5cd90f5826
until around 7fe6881 the way to define well-founded recursions was to
specify a `WellFoundedRelation` on the argument explicitly. This was
rather low-level, for example one had to predict the packing of multiple
arguments into `PProd`s, the packing of mutual functions into `PSum`s,
and the cliques that were calculated.
Then the current `termination_by` syntax was introduced, where you
specify the termination argument at a higher level (one clause per
functions, unpacked arguments), and the `WellFoundedRelation` is found
using type class resolution.
The old syntax was kept around as `termination_by'`. This is not used
anywhere in the lean, std, mathlib or the theorem-proving-in-lean
repositories,
and three occurrences I found in the wild can do without
In particular, it should be possible to express anything that the old
syntax
supported also with the new one, possibly requiring a helper type with a
suitable instance, or the following generic wrapper that now lives in
std
```
def wrap {α : Sort u} {r : α → α → Prop} (h : WellFounded r) (x : α) : {x : α // Acc r x}
```
Since the old syntax is unused, has an unhelpful name and relies on
internals, this removes the support. Now is a good time before the
refactoring that's planned in #2921.
The test suite was updated without particular surprises.
The parametric `terminationHint` parser is gone, which means we can
match on syntax more easily now, in `expandDecreasingBy?`.
37 lines
629 B
Text
37 lines
629 B
Text
import Lean
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open Lean
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open Lean.Meta
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def tst (declName : Name) : MetaM Unit := do
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IO.println (← getUnfoldEqnFor? declName)
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mutual
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def g (i j : Nat) : Nat :=
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if i < 5 then 0 else
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match j with
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| Nat.zero => 1
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| Nat.succ j => h i j
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def h (i j : Nat) : Nat :=
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match j with
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| 0 => g i 0
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| Nat.succ j => g i j
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end
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termination_by
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g i j => (i + j, 0)
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h i j => (i + j, 1)
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decreasing_by
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simp_wf
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first
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| apply Prod.Lex.left
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apply Nat.lt_succ_self
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| apply Prod.Lex.right
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decide
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#eval tst ``g
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#check g._eq_1
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#check g._eq_2
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#check g._unfold
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#eval tst ``h
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#check h._eq_1
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#check h._eq_2
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#check h._unfold
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