provides a collection of optimization strategies whose applicability to a given type system is checked through verification on a case-by-case basis. We have developed a prototypical implementation of Veritas and used it to verify type soundness of the simply-typed lambda calculus and of parts of typed SQL. Our experience suggests that many of the individual verification steps can be automated and, in particular, that a high degree of automation is possible for type systems of DSLs.

show abstract

Section: Automated Metatheorymentioning

confidence: 99%

“…The source code of our prototype is available online. 1 Figure 6 shows a screenshot of our prototype.…”

Section: Prototypical Implementationmentioning

confidence: 99%

Type systems for the masses: deriving soundness proofs and efficient checkers

Grewe

Erdweg

Wittmann

et al. 2015

2015 ACM International Symposium on New Ideas, New Paradigms, and Reflections on Programming and Software (Onward!)

View full text Add to dashboard Cite

show abstract

“…4.1, we describe the concept of quantification procedures that were introduced in [2] to synthesize induction axioms for procedures that involve second-order procedures. In Sect.…”

Section: Static Analysis Of Second-order Programsmentioning

confidence: 99%

“…The corresponding definition in [2] considered second-order procedures without preconditions, so we generalize this definition as follows: Definition 3. For each second-order procedure procedure proc(f : τ 1 × .…”

Section: Quantification Proceduresmentioning

confidence: 99%

Second-Order Programs with Preconditions

Aderhold

2010

Verification, Induction, Termination Analysis

Self Cite

View full text Add to dashboard Cite

Abstract. In the implementation of procedures, developers often assume that the input satisfies certain properties; for example, binary search assumes the array to be sorted. Such requirements on the input can be formally expressed as preconditions of procedures. If a secondorder procedure p (e.g., map or foldl ) is called with a first-order procedure f that has a precondition, the question arises whether p will call f only with arguments that satisfy the precondition of f . In this paper, we propose a method to statically analyze if all procedure calls in a given second-order program satisfy the respective preconditions. In particular, we consider indirect calls of procedures that are passed as an argument to a second-order procedure.

show abstract

“…Lorenzen and Erdweg present an automated method for type-soundness proofs that is limited to desugared language extensions [11]. More generally, there are various techniques for automated verification [1,9,17], some of which we plan to incorporate into our tool as proof strategies.…”

Section: Related Workmentioning

confidence: 99%

Using Vampire in Soundness Proofs of Type Systems

Grewe¹,

Erdweg²,

Mezini³

EPiC Series in Computing

View full text Add to dashboard Cite

Type systems for programming languages shall detect type errors in programs before runtime. To ensure that a type system meets this requirement, its soundness must be formally verified. We aim at automating soundness proofs of type systems to facilitate the development of sound type systems for domain-specific languages.Soundness proofs for type systems typically require induction. However, many of the proofs of individual induction cases only require first-order reasoning. For the development of our workbench Veritas, we build on this observation by combining automated first-order theorem provers such as Vampire with automated proof strategies specific to type systems. In this paper, we describe how we encode type soundness proofs in first-order logic using TPTP. We show how we use Vampire to prove the soundness of type systems for the simply-typed lambda calculus and for parts of a typed SQL. We report on which parts of the proofs are handled well by Vampire, and what parts work less well with our current approach.

show abstract

Automated Synthesis of Induction Axioms for Programs with Second-Order Recursion

Cited by 3 publications

References 9 publications

Type systems for the masses: deriving soundness proofs and efficient checkers

Type systems for the masses: deriving soundness proofs and efficient checkers

Second-Order Programs with Preconditions

Using Vampire in Soundness Proofs of Type Systems

Contact Info

Product

Resources

About