Combining interactive and automatic reasoning in first order theories of functional programs

Authors:
Ana Bove;Peter Dybjer;Andrés Sicard-Ramírez
Affiliations:
Chalmers University of Technology, Gothenburg, Sweden;Chalmers University of Technology, Gothenburg, Sweden;EAFIT University, Medellín, Colombia
Venue:
FOSSACS'12 Proceedings of the 15th international conference on Foundations of Software Science and Computational Structures
Year:
2012

Citing 15
Cited 2

Program verification in a logical theory of construction

Proc. of a conference on Functional programming languages and computer architecture
An overview of Miranda

ACM SIGPLAN Notices
A functional programming approach to the specification and verification of concurrent systems

Formal Aspects of Computing
Comparing integrated and external logics of functional programs

Science of Computer Programming
A framework for defining logics

Journal of the ACM (JACM)
Optimized Encodings of Fragments of Type Theory in First Order Logic

TYPES '95 Selected papers from the International Workshop on Types for Proofs and Programs
Theorem Proving for Functional Programmers

IFL '02 Selected Papers from the 13th International Workshop on Implementation of Functional Languages
Modelling general recursion in type theory

Mathematical Structures in Computer Science
The logic of demand in Haskell

Journal of Functional Programming
Automation for interactive proof: first prototype

Information and Computation - Special issue: Combining logical systems
Embedding a logical theory of constructions in Agda

Proceedings of the 3rd workshop on Programming languages meets program verification
The TPTP Problem Library and Associated Infrastructure

Journal of Automated Reasoning
Partial and Nested Recursive Function Definitions in Higher-order Logic

Journal of Automated Reasoning
Connecting a logical framework to a first-order logic prover

FroCoS'05 Proceedings of the 5th international conference on Frontiers of Combining Systems
A tool for automated theorem proving in agda

TYPES'04 Proceedings of the 2004 international conference on Types for Proofs and Programs

Dependently typed programming based on automated theorem proving

MPC'12 Proceedings of the 11th international conference on Mathematics of Program Construction
HALO: haskell to logic through denotational semantics

POPL '13 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages

Quantified Score

Hi-index	0.00

Visualization

Abstract

We propose a new approach to the computer-assisted verification of functional programs. We work in first order theories of functional programs which are obtained by extending Aczel's first order theory of combinatory formal arithmetic with positive inductive and coinductive predicates. Rather than building a special purpose system we implement our theories in Agda, a proof assistant for dependent type theory which can be used as a generic theorem prover. Agda provides support for interactive reasoning by encoding first order theories using the formulae-as-types principle. Further support is provided by off-the-shelf automatic theorem provers for first order logic which can be called by a program which translates Agda representations of first order formulae into the TPTP language understood by the provers. We show some examples where we combine interactive and automatic reasoning, covering both proof by induction and coinduction.