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18
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 77 (8 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 definition (in the style of LF, the Edinburgh Logical Framework) with logic programming (in the style of Prolog). It achieves this unification by giving types an operational interpretation, much the same way that Prolog gives certain formulas (Hornclauses) an operational interpretation. Novel features of Elf include: (1) the Elf search process automatically constructs terms that can represent objectlogic proofs, and thus a program need not construct them explicitly, (2) the partial correctness of metaprograms with respect to a given logic can be expressed and proved in Elf itself, and (3) Elf exploits Elliott's unification algorithm for a calculus with dependent types. This research was...
Natural Deduction as HigherOrder Resolution
 Journal of Logic Programming
, 1986
"... An interactive theorem prover, Isabelle, is under development. In LCF, each inference rule is represented by one function for forwards proof and another (a tactic) for backwards proof. In Isabelle, each inference rule is represented by a Horn clause. ..."
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Cited by 54 (8 self)
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An interactive theorem prover, Isabelle, is under development. In LCF, each inference rule is represented by one function for forwards proof and another (a tactic) for backwards proof. In Isabelle, each inference rule is represented by a Horn clause.
Formalized mathematics
 TURKU CENTRE FOR COMPUTER SCIENCE
, 1996
"... It is generally accepted that in principle it’s possible to formalize completely almost all of presentday mathematics. The practicability of actually doing so is widely doubted, as is the value of the result. But in the computer age we believe that such formalization is possible and desirable. In c ..."
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Cited by 23 (0 self)
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It is generally accepted that in principle it’s possible to formalize completely almost all of presentday mathematics. The practicability of actually doing so is widely doubted, as is the value of the result. But in the computer age we believe that such formalization is possible and desirable. In contrast to the QED Manifesto however, we do not offer polemics in support of such a project. We merely try to place the formalization of mathematics in its historical perspective, as well as looking at existing praxis and identifying what we regard as the most interesting issues, theoretical and practical.
Verbalization of highlevel formal proofs
 In Proceedings of the Sixteenth National Conference on Artificial Intelligence
, 1999
"... We propose a new approach to text generation from formal proofs that exploits the highlevel and interactive features of a tacticstyle theorem prover. The design of our system is based on communication conventions identified in a corpus of texts. We show how to use dialogue with the theorem prover ..."
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Cited by 18 (4 self)
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We propose a new approach to text generation from formal proofs that exploits the highlevel and interactive features of a tacticstyle theorem prover. The design of our system is based on communication conventions identified in a corpus of texts. We show how to use dialogue with the theorem prover to obtain information that is required for communication but is not explicitly used in reasoning.
The Ergo Support System: An integrated set of tools for prototyping integrated environments
 SCHOOL OF COMPUTER SCIENCE, CARNEGIE MELLON UNIVERSITY, PITTSBURGH
, 1988
"... The Ergo Support System (ESS) is an engineering framework for experimentation and prototyping to support the application of formal methods to program development, ranging from program analysis and derivation to prooftheoretic approaches. The ESS is a growing suite of tools that are linked together ..."
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Cited by 14 (3 self)
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The Ergo Support System (ESS) is an engineering framework for experimentation and prototyping to support the application of formal methods to program development, ranging from program analysis and derivation to prooftheoretic approaches. The ESS is a growing suite of tools that are linked together by means of a set of abstract interfaces. The principal engineering challenge is the design of abstract interfaces that are semantically rich and yet flexible enough to permit experimentation with a wide variety of formallybased program and proof development paradigms and associated languages. As part of the design of ESS, several abstract interface designs have been developed that provide for more effective component integration while preserving flexibility and the potential for scaling. A benefit of the open architecture approach of ESS is the ability to mix formal and informal approaches in the same environment architecture. The ESS has already been applied in a number of formal methods experiments.
Proof Style
 University of Cambridge Computer Laboratory
, 1997
"... We are concerned with how to communicate a mathematical proof to a computer theorem prover. This can be done in many ways, while allowing the machine to generate a completely formal proof object. The most obvious choice is the amount of guidance required from the user, or from the machine perspe ..."
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Cited by 13 (3 self)
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We are concerned with how to communicate a mathematical proof to a computer theorem prover. This can be done in many ways, while allowing the machine to generate a completely formal proof object. The most obvious choice is the amount of guidance required from the user, or from the machine perspective, the degree of automation provided. But another important consideration, which we consider particularly significant, is the bias towards a `procedural' or `declarative' proof style. We will explore this choice in depth, and discuss the strengths and weaknesses of declarative and procedural styles for proofs in pure mathematics and for verification applications. We conclude with a brief summary of our own experiments in trying to combine both approaches. This is the text accompanying my invited talk at the European BRA Types annual meeting in Aussois. This talk was given on the 16th of December 1996, and the present text has been slightly modified in the light of some of the subs...
Fast Tacticbased Theorem Proving
 TPHOLs 2000, LNCS 1869
, 2000
"... Theorem provers for higherorder logics often use tactics to implement automated proof search. Tactics use a generalpurpose metalanguage to implement both generalpurpose reasoning and computationally intensive domainspecific proof procedures. The generality of tactic provers has a performance pe ..."
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Cited by 9 (4 self)
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Theorem provers for higherorder logics often use tactics to implement automated proof search. Tactics use a generalpurpose metalanguage to implement both generalpurpose reasoning and computationally intensive domainspecific proof procedures. The generality of tactic provers has a performance penalty; the speed of proof search lags far behind specialpurpose provers. We present a new modular proving architecture that significantly increases the speed of the core logic engine.
Writing Constructive Proofs Yielding Efficient Extracted Programs
"... The NuPRL system [3] was designed for interactive writing of machinechecked constructive proofs and for extracting algorithms from the proofs. The extracted algorithms are guaranteed to be correct * which makes it possible to use NuPRL as a programming language with builtin verification[1,5,7,8,9, ..."
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Cited by 6 (0 self)
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The NuPRL system [3] was designed for interactive writing of machinechecked constructive proofs and for extracting algorithms from the proofs. The extracted algorithms are guaranteed to be correct * which makes it possible to use NuPRL as a programming language with builtin verification[1,5,7,8,9,10]. However it turned out that proofs written without algorithmic efficiency in mind often produce very inefficient algorithms  exponential and doubleexponential ones for problems that can be solved in polynomial time. In this paper we present...
Program development through proof transformation
 CONTEMPORARY MATHEMATICS
, 1990
"... We present a methodology for deriving verified programs that combines theorem proving and proof transformation steps. It extends the paradigm employed in systems like NuPrl where a program is developed and verified through the proof of the specification in a constructive type theory. We illustrate ..."
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Cited by 4 (1 self)
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We present a methodology for deriving verified programs that combines theorem proving and proof transformation steps. It extends the paradigm employed in systems like NuPrl where a program is developed and verified through the proof of the specification in a constructive type theory. We illustrate our methodology through an extended example  a derivation of Warshall's algorithm for graph reachability. We also outline how our framework supports the definition, implementation, and use of abstract data types.
Incremental Proof Planning by MetaRules
 Proc. FLAIRS97, Daytona Beach, ISBN
, 1997
"... We propose a new approach to automated tactical theorem proving and proof planning: By using metarules to control the search for a proof, heuristic knowledge is declaratively collected. This eases the user's understanding of the system's search for a proof thus making userinteractions easier. The ..."
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Cited by 1 (0 self)
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We propose a new approach to automated tactical theorem proving and proof planning: By using metarules to control the search for a proof, heuristic knowledge is declaratively collected. This eases the user's understanding of the system's search for a proof thus making userinteractions easier. The system's heuristics can be modified by simply using different sets of metarules. Via metarules contextual preconditions for tactics can be formulated in a transparent way. The metarule interpreter interleaves proof planning, plan execution (tactic application), and reasoning about the tactic's results. In our framework the planner has access to more information, because the metarule interpreter knows about the history of the proof resp. the proof plan by being able to access the (partial) prooftree. 1 Introduction Albeit we focus here on the domain of automated induction theorem proving, our method is not limited to this domain. An automated induction theorem proving system has various...