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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. LLF c ..."
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Cited by 215 (44 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...
Structuring Metatheory on Inductive Definitions
, 2000
"... We examine a problem for machine supported metatheory. There are statements true about a theory that are true of some (but only some) extensions; however standard theorystructuring facilities do not support selective inheritance. We use the example of the deduction theorem for modal logic and s ..."
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Cited by 7 (0 self)
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We examine a problem for machine supported metatheory. There are statements true about a theory that are true of some (but only some) extensions; however standard theorystructuring facilities do not support selective inheritance. We use the example of the deduction theorem for modal logic and show how a statement about a theory can explicitly formalize the closure conditions extensions should satisfy for it to remain true. We show how metatheories based on inductive denitions allow theories and general metatheorems to be organized this way, and report on a case study using the theory FS0 . 1 Introduction Hierarchical theory structuring plays an important role in the application of theorem provers to nontrivial problems, and many systems provide support for it. For example HOL [6], Isabelle [13] and their predecessor LCF [7] support simple theory hierarchies. In these systems a theory is a specication of a language, using types and typed constants, and a collection of rules...
Pure type systems in rewriting logic: Specifying typed higherorder languages in a firstorder logical framework
 In Essays in Memory of OleJohan Dahl, volume 2635 of LNCS
, 2004
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Scoped Metatheorems
, 1998
"... Proof development systems traditionally structure theories hierarchically: Theorems established in a subtheory hold in all supertheories. While often eective, this is sometimes too restrictive as there are certain facts that are true of some but not all extensions. We present a solution where instea ..."
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Cited by 3 (2 self)
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Proof development systems traditionally structure theories hierarchically: Theorems established in a subtheory hold in all supertheories. While often eective, this is sometimes too restrictive as there are certain facts that are true of some but not all extensions. We present a solution where instead of rst formalizing a theory and then establishing facts, we parameterize each statement with its scope of application. We present this idea abstractly and consider concrete implementations based on parameterized inductive denitions. 1 Introduction It is a truism of software engineering that large programming projects should be factored into modular subdevelopments. The same holds for large formal mathematical projects carried out using computer support in the form of a proof development system, as we see if look at what has been achieved by the user communities of, e.g., Nuprl, HOL, Coq, Isabelle, or Mizar. However the nature of facilities for structuring developments varies from syst...
Metatheory in the HigherOrder Logic Framework Isabelle
, 1996
"... Isabelle [Pau94] is a generic theorem proving environment. It is written in ML, and is part of the LCF [GMW79] family of tacticbased theorem provers. The core system uses a metalogic consisting of the implicational/universal fragment of an intuitionistic higherorder logic with equality. Within thi ..."
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Cited by 1 (1 self)
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Isabelle [Pau94] is a generic theorem proving environment. It is written in ML, and is part of the LCF [GMW79] family of tacticbased theorem provers. The core system uses a metalogic consisting of the implicational/universal fragment of an intuitionistic higherorder logic with equality. Within this system, a large number object logics can be represented. A general method of encoding a sequent calculus as an object logic in a form suitable for proving properties of the calculus is presented. Some suggestions about general use of Isabelle in this area are made. 1 Introduction As with most Logical Frameworks, Isabelle uses an ASCII notation for the symbols of logic not available on a keyboard. Appendix A gives a basic introduction to this, but throughout this paper standard logical notations will be used for ease of reading. Isabelle represents a highly modular system with many incompatible object logics having been developed based on a single core, the Pure core system. The Pure syst...
Proving Correctness of Modular Functional Programs
"... and for Mum. I whacked the back of the driver’s seat with my fist. “This is important, goddamnit! This is a true story! ” The car swerved sickeningly, thenstraightenedout....Thekidinthebacklookedlikehewasready to jump right out of the car and take his chances. Our vibrations were getting nasty—but w ..."
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and for Mum. I whacked the back of the driver’s seat with my fist. “This is important, goddamnit! This is a true story! ” The car swerved sickeningly, thenstraightenedout....Thekidinthebacklookedlikehewasready to jump right out of the car and take his chances. Our vibrations were getting nasty—but why? I was puzzled, frustrated. Was there no communication in this car? Had we deteriorated to the level of dumb beasts? Because my story was true. I was certain of that. And it was extremely important, I felt, for the meaning of our journey to be made absolutelyclear....Andwhenthecallcame, I wasready. One reason for studying and programming in functional programming languages is that they are easy to reason about, yet there is surprisingly little work on proving the correctness of large functional programs. In this dissertation I show