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- Jonathan Sterling, Darin Morrison
- ArXiv
- 2016

binding trees (abts) are a generalization of abstract syntax trees where operators may express variable binding structure as part of their arities. Originally formulated by Peter Aczel [1], unisorted abts have been deployed successfully as the uniform syntactic framework for several implementations of Constructive Type Theory, including Nuprl [3], MetaPRL… (More)

- Jonathan Sterling, Robert Harper
- ArXiv
- 2017

We contribute a general apparatus for dependent<lb>tactic-based proof refinement in the LCF tradition, in which the<lb>statements of subgoals may express a dependency on the proofs of<lb>other subgoals; this form of dependency is extremely useful and<lb>can serve as an algorithmic alternative to extensions of LCF based<lb>on non-local instantiation of… (More)

- Darryl McAdams, Jonathan Sterling
- ArXiv
- 2014

This paper proposes the use of dependent types for pragmatic phenomena such as pronoun binding and presupposition resolution as a typetheoretic alternative to formalisms such as Discourse Representation Theory and Dynamic Semantics.

- Norman M. Robertson, Diane M Allen, +11 authors Barbara B. Comerford
- 2002

No part of this publication may be reproduced, displayed on a computer system, transmitted, transcribed, stored in a retrieval system, or translated into any language or computer language, in any form or by any means, electronic, mechanical, magnetic, optical, chemical, manual or otherwise , without the prior written consent of The Academy of Medicine of… (More)

- Jonathan Sterling
- ArXiv
- 2015

What is the proper explanation of intuitionistic hypothetical judgment, and thence propositional implication? The answer is unclear from the writings of Brouwer and Heyting, who in their lifetimes propounded multiple (sometimes conflicting) explanations of the hypothetical judgment. To my mind, the determination of an acceptable explanation must take into… (More)

- Jonathan Sterling
- ArXiv
- 2016

Using Martín Escardó’s « effectful forcing » technique, we demonstrate the constructive validity of Brouwer’s monotone Bar Theorem for any System T-definable bar. We have not assumed any non-constructive (Classical or Brouwerian) principles in this proof, and have carried out the entire development formally in the Agda proof assistant [13] for Martin-Löf ’s… (More)

- Jonathan Sterling
- ArXiv
- 2016

The syntax and semantics of user-supplied hypothesis names in tactic languages is a thorny problem, because the binding structure of a proof is a function of the goal at which a tactic script is executed. We contribute a new language to deal with the dynamic and interactive character of names in tactic scripts called Nominal LCF, and endow it with a… (More)

- Jonathan Sterling
- ArXiv
- 2015

At the heart of intuitionistic type theory lies an intuitive semantics called the “meaning explanations”; crucially, when meaning explanations are taken as definitive for type theory, the core notion is no longer “proof” but “verification”. We’ll explore how type theories of this sort arise naturally as enrichments of logical theories with further… (More)

We develop a computational interpretation of guarded dependent type theory with clocks called CTT which enjoys a straightforward operational semantics and immediate canonicity result for base types. Our realizability-style presentation of guarded type theory is a computational and syntactic alternative to category-theoretic accounts of guarded recursion,… (More)

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