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Knowledgebased synthesis of distributed systems using event structures
 In Proc. 11th Int. Conf. on Logic for Programming, Artificial Intelligence, and Reasoning (LPAR 2004), Lecture Notes in Computer Science
, 2005
"... To produce a program guaranteed to satisfy a given specification one can synthesize it from a formal constructive proof that a computation satisfying that specification exists. This process is particularly effective if the specifications are written in a highlevel language that makes it easy for de ..."
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To produce a program guaranteed to satisfy a given specification one can synthesize it from a formal constructive proof that a computation satisfying that specification exists. This process is particularly effective if the specifications are written in a highlevel language that makes it easy for designers to specify their goals. We consider a highlevel specification language that results from adding knowledge to a fragment of Nuprl specifically tailored for specifying distributed protocols, called event theory. We then show how highlevel knowledgebased programs can be synthesized from the knowledgebased specifications using a proof development system such as Nuprl. Methods of Halpern and Zuck [1992] then apply to convert these knowledgebased protocols to ordinary protocols. These methods can be expressed as heuristic transformation tactics in Nuprl. 1
INTEGRATION OF DECISION PROCEDURES INTO HIGHORDER INTERACTIVE PROVERS
, 2006
"... An efficient proof assistant uses a wide range of decision procedures, including automatic verification of validity of arithmetical formulas with linear terms. Since the final product of a proof assistant is a formalized and verified proof, it prompts an additional task of building proofs of formula ..."
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An efficient proof assistant uses a wide range of decision procedures, including automatic verification of validity of arithmetical formulas with linear terms. Since the final product of a proof assistant is a formalized and verified proof, it prompts an additional task of building proofs of formulas, which validity is established by such a decision procedure. We present an implementation of several decision procedures for arithmetical formulas with linear terms in the MetaPRL proof assistant in a way that provides formal proofs of formulas found valid by those procedures. We also present an implementation of a theorem prover for the logic of justified common knowledge S4 J n introduced in [Artemov, 2004]. This system captures the notion of justified common knowledge, which is free of some of the deficiencies of the usual common knowledge operator, and is yet sufficient for the analysis of epistemic problems where common knowledge has been traditionally applied. In particular, S4 J n enjoys cutelimination, which introduces the possibility of automatic proof search in the logic of common
λµPRL – A Proof Refinement Calculus for Classical Reasoning
 in Computational Type Theory Diploma thesis, Institut für Informatik, Universität Potsdam
, 2009
"... Abstract. We present a hybrid proof calculus λµPRL that combines the propositional fragment of computational type theory with classical reasoning rules from the λµcalculi. The calculus supports the topdown development of proofs as well as the extraction of proof terms in a functional programming l ..."
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Abstract. We present a hybrid proof calculus λµPRL that combines the propositional fragment of computational type theory with classical reasoning rules from the λµcalculi. The calculus supports the topdown development of proofs as well as the extraction of proof terms in a functional programming language extended by a nonconstructive binding operator. It enables a user to employ a mix of constructive and classical reasoning techniques and to extract algorithms from proofs of specification theorems that are fully executable if classical arguments occur only in proof parts related to the validation of the algorithm. We prove the calculus sound and complete for classical propositional logic, introduce the concept of µsafe terms to identify proof terms corresponding to constructive proofs and show that the restriction of λµPRL to µsafe proof terms is sound and complete for intuitionistic propositional logic. We also show that an extension of λµPRL to arithmetical and firstorder expressions is isomorphic to Murthy’s calculus P ROGK.
Abstraction and Ontology: Questions as Propositional Abstracts in Type Theory with Records

, 2005
"... The paper develops a semantics for natural language interrogatives which identifies questions— the denotations of interrogatives—with propositional abstracts. The paper argues that a theory of Questions as Propositional Abstracts (QPA), is a simple, transparently implementable theory that has signif ..."
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The paper develops a semantics for natural language interrogatives which identifies questions— the denotations of interrogatives—with propositional abstracts. The paper argues that a theory of Questions as Propositional Abstracts (QPA), is a simple, transparently implementable theory that has significant empirical coverage. However, until recently QPA has been abandoned in formal semantic treatments of questions, due to a number of significant problems QPA encountered when formulated within the type system of Montague Semantics. In recent work, Ginzburg and Sag provided a a situation theoretic implementation of QPA that succeeded in overcoming cerain of the original problems for QPA. However, Ginzburg and Sag’s proposal relied on a special purpose account of λabstraction, raising the question to what extent QPA can be sustained using standard notions of abstraction. In this paper such doubts are allayed by implementing QPA in a version of Type Theory that provides record types. These latter allow one to develop notions of simultaneous/vacuous abstraction with restrictions and an ontology with various ‘informational entities’. Moreover, the intrinsic polymorphism of this theory plays a crucial role in enabling the definition of a general type for questions, one of the main stumbling blocks for earlier versions of QPA.
A Causal Logic of Events in Formalized Computational Type Theory ∗
"... We provide a logic for distributed computing that has the explanatory and technical power of constructive logics of computation. In particular, we establish a proof technology that supports correctbyconstruction programming based on the notion that concurrent processes can be extracted from proofs ..."
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We provide a logic for distributed computing that has the explanatory and technical power of constructive logics of computation. In particular, we establish a proof technology that supports correctbyconstruction programming based on the notion that concurrent processes can be extracted from proofs that specifications are achievable. 1
Generalized Support and Formal Development of Constraint Propagators
"... Abstract The concept of support is pervasive in constraint programming. Traditionally, when a domain value ceases to have support, it may be removed because it takes part in no solutions. Arcconsistency algorithms such as AC2001 [8] make use of support in the form of a single domain value. GAC alg ..."
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Abstract The concept of support is pervasive in constraint programming. Traditionally, when a domain value ceases to have support, it may be removed because it takes part in no solutions. Arcconsistency algorithms such as AC2001 [8] make use of support in the form of a single domain value. GAC algorithms such as GACSchema We design a methodology for developing correct propagators using generalized support. A constraint is expressed as a family of support properties, which may be proven correct against the formal semantics of the constraint. Using CurryHoward isomorphism to interpret constructive proofs as programs, we show how to derive correct propagators from the constructive proofs of the support properties. The framework is carefully designed to allow efficient algorithms to be produced. Derived algorithms may make use of dynamic literal triggers or watched literals
Two Lectures on Constructive Type Theory
, 2015
"... Main Goal: One goal of these two lectures is to explain how important ideas and problems from computer science and mathematics can be expressed well in constructive type theory and how proof assistants for type theory help us solve them. Another goal is to note examples of abstract mathematical idea ..."
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Main Goal: One goal of these two lectures is to explain how important ideas and problems from computer science and mathematics can be expressed well in constructive type theory and how proof assistants for type theory help us solve them. Another goal is to note examples of abstract mathematical ideas currently not expressed well enough in type theory. The two lectures will address the following three specific questions related to this goal. Three Questions: One, what are the most important foundational ideas in computer science and mathematics that are expressed well in constructive type theory, and what concepts are more difficult to express? Two, how can proof assistants for type theory have a large impact on research and education, specifically in computer science, mathematics, and beyond? Three, what key ideas from type theory are students missing if they know only one of the modern type theories? The lectures are intended to complement the handson Nuprl tutorials by Dr. Mark Bickford that will introduce new topics as well as address these questions. The lectures refer to recent educational material posted on the PRL project web page, www.nuprl.org, especially the online article Logical Investigations, July 2014 on the front page of the web cite.
Nuprl as Logical Framework for Automating Proofs in Category Theory
, 2012
"... We describe the construction of a semiautomated proof system for elementary category theory using the Nuprl proof development system as logical framework. We have used Nuprl’s display mechanism to implement the basic vocabulary and Nuprl’s rule compiler to implemented a firstorder proof calculus f ..."
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We describe the construction of a semiautomated proof system for elementary category theory using the Nuprl proof development system as logical framework. We have used Nuprl’s display mechanism to implement the basic vocabulary and Nuprl’s rule compiler to implemented a firstorder proof calculus for reasoning about categories, functors and natural transformations. To automate proofs we have formalized both standard techniques from automated theorem proving and reasoning patterns that are specific to category theory and used Nuprl’s tactic mechanism for the actual implementation. We illustrate our approach by automating proofs of natural isomorphisms between categories.