Self-Representation in Girard's System U

Brown, Marianne; Palsberg, Jens

doi:10.1145/2676726.2676988

Cited by 9 publications

(9 citation statements)

References 30 publications

(38 reference statements)

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“…Hence what we are doing is different from e.g. [10] which defines a higher order syntax for reflection. We also diverge from [24] which exploits the metatheoretic equality to make reflection feasible because we would like to have the freedom to interpret equality in any way we would like.…”

Section: Related Workmentioning

confidence: 99%

Type theory in type theory using quotient inductive types

Altenkirch

Kaposi

2016

Proceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

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A note on versions:The version presented here may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher's version. Please see the repository url above for details on accessing the published version and note that access may require a subscription. AbstractWe present an internal formalisation of a type heory with dependent types in Type Theory using a special case of higher inductive types from Homotopy Type Theory which we call quotient inductive types (QITs). Our formalisation of type theory avoids referring to preterms or a typability relation but defines directly well typed objects by an inductive definition. We use the elimination principle to define the set-theoretic and logical predicate interpretation. The work has been formalized using the Agda system extended with QITs using postulates.

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Section: Related Workmentioning

confidence: 99%

Type theory in type theory using quotient inductive types

Altenkirch

Kaposi

2016

Proceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

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“…Nevertheless these representations were only partially typed. The finally tagless approach to embedded representations [29] kicked off a series of papers on typed selfrepresentation [4,5,18,19,20,21,81,107] which eventually succeeded at providing elegant solutions.…”

Section: Reasoning In the Lambda Calculus About Syntaxmentioning

confidence: 99%

Incorporating quotation and evaluation into Church's type theory

Farmer

2018

Information and Computation

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cttqe is a version of Church's type theory that includes quotation and evaluation operators that are similar to quote and eval in the Lisp programming language. With quotation and evaluation it is possible to reason in cttqe about the interplay of the syntax and semantics of expressions and, as a result, to formalize syntax-based mathematical algorithms. We present the syntax and semantics of cttqe as well as a proof system for cttqe. The proof system is shown to be sound for all formulas and complete for formulas that do not contain evaluations. We give several examples that illustrate the usefulness of having quotation and evaluation in cttqe.

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“…Like the STLC representation in Figure 10, we use a typed Mogensen-Scott encoding, though there are several important differences. Following previous work on typed self-representation [7,8,31], we use Parametric Higher-Order Abstract Syntax (PHOAS) [12,40] to give our representation more expressiveness. The type PExp is parametric in V, which determines the type of free variables in a representation.…”

Section: Our Representation Schemementioning

confidence: 99%

Typed self-evaluation via intensional type functions

Brown

Palsberg

2017

Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages

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Many popular languages have a self-interpreter, that is, an interpreter for the language written in itself. So far, work on polymorphically-typed self-interpreters has concentrated on self-recognizers that merely recover a program from its representation. A larger and until now unsolved challenge is to implement a polymorphicallytyped self-evaluator that evaluates the represented program and produces a representation of the result. We present F µi ω , the first λcalculus that supports a polymorphically-typed self-evaluator. Our calculus extends Fω with recursive types and intensional type functions and has decidable type checking. Our key innovation is a novel implementation of type equality proofs that enables us to define a versatile representation of programs. Our results establish a new category of languages that can support polymorphically-typed selfevaluators.

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Self-Representation in Girard's System U

Cited by 9 publications

References 30 publications

Type theory in type theory using quotient inductive types

Type theory in type theory using quotient inductive types

Incorporating quotation and evaluation into Church's type theory

Typed self-evaluation via intensional type functions

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