On the Semantics of Intensionality

Kavvos, G. A.

doi:10.1007/978-3-662-54458-7_32

Cited by 7 publications

(3 citation statements)

References 188 publications

(330 reference statements)

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“…From a programming perspective, the discussion and extensive bibliography of Kavvos' D.Phil. thesis [44] are well worth reading. Focusing just on interactive proof assistants, we find that Boyer and Moore developed a global infrastructure [7] for incorporating symbolic algorithms into Nqthm [8].…”

Section: Related Workmentioning

confidence: 98%

HOL Light QE

Carette

Farmer

Laskowski

2018

Interactive Theorem Proving

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We are interested in algorithms that manipulate mathematical expressions in mathematically meaningful ways. Expressions are syntactic, but most logics do not allow one to discuss syntax. cttqe is a version of Church's type theory that includes quotation and evaluation operators, akin to quote and eval in the Lisp programming language. Since the HOL logic is also a version of Church's type theory, we decided to add quotation and evaluation to HOL Light to demonstrate the implementability of cttqe and the benefits of having quotation and evaluation in a proof assistant. The resulting system is called HOL Light QE. Here we document the design of HOL Light QE and the challenges that needed to be overcome. The resulting implementation is freely available.

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Section: Related Workmentioning

confidence: 98%

HOL Light QE

Carette

Farmer

Laskowski

2018

Interactive Theorem Proving

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“…Of particular note is that, even in a pure programming context, unrestricted reflection leads to problems [123]. Kavvos' recent D.Phil thesis [84] has a very interesting overview of the impossibility of building a quotation operator (with certain properties) and other dangers. His literature review is also quite extensive.…”

Section: Meaning Formulasmentioning

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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“…As discussed before, the modal types work in our favour by separating intension from extension, so that the latter does not leak into the former. Given the logical nature of the categorical constructs used in our previous work on intensionality [15], we shall model the types of iPCF after the constructive modal logic S4, in the dual-context style pioneered by Pfenning and Davies [19,7]. Let us seize this opportunity to remark that (a) there are also other ways to capture S4, for which see the survey [13], and that (b) dual-context formulations are not by any means limited to S4: they began in the context of intuitionistic linear logic, but have recently been shown to also encompass other modal logics; see [14].…”

Section: Introducing Intensional Pcfmentioning

confidence: 99%

Intensionality, Intensional Recursion, and the Gödel-Löb axiom

Kavvos

2017

Preprint

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The use of a necessity-like modality in a typed λ -calculus can be used as a device for separating the calculus in two separate regions. These can be thought of as intensional vs. extensional data: data in the first region, the modal one, are available as code, and their description can be examined, whereas data in the second region are only available as values up to ordinary equality. This allows us to add seemingly non-functional operations at modal types, whilst maintaining consistency. In this setting the Gödel-Löb axiom acquires a novel constructive reading: it affords the programmer the possibility of a very strong kind of recursion, by enabling him to write programs that have access to their own code. This is a type of computational reflection that is strongly reminiscent of Kleene's Second Recursion Theorem. We prove that it is consistent with the rest of the system.

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On the Semantics of Intensionality

Cited by 7 publications

References 188 publications

HOL Light QE

HOL Light QE

Incorporating quotation and evaluation into Church's type theory

Intensionality, Intensional Recursion, and the Gödel-Löb axiom

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