F. Kamareddine. Reviewing the classical and the de Bruijn notation for -calculus and pure type systems. Logic and Computation, 11(3):363-394.

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Faster Proof Checking in the Edinburgh Logical Framework - Stump, Dill (2002)   (2 citations)  (Correct)

....So there is no need to compute e[ if this intersection is empty. 5.1 de Bruijn indices The optimizations of safe substitution are described for the version of LF that uses named variables; this is what is implemented in ea. An alternative is to use de Bruijn indices for variables (see, e.g. [13]) The optimization of returning e for e[ without actually applying the substitution in the case where FV (e) Def( is still relevant with de Bruijn indices. The de nition of FS( x : M) for 2 f ; g is changed to be the following: FS( x : M) FS( fv 1jv 2 FS(M)g The ....

F. Kamareddine. Reviewing the classical and the de Bruijn notation for -calculus and pure type systems. Logic and Computation, 11(3):363-394.

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