Tuesday, April 10, 2007

HOAS vs. Nominal Logic

I don't yet have a deep understanding in the debate between higher-order abstract syntax and nominal logic, but this is an interesting summary from Karl Crary and Bob Harper in a short article in the Logic Column for SIGACT News:
“The real contrast between HOAS and nominal logic lies in their philosophy toward binding structure. Both HOAS and nominal logic provide a sophisticated treatment of binding structure not enjoyed by first-order accounts, but ones of very different character. The philosophy of LF is that binding and alpha-conversion are fundamental concepts, and thus builds them in at the lowest level. Consequently, name management in LF is ordinarily a non-issue. In contrast, nominal logic promotes name management as an object of study. It makes binding into a sophisticated artifact, rather than a primitive concept as in LF.”

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