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Intensional Joy (a concatenative account of internal structure)

programming languages (no, I didn’t say intentional) have had a bit of a moment in the spotlight recently. Specifically, back in December, Johannes Bader’s website on tree calculus popularized some work on intensional rewriting systems which was largely spearheaded by Dr.

Specifically, back in December, Johannes Bader’s website on tree calculus popularized some work on intensional rewriting systems which was largely spearheaded by Dr. Barry Jay. [a]dup→[a][a][a][b]swap→[b][a][a]pop→ϵ[a][b]cat→[ab][a]quote→[[a]][a]eval→a \begin{aligned} [a] \, \text{dup} &\to [a] \, [a] \\ [a] \, [b] \, \text{swap} &\to [b] \, [a] \\ [a] \, \text{pop} &\to \epsilon \\ [a] \, [b] \, \text{cat} &\to [a b] \\ [a] \, \text{quote} &\to [[a]] \\ [a] \, \text{eval} &\to a \\ \end{aligned} [a]dup[a][b]swap[a]pop[a][b]cat[a]quote[a]eval​→[a][a]→[b][a]→ϵ→[ab]→[[a]]→a​If we always apply the leftmost rewrite which is not inside a quotation, then we get a notion of “applicative order reduction” which simulates the stack-based semantics. I think that it would be valuable for future researchers to come up with a weaker general notion of equivalence that allows us to talk about intensional languages.

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