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A Linear Logical Framework
, 1996
"... We present the linear type theory LLF as the forAppeared in the proceedings of the Eleventh Annual IEEE Symposium on Logic in Computer Science  LICS'96 (E. Clarke editor), pp. 264275, New Brunswick, NJ, July 2730 1996. mal basis for a conservative extension of the LF logical framework. ..."
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Cited by 222 (45 self)
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We present the linear type theory LLF as the forAppeared in the proceedings of the Eleventh Annual IEEE Symposium on Logic in Computer Science  LICS'96 (E. Clarke editor), pp. 264275, New Brunswick, NJ, July 2730 1996. mal basis for a conservative extension of the LF logical framework. LLF combines the expressive power of dependent types with linear logic to permit the natural and concise representation of a whole new class of deductive systems, namely those dealing with state. As an example we encode a version of MiniML with references including its type system, its operational semantics, and a proof of type preservation. Another example is the encoding of a sequent calculus for classical linear logic and its cut elimination theorem. LLF can also be given an operational interpretation as a logic programming language under which the representations above can be used for type inference, evaluation and cutelimination. 1 Introduction A logical framework is a formal system desig...
Requirements for a Program Refinement Engine
 PATTER RECOGNITION LETTERS
, 1995
"... Refinement is a mathematicallybased technique for developing a program from an abstract specification so that the program satisfies the specification. The aim of the Program Refinement Tool project is to develop a generic refinement tool suitable for supporting a methodology for the interactive ..."
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Cited by 2 (1 self)
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Refinement is a mathematicallybased technique for developing a program from an abstract specification so that the program satisfies the specification. The aim of the Program Refinement Tool project is to develop a generic refinement tool suitable for supporting a methodology for the interactive development of programs based on the refinement calculus. This report summarizes our investigation into an appropriate engine to use for the refinement calculator and theorem prover in this tool.
Tactics for reasoning modulo AC in Coq
 In First International Conf. on Certified Programs and Proofs
, 2011
"... Abstract. We present a set of tools for rewriting modulo associativity and commutativity (AC) in Coq, solving a longstanding practical problem. We use two building blocks: first, an extensible reflexive decision procedure for equality modulo AC; second, an OCaml plugin for pattern matching modulo ..."
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Cited by 1 (0 self)
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Abstract. We present a set of tools for rewriting modulo associativity and commutativity (AC) in Coq, solving a longstanding practical problem. We use two building blocks: first, an extensible reflexive decision procedure for equality modulo AC; second, an OCaml plugin for pattern matching modulo AC. We handle associative only operations, neutral elements, uninterpreted function symbols, and userdefined equivalence relations. By relying on typeclasses for thereification phase, we can infer these properties automatically, so that endusers do not need to specify which operation is A or AC, or which constant is a neutral element. 1
Generalized Rewriting in Type Theory
"... While type theories such as Nuprl are expressive logics for theorem proving, they present difficulties for designers of term rewriting systems. The two most serious difficulties are: 1) They do not provide a global equality. Instead users rewrite over arbitrary userdefined relations. 2) Each rewrit ..."
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While type theories such as Nuprl are expressive logics for theorem proving, they present difficulties for designers of term rewriting systems. The two most serious difficulties are: 1) They do not provide a global equality. Instead users rewrite over arbitrary userdefined relations. 2) Each rewrite step must be proved valid. In general, these proofs cannot be recursively generated. We have overcome these difficulties and designed a package for the Nuprl system that works well in practice. Our solution is an extensible set of functions for directing and validating relational inferences. The heart of our package is a set of operators that use a usersupplied lemma database to create new rewrites from old ones. These routines place no restrictions on relations; a rewrite's success depends on the strength of the database. Overall, the package allows rewrites to be pieced together in numerous ways, providing the user with a tool to construct sophisticated rewrite strategies. 1 Introductio...
DECIDING KLEENE ALGEBRAS IN COQ
, 2011
"... braries to assist in the mechanization of formal proofs in Coq. The first library provides algebraic tools for reasoning about binary relations and can be found at ..."
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braries to assist in the mechanization of formal proofs in Coq. The first library provides algebraic tools for reasoning about binary relations and can be found at
HigherOrder Automated Theorem Provers
"... The automation of simple type theory, also referred to as classical higherorder logic (HOL), has significantly progressed recently. This paper provides an allowedly slightly biased survey on these developments. One distinguishing characteristics of HOL is its support for higherorder ..."
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The automation of simple type theory, also referred to as classical higherorder logic (HOL), has significantly progressed recently. This paper provides an allowedly slightly biased survey on these developments. One distinguishing characteristics of HOL is its support for higherorder
HigherOrder Automated Theorem Provers
"... The automation of simple type theory, also referred to as classical higherorder logic (HOL), has significantly progressed recently. This paper provides an allowedly slightly biased survey on these developments. A distinguishing characteristic of HOL is its support for higherorder quan ..."
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The automation of simple type theory, also referred to as classical higherorder logic (HOL), has significantly progressed recently. This paper provides an allowedly slightly biased survey on these developments. A distinguishing characteristic of HOL is its support for higherorder quan