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On Equivalence and Canonical Forms in the LF Type Theory [article]

Robert Harper, Frank Pfenning
2001 arXiv   pre-print
In this paper we present a new, type-directed equivalence algorithm for the LF type theory that overcomes the weaknesses of previous approaches.  ...  Decidability of definitional equality and conversion of terms into canonical form play a central role in the meta-theory of a type-theoretic logical framework.  ...  We would also like to thank the anonymous referees for a number of helpful suggestions and pointers to the literature.  ... 
arXiv:cs/0110028v1 fatcat:xpano6fmlbhcdipxuavi7exxbm

On equivalence and canonical forms in the LF type theory

Robert Harper, Frank Pfenning
2005 ACM Transactions on Computational Logic  
In this paper we present a new, type-directed equivalence algorithm for the LF type theory that overcomes the weaknesses of previous approaches.  ...  Decidability of de nitional equality and conversion of terms into canonical form play a central role in the meta-theory of a type-theoretic logical framework.  ...  This result shows that all adequacy proofs for LF representation on canonical forms still hold. In fact, they can be carried out directly on quasi-canonical forms.  ... 
doi:10.1145/1042038.1042041 fatcat:qn535ytk2zhlfmhnwk2kz2gdra

LF in LF

Chris Martens, Karl Crary
2012 Proceedings of the seventh international workshop on Logical frameworks and meta-languages, theory and practice - LFMTP '12  
We present a mechanized metatheoretic development of two presentations of LF: the Canonical presentation (in which only betashort, eta-long terms are well-formed) and the original version based on definitional  ...  We prove the standard metatheory, i.e. that type checking is decidable and canonical forms exist uniquely.  ...  We also thank the anonymous reviewers for their thorough reading and helpful suggestions.  ... 
doi:10.1145/2364406.2364410 fatcat:qo6mulfcujevddg6hf7fg5lqxe

A dependent nominal type theory

James Cheney, Pawel Urzyczyn
2012 Logical Methods in Computer Science  
We present a LF-style dependent type theory extended with name-abstraction types, prove soundness and decidability of beta-eta-equivalence checking, discuss adequacy and canonical forms via an example,  ...  So far nominal techniques have mostly been studied using classical logic or model theory, not type theory.  ...  Acknowledgements Thanks to Frank Nebel, Andrew Pitts, Aaron Stump, Stephanie Weirich, and Edwin Westbrook for helpful discussions on this work.  ... 
doi:10.2168/lmcs-8(1:8)2012 fatcat:mb5ugrcs4ncptamcquh2ymuqry

A framework for defining logics

Robert Harper, Furio Honsell, Gordon Plotkin
1993 Journal of the ACM  
Logics are represented in LF via a new principle, the judgements as types principle, whereby each judgement is identified with the type of its proofs.  ...  Building on the experience of AUTOMATH and LCF, the NuPRL system [9] is a full-scale interactive proof development environment for type theory that provides support not only for interactive proof construction  ...  Definition of the Type Theory The LF type theory is a calculus for deriving typing and equivalence (i.e.definitional equality) assertions.  ... 
doi:10.1145/138027.138060 fatcat:xht7p7hyyjh4hpzuvfuycskwje

Producing Proofs from an Arithmetic Decision Procedure in Elliptical LF

Aaron Stump, Clark W. Barrett, David L. Dill
2002 Electronical Notes in Theoretical Computer Science  
Software that can produce independently checkable evidence for the correctness of its output has received recent attention for use in certifying compilers and proofcarrying code.  ...  It is shown how extensions to LF which support proof rules schematic in an arity ("elliptical" rules) are very convenient for this purpose.  ...  One thing that is known is that just adding the type nat and subrange types to LF makes type-checking undecidable in general.  ... 
doi:10.1016/s1571-0661(04)80504-8 fatcat:axotixwzt5ddtl4kzu26i7z6ii

QED(1+1) on the Light Front and its implications for semiphenomenological methods in QCD(3+1) [article]

V.A. Franke, S.A. Paston, E.V. Prokhvatilov
2006 arXiv   pre-print
A modification of the canonical LF Hamiltonian for QCD is proposed, basing on the detailed study of the exact description of vacuum condensate in QED(1+1) that uses correct form of LF Hamiltonian.  ...  A possibility of semiphenomenological description of vacuum effects in QCD quantized on the Light Front (LF) is discussed.  ...  We quantized this boson theory on the LF with the p − ≥ ε > 0 regularization and considered the difference between LF perturbation theory and corresponding covariant one (in Lorentz coordinates) to all  ... 
arXiv:hep-th/0610160v1 fatcat:bzngenu5pzcbra4gtkgnagjuwm

On the construction of corrected Light-Front Hamiltonian for QED_2 [article]

S.A. Paston, E.V. Prokhvatilov, V.A. Franke
2001 arXiv   pre-print
The obtained Light-Front Hamiltonian contains all terms, present in the QED_2 theory, canonically (naively) quantized on the Light-Front (in the Light-Front gauge) and an unusual counterterm.  ...  This is done to all orders of perturbation theory in fermion mass, using the bosonization at intermediate steps and comparing Light-Front and Lorentz-covariant perturbation theories for bosonized model  ...  The form of the obtained LF Hamiltonian allows simple transformation to original canonical fermion variables on the LF and the direct comparison with the original canonical LF Hamiltonian.  ... 
arXiv:hep-th/0011224v2 fatcat:cyzpvmo2pzampbodyigmuv7q74

Mechanizing metatheory in a logical framework

2007 Journal of functional programming  
In this methodology, the syntactic and deductive apparatus of a system is encoded as the canonical forms of associated LF types; an encoding is correct (adequate) if and only if it defines a compositional  ...  We begin by defining a variant of the original LF language, called Canonical LF, in which only canonical forms (long βη-normal forms) are permitted.  ...  We thank the anonymous referees for their helpful feedback on previous drafts.  ... 
doi:10.1017/s0956796807006430 fatcat:g3t4uybplvhdrh2l4tcwaaisqq

Some normalization properties of martin-löf's type theory, and applications [chapter]

David A. Basin, Douglas J. Howe
1991 Lecture Notes in Computer Science  
For type theories such as LF, such properties can be established via an analysis of normal forms and types.  ...  For certain kinds of applications of type theories, the faithfulness of formalization in the theory depends on intensional, or structural, properties of objects constructed in the theory.  ...  The subtheory we deal with in this paper is based on the LF type theory. It is suitably well-behaved and is expressive enough for the examples we have in mind.  ... 
doi:10.1007/3-540-54415-1_60 fatcat:3s2533qtijhpzb7ajc32dsqliu

QED_2 Light-Front Hamiltonian reproducing all orders of covariant chiral perturbation theory [article]

S. A. Paston, E. V. Prokhvatilov, V. A. Franke
1999 arXiv   pre-print
The obtained LF Hamiltonian depends explicitly on chiral condensate parameters which enter in a form of some coupling constants.  ...  Light-Front (LF) Hamiltonian for QED in (1+1)-dimensions is constructed using the boson form of this model with additional Pauli-Villars type ultraviolet regularization.  ...  Acknowledgements The author (E. V. P.) is grateful to the DAAD for financial support. The present work was supported also in part (for one of authors S. A.  ... 
arXiv:hep-th/9910114v4 fatcat:rqzertxg2ve4ndyiwieudipjmi

A Concurrent Logical Framework: The Propositional Fragment [chapter]

Kevin Watkins, Iliano Cervesato, Frank Pfenning, David Walker
2004 Lecture Notes in Computer Science  
The underlying type theory uses monadic types to segregate values from computations.  ...  From a logical point of view our type theory can be seen as a novel combination of lax logic and dual intuitionistic linear logic.  ...  It is based on the observation that, since LF-style representations rely exclusively on canonical forms, there is no need for the framework to define-or the meta-theory to investigate-anything but canonical  ... 
doi:10.1007/978-3-540-24849-1_23 fatcat:lzh5gunf7re2zbjc5yqzwwxdf4

Coercive subtyping: Theory and implementation

Z. Luo, S. Soloviev, T. Xue
2013 Information and Computation  
In this paper, we give a new and adequate formulation of T [C], the system that extends a type theory T with coercive subtyping based on a set C of basic subtyping judgements, and show that coercive subtyping  ...  We also compare coercive subtyping with the 'ordinary' notion of subtyping -subsumptive subtyping, and show that the former is adequate for type theories with canonical objects while the latter is not.  ...  Assume T be a type theory specified in the logical framework LF 9 and C be a (possibly infinite) set of subtyping judgements of the form Γ ⊢ A < c B : T ype.  ... 
doi:10.1016/j.ic.2012.10.020 fatcat:lmuvh3rwqjeubdygevnuezqigm

Quantization of Field Theory on the Light Front [article]

V.A. Franke, Yu.V. Novozhilov, S.A. Paston, E.V. Prokhvatilov
2005 arXiv   pre-print
Canonical formulation of quantum field theory on the Light Front (LF) is reviewed.  ...  The problem of constructing the LF Hamiltonian which gives the theory equivalent to original Lorentz and gauge invariant one is considered.  ...  The work was supported by the Russian Foundation for Basic Research, grant no. 05-02-17477 (S.A.P. and E.V.P.).  ... 
arXiv:hep-th/0404031v2 fatcat:znuu6yljinbbtide4abnrgay6u

The Light-Front Hamiltonian formalism for two-dimensional Quantum Electrodynamics equivalent to the Lorentz-covariant approach [article]

S.A. Paston, E.V. Prokhvatilov, V.A. Franke
2003 arXiv   pre-print
theory in all orders in the fermion mass.  ...  The coefficient of the counterterm has no ultraviolet divergence, depends on the value of the fermion condensate in the \theta-vacuum, and is linear in this value for a small fermion mass.  ...  For nongauge field theories of the type of the Yukawa model, it is possible to find the counterterms required for improving the canonical LF Hamiltonian [9, 11] including all PT orders in the coupling  ... 
arXiv:hep-th/0302016v1 fatcat:cnkhtgaedndmvljurocp3r433m
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