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?`.
25 lines
419 B
Text
25 lines
419 B
Text
namespace Ex1
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mutual
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def f : Nat → α → α → α
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| 0, a, b => a
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| n, a, b => g a n b |>.1
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def g : α → Nat → α → (α × α)
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| a, 0, b => (a, b)
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| a, n, b => (h a b n, a)
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def h : α → α → Nat → α
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| a, b, 0 => b
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| a, b, n+1 => f n a b
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end
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termination_by
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f n _ _ => (n, 2)
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g _ n _ => (n, 1)
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h _ _ n => (n, 0)
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#print f
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#print g
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#print h
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#eval f 5 'a' 'b'
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end Ex1
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