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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.
NuPRL’s class theory and its applications
 Foundations of Secure Computation, NATO ASI Series, Series F: Computer & System Sciences
, 2000
"... This article presents a theory of classes and inheritance built on top of constructive type theory. Classes are defined using dependent and very dependent function types that are found in the Nuprl constructive type theory. Inheritance is defined in terms of a general subtyping relation over the und ..."
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Cited by 15 (7 self)
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This article presents a theory of classes and inheritance built on top of constructive type theory. Classes are defined using dependent and very dependent function types that are found in the Nuprl constructive type theory. Inheritance is defined in terms of a general subtyping relation over the underlying types. Among the basic types is the intersection type which plays a critical role in the applications because it provides a method of composing program components. The class theory is applied to defining algebraic structures such as monoids, groups, rings, etc. and relating them. It is also used to define communications protocols as infinite state automata. The article illustrates the role of these formal automata in defining the services of a distributed group communications system. In both applications the inheritance mechanisms allow reuse of proofs and the statement of general properties of system composition. 1
Formal reasoning about communication systems I: Embedding ML into type theory
, 1997
"... Abstract. We present a semantically correct embedding of a subset of the Ocaml programming language into the type theory of NuPRL. The subset is that needed to build the Ensemble group communication system. We describe the essential methodologies for representing language constructs by typetheoreti ..."
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Cited by 12 (9 self)
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Abstract. We present a semantically correct embedding of a subset of the Ocaml programming language into the type theory of NuPRL. The subset is that needed to build the Ensemble group communication system. We describe the essential methodologies for representing language constructs by typetheoretical expressions. Tactics representing derived inference rules and a programming logic for these constructs will be discussed as well as algorithms for translating an Ocamlprogram into NuPRLobjects and vice versa. The formal representations and the translation algorithms will serve as the foundation for the development of automated reasoning tools for the
Unguessable Atoms: A Logical Foundation for Security
"... Abstract. We show how a type of atoms, which behave like urelements, and a new proposition that expresses the independence of a term from an atom can be added to any logical system after imposing minor restrictions on definitions and computations. Working in constructive type theory, we give rules f ..."
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Cited by 4 (3 self)
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Abstract. We show how a type of atoms, which behave like urelements, and a new proposition that expresses the independence of a term from an atom can be added to any logical system after imposing minor restrictions on definitions and computations. Working in constructive type theory, we give rules for the independence proposition and show how cryptographic protocols can be modeled as automata exchanging atoms. This model provides a unifying framework for reasoning about security and allows us to combine a general model of computation with a simple model of acquisition of secret information. As an application, we prove a fundamental property of nonces that justifies the axioms for nonces used in the protocol composition logic (PCL) of Datta, Derek, Mitchell and Roy. The example shows that basic security properties are naturally expressed in terms of independence and the causal ordering of events. The rules and example proofs are fully implemented in the Nuprl proof development system. 1
Formalizing Automata II: Decidable Properties
"... Is it possible to create formal proofs of interesting mathematical theorems which are mechanically checked in every detail and yet are readable and even faithful to the best expositions of those results in the literature? This paper answers that question positively for theorems about decidable prope ..."
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Cited by 2 (0 self)
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Is it possible to create formal proofs of interesting mathematical theorems which are mechanically checked in every detail and yet are readable and even faithful to the best expositions of those results in the literature? This paper answers that question positively for theorems about decidable properties of nite automata. The exposition is from Hopcroft and Ullman's classic 1969 textbook Formal Languages and Their Relation to Automata. This paper describes a successful formalization which is faithful to that book. The requirement of being faithful to the book has unexpected consequences, namely that the underlying formal theory must include primitive notions of computability. This requirement makes a constructive formalization especially suitable. It also opens the possibility ofusingthe formal proofs to decide properties of automata. The paper shows how to do this. 1
RESTRUCTURING FORMAL MATHEMATICS FOR NATURAL TEXTS
, 2004
"... In the presence of growing collections of formal mathematics, and renewed interest in formal mathematics and automated theorem proving for new domains such as hardware or code verification, it is vital to be able to present formal content accessibly to broad audiences. We propose a novel approach to ..."
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In the presence of growing collections of formal mathematics, and renewed interest in formal mathematics and automated theorem proving for new domains such as hardware or code verification, it is vital to be able to present formal content accessibly to broad audiences. We propose a novel approach to constructing a content planner for formal mathematics produced by a tacticstyle prover which capitalizes on the inherent structure of the formal proofs. Though it had been posited that highlevel formal structure is unsuitable as a source of information for text generation, due to its heuristic nature and necessary lack of details, we are able to show that this is not the case. Tacticstyle proofs share significant structural commonality with the discourse structure of corresponding texts. These commonalities allow a content planner to be constructed which need only use lowlevel logical content as a supplementary information source to the generation process. To show that this is the case, we collected two corpora of texts generated to communicate the proof content of a series of formal proofs produced by the Nuprl
The MetaPRL Logical Programming Environment  Volume I
, 2001
"... This thesis is primarily about the design of formal programming environments for building large software systems. This work articulates two principles and uses them to guide the design, implementation, and study of a specific formal programming environment. First, design methods for large software s ..."
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This thesis is primarily about the design of formal programming environments for building large software systems. This work articulates two principles and uses them to guide the design, implementation, and study of a specific formal programming environment. First, design methods for large software systems will include multiple languages, methodologies, and refinement techniques that are suited to problem subdomains. This means that any formal system must provide the ability to define multiple logics, and it is by definition a logical framework. Second, the framework must provide the ability to express formal relations between logical theories to address the problem of system decomposition. This thesis also presents the the MetaPRL formal system. MetaPRL was built to provide a modular, abstract logical framework where multiple designs can be expressed and related. The MetaPRL design builds on our experience with logical frameworks and with structured programming concepts like inheritance and reuse to provide an efficient, highly abstract, logical machine. The contribution includes several parts. • The development of an untyped metalogic using explicit substitution. • The definition of a verydependent function type in the Nuprl type theory. • A system architecture for generic multilogical development. • A generic refiner that provides automation and enforcement for the multiple logical theories in logical environment. • A module system for logics and theories. • A generic distributed interactive theorem prover.