# A nonstandard standardization theorem

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### Cites background or methods from "A nonstandard standardization theor..."

...Explicit substitutions (ES) have been connected to linear logic by Kesner and co-authors in a sequence of works [26, 32, 33], culminating in the linear substitution calculus (LSC), a new formalism with ES behaviorally isomorphic to proof nets (introduced in [6], developed in [1, 3, 4, 7, 10], and bearing similarities with calculi by De Bruijn [25], Nederpelt [42], and Milner [41])....

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...Plotkin’s Approach: our study complements the recent [10], where it is shown that WLHR is a standard strategy of the LSC....

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...The presentation in use here has already appeared in [3, 10] (see also [1, 4]) as the weak head strategy of the linear substitution calculus (which is obtained by considering all contexts as evaluation contexts), and it avoids many technicalities of the original one....

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53 citations

### Cites background from "A nonstandard standardization theor..."

...For example, linear-head, head, weak and strong normalization are characterized in [40] by means of appropriate non-idempotent types in the framework of the linear substitution calculus [1], a calculus with explicit substitution at a distance....

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48 citations

### Cites background or methods or result from "A nonstandard standardization theor..."

...While the study of standardisation for the LSC [6] uses the string approach (and thus only talks about the left-to-right order and the leftmost redex), here some of the proofs (see the long version [2]) require a delicate analysis of the relative positions of redexes and so we prefer the more informative tree approach and define the order formally....

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...Using the lemma above and a technical property of standard derivations (the enclave axiom, see [6]) we obtain:...

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...In [6] it is showed that in the full LSC standard derivations are complete, i....

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...As in our previous work [3], we prove our result by means of the linear substitution calculus (see also [1, 6]), a simple calculus of explicit substitutions (ES, for short) arising from linear logic and graphical syntaxes and similar to calculi studied by De Bruijn [16], Nederpelt [22], and Milner [21]....

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...Unfortunately, the linear LO strategy, noted →LO and first defined in [6], is mechanisable but the pair (→LOβ ,→LO) is not a high-level implementation system....

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##### References

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### "A nonstandard standardization theor..." refers methods in this paper

...The linear substitution calculus has been designed to mimic the representation of λ-calculus in linear logic proofnets [18], where β-reduction is decomposed into small steps....

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### "A nonstandard standardization theor..." refers background in this paper

...In order to give an intuition on such a phenomenon let us consider a calculus with ES such as λσ [1] or λx [9] containing at least the following reduction rules:...

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