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322
Dependent Types Ensure Partial Correctness of Theorem Provers
, 2002
"... Static type systems in programming languages allow many errors to be detected at compile time that wouldn't be detected until runtime otherwise. Dependent types are more expressive than the type systems in most programming languages, so languages that have them should allow programmers to detec ..."
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Cited by 13 (1 self)
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to detect more errors earlier. In this paper, using the Twelf system, we show that dependent types in the logic programming setting can be used to ensure partial correctness of programs which implement theorem provers, and thus avoid runtime errors in proof search and proof construction. We present two
Partiality and Recursion in Interactive Theorem Provers  An Overview
 UNDER CONSIDERATION FOR PUBLICATION IN MATH. STRUCT. IN COMP. SCIENCE
, 2011
"... The use of interactive theorem provers to establish the correctness of critical parts of a software development or for formalising mathematics is becoming more common and feasible in practice. However, most mature theorem provers lack a direct treatment of partial and general recursive functions; ov ..."
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Cited by 2 (0 self)
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The use of interactive theorem provers to establish the correctness of critical parts of a software development or for formalising mathematics is becoming more common and feasible in practice. However, most mature theorem provers lack a direct treatment of partial and general recursive functions
G.: Integrating an automated theorem prover into Agda
 NASA Formal Methods (NFM 2011), LNCS
, 2011
"... Abstract. Agda is a dependently typed functional programming language and a proof assistant in which developing programs and proving their correctness is one activity. We show how this process can be enhanced by integrating external automated theorem provers, provide a prototypical integration of th ..."
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Cited by 6 (2 self)
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Abstract. Agda is a dependently typed functional programming language and a proof assistant in which developing programs and proving their correctness is one activity. We show how this process can be enhanced by integrating external automated theorem provers, provide a prototypical integration
Termination checking in the presence of nested inductive and coinductive types. Note supporting presentation given at the Workshop on Partiality and Recursion in Interactive Theorem Provers
 In Preliminary Proceedings of the Ninth Workshop on Language Descriptions Tools and Applications, LDTA 2009
, 2009
"... In the dependently typed functional programming language Agda one can easily mix induction and coinduction. The implementation of the termination/productivity checker is based on a simple extension of a termination checker for a language with inductive types. However, this simplicity comes at a pric ..."
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Cited by 11 (5 self)
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In the dependently typed functional programming language Agda one can easily mix induction and coinduction. The implementation of the termination/productivity checker is based on a simple extension of a termination checker for a language with inductive types. However, this simplicity comes at a
Dependently Typed Functional Programs and their Proofs
, 1999
"... Research in dependent type theories [ML71a] has, in the past, concentrated on its use in the presentation of theorems and theoremproving. This thesis is concerned mainly with the exploitation of the computational aspects of type theory for programming, in a context where the properties of programs ..."
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Cited by 81 (13 self)
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Research in dependent type theories [ML71a] has, in the past, concentrated on its use in the presentation of theorems and theoremproving. This thesis is concerned mainly with the exploitation of the computational aspects of type theory for programming, in a context where the properties
Dependent Types, Theorem Proving, and Applications for a Verifying Compiler
, 2005
"... One approach to Prof. Hoare’s challenge is to view the development of verified software from the perspective of interactive theorem provers. This idea is already commonly developed and many mediumscale software systems have been developed and verified in this manner. Developments based on HOL, ACL2 ..."
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Cited by 1 (0 self)
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then be compiled into traditional executable code. In this sense, we already have a small scale example of a verification aware programming language. We propose to take advantage of the notion of “dependent types ” to ensure that this programming language combines powerful logical capabilities, reasonable
IEEE.1 An Industrial Strength Theorem Prover for a Logic Based on Common Lisp
"... Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be ..."
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of the Motorola CAP digital signal processing chip and the proof of the correctness of the kernel of the floating point division algorithm on the AMD5K86 microprocessor by Advanced Micro Devices, Inc. Index terms—formal verification, automatic theorem proving, computational logic, partial functions, total
Elf: A Language for Logic Definition and Verified Metaprogramming
 In Fourth Annual Symposium on Logic in Computer Science
, 1989
"... We describe Elf, a metalanguage for proof manipulation environments that are independent of any particular logical system. Elf is intended for metaprograms such as theorem provers, proof transformers, or type inference programs for programming languages with complex type systems. Elf unifies logic ..."
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Cited by 80 (7 self)
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We describe Elf, a metalanguage for proof manipulation environments that are independent of any particular logical system. Elf is intended for metaprograms such as theorem provers, proof transformers, or type inference programs for programming languages with complex type systems. Elf unifies logic
Dependent Types from Counterexamples
, 2010
"... Motivated by recent research in abstract model checking, we present a new approach to inferring dependent types. Unlike many of the existing approaches, our approach does not rely on programmers to supply the candidate (or the correct) types for the recursive functions and instead does counterexampl ..."
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Cited by 17 (4 self)
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counterexampleguided refinement to automatically generate the set of candidate dependent types. The main idea is to extend the classical fixedpoint type inference routine to return a counterexample if the program is found untypable with the current set of candidate types. Then, an interpolating theorem prover
Machine Assisted Proofs for Generic Semantics to Compiler Transformation Correctness Theorems
"... This thesis investigates the issues involved in the creation of a “general theory of operational semantics ” in LEGO, a typetheoretic theorem proving environment implementing a constructionist logic. Such a general theory permits the ability to manipulate and reason about operational semantics both ..."
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that quantify over the class of operational semantics. In implementation terms this indicates the need to ensure both the class of operational semantics and the means of inferring results thereon remain at the theorem prover level. The endeavour of this thesis can be seen as assessing both the requirements
Results 1  10
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