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?`.
8 lines
215 B
Text
8 lines
215 B
Text
def sum (as : Array Nat) : Nat :=
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let rec go (i : Nat) (s : Nat) : Nat :=
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if h : i < as.size then
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go (i+2) (s + as.get ⟨i, h⟩) -- Error
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else
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s
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go 0 0
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termination_by go i _ => as.size - i
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