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feat(untyped): the Leftmost Reduction Theorem#700

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m-ow wants to merge 11 commits into
leanprover:mainfrom
m-ow:leftmost-reduction
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feat(untyped): the Leftmost Reduction Theorem#700
m-ow wants to merge 11 commits into
leanprover:mainfrom
m-ow:leftmost-reduction

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@m-ow

@m-ow m-ow commented Jul 8, 2026

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Introduces leftmost reduction ⭢ℓ, a beta-step contracting the redex at position 0, together with normal forms, and proves the Leftmost Reduction Theorem: if a term beta-reduces to a normal form, the leftmost strategy reaches it too.
The result falls out of standardization, following Copes (2018).

Builds on top of #679

@lengyijun

lengyijun commented Jul 8, 2026

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Can you add 2 theorems :

  1. NormalForm M <-> Normal FullBeta M
  2. Decidable Normal FullBeta

@m-ow m-ow force-pushed the leftmost-reduction branch from 5d41ee8 to d1fadfa Compare July 8, 2026 19:13
@m-ow

m-ow commented Jul 8, 2026

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@lengyijun Sounds good, I'll get both into a separate PR soon :)

@lengyijun

lengyijun commented Jul 9, 2026

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Should we rename Normal to NormalBeta ?
Or put it in namespace "FullBeta"

Normal may also refer to Normal FullBetaEta or Normal FullEta

@m-ow m-ow force-pushed the leftmost-reduction branch from 8e88dc3 to 09edd8f Compare July 9, 2026 14:29
@m-ow m-ow force-pushed the leftmost-reduction branch from 09edd8f to 6ed85b7 Compare July 9, 2026 14:47
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3 participants