Results 11  20
of
28
Encoding the HOL Light logic in Coq
"... Abstract. We show how to encode the HOL Light logic in Coq. This makes an automatic translation of HOL proofs to Coq possible. The translated HOL proofs refer to translated HOL data types but those data types can be related to the standard Coq data types, making the HOL results useful for Coq. The t ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
Abstract. We show how to encode the HOL Light logic in Coq. This makes an automatic translation of HOL proofs to Coq possible. The translated HOL proofs refer to translated HOL data types but those data types can be related to the standard Coq data types, making the HOL results useful for Coq. The translated proofs have a size linear in the time HOL takes to process the original proofs. However the constant of linearity is large. The approach described in this paper is similar to the method of Pavel Naumov, MarkOliver Stehr and José Mesequer for translating HOL98 proofs to Nuprl [10].
Checking Nuprl Proofs in ACL2: A Progress Report
"... Abstract. Stipulations on the correctness of proofs produced in a formal system include that the axioms and proof rules are the intended ones and that the proof has been properly constructed (i.e. it is a correct instantiation of the axioms and proof rules.) In software implementations of formal sys ..."
Abstract
 Add to MetaCart
Abstract. Stipulations on the correctness of proofs produced in a formal system include that the axioms and proof rules are the intended ones and that the proof has been properly constructed (i.e. it is a correct instantiation of the axioms and proof rules.) In software implementations of formal systems, correctness additionally depends both on the correctness of the program implementing the system and on the hardware it is executed on. Once we implement a system in software and execute it on a computer, we have moved from the abstract world of mathematics into the physical world; absolute correctness can never be achieved here. We can only strive to increase our confidence that the system is producing correct results. In the process of creating proofs, foundational systems like Nuprl construct formal proof objects. These proof objects can be independently checked to verify they are correct instantiations of the axioms and proof rules thereby increasing confidence that the putative proof object faithfully represents a proof in the formal system. Note that this kind of proof checking does not address issues related to the models of the proof system, it simply provides more evidence that a proof has been correctly constructed. The Nuprl implementation consists of more than 100K lines of LISP and tactic code implemented in ML. Although parts of the system consist of legacy codes going as far back as the late 1970’s (Edinburgh LCF), and even though the Nuprl system has been extensively used since 1986 in formalizing a significant body of mathematics, the chances that the implementation is correct are slim. Verifying the system itself is infeasible, instead we propose to increase confidence in Nuprl proofs by independently checking them in ACL2. In this paper we describe: (i.) the ACL2 formalization of Nuprl terms, proof rules, and proofs, (ii.) first steps in the implementation of a proof checker, and (iii.) discuss issues related to the future of the project. 1
UITP 2010 Pollackinconsistency
"... For interactive theorem provers a very desirable property is consistency: it should not be possible to prove false theorems. However, this is not enough: it also should not be possible to think that a theorem that actually is false has been proved. More precisely: the user should be able to know wha ..."
Abstract
 Add to MetaCart
(Show Context)
For interactive theorem provers a very desirable property is consistency: it should not be possible to prove false theorems. However, this is not enough: it also should not be possible to think that a theorem that actually is false has been proved. More precisely: the user should be able to know what it is that the interactive theorem prover is proving. To make these issues concrete we introduce the notion of Pollackconsistency. This property is related to a system being able to correctly parse formulas that it printed itself. In current systems it happens regularly that this fails. We argue that a good interactive theorem prover should be Pollackconsistent. We show with examples that many interactive theorem provers currently are not Pollackconsistent. Finally we describe a simple approach for making a system Pollackconsistent, which only consists of a small modification to the printing code of the system. The most intelligent creature in the universe is a rock. None would know it because they have lousy I/O. — quote from the Internet
Author manuscript, published in "39th ACM SIGPLANSIGACT Symposium on Principles of Programming Languages POPL'12 (2012)" SelfCertification Bootstrapping Certified Typecheckers in F ⋆ with Coq
, 2011
"... Wellestablished dependentlytyped languages like Agda and Coq provide reliable ways to build and check formal proofs. Several other dependentlytyped languages such as Aura, ATS, Cayenne, Epigram, F ⋆ , F7, Fine, Guru, PCML5, and Ur also explore reliable ways to develop and verify programs. All the ..."
Abstract
 Add to MetaCart
(Show Context)
Wellestablished dependentlytyped languages like Agda and Coq provide reliable ways to build and check formal proofs. Several other dependentlytyped languages such as Aura, ATS, Cayenne, Epigram, F ⋆ , F7, Fine, Guru, PCML5, and Ur also explore reliable ways to develop and verify programs. All these languages shine in their own regard, but their implementations do not themselves enjoy the degree of safety provided by machinechecked verification. We propose a general technique called selfcertification that allows a typechecker for a suitably expressive language to be certified for correctness. We have implemented this technique for F ⋆ , a dependently typed language on the.NET platform. Selfcertification involves implementing a typechecker for F ⋆ in F ⋆ , while using all the conveniences F ⋆ provides for the compilerwriter (e.g., partiality, effects, implicit conversions, proof automation, libraries). This
This document in subdirectoryRS/97/24/ Relational Reasoning about Contexts ∗
, 909
"... See back inner page for a list of recent BRICS Report Series publications. Copies may be obtained by contacting: BRICS ..."
Abstract
 Add to MetaCart
See back inner page for a list of recent BRICS Report Series publications. Copies may be obtained by contacting: BRICS
116 Linear λCalculus 6.2 Linear Type Checking
"... The typing rules for the linear λcalculus are syntaxdirected in that the principal term constructor determines the typing rule which must be used. Nonetheless, the typing rules are not immediately suitable for an efficient typechecking algorithm since we would have to guess how the linear hypothe ..."
Abstract
 Add to MetaCart
The typing rules for the linear λcalculus are syntaxdirected in that the principal term constructor determines the typing rule which must be used. Nonetheless, the typing rules are not immediately suitable for an efficient typechecking algorithm since we would have to guess how the linear hypotheses are to be split between the hypothesis in a number of rules. The occurrence constraints introduced in Section?? would be sufficient to avoid this choice, but they are rather complex, jeopardizing our goal of designing a simple procedure which is easy to trust. Fortunately, we have significantly more information here, since the proof term is given to us. This determines the amount of work we have to do in each branch of a derivation, and we can resolve the don’tcare nondeterminism directly. Instead of guessing a split of the linear hypotheses between two premisses of a rule, we pass all linear variables to the first premiss. Checking the corresponding subterm will consume some of these variables, and we pass the remaining ones one to check the second subterms. This idea requires a judgment Γ; ∆I \ ∆O ⊢ M: A where ∆I represents the available linear hypotheses and ∆O ⊆ ∆I the linear hypotheses not used in M. For example, the rules for the simultaneous conjunction and unit would be
Linear Type Checking
"... but ag it to indicate that it may not be exact, but that some of these linear hypotheses may be absorbed if necessary. In other words, in the judgment any of the remaining hypotheses in O need not be consumed in the other branches of the typing derivation. On the other hand, the judgment ; I n O ` ..."
Abstract
 Add to MetaCart
but ag it to indicate that it may not be exact, but that some of these linear hypotheses may be absorbed if necessary. In other words, in the judgment any of the remaining hypotheses in O need not be consumed in the other branches of the typing derivation. On the other hand, the judgment ; I n O ` 0 M : A indicates the M uses exactly the variables in I O . When we think of the judgment ; I n O ` i M : A as describing an algorithm, we think of , I and M as given, and O and the slack indicator i as part of the result of the computation. The type A may or may not be givenin one case it is synthesized, in the other case checked. This re nes our view as computation being described as the bottomup construction of a derivation to include parts of the judgment in dierent roles (as input, output, or bidirectional components). In logic programming, which is based on the notion of computationasproofsearch, these roles of the syntactic constituents of a judgment are called