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?`.
61 lines
924 B
Text
61 lines
924 B
Text
namespace Ex1
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mutual
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def h (c : Nat) (x : Nat) := match g c x c c with
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| 0 => 1
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| r => r + 2
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def g (c : Nat) (t : Nat) (a b : Nat) : Nat := match t with
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| (n+1) => match g c n a b with
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| 0 => 0
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| m => match g c (n - m) a b with
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| 0 => 0
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| m + 1 => g c m a b
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| 0 => f c 0
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def f (c : Nat) (x : Nat) := match h c x with
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| 0 => 1
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| r => f c r
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end
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termination_by
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g x a b => 0
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f c x => 0
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h c x => 0
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decreasing_by sorry
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attribute [simp] g
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attribute [simp] h
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attribute [simp] f
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#check g._eq_1
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#check g._eq_2
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#check h._eq_1
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#check f._eq_1
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end Ex1
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namespace Ex2
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def g (t : Nat) : Nat := match t with
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| (n+1) => match g n with
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| 0 => 0
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| m + 1 => match g (n - m) with
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| 0 => 0
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| m + 1 => g n
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| 0 => 0
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decreasing_by sorry
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theorem ex1 : g 0 = 0 := by
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rw [g]
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#check g._eq_1
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#check g._eq_2
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theorem ex2 : g 0 = 0 := by
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unfold g
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simp
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#check g._unfold
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end Ex2
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