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feat(Order/OmegaCompletePartialOrder): least fixed point and Scott induction#38316

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tannerduve:lfp-scott-induction
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feat(Order/OmegaCompletePartialOrder): least fixed point and Scott induction#38316
tannerduve wants to merge 2 commits intoleanprover-community:masterfrom
tannerduve:lfp-scott-induction

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@tannerduve tannerduve commented Apr 20, 2026

Add lfp for endomorphisms on an ωCPO with a least element and its basic API (map_lfp, isFixedPt_lfp, lfp_le_fixed, isLeast_lfp) and the Scott induction theorem lfp_induction

Also add corresponding induction principles for Part.fix: fix_scott_induction (ω-Scott continuous functional, admissible predicate) and fix_scott_induction_pointwise

@github-actions github-actions bot added the new-contributor This PR was made by a contributor with at most 5 merged PRs. Welcome to the community! label Apr 20, 2026
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github-actions bot commented Apr 20, 2026

PR summary 98261a9c88

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference

Declarations diff

+ exists_mem_approx_of_mem_fix
+ fix_eq_lfp
+ fix_scott_induction
+ fix_scott_induction_pointwise
+ isFixedPt_lfp
+ isLeast_lfp
+ lfp
+ lfp_induction
+ lfp_le_fixed
+ map_lfp

You can run this locally as follows
## summary with just the declaration names:
./scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh contains some details about this script.


No changes to technical debt.

You can run this locally as

./scripts/reporting/technical-debt-metrics.sh pr_summary
  • The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
  • The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

@tannerduve tannerduve force-pushed the lfp-scott-induction branch from 0a8df7a to 70a968c Compare April 21, 2026 00:52
…duction

Add `lfp` for ω-Scott continuous endofunctions on an ωCPO with `⊥`, defined
as the supremum of the iteration chain from `⊥`, together with its basic API
(`map_lfp`, `isFixedPt_lfp`, `lfp_le_fixed`, `isLeast_lfp`) and a Scott
induction principle `lfp_induction`.

Also add corresponding induction principles for `Part.fix`:
`fix_scott_induction` (ω-Scott continuous functional, admissible predicate)
and `fix_scott_induction_pointwise` (no continuity hypothesis, conclusion
of the form `Part.fix g x = some y → P x y`), supported by a helper
`exists_approx_eq_of_fix_eq_some`.
@tannerduve tannerduve force-pushed the lfp-scott-induction branch from 70a968c to 2bee3da Compare April 21, 2026 00:53
…ction

Add `fix_eq_lfp` identifying `Part.fix g` with `ContinuousHom.lfp` of the
associated continuous map, and reduce `fix_scott_induction` to a direct
application of `ContinuousHom.lfp_induction`.
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