ac7b95da86
This PR ports Batteries.WF to Init.WFC for executable well-founded fixpoints. It introduces `csimp` theorems to replace the recursors and non-executable definitions with executable definitions. This ocassionally comes up on Zulip as it prevents admiting definitions generated from well-founded induction. (e.g., [#lean4 > Computable WellFounded.fix](https://leanprover.zulipchat.com/#narrow/channel/270676-lean4/topic/Computable.20WellFounded.2Efix/with/529347861) and [#mathlib4 > Why Nat.find is computable, when Wellfounded.fix isn't?](https://leanprover.zulipchat.com/#narrow/channel/287929-mathlib4/topic/Why.20Nat.2Efind.20is.20computable.2C.20when.20Wellfounded.2Efix.20isn't.3F/with/545143617)). This was motivated by running into poor elaboration performance with recursive definitions involving complex inductive types generated by a custom elaborator. It would be helpful to explore bypassing the elaborator and generating elaborated terms directly, but this requires an executable fixpoint (such as `WellFounded.fixC` introduced in batteries).
14 lines
265 B
Text
14 lines
265 B
Text
prelude
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import Init.Guard
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import Init.WFComputable
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-- Test wellfounded fix call is executable
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def log2p1 : Nat → Nat :=
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WellFounded.fix Nat.lt_wfRel.2 fun n IH =>
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let m := n / 2
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if h : m < n then
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IH m h + 1
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else
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0
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#guard log2p1 4 == 3
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