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Over the last decades, deep neural networks based-models became the dominantparadigm in machine learning. Further, the use of artificial neural networks insymbolic learning has been seen as increasingly relevant recently. To study thecapabilities of neural networks in the symbolic AI domain, researchers haveexplored the ability of deep neural networks to learn mathematicalconstructions, such as addition and multiplication, logic inference, such astheorem provers, and even the execution of computer programs. The latter isknown to be too complex a task for neural networks. Therefore, the results werenot always successful, and often required the introduction of biased elementsin the learning process, in addition to restricting the scope of possibleprograms to be executed. In this work, we will analyze the ability of neuralnetworks to learn how to execute programs as a whole. To do so, we propose adifferent approach. Instead of using an imperative programming language, withcomplex structures, we use the Lambda Calculus ({\lambda}-Calculus), a simple,but Turing-Complete mathematical formalism, which serves as the basis formodern functional programming languages and is at the heart of computabilitytheory. We will introduce the use of integrated neural learning and lambdacalculi formalization. Finally, we explore execution of a program in{\lambda}-Calculus is based on reductions, we will show that it is enough tolearn how to perform these reductions so that we can execute any program.Keywords: Machine Learning, Lambda Calculus, Neurosymbolic AI, Neural Networks,Transformer Model, Sequence-to-Sequence Models, Computational Models

A Neural Lambda Calculus: Neurosymbolic AI meets the foundations of computing and functional programming