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Soundness of the simply typed lambda calculus in ACL2

Sol Swords, William R. Cook
2006 Proceedings of the sixth international workshop on the ACL2 theorem prover and its applications - ACL2 '06  
To illustrate this method, we present a proof in ACL2 of the soundness of the simply typed λ-calculus.  ...  We introduce a method for performing these proofs in ACL2, including a macro which automates the process of defining functions and theorems to facilitate reasoning about recursive data types.  ...  In this paper we examine a proof in ACL2 of the soundness of the simply-typed λ-calculus, discussing problems which present themselves in going from the well-known hand proof to a mechanized proof.  ... 
doi:10.1145/1217975.1217982 dblp:conf/acl2/SwordsC06 fatcat:gn6sbcjvgbbyfc7pgjgnmr2sfq

The Right Tools for the Job: Correctness of Cone of Influence Reduction Proved Using ACL2 and HOL4

Michael J. C. Gordon, Matt Kaufmann, Sandip Ray
2010 Journal of automated reasoning  
Our proof exploits a link between the HOL4 and ACL2 proof systems to show correctness of a cone of influence reduction algorithm, implemented in ACL2, with respect to the classical semantics of linear  ...  We present a case study illustrating how to exploit the expressive power of higher-order logic to complete a proof whose main lemma is already proved in a firstorder theorem prover.  ...  Kaufmann also thanks the Texas-United Kingdom Collaborative for travel support to Cambridge, England, and the Computer Laboratory at the University of Cambridge for hosting him during the course of this  ... 
doi:10.1007/s10817-010-9169-y fatcat:rblnzquszzatfogsbdrexvtbyy

A Survey on Theorem Provers in Formal Methods [article]

M. Saqib Nawaz, Moin Malik, Yi Li, Meng Sun, M. Ikram Ullah Lali
2019 arXiv   pre-print
In literature, there is a shortage of comprehensive documents that can provide proper guidance about the preferences of theorem provers with respect to their designs, performances, logical frameworks,  ...  Mechanical reasoning is a key area of research that lies at the crossroads of mathematical logic and artificial intelligence.  ...  ACKNOWLEDGMENTS The work has been supported by the National Natural Science Foundation of China under grant no. 61772038, 61532019 and 61272160, and the Guandong Science and Technology Department (Grant  ... 
arXiv:1912.03028v1 fatcat:fabxqg75xjhxlh7u3uyypgyzdy

An industrial strength theorem prover for a logic based on Common Lisp

M. Kaufmann, J.S. Moore
1997 IEEE Transactions on Software Engineering  
For users happy with an essentially quantifier-free, first-order logic, we believe that ACL2 offers more overall convenience for the type of reasoning required to model and prove properties of digital  ...  Axioms for Primitive Data Types The following primitive data types are axiomatized. ©  ...  This paper is an extended version the paper "ACL2: An Industrial Strength Version of Nqthm," which appeared in  ... 
doi:10.1109/32.588534 fatcat:bzb42znaqrfg7jn4ybn4ptyk5y

Semantics of the reFLect language

Sava Krstić, John Matthews
2004 Proceedings of the 6th ACM SIGPLAN international conference on Principles and practice of declarative programming - PPDP '04  
In this paper, we consider core reFL ect -a language that extends a polymorphically typed λ-calculus with a datatype for programs and with constructs for splicing programs into programs and for defining  ...  These results provide the basis for developing the semantics of reFL ect 's extension of higher order logic and proving its soundness.  ...  Handling Polymorphism The denotational semantics of the monomorphic fragment of reFL ect presented in Section 6.1 extends to the full language in the same way the frame semantics of the simply typed λ-calculus  ... 
doi:10.1145/1013963.1013971 dblp:conf/ppdp/KrsticM04 fatcat:33fjhbnstjf7zku37hhdjkixia

Foundations [article]

Jeremy Avigad
2021 arXiv   pre-print
This is a draft of a chapter on mathematical logic and foundations for an upcoming handbook of computational proof assistants.  ...  Extensions The simply typed lambda calculus can be extended in various ways.  ...  The notion of -equivalence for terms in the simply typed lambda calculus is a prototypical example of a notion of definitional equality.  ... 
arXiv:2009.09541v4 fatcat:yatuz32vondo3eburgtj6jmp6e

Size-Change Termination as a Contract [article]

Phuc C. Nguyen, Thomas Gilray, Sam Tobin-Hochstadt, David Van Horn
2018 arXiv   pre-print
We formulate run-time size-change checks as contracts in the style of Findler and Felleisen.  ...  One such method is the size-change termination approach of Lee, Jones, and Ben-Amram, which operates in two phases: (1) abstract programs into "size-change graphs," and (2) check these graphs for the size-change  ...  Nguyễn, Thomas Gilray, Sam Tobin-Hochstadt, and David Van Horn Lambda-calculus interpreter Checking termination of an interpreter for a turing-complete language is challenging-after all, the interpreter  ... 
arXiv:1808.02101v1 fatcat:uowsryeo7jdgbajc5zhhaxqhoy

Formal verification of a generic framework to synthesize SAT-provers

Francisco -Jesús Martín-Mateos, José -Antonio Alonso, María -José Hidalgo, José -Luis Ruiz-Reina
2004 Journal of automated reasoning  
We present in this paper an application of the ACL2 system to generate and reason about propositional satisfiability provers.  ...  For that purpose, we develop a framework where we define a generic SAT-prover based on transformation rules, and we formalize this generic framework in the ACL2 logic, carrying out a formal proof of its  ...  We will call O G the set of propositional objects (or simply objects) and G the set of expansion rules.  ... 
doi:10.1007/bf03177742 fatcat:kw6a66uco5faxntunbwxprzgpa

Mechanized Metatheory for the Masses: The PoplMark Challenge [chapter]

Brian E. Aydemir, Aaron Bohannon, Matthew Fairbairn, J. Nathan Foster, Benjamin C. Pierce, Peter Sewell, Dimitrios Vytiniotis, Geoffrey Washburn, Stephanie Weirich, Steve Zdancewic
2005 Lecture Notes in Computer Science  
of Featherweight Java, proving type soundness of variants of the simply typed λ-calculus and F <: , and a substantial formalization of the behavior of TCP, UDP, and the Sockets API.  ...  Based on the metatheory of System F<:, a typed lambda-calculus with second-order polymorphism, subtyping, and records, these benchmarks embody many aspects of programming languages that are challenging  ...  This language is of moderate scale-significantly more complex than simply typed lambda-calculus or "mini ML," but much smaller than a full-blown programming language-to keep the work involved in attempting  ... 
doi:10.1007/11541868_4 fatcat:6eprs3kxvjg67ak2zhuipl5qyu

Directly reflective meta-programming

Aaron Stump
2008 Higher-Order and Symbolic Computation  
This paper presents a new meta-programming language, based on an untyped lambda calculus, in which structurally reflective programming is supported directly, without any encoding.  ...  The language features call-by-value and call-by-name lambda abstractions, as well as novel reflective features enabling the intensional manipulation of arbitrary program terms.  ...  Many thanks to the anonymous reviewers of previous versions of this paper for their thorough reading and insightful criticisms.  ... 
doi:10.1007/s10990-007-9022-0 fatcat:tmg23rwsqjhuxb6qdgquvxrdhq

Lifted-FL: A Pragmatic Implementation of Combined Model Checking and Theorem Proving [chapter]

Mark D. Aagaard, Robert B. Jones, Carl-Johan H. Seger
1999 Lecture Notes in Computer Science  
The approach is made possible by using the same programming language ( ) as both the meta and object language of theorem proving.  ...  Combining theorem proving and model checking o ers the tantalizing possibility of e ciently reasoning about large circuits at high levels of abstraction.  ...  Additionally, John Harrison and Ching-Tsun Chou read a draft of the paper and provided helpful comments.  ... 
doi:10.1007/3-540-48256-3_22 fatcat:hykbeosjcvgcrlrnwx76oulviq

PhD Abstracts

2014 Journal of functional programming  
A dissertation is eligible if parts of it have or could have appeared in JFP, that is, if it is in the general area of functional programming. The abstracts are not reviewed.  ...  As a service to the community, JFP is launching a new feature, in the form of a regular publication of abstracts from PhD dissertations that were completed during the previous year.  ...  We give a gentle introduction to our approach which only assumes elementary knowledge of simply-typed λ calculus and rewriting.  ... 
doi:10.1017/s0956796814000215 fatcat:rs2j5wgm5ndf7ek2zls5pmg2w4

Mathematical Induction in Otter-Lambda

Michael Beeson
2006 Journal of automated reasoning  
This is the first time that such a first-order prover has been combined in one program with a unification algorithm capable of instantiating variables to lambda terms to assist in the deductions.  ...  The resulting prover has all the advantages of the proof-search algorithm of Otter (speed, variety of inference rules, excellent handling of equality) and also the power of lambda unification.  ...  be found; but we can also simply observe that if we do use 0, the proof that is found is in fact correctly typed.  ... 
doi:10.1007/s10817-006-9036-z fatcat:5qz2fpqpdrcinhzdbbh5g63ap4

Programmed Strategies for Program Verification

Richard B. Kieburtz
2007 Electronical Notes in Theoretical Computer Science  
Properties refine the type system of Haskell but cannot be verified by type-checking alone; a more powerful logical verifier is needed.  ...  In Programatica, predicate definitions and property assertions written in P-logic, a programming logic for Haskell, can be embedded in the text of a Haskell program module.  ...  Three such definitions are given in Fig. 5 , each corresponding to one of the three specifications of normal forms for the lambda calculus that were mentioned in the preceding paragraph.  ... 
doi:10.1016/j.entcs.2007.02.045 fatcat:3gnit7ab3zd4hilkj7h2ahsjmu

Formalizing the metatheory of logical calculi and automatic provers in Isabelle/HOL (invited talk)

Jasmin Christian Blanchette
2019 Proceedings of the 8th ACM SIGPLAN International Conference on Certified Programs and Proofs - CPP 2019  
At the heart of the project is the conviction that proof assistants have become mature enough to actually help researchers in automated reasoning when they develop new calculi and tools.  ...  IsaFoL (Isabelle Formalization of Logic) is an undertaking that aims at developing formal theories about logics, proof systems, and automatic provers, using Isabelle/HOL.  ...  Barras [5] took this idea to its logical extreme with his "Coq in Coq" Ph.D. project: a verification in Coq of a type checker for the calculus of inductive constructions underlying Coq.  ... 
doi:10.1145/3293880.3294087 dblp:conf/cpp/Blanchette19 fatcat:n7delklh2nejvh4zspbcljamwy
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