#### 42 Citations

The formal system λΔ

- Mathematics, Computer Science
- TOCL
- 2009

The formal system λΔ is a typed λ-calculus that pursues the unification of terms, types, environments, and contexts as the main goal and enjoys some important desirable properties. Expand

A Distributed and Trusted Web of Formal Proofs

- Computer Science
- ICDCIT
- 2020

This talk proposes that proof assistants should sit on the edge of a web of formal proofs and that proof assistant should be exporting their proofs so that they can exist independently of any theorem prover. Expand

A Formal System for the Universal Quantification of Schematic Variables.

- Computer Science, Mathematics
- 2020

This calculus belongs to the $\lambda\delta$ family of formal systems, which borrow some features from the pure type systems and some from the languages of the Automath tradition, but stand outside both families. Expand

Two Formal Systems of the $\lambda\delta$ Family Revised

- Mathematics
- 2019

We present the framework $\lambda\delta$-2B that significantly improves and generalizes two previous formal systems of the $\lambda\delta$ family, i.e., $\lambda\delta$-1A and $\lambda\delta$-2A. Our… Expand

Two Formal Systems of the $λδ$ Family Revised

- Computer Science
- ArXiv
- 2019

A short definition for the framework λδ -2B stands just on two notions, i.e., bound rt-reduction and parametric validity and some important results are presented that are presented here for the first time. Expand

Extending the Applicability Condition in the Formal System \lambda\delta

- Mathematics, Computer Science
- 2015

The formal system \lambda\delta is a typed lambda calculus
derived from \Lambda\infinity, aiming to support the foundations of Mathematics that require an underlying theory of expressions (for… Expand

The Next 700 Challenge Problems for Reasoning with Higher-Order Abstract Syntax Representations

- Computer Science
- Journal of Automated Reasoning
- 2015

This paper survey and compare four meta-reasoning systems, Twelf, Beluga, Abella and Hybrid, using several benchmarks from the open repository ORBI that describes challenge problems for reasoning with higher-order abstract syntax representations to investigate how these systems mechanize and support reasoning using a context of assumptions. Expand

Veried Representations of Landau's \Grundlagen" in the Family and in the Calculus of Constructions

- Mathematics
- 2015

ion λC CC unrestricted (◻,◻) (◻T ,◻T ) (◻T ,◻P ) (◻P ,◻T ) (◻P ,◻P ) (◻,⋆) (◻T ,Type) (◻T ,Prop) (◻P ,Type) (◻P ,Prop) (⋆,◻) (Type,◻T ) (Type,◻P ) (Prop,◻T ) (Prop,◻P ) (⋆,⋆) (Type,Type) (Type,Prop)… Expand

The Formal System λδ Revised - Stage A: Extending the Applicability Condition

- Computer Science
- ArXiv
- 2014

This article presents a revised version of the λδ calculus, a typed λ-calculus derived from Λ∞, and proves three relevant desired properties: the confluence of reduction, the strong normalization of an extended form of Reduction, known as the “big tree” theorem, and the preservation of validity by reduction. Expand

lowing result of Kreisel and ( Girard 1981 ) : Any function

- 2014

Suppose a formal proof of ∀x∃y Spec(x, y) is given, where Spec(x, y) is an atomic formula expressing some specification for naturalnumbers x, y. For any particular number n we then obtain a formal… Expand