Abstract
The introduction of a general definition of function was key to Frege’s formalisation of logic. Self-application of functions was at the heart of Russell’s paradox in 1902. This led Russell to introduce type theory in order to control the application of functions and hence to avoid the paradox. Since, different type systems have been introduced, each allowing different functional power. Eight of these influential systems have been unified in the so-called Barendregt cube. These eight systems use different binders for functions and types and do not allow types to have the same instantiation right as functions. De Bruijn in his Automath did not make these distinctions. In this tutorial, we discuss the modern, as well as de Bruijn’s framework of functions and types and study the cube in different frameowrks.
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Kamareddine, F. (2002). On Functions and Types: A Tutorial. In: Grosky, W.I., Plášil, F. (eds) SOFSEM 2002: Theory and Practice of Informatics. SOFSEM 2002. Lecture Notes in Computer Science, vol 2540. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36137-5_4
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