A new approach to abstract syntax involving binders

Gabbay, Murdoch J.; Pitts, Andrew M.

doi:10.1109/lics.1999.782617

Cited by 148 publications

(148 citation statements)

References 22 publications

Supporting

Mentioning

148

Contrasting

Order By: Relevance

“…Taking for U the set of terms without hnf, one can show using the confluence property that the normal forms of the corresponding infinite λ-calculus satisfy the equations in (11). That is, the Böhm tree of a term M is the normal form of M in the infinitary λ-calculus that equates all terms without head normal form with ⊥ [5,17].…”

Section: Böhm Lévy-longo and Berarducci Treesmentioning

confidence: 99%

“…The informal definitions of Böhm, Lévy-Longo and Berarducci trees given in (11), (12) and (13) use the notion of β-reduction relation which is not a function. To formally define the notions of trees, we need to define evaluation strategies, i.e.…”

Section: Notation 25 (Injections)mentioning

confidence: 99%

“…Nominal sets [11] provide an elegant way for establishing an α-structural recursion principle [23] that allows one to define substitution on α-equivalence classes of finite λ-terms starting from a partial function with a side-condition [14,23]. It is one of the aims of this paper to establish an α-corecursion principle, which allows us to view (3) as a corecursive definition of substitution on α-equivalence classes of terms in Λ ∞ .…”

Section: Introductionmentioning

confidence: 99%

“…To come back to α-(co)recursion, Pitts [23] derives structural recursion and induction principles for syntax with binding by using the result from [11] that the set Λ/= α of α-equivalence classes of finite λ-terms is the initial algebra for the functor L α on the category Nom of nominal sets defined by…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

An Alpha-Corecursion Principle for the Infinitary Lambda Calculus

Kurz

Petrişan

Severi

et al. 2012

Coalgebraic Methods in Computer Science

View full text Add to dashboard Cite

Abstract. Gabbay and Pitts proved that lambda-terms up to alphaequivalence constitute an initial algebra for a certain endofunctor on the category of nominal sets. We show that the terms of the infinitary lambda-calculus form the final coalgebra for the same functor. This allows us to give a corecursion principle for alpha-equivalence classes of finite and infinite terms. As an application, we give corecursive definitions of substitution and of infinite normal forms (Böhm, Lévy-Longo and Berarducci trees).

show abstract

Section: Böhm Lévy-longo and Berarducci Treesmentioning

confidence: 99%

Section: Notation 25 (Injections)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An Alpha-Corecursion Principle for the Infinitary Lambda Calculus

Kurz

Petrişan

Severi

et al. 2012

Coalgebraic Methods in Computer Science

View full text Add to dashboard Cite

show abstract

“…A limited form of recursion over HOAS syntax is also assumed. Similarly the FM approach [7] aims to be a foundation of programming and reasoning with names in a onelevel architecture. It would be interesting to look at using a version of the "New" quantifier in the specification logic, especially for those applications where the behavior of the object-logic binder is not faithfully mirrored by a traditional universal quantification at the SL-level, for example the π-calculus.…”

Section: Related Workmentioning

confidence: 99%

Multi-level Meta-reasoning with Higher-Order Abstract Syntax

Momigliano

Ambler

2003

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. Combining Higher Order Abstract Syntax (HOAS) and (co)-induction is well known to be problematic. In previous work [1] we have described the implementation of a tool called Hybrid, within Isabelle HOL, which allows object logics to be represented using HOAS, and reasoned about using tactical theorem proving and principles of (co)induction. Moreover, it is definitional, which guarantees consistency within a classical type theory. In this paper we describe how to use it in a multi-level reasoning fashion, similar in spirit to other meta-logics such F Oλ ∆I N and Twelf. By explicitly referencing provability, we solve the problem of reasoning by (co)induction in presence of non-stratifiable hypothetical judgments, which allow very elegant and succinct specifications. We demonstrate the method by formally verifying the correctness of a compiler for (a fragment) of Mini-ML, following [10]. To further exhibit the flexibility of our system, we modify the target language with a notion of non-well-founded closure, inspired by Milner & Tofte [16] and formally verify via co-induction a subject reduction theorem for this modified language.

show abstract

Mechanized Metatheory for the Masses: The PoplMark Challenge

Aydemir

Bohannon

Fairbairn

et al. 2005

Lecture Notes in Computer Science

229

201

View full text Add to dashboard Cite

How close are we to a world where every paper on programming languages is accompanied by an electronic appendix with machinechecked proofs? We propose an initial set of benchmarks for measuring progress in this area. Based on the metatheory of System F , a typed lambda-calculus with second-order polymorphism, subtyping, and records, these benchmarks embody many aspects of programming languages that are challenging to formalize: variable binding at both the term and type levels, syntactic forms with variable numbers of components (including binders), and proofs demanding complex induction principles. We hope that these benchmarks will help clarify the current state of the art, provide a basis for comparing competing technologies, and motivate further research.

show abstract

A new approach to abstract syntax involving binders

Cited by 148 publications

References 22 publications

An Alpha-Corecursion Principle for the Infinitary Lambda Calculus

An Alpha-Corecursion Principle for the Infinitary Lambda Calculus

Multi-level Meta-reasoning with Higher-Order Abstract Syntax

Mechanized Metatheory for the Masses: The PoplMark Challenge

Contact Info

Product

Resources

About