Results 1 - 10 of 13

Categorical Logic

by Andrew M. Pitts - A CHAPTER IN THE FORTHCOMING VOLUME VI OF HANDBOOK OF LOGIC IN COMPUTER SCIENCE , 1995
"... ..."
Abstract - Cited by 112 (2 self) - Add to MetaCart
Abstract not found

Semantic Foundations for Embedding HOL in Nuprl

by Douglas J. Howe - ALGEBRAIC METHODOLOGY AND SOFTWARE TECHNOLOGY , 1996
"... We give a new semantics for Nuprl's constructive type theory that justifies a useful embedding of the logic of the HOL theorem prover inside Nuprl. The embedding gives Nuprl effective access to most of the large body of formalized mathematics that the HOL community has amassed over the las ..."
Abstract - Cited by 32 (2 self) - Add to MetaCart
We give a new semantics for Nuprl's constructive type theory that justifies a useful embedding of the logic of the HOL theorem prover inside Nuprl. The embedding gives Nuprl effective access to most of the large body of formalized mathematics that the HOL community has amassed over the last decade. The new semantics is dramatically simpler than the old, and gives a novel and general way of adding set-theoretic equivalence classes to untyped functional programming languages.

The Seven Virtues of Simple Type Theory

by William M. Farmer - JOURNAL OF APPLIED LOGIC , 2003
"... ..."
Abstract - Cited by 30 (6 self) - Add to MetaCart
Abstract not found
(Show Context)

Importing mathematics from hol into Nuprl

by Douglas J. Howe - Theorem Proving in Higher Order Logics (TPHOLs 1996), volume 1125 of LNCS , 1996
"... Abstract. Nuprl and HOL are both tactic-based interactive theorem provers for higher-order logic, and both have been used in many substantial applications over the last decade. However, the HOL community has accumulated a much larger collection of formalized mathematics of the kind useful for hardwa ..."
Abstract - Cited by 29 (2 self) - Add to MetaCart
Abstract. Nuprl and HOL are both tactic-based interactive theorem provers for higher-order logic, and both have been used in many substantial applications over the last decade. However, the HOL community has accumulated a much larger collection of formalized mathematics of the kind useful for hardware and software veri cation. This collection would be of great bene t in applying Nuprl to veri cation problems of real practical interest. This paper describes a connection we have implemented between HOL and Nuprl that gives Nuprl e ective access to mathematics formalized in HOL. In designing this connection, we had to overcome a number of problems related to di erences in the logics, logical infrastructures and stylistic conventions of Nuprl and HOL. 1
(Show Context)

A HOL basis for reasoning about functional programs

by Sten Agerholm , 1994
"... ..."
Abstract - Cited by 24 (6 self) - Add to MetaCart
Abstract not found

Modular Reasoning in Isabelle

by Florian Kammüller , 1999
"... The concept of locales for Isabelle enables local definition and assumption for interactive mechanical proofs. Furthermore, dependent types are constructed in Isabelle/HOL for first class representation of structure. These two concepts are introduced briefly. Although each of them has proved use ..."
Abstract - Cited by 13 (2 self) - Add to MetaCart
The concept of locales for Isabelle enables local definition and assumption for interactive mechanical proofs. Furthermore, dependent types are constructed in Isabelle/HOL for first class representation of structure. These two concepts are introduced briefly. Although each of them has proved useful in itself, their real power lies in combination. This paper illustrates by examples from abstract algebra how this combination works and argues that it enables modular reasoning.
(Show Context)

A Classical Set-Theoretic Model of Polymorphic Extensional Type Theory

by Douglas J. Howe , 1997
"... . We give a new semantic foundation for type theories in the lineage of Martin-Lof's "polymorphic extensional" type theory, and use it to give a model of the constructive type theory of the interactive theorem proving system Nuprl. These type theories are based on an operational seman ..."
Abstract - Cited by 6 (1 self) - Add to MetaCart
. We give a new semantic foundation for type theories in the lineage of Martin-Lof's "polymorphic extensional" type theory, and use it to give a model of the constructive type theory of the interactive theorem proving system Nuprl. These type theories are based on an operational semantics of an untyped programming language. We show how to integrate classical set-theoretic objects, such as functions-as-graphs and equivalence classes, into this operational framework. The new semantics is dramatically simpler than the previous ones, and enables direct reasoning about classical mathematics. A practical consequence is that it justifies a useful embedding of the logic of the HOL theorem prover that gives Nuprl effective access to most of the large body of formalized mathematics that the HOL community has amassed over the years. 1 Introduction The so-called "polymorphic extensional" type theory of Martin-Lof (Martin-Lof, 1982) has two features that set it apart from other constructive type t...
(Show Context)

A comparative study of Coq and HOL

by Vincent Zammit - In Proceedings of the 10th International Conference on Theorem Proving in Higher Order Logics, Lecture Notes in Computer Science , 1997
"... Abstract. This paper illustrates the dierences between the style of theory mechanisation of Coq and of HOL. This comparative study is based on the mechanisation of fragments of the theory of computation in these systems. Examples from these implementations are given to sup-port some of the arguments ..."
Abstract - Cited by 5 (1 self) - Add to MetaCart
Abstract. This paper illustrates the dierences between the style of theory mechanisation of Coq and of HOL. This comparative study is based on the mechanisation of fragments of the theory of computation in these systems. Examples from these implementations are given to sup-port some of the arguments discussed in this paper. The mechanisms for specifying denitions and for theorem proving are discussed separately, building in parallel two pictures of the dierent approaches of mechani-sation given by these systems. 1
(Show Context)

Quotients in Simple Type Theory

by Bart Jacobs - Manuscript, Math. Inst , 1994
"... Introduction Quotients are used throughout mathematics for constructing new objects from old, by collapsing part of the structure, see for example any textbook on algebra or topology. Here we give a completely general description of such quotients in a type theoretic language. We assume a simple ty ..."
Abstract - Cited by 3 (1 self) - Add to MetaCart
Introduction Quotients are used throughout mathematics for constructing new objects from old, by collapsing part of the structure, see for example any textbook on algebra or topology. Here we give a completely general description of such quotients in a type theoretic language. We assume a simple type theory, together with a predicate logic to reason about types and terms. Then quotients can be described as a left adjoint to a certain equality-predicate functor. This gives us all the rules we need: formation, introduction, elimination and (fi)- and (j)-conversions for quotients. These will be described in the next section below. Subsequently, the new syntax is put to use in constructing Z from N, a poset from a preorder, the abelianization of a group, and tensor products\Omega and sums \Phi of abelian groups. All these constructions involve taking a suitable quotient. They will be de
(Show Context)

Strongly-typed Theory of Structures And Behaviours

by Keith Hanna, Neil Daeche - Correct Hardware Design and Verification Methods, Lecture Notes In Computer Science , 1993
"... This paper describes an approach to capturing the relation between circuits and their behaviours within a formal theory. The method exploits dependent types to achieve a rigorous yet theoretically simple connection between circuits (treated as graphs) and their behavioural specifications (treate ..."
Abstract - Cited by 2 (1 self) - Add to MetaCart
This paper describes an approach to capturing the relation between circuits and their behaviours within a formal theory. The method exploits dependent types to achieve a rigorous yet theoretically simple connection between circuits (treated as graphs) and their behavioural specifications (treated as predicates). An example is given of a behavioural extraction function and it is shown how a type for modules can be defined that is sufficiently fine to guarantee that the behaviour of a module will satisfy its behavioural specification. The method is discussed in relation to VHDL and in relation to formal synthesis, (a process whereby one starts with a behavioural specification and, using an interactive goal-directed approach, ends up with a circuit and a formal proof that it satisfies the given behavioural specification).
(Show Context)