scholarly journals Backpropagation in the simply typed lambda-calculus with linear negation

2020 ◽  
Vol 4 (POPL) ◽  
pp. 1-27 ◽  
Author(s):  
Aloïs Brunel ◽  
Damiano Mazza ◽  
Michele Pagani
Keyword(s):  
Lambda Calculus ◽  
Typed Lambda Calculus

The Simply Typed Lambda Calculus

2013 ◽  
pp. 5-54
Author(s):  
Henk Barendregt ◽  
Wil Dekkers ◽  
Richard Statman
Keyword(s):  
Lambda Calculus ◽  
Typed Lambda Calculus

scholarly journals The computational content of atomic polymorphism

2018 ◽  
Vol 27 (5) ◽  
pp. 625-638
Author(s):  
Gilda Ferreira ◽  
Vasco T Vasconcelos
Keyword(s):  
Lambda Calculus ◽  
The Other ◽  
Typed Lambda Calculus ◽  
Polymorphic System

AbstractWe show that the number-theoretic functions definable in the atomic polymorphic system (${\mathbf{F}}_{\mathbf{at}}$) are exactly the extended polynomials. Two proofs of the above result are presented: one, reducing the functions’ definability problem in ${\mathbf{F}}_{\mathbf{at}}$ to definability in the simply typed lambda calculus ($\lambda ^{\rightarrow }$) and the other, directly adapting Helmut Schwichtenberg’s strategy for definability in $\lambda ^{\rightarrow }$ to the atomic polymorphic setting. The uniformity granted in the polymorphic system, when compared with the simply typed lambda calculus, is emphasized.

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