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feat(data/rat/floor): add norm_num support for int.{floor,ceil,fract}
#16502
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eric-wieser
added
awaiting-review
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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
+172
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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
added
awaiting-author
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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.