ffbea840bf
If here is only one plausible measure, there is no point having the `GuessLex` code see if it is terminating, running all the tactics, only for the `MkFix` code then run the tactics again. So if there is only one plausible measure (non-mutual recursion with only one varying parameter), just use that measure. Side benefit: If the function isn’t terminating, more detailed error messages are shown (failing proof goals), located at the recursive calls.
37 lines
1.5 KiB
Text
37 lines
1.5 KiB
Text
/-!
|
|
A few cases where guessing the lexicographic order fails, and
|
|
where we want to keep tabs on the output.
|
|
|
|
All functions take more than one changing argument, because the guesslex
|
|
code skips non-mutuals unary functions with only one plausible measure.
|
|
-/
|
|
|
|
def nonTerminating : Nat → Nat → Nat
|
|
| 0, _ => 0
|
|
| n, m => nonTerminating (.succ n) (.succ m)
|
|
|
|
-- Saying decreasing_by forces Lean to use structural recursion, which gives a different
|
|
-- error message
|
|
def nonTerminating2 : Nat → Nat → Nat
|
|
| 0, _ => 0
|
|
| n, m => nonTerminating2 (.succ n) (.succ m)
|
|
decreasing_by decreasing_tactic
|
|
|
|
|
|
-- The GuessLex code does not like eta-contracted motives in `casesOn`.
|
|
-- At the time of writing, the error message is swallowed
|
|
-- When guessing the lexicographic order becomes more verbose this will improve.
|
|
def FinPlus1 n := Fin (n + 1)
|
|
def badCasesOn (n m : Nat) : Fin (n + 1) :=
|
|
Nat.casesOn (motive := FinPlus1) n (⟨0,Nat.zero_lt_succ _⟩) (fun n => Fin.succ (badCasesOn n (.succ m)))
|
|
decreasing_by decreasing_tactic
|
|
-- termination_by badCasesOn n => n
|
|
|
|
|
|
-- Like above, but now with a `casesOn` alternative with insufficient lambdas
|
|
def Fin_succ_comp (f : (n : Nat) → Fin (n + 1)) : (n : Nat) → Fin (n + 2) := fun n => Fin.succ (f n)
|
|
def badCasesOn2 (n m : Nat) : Fin (n + 1) :=
|
|
Nat.casesOn (motive := fun n => Fin (n + 1)) n (⟨0,Nat.zero_lt_succ _⟩)
|
|
(Fin_succ_comp (fun n => badCasesOn2 n (.succ m)))
|
|
decreasing_by decreasing_tactic
|
|
-- termination_by badCasesOn2 n => n
|