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The following category theory inspired analysis (adapted from Plotkin's A Note on Inductive Generalization) explains a sense in which unification and anti-unification are dual concepts. As notation, l …

Dave Clarke's answer basically says it all: this is the standard convention in classical and constructive mathematics. Nonetheless, your objection is the source of a century-old subdiscipline of phil …

I'll just add another perspective to augment the above responses. First, these reflections are worthwhile, and many people have had similar ideas. In philosophy this is sometimes called "proof-theor …

You could have a look at McDowell and Miller's Cut-Elimination for a Logic with Definitions and Induction, which shows how to adopt Tait's method to a first-order intuitionistic sequent calculus with …

These kind of logics are considered in linguistics: you can have a look at Michael Moortgat's article, Categorial Type Logic.

Again I'm not exactly sure what you are looking for because there are potentially many "similar" systems, but for recent work that I think is very related you can read Part II ("Mixing Derivability an …

[Expanding the comment into an answer.] First, just a clarification about counting bound variables in a combinator (= closed term) $t$. I interpret the question as asking about $$ \text{the total num …

Andrej's and Łukasz's answers make good points, but I wanted to add additional comments. To echo what Damiano said, this way of representing binding using pointers is the one suggested by proof-nets, …

I can think of one instance where category theory was directly "applied" to solve an open problem in programming languages: Thorsten Altenkirch, Peter Dybjer, Martin Hofmann, and Phil Scott, "Normaliz …

One reference: Automating Proofs in Category Theory by Dexter Kozen, Christoph Kreitz, and Eva Richter.