feat(data/rat/floor): add norm_num support for int.{floor,ceil,fract}
#16502
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eric-wieser
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Does |
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Edited :) |
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🤣 I actually meant that the floor of |
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I am not sure if this is better code, but it avoids some duplication: /-- A norm_num extension for `int.floor`, `int.ceil`, and `int.fract`. -/
@[norm_num] meta def eval_floor_ceil (e : expr) : tactic (expr × expr) := do
let (f, args) := e.get_app_fn_args,
let val := [`int.floor, `int.ceil, `int.fract].index_of f.const_name,
guard $ val ≠ 3,
some x ← pure args.last',
q ← x.to_rat,
let z := if val ≠ 1 then int.floor q else int.ceil q,
let ze := `(z),
if val ≠ 2 then do
t ← to_expr ``(%%e = %%ze),
((), p) ← solve_aux t (do
mk_mapp (ite (val = 0) `int.floor_eq_iff `int.ceil_eq_iff) ((args.take 3).map some) >>=
rewrite_target,
tactic.interactive.norm_num [] (interactive.loc.ns [none])),
p ← instantiate_mvars p,
pure (ze, p)
else do
let q' := int.fract q,
some R ← pure args.head',
ic ← mk_instance_cache R,
(ic, q'e) ← ic.of_rat q',
t ← to_expr ``(%%e = %%q'e),
((), p) ← tactic.solve_aux t (do
`[rw int.fract_eq_iff; norm_num],
refine ``(⟨%%ze, _⟩),
tactic.interactive.norm_num [] (interactive.loc.ns [none])),
p ← instantiate_mvars p,
pure (q'e, p)[I edited the code above]. |
adomani
reviewed
Sep 15, 2022
| open tactic | ||
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| /-- A norm_num extension for `int.floor`, `int.ceil`, and `int.fract`. -/ | ||
| @[norm_num] meta def eval_floor_ceil : expr → tactic (expr × expr) |
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Suggested change
| @[norm_num] meta def eval_floor_ceil : expr → tactic (expr × expr) | |
| @[norm_num] meta def eval_floor_ceil_fract : expr → tactic (expr × expr) |
maybe, since it deals with int.fract as well.
adomani
reviewed
Sep 15, 2022
| example : int.ceil (-15 / 16 : R) + 1 = 1 := by norm_num | ||
| example : int.fract (-17 / 16 : R) - 1 = -1 / 16 := by norm_num | ||
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| end |
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Suggested change
| end | |
| end floor |
to please the linter
adomani
reviewed
Sep 15, 2022
Comment on lines
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| ((), p) ← tactic.solve_aux t (do | ||
| tactic.mk_mapp `int.ceil_eq_iff [some R, some inst_1, some inst_2] >>= tactic.rewrite_target, | ||
| `[norm_num]), |
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Should the tactic input to solve_aux end with a done, to make sure that it proves t, or is it unnecessary in this case, since this is an extension anyway?
(Most of my comments are also for my own understanding!)
alexjbest
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semorrison
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the
too-late
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Ported to leanprover-community/mathlib4#13647 |
YaelDillies
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This is super sloppy code, but is a working version to improve upon.
It's unfortunate that where in a proof it's often sufficient to do:
the idiomatic norm_num handler is much more painful to write.
Closes #15992.