Results 1  10
of
12
A Framework for Defining Logics
 JOURNAL OF THE ASSOCIATION FOR COMPUTING MACHINERY
, 1993
"... The Edinburgh Logical Framework (LF) provides a means to define (or present) logics. It is based on a general treatment of syntax, rules, and proofs by means of a typed calculus with dependent types. Syntax is treated in a style similar to, but more general than, MartinLof's system of ariti ..."
Abstract

Cited by 716 (39 self)
 Add to MetaCart
The Edinburgh Logical Framework (LF) provides a means to define (or present) logics. It is based on a general treatment of syntax, rules, and proofs by means of a typed calculus with dependent types. Syntax is treated in a style similar to, but more general than, MartinLof's system of arities. The treatment of rules and proofs focuses on his notion of a judgement. Logics are represented in LF via a new principle, the judgements as types principle, whereby each judgement is identified with the type of its proofs. This allows for a smooth treatment of discharge and variable occurrence conditions and leads to a uniform treatment of rules and proofs whereby rules are viewed as proofs of higherorder judgements and proof checking is reduced to type checking. The practical benefit of our treatment of formal systems is that logicindependent tools such as proof editors and proof checkers can be constructed.
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. ..."
Abstract

Cited by 55 (8 self)
 Add to MetaCart
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.
Using Reflection to Build Efficient and Certified Decision Procedures
 TACS'97. SpringerVerlag LNCS 1281
, 1997
"... In this paper we explain how computational reflection can help build efficient certified decision procedure in reduction systems. We have developped a decision procedure on abelian rings in the Coq system but the approach we describe applies to all reduction systems that allow the definition of c ..."
Abstract

Cited by 51 (0 self)
 Add to MetaCart
In this paper we explain how computational reflection can help build efficient certified decision procedure in reduction systems. We have developped a decision procedure on abelian rings in the Coq system but the approach we describe applies to all reduction systems that allow the definition of concrete types (or datatypes). We show that computational reflection is more efficient than an LCFlike approach to implement decision procedures in a reduction system. We discuss the concept of total reflection, which we have investigated in Coq using two facts: the extraction process available in Coq and the fact that the implementation language of the Coq system can be considered as a sublanguage of Coq. Total reflection is not yet implemented in Coq but we can test its performance as the extraction process is effective. Both reflection and total reflection are conservative extensions of the reduction system in which they are used. We also discuss performance and related approaches....
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 m ..."
Abstract

Cited by 13 (5 self)
 Add to MetaCart
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...
Bidirectional Natural Deduction
 AI*IA Notizie
, 1993
"... The goal of this paper is to present a theorem prover able to perform both forward and backward reasoning supported by a well defined formal system. This system for bidirectional reasoning has been proved equivalent to Gentzen's classical system of propositional natural deduction. Thi ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
The goal of this paper is to present a theorem prover able to perform both forward and backward reasoning supported by a well defined formal system. This system for bidirectional reasoning has been proved equivalent to Gentzen's classical system of propositional natural deduction. This paper, primarily aimed at developing a deeper theoretical understanding of bidirectional reasoning, provides basic concepts to be incorporated into an innovative theorem prover to support interactive proofs construction in general domains. 1
A framework for defining logical frameworks
 University of Udine
, 2006
"... Replace this file with prentcsmacro.sty for your meeting, or with entcsmacro.sty for your meeting. Both can be ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
Replace this file with prentcsmacro.sty for your meeting, or with entcsmacro.sty for your meeting. Both can be
AND
"... Abstract. The Edinburgh Logical Framework (LF) provides a means to define (or present) logics. It is based on a general treatment of syntax, rules, and proofs by means of a typed Acalculus with dependent types. Syntax is treated in a style similar to, but more general than, MartinLof’s system of a ..."
Abstract
 Add to MetaCart
Abstract. The Edinburgh Logical Framework (LF) provides a means to define (or present) logics. It is based on a general treatment of syntax, rules, and proofs by means of a typed Acalculus with dependent types. Syntax is treated in a style similar to, but more general than, MartinLof’s system of arities. The treatment of rules and proofs focuses on his notion of a judgment. Logics are represented in LF via a new principle, the judgrrzents as ~pes principle, whereby each judgment is identified with the type of its proofs. This allows for a smooth treatment of discharge and variable occurrence conditions and leads to a uniform treatment of rules and proofs whereby rules are viewed as proofs of higherorder judgments and proof checking is reduced to type checking. The practical benefit of our treatment of formal systems is that logicindependent tools,
Bidirectional Reasoning
"... The goal of this paper is to present a formal system FB for bidirectional reasoning which integrates forward and backward deduction. FB is proved equivalent to Gentzen's classical system of propositional natural deduction. FB is the logic of a theorem prover which supports interactive proof ..."
Abstract
 Add to MetaCart
The goal of this paper is to present a formal system FB for bidirectional reasoning which integrates forward and backward deduction. FB is proved equivalent to Gentzen's classical system of propositional natural deduction. FB is the logic of a theorem prover which supports interactive proof construction in general domains. 1