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39
The Implementation of ALF  a Proof Editor based on MartinLöf's Monomorphic Type Theory with Explicit Substitution
, 1995
"... This thesis describes the implementation of ALF, which is an interactive proof editor based on MartinLöf's type theory with explicit substitutions. ALF is a general purpose proof assistant, in which different logics can be represented. Proof objects are manipulated directly, by the usual editing op ..."
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Cited by 43 (0 self)
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This thesis describes the implementation of ALF, which is an interactive proof editor based on MartinLöf's type theory with explicit substitutions. ALF is a general purpose proof assistant, in which different logics can be represented. Proof objects are manipulated directly, by the usual editing operations. A partial proof is represented as an incomplete proof object, i.e., a proof object containing placeholders. A modular type/proof checking algorithm for complete proof objects is presented, and it is proved sound and complete assuming some basic meta theory properties of the substitution calculus. The algorithm is extended to handle incomplete objects in such a way that the type checking problem is reduced to a unication problem, i.e., the problem of finding instantiations to the placeholders in the object. Placeholders are represented together with their expected type and local context. We show that checking the correctness of instantiations can be localised, which means that it is e...
Proof by Pointing
, 1994
"... This paper presents a principle for using locations in logical expressions to guide the process of building proofs. Using a sequentstyle presentation of theorem provers, we annotate the inference rules to specify an algorithm that associates the construction of a proof tree to a location within ..."
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Cited by 40 (8 self)
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This paper presents a principle for using locations in logical expressions to guide the process of building proofs. Using a sequentstyle presentation of theorem provers, we annotate the inference rules to specify an algorithm that associates the construction of a proof tree to a location within a goal sequent. This principle provides a natural and effective use of the mouse in the userinterface of computer proof assistants. The implementation of the algorithm in a variety of theorem provers is discussed.
TAME: A PVS Interface to Simplify Proofs for Automata Models
 In Proc. User Interfaces for Theorem Provers 1998 (UITP '98
, 1998
"... Although a number of mechanical provers have been introduced and applied widely by academic researchers, these provers are rarely used in the practical development of software. For mechanical provers to be used more widely in practice, two major barriers must be overcome. First, the languages provid ..."
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Cited by 39 (12 self)
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Although a number of mechanical provers have been introduced and applied widely by academic researchers, these provers are rarely used in the practical development of software. For mechanical provers to be used more widely in practice, two major barriers must be overcome. First, the languages provided by the mechanical provers for expressing the required system behavior must be more natural for software developers. Second, the reasoning steps supported by mechanical provers are usually at too low and detailed a level and therefore discourage use of the prover. To help remove these barriers, we are developing a system called TAME, a highlevel user interface to PVS for specifying and proving properties of automata models. TAME provides both a standard specification format for automata models and numerous highlevel proof steps appropriate for reasoning about automata models. In previous work, we have shown how TAME can be useful in proving properties about systems described as LynchVaa...
CAS/PI: a Portable and Extensible Interface for Computer Algebra Systems
 In Proc. of ISSAC'92
, 1992
"... CAS/ß is a Computer Algebra System graphic user interface designed to be highly portable and extensible. It has been developed by composition of preexisting software tools such as Maple, Sisyphe, or Ulysse systems, ZicVis 3D plotting library, etc, using control integration technology and a set of ..."
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Cited by 38 (6 self)
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CAS/ß is a Computer Algebra System graphic user interface designed to be highly portable and extensible. It has been developed by composition of preexisting software tools such as Maple, Sisyphe, or Ulysse systems, ZicVis 3D plotting library, etc, using control integration technology and a set of high level graphic toolkits to build the formula editor and the dialog manager. The main aim of CAS/ß is to allow a wide range of runtime reconfigurations and extensions. For instance, it is possible to add new tools to a running system, to modify connections between working tools, to extend the set of graphic symbols managed by the formula editor, to design new high level editing commands based on the syntax or semantics of mathematical formulas, to customize and extend the menubutton based user interface, etc. More generally, CAS/ß can be seen equally as a powerful systemindependent graphic user interface enabling intersystems communications, a toolkit to allow fast development of custo...
A blackboard architecture for guiding interactive proofs
 Artificial Intelligence: Methodology, Systems and Applications
, 1998
"... Abstract. The acceptance and usability of current interactive theorem proving environments is, among other things, strongly influenced by the availability of an intelligent default suggestion mechanism for commands. Such mechanisms support the user by decreasing the necessary interactions during the ..."
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Cited by 24 (19 self)
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Abstract. The acceptance and usability of current interactive theorem proving environments is, among other things, strongly influenced by the availability of an intelligent default suggestion mechanism for commands. Such mechanisms support the user by decreasing the necessary interactions during the proof construction. Although many systems offer such facilities, they are often limited in their functionality. In this paper we present a new agentbased mechanism that independently observes the proof state, steadily computes suggestions on how to further construct the proof, and communicates these suggestions to the user via a graphical user interface. We furthermore introduce a focus technique in order to restrict the search space when deriving default suggestions. Although the agents we discuss in this paper are rather simple from a computational viewpoint, we indicate how the presented approach can be extended in order to increase its deductive power. 1
Type Theory and Programming
, 1994
"... This paper gives an introduction to type theory, focusing on its recent use as a logical framework for proofs and programs. The first two sections give a background to type theory intended for the reader who is new to the subject. The following presents MartinLof's monomorphic type theory and an im ..."
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Cited by 21 (2 self)
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This paper gives an introduction to type theory, focusing on its recent use as a logical framework for proofs and programs. The first two sections give a background to type theory intended for the reader who is new to the subject. The following presents MartinLof's monomorphic type theory and an implementation, ALF, of this theory. Finally, a few small tutorial examples in ALF are given.
Tecton: A Framework for Specifying and Verifying Generic System Components
, 1992
"... This paper presents the syntax and semantics of a small language for describing and using abstract concepts in formal software development and hardware design. The language provides definition, abbreviation, extension, and lemma constructs, which have general mathematical descriptive power, plus a c ..."
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Cited by 20 (6 self)
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This paper presents the syntax and semantics of a small language for describing and using abstract concepts in formal software development and hardware design. The language provides definition, abbreviation, extension, and lemma constructs, which have general mathematical descriptive power, plus a computationspecific realization construct. The semantics, which is denotational, includes specification of the requirements ("legality conditions ") that must be met when using each construct. The syntax and semantics are such that a corresponding proof theory requires only first order and inductive proof methods, rather than general higher order techniques as required in some frameworks. The language and some of the main proof issues are illustrated with an extended example of a behavioral and structural description of a carrylookahead adder circuit, with the circuit realization given in terms of a generic parallelprefix circuit. Partially supported by NSF Grant Number CCR8906678. A pr...
An Overview of the Tecton Proof System
, 1992
"... The Tecton Proof System is an experimental tool for constructing proofs of first order logic formulas and of program specifications expressed using formulas in Hoare's axiomatic proof formalism. It is designed to make interactive proof construction easier than with previous proof tools, by mainta ..."
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Cited by 13 (5 self)
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The Tecton Proof System is an experimental tool for constructing proofs of first order logic formulas and of program specifications expressed using formulas in Hoare's axiomatic proof formalism. It is designed to make interactive proof construction easier than with previous proof tools, by maintaining multiple proof attempts internally in a structured form called a proof forest; displaying them in an easy to comprehend form, using a combination of tabular formats, graphical representations, and hypertext links; and automating substantial parts of proofs through rewriting, induction, case analysis, and generalization inference mechanisms, along with a linear arithmetic decision procedure. Further development of the system is planned as part of an overall framework aimed at supporting the kind of abstractions and specializations necessary for building libraries of generic software and hardware components. Partially supported by National Science Foundation Grants CCR8906678...
Interactive Theorem Proving: An Empirical Study of User Activity
 Journal of Symbolic Computation
, 1995
"... In this paper the interaction between users and the interactive theorem prover HOL is investigated from a humancomputer interaction perspective. First, we outline three possible views of interaction, and give a brief survey of some current interfaces and how they may be described in terms of the ..."
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Cited by 12 (3 self)
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In this paper the interaction between users and the interactive theorem prover HOL is investigated from a humancomputer interaction perspective. First, we outline three possible views of interaction, and give a brief survey of some current interfaces and how they may be described in terms of these views. Second, we describe and present the results of an empirical study of intermediate and expert HOL users. The results are analysed for evidence in support of the proposed view of proof activity in HOL. We believe that this approach provides a principled basis for the assessment and design of interfaces to theorem provers.
Constructively Formalizing Automata Theory
 Proof, Language and Interaction: Essays in Honour of Robert Milner
, 1997
"... We present a constructive formalization of the MyhillNerode theorem on the minimization of finite automata that follows the account in Hopcroft and Ullman's book Formal Languages and Their Relation to Automata. We chose to formalize this theorem because it illustrates many points critical to formal ..."
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Cited by 11 (0 self)
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We present a constructive formalization of the MyhillNerode theorem on the minimization of finite automata that follows the account in Hopcroft and Ullman's book Formal Languages and Their Relation to Automata. We chose to formalize this theorem because it illustrates many points critical to formalization of computational mathematics, especially the extraction of an important algorithm from a proof as a method of knowing that the algorithm is correct. It also gave us an opportunity to experiment with a constructive implementation of quotient sets. We carried out the formalization in Nuprl, an interactive theorem prover based on constructive type theory. Nuprl borrows an implementation of the ML language from the LCF system of Milner, Gordon, and Wadsworth, and makes heavy use of the notion of tactic pioneered by Milner in LCF. We are interested in the pedagogical value of electronic formal mathematical texts and have put our formalization on the World Wide Web. Readers are invited to ...