# Lambda calculus notation with nameless dummies, a tool for automatic formula manipulation, with application to the Church-Rosser theorem

@article{Bruijn1972LambdaCN, title={Lambda calculus notation with nameless dummies, a tool for automatic formula manipulation, with application to the Church-Rosser theorem}, author={de Ng Dick Bruijn}, journal={Studies in logic and the foundations of mathematics}, year={1972}, volume={133}, pages={375-388} }

## 1,193 Citations

### The fine-structure of lambda calculus

- Computer Science
- 1992

This paper starts by setting the ground for a lambda calculus notation that strongly mirrors the two fundamental operations of term construction, namely abstraction and application, and provides a type operator which gives a representative type for a typeable tenll.

### A Lambda Term Representation Inspired by Linear Ordered Logic

- Computer ScienceLFMTP
- 2011

A new nameless representation of lambda terms inspired by ordered logic is introduced and an experimental evaluation of its performance in a proof checker for the Edinburgh Logical Framework is presented.

### Formal metatheory of the Lambda calculus using Stoughton's substitution

- MathematicsTheor. Comput. Sci.
- 2017

### C-Expressions: A Variable-Free Calculus for Equational Logic Programming

- Computer ScienceTheor. Comput. Sci.
- 1993

### A Consistent Extension of the Lambda-Calculus as a Base for Functional Programming Languages

- Computer ScienceInf. Control.
- 1982

### INTERSECTION TYPE SYSTEM AND LAMBDA CALCULUS WITH DIRECTOR STRINGS

- Computer Science, MathematicsComputer Science & Information Technology (CS & IT )
- 2019

An intersection type system for 𝜆𝑜-calculus is presented and it is shown it satisfies the subject reduction property and is presented as a model for explicit substitution in programming languages and proof assistants.

### Alpha Conversion in Simply Typed Lambda CalculusAna

- Mathematics
- 2007

In the usual presentations of simply typed-calculus, it is usual to identify terms that are-convertible. However, this is not at all a practise in most (typed) functional languages, for which simply…

### A Mechanisation of Name-Carrying Syntax up to Alpha-Conversion

- Computer ScienceHUG
- 1993

We present a new strategy for representing syntax in a, mechanised logic. We define an underlying type of de Bruijn terms, define an operation of named lambda-abstraction, and hence inductively…

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