scholarly journals Machine-checked Proof of the Church-Rosser Theorem for the Lambda Calculus Using the Barendregt Variable Convention in Constructive Type Theory

2018 ◽  
Vol 338 ◽  
pp. 79-95 ◽  
Author(s):  
Ernesto Copello ◽  
Nora Szasz ◽  
Álvaro Tasistro
Keyword(s):  
Type Theory ◽  
Lambda Calculus ◽  
Constructive Type Theory ◽  
Constructive Type ◽  
The Church

Formalization of metatheory of the Lambda Calculus in constructive type theory using the Barendregt variable convention

2021 ◽  
pp. 1-20
Author(s):  
Ernesto Copello ◽  
Nora Szasz ◽  
Álvaro Tasistro
Keyword(s):  
Type Theory ◽  
Lambda Calculus ◽  
Proof Assistant ◽  
First Order ◽  
Constructive Type Theory ◽  
Fundamental Part ◽  
Constructive Type ◽  
Free Variables ◽  
The Church ◽  
Theoretical Results

Abstarct We formalize in Constructive Type Theory the Lambda Calculus in its classical first-order syntax, employing only one sort of names for both bound and free variables, and with α-conversion based upon name swapping. As a fundamental part of the formalization, we introduce principles of induction and recursion on terms which provide a framework for reproducing the use of the Barendregt Variable Convention as in pen-and-paper proofs within the rigorous formal setting of a proof assistant. The principles in question are all formally derivable from the simple principle of structural induction/recursion on concrete terms. We work out applications to some fundamental meta-theoretical results, such as the Church–Rosser Theorem and Weak Normalization for the Simply Typed Lambda Calculus. The whole development has been machine checked using the system Agda.

The calculus of dependent lambda eliminations

2017 ◽  
Vol 27 ◽  
Author(s):  
AARON STUMP
Keyword(s):  
Type Theory ◽  
Lambda Calculus ◽  
Denotational Semantics ◽  
Prototype Implementation ◽  
Constructive Type Theory ◽  
Typed Lambda Calculus ◽  
Constructive Type

AbstractModern constructive type theory is based on pure dependently typed lambda calculus, augmented with user-defined datatypes. This paper presents an alternative called the Calculus of Dependent Lambda Eliminations, based on pure lambda encodings with no auxiliary datatype system. New typing constructs are defined that enable induction, as well as large eliminations with lambda encodings. These constructs are constructor-constrained recursive types, and a lifting operation to lift simply typed terms to the type level. Using a lattice-theoretic denotational semantics for types, the language is proved logically consistent. The power of CDLE is demonstrated through several examples, which have been checked with a prototype implementation called Cedille.

scholarly journals Alpha-Structural Induction and Recursion for the Lambda Calculus in Constructive Type Theory

2016 ◽  
Vol 323 ◽  
pp. 109-124 ◽  
Author(s):  
Ernesto Copello ◽  
Álvaro Tasistro ◽  
Nora Szasz ◽  
Ana Bove ◽  
Maribel Fernández
Keyword(s):  
Type Theory ◽  
Lambda Calculus ◽  
Constructive Type Theory ◽  
Structural Induction ◽  
Constructive Type

Recursively Defined Types in Constructive Type Theory

1989 ◽  
pp. 369-410 ◽  
Author(s):  
PRAKASH PANANGADEN ◽  
PAUL MENDLER ◽  
MICHAEL I. SCHWARTZBACH
Keyword(s):  
Type Theory ◽  
Constructive Type Theory ◽  
Constructive Type
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