e2983e44ef
Because of the last-added-tried-first rule for macros, all the special purpose `decreasing_trivial` rules are tried for most recursive definitions out there, and because they use `apply` and `assumption` with default transparency may cause some definitoins to be unfolded over and over again. A quick test with one of the functions in the leansat project shows that elaboration time goes down from 600ms to 375ms when using ``` decreasing_by all_goals decreasing_with with_reducible decreasing_trivial ``` instead of ``` decreasing_by all_goals decreasing_with decreasing_trivial ``` This change uses `with_reducible` in most of these macros. This means that these tactics will no longer work when the relations/definitions they look for is hidden behind a definition. This affected in particular `Array.sizeOf_get`, which now has a companion `sizeOf_getElem`. In addition, there were three tactics using `apply` to apply Nat-related lemmas that we now expect `omega` to solve. We still need them when building `Init` modules that don’t have access to `omega`, but they now live in `decreasing_trivial_pre_omega`, meant to be only used internally.
62 lines
2.9 KiB
Text
62 lines
2.9 KiB
Text
/-
|
|
Copyright (c) 2022 Microsoft Corporation. All rights reserved.
|
|
Released under Apache 2.0 license as described in the file LICENSE.
|
|
Author: Leonardo de Moura
|
|
-/
|
|
prelude
|
|
import Init.SizeOf
|
|
import Init.MetaTypes
|
|
import Init.WF
|
|
|
|
/-- Unfold definitions commonly used in well founded relation definitions.
|
|
This is primarily intended for internal use in `decreasing_tactic`. -/
|
|
macro "simp_wf" : tactic =>
|
|
`(tactic| try simp (config := { unfoldPartialApp := true, zetaDelta := true }) [invImage, InvImage, Prod.lex, sizeOfWFRel, measure, Nat.lt_wfRel, WellFoundedRelation.rel])
|
|
|
|
/-- Extensible helper tactic for `decreasing_tactic`. This handles the "base case"
|
|
reasoning after applying lexicographic order lemmas.
|
|
It can be extended by adding more macro definitions, e.g.
|
|
```
|
|
macro_rules | `(tactic| decreasing_trivial) => `(tactic| linarith)
|
|
```
|
|
-/
|
|
syntax "decreasing_trivial" : tactic
|
|
|
|
macro_rules | `(tactic| decreasing_trivial) => `(tactic| (simp (config := { arith := true, failIfUnchanged := false })) <;> done)
|
|
macro_rules | `(tactic| decreasing_trivial) => `(tactic| omega)
|
|
macro_rules | `(tactic| decreasing_trivial) => `(tactic| assumption)
|
|
|
|
/--
|
|
Variant of `decreasing_trivial` that does not use `omega`, intended to be used in core modules
|
|
before `omega` is available.
|
|
-/
|
|
syntax "decreasing_trivial_pre_omega" : tactic
|
|
macro_rules | `(tactic| decreasing_trivial_pre_omega) => `(tactic| apply Nat.sub_succ_lt_self; assumption) -- a - (i+1) < a - i if i < a
|
|
macro_rules | `(tactic| decreasing_trivial_pre_omega) => `(tactic| apply Nat.pred_lt'; assumption) -- i-1 < i if j < i
|
|
macro_rules | `(tactic| decreasing_trivial_pre_omega) => `(tactic| apply Nat.pred_lt; assumption) -- i-1 < i if i ≠ 0
|
|
|
|
|
|
/-- Constructs a proof of decreasing along a well founded relation, by applying
|
|
lexicographic order lemmas and using `ts` to solve the base case. If it fails,
|
|
it prints a message to help the user diagnose an ill-founded recursive definition. -/
|
|
macro "decreasing_with " ts:tacticSeq : tactic =>
|
|
`(tactic|
|
|
(simp_wf
|
|
repeat (first | apply Prod.Lex.right | apply Prod.Lex.left)
|
|
repeat (first | apply PSigma.Lex.right | apply PSigma.Lex.left)
|
|
first
|
|
| done
|
|
| $ts
|
|
| fail "failed to prove termination, possible solutions:
|
|
- Use `have`-expressions to prove the remaining goals
|
|
- Use `termination_by` to specify a different well-founded relation
|
|
- Use `decreasing_by` to specify your own tactic for discharging this kind of goal"))
|
|
|
|
/-- `decreasing_tactic` is called by default on well-founded recursions in order
|
|
to synthesize a proof that recursive calls decrease along the selected
|
|
well founded relation. It can be locally overridden by using `decreasing_by tac`
|
|
on the recursive definition, and it can also be globally extended by adding
|
|
more definitions for `decreasing_tactic` (or `decreasing_trivial`,
|
|
which this tactic calls). -/
|
|
macro "decreasing_tactic" : tactic =>
|
|
`(tactic| decreasing_with first | decreasing_trivial | subst_vars; decreasing_trivial)
|