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Presentable signatures and initial semantics

Benedikt Ahrens ; André Hirschowitz ; Ambroise Lafont ; Marco Maggesi.

We present a device for specifying and reasoning about syntax for datatypes, programming languages, and logic calculi. More precisely, we study a notion of "signature" for specifying syntactic constructions. In the spirit of Initial Semantics, we define the "syntax generated by a signature" to be&nbsp;[&hellip;]

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Variable binding and substitution for (nameless) dummies

André Hirschowitz ; Tom Hirschowitz ; Ambroise Lafont ; Marco Maggesi.

By abstracting over well-known properties of De Bruijn's representation with nameless dummies, we design a new theory of syntax with variable binding and capture-avoiding substitution. We propose it as a simpler alternative to Fiore, Plotkin, and Turi's approach, with which we establish a strong&nbsp;[&hellip;]

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