On the Notion of Substitution
@article{Crabb2004OnTN,
title={On the Notion of Substitution},
author={Marcel Crabb{\'e}},
journal={Log. J. IGPL},
year={2004},
volume={12},
pages={111-124}
}We consider a concept of substitutive structure, called "logos", in order to study simple substitution, independently of formal or programming languages. We provide a definition of simultaneous substitution in an arbitrary logos and use it to prove a completeness theorem expressing that the equational properties of the usual substitution can be proved from the logos axioms only.
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