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37
Grammatical Framework: A TypeTheoretical Grammar Formalism
, 2003
"... Grammatical Framework (GF) is a specialpurpose functional language for defining grammars. It uses a Logical Framework (LF) for a description of abstract syntax, and adds to this a notation for defining concrete syntax. GF grammars themselves are purely declarative, but can be used both for lineariz ..."
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Cited by 72 (19 self)
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Grammatical Framework (GF) is a specialpurpose functional language for defining grammars. It uses a Logical Framework (LF) for a description of abstract syntax, and adds to this a notation for defining concrete syntax. GF grammars themselves are purely declarative, but can be used both for linearizing syntax trees and parsing strings. GF can describe both formal and natural languages. The key notion of this description is a grammatical object, which is not just a string, but a record that contains all information on inflection and inherent grammatical features such as number and gender in natural languages, or precedence in formal languages. Grammatical objects have a type system, which helps to eliminate runtime errors in language processing. In the same way as an LF, GF uses...
Some lambda calculus and type theory formalized
 Journal of Automated Reasoning
, 1999
"... Abstract. We survey a substantial body of knowledge about lambda calculus and Pure Type Systems, formally developed in a constructive type theory using the LEGO proof system. On lambda calculus, we work up to an abstract, simplified, proof of standardization for beta reduction, that does not mention ..."
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Cited by 52 (7 self)
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Abstract. We survey a substantial body of knowledge about lambda calculus and Pure Type Systems, formally developed in a constructive type theory using the LEGO proof system. On lambda calculus, we work up to an abstract, simplified, proof of standardization for beta reduction, that does not mention redex positions or residuals. Then we outline the meta theory of Pure Type Systems, leading to the strengthening lemma. One novelty is our use of named variables for the formalization. Along the way we point out what we feel has been learned about general issues of formalizing mathematics, emphasizing the search for formal definitions that are convenient for formal proof and convincingly represent the intended informal concepts.
Proofassistants using Dependent Type Systems
, 2001
"... this article we will not attempt to describe all the dierent possible choices of type theories. Instead we want to discuss the main underlying ideas, with a special focus on the use of type theory as the formalism for the description of theories including proofs ..."
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Cited by 48 (4 self)
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this article we will not attempt to describe all the dierent possible choices of type theories. Instead we want to discuss the main underlying ideas, with a special focus on the use of type theory as the formalism for the description of theories including proofs
Termination Checking with Types
, 1999
"... The paradigm of typebased termination is explored for functional programming with recursive data types. The article introduces , a lambdacalculus with recursion, inductive types, subtyping and bounded quanti cation. Decorated type variables representing approximations of inductive types ..."
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Cited by 28 (6 self)
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The paradigm of typebased termination is explored for functional programming with recursive data types. The article introduces , a lambdacalculus with recursion, inductive types, subtyping and bounded quanti cation. Decorated type variables representing approximations of inductive types are used to track the size of function arguments and return values. The system is shown to be type safe and strongly normalizing. The main novelty is a bidirectional type checking algorithm whose soundness is established formally.
Normalization by evaluation for MartinLöf type theory with one universe
 IN 23RD CONFERENCE ON THE MATHEMATICAL FOUNDATIONS OF PROGRAMMING SEMANTICS, MFPS XXIII, ELECTRONIC NOTES IN THEORETICAL COMPUTER SCIENCE
, 2007
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The Gentle Art of Levitation
"... We present a closed dependent type theory whose inductive types are given not by a scheme for generative declarations, but by encoding in a universe. Each inductive datatype arises by interpreting its description—a firstclass value in a datatype of descriptions. Moreover, the latter itself has a de ..."
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Cited by 20 (4 self)
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We present a closed dependent type theory whose inductive types are given not by a scheme for generative declarations, but by encoding in a universe. Each inductive datatype arises by interpreting its description—a firstclass value in a datatype of descriptions. Moreover, the latter itself has a description. Datatypegeneric programming thus becomes ordinary programming. We show some of the resulting generic operations and deploy them in particular, useful ways on the datatype of datatype descriptions itself. Surprisingly this apparently selfsupporting setup is achievable without paradox or infinite regress. 1.
Untyped algorithmic equality for MartinLöf’s logical framework with surjective pairs (extended version
, 2005
"... Abstract. An untyped algorithm to test βηequality for MartinLöf’s Logical Framework with strong Σtypes is presented and proven complete using a model of partial equivalence relations between untyped terms. 1 ..."
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Cited by 9 (4 self)
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Abstract. An untyped algorithm to test βηequality for MartinLöf’s Logical Framework with strong Σtypes is presented and proven complete using a model of partial equivalence relations between untyped terms. 1
A Pointfree approach to Constructive Analysis in Type Theory
, 1997
"... The first paper in this thesis presents a machine checked formalisation, in MartinLöf's type theory, of pointfree topology with applications to domain theory. In the other papers pointfree topology is used in an approach to constructive analysis. The continuum is defined as a formal space from a ba ..."
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Cited by 7 (0 self)
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The first paper in this thesis presents a machine checked formalisation, in MartinLöf's type theory, of pointfree topology with applications to domain theory. In the other papers pointfree topology is used in an approach to constructive analysis. The continuum is defined as a formal space from a base of rational intervals. Then the closed rational interval [a, b] is defined as a formal space, in terms of the continuum, and the HeineBorel covering theorem is proved constructively. The basic definitions for a pointfree approach to functional analysis are given in such a way that the linear functionals from a seminormed linear space to the reals are points of a particular formal space, and in this setting the Alaoglu and the HahnBanach theorems are proved in an entirely constructive way. The proofs have been carried out in intensional MartinLöf type theory with one universe and finitary inductive definitions, and the proofs have also been mechanically checked in an implementation of that system. ...
A modular typechecking algorithm for type theory with singleton types and proof irrelevance
 IN TLCA’09, VOLUME 5608 OF LNCS
, 2009
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Irrelevance in Type Theory with a Heterogeneous Equality Judgement
"... Abstract. Dependently typed programs contain an excessive amount of static terms which are necessary to please the type checker but irrelevant for computation. To obtain reasonable performance of not only the compiled program but also the type checker such static terms need to be erased as early as ..."
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Cited by 7 (1 self)
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Abstract. Dependently typed programs contain an excessive amount of static terms which are necessary to please the type checker but irrelevant for computation. To obtain reasonable performance of not only the compiled program but also the type checker such static terms need to be erased as early as possible, preferably immediately after type checking. To this end, Pfenning’s type theory with irrelevant quantification, that models a distinction between static and dynamic code, is extended to universes and large eliminations. Novel is a heterogeneously typed implementation of equality which allows the smooth construction of a universal Kripke model that proves normalization, consistency and decidability.