f40c999f68
as suggested in <https://leanprover.zulipchat.com/#narrow/stream/270676-lean4/topic/termination_by.20regression/near/419786430> Also refactored the code a bit and removed the code smell around `GuessLex`-produced termination arguments (which may not be surface-syntactically expressible) a bit by introducing an explicit flag for those.
138 lines
3 KiB
Text
138 lines
3 KiB
Text
/-!
|
|
Various tests about `decreasing_by`.
|
|
-/
|
|
|
|
-- For concise recursive definition that need well-founded recursion
|
|
-- and `decreasing_by` tactics that would fail if run on the subgoal
|
|
opaque dec1 : Nat → Nat
|
|
axiom dec1_lt (n : Nat) : dec1 n < n
|
|
opaque dec2 : Nat → Nat
|
|
axiom dec2_lt (n : Nat) : dec2 n < n
|
|
|
|
|
|
def simple (n : Nat) := n + simple (dec1 n)
|
|
decreasing_by apply dec1_lt
|
|
|
|
namespace Ex1
|
|
|
|
-- Multiple goals, explicit termination_By
|
|
def foo (n m : Nat) : Nat := foo n (dec2 m) + foo (dec1 n) 100
|
|
termination_by (n, m)
|
|
decreasing_by
|
|
· simp_wf
|
|
apply Prod.Lex.right
|
|
apply dec2_lt
|
|
· simp_wf
|
|
apply Prod.Lex.left
|
|
apply dec1_lt
|
|
|
|
end Ex1
|
|
|
|
namespace Ex2
|
|
|
|
-- Multiple goals, no termination_By
|
|
-- This does *not* work, because GuessLex does not pass multiple goals to the tactic.
|
|
-- so this tactic script fails.
|
|
def foo (n m : Nat) : Nat := foo n (dec2 m) + foo (dec1 n) 100 -- Error
|
|
decreasing_by
|
|
· simp_wf
|
|
apply Prod.Lex.right
|
|
apply dec2_lt
|
|
· simp_wf
|
|
apply Prod.Lex.left
|
|
apply dec1_lt
|
|
|
|
end Ex2
|
|
|
|
namespace Ex3
|
|
-- Using `all_goals`, explicit termination_By
|
|
def foo (n m : Nat) : Nat := foo n (dec2 m) + foo (dec1 n) 100
|
|
termination_by (n, m)
|
|
decreasing_by all_goals
|
|
simp_wf
|
|
first
|
|
| apply Prod.Lex.right
|
|
apply dec2_lt
|
|
| apply Prod.Lex.left
|
|
apply dec1_lt
|
|
|
|
end Ex3
|
|
|
|
namespace Ex4
|
|
|
|
-- Multiple goals, no termination_By
|
|
-- This does work, because the tactic is flexible enough
|
|
-- (Not a recommended way; complex `decrasing_by` should go along with `termination_by`.)
|
|
def foo (n m : Nat) : Nat := foo n (dec2 m) + foo (dec1 n) 100 -- Error
|
|
decreasing_by all_goals
|
|
simp_wf
|
|
first
|
|
| apply Prod.Lex.right
|
|
apply dec2_lt
|
|
| apply Prod.Lex.left
|
|
apply dec1_lt
|
|
|
|
end Ex4
|
|
|
|
namespace Ex5
|
|
-- Empty proof. Produces parse error and unsolved goals.
|
|
def foo (n m : Nat) : Nat := foo n (dec2 m) + foo (dec1 n) 100
|
|
termination_by (n, m)
|
|
decreasing_by -- Error
|
|
|
|
end Ex5
|
|
|
|
namespace Ex6
|
|
|
|
-- Incomplete tactic
|
|
-- Unsolved goals reported
|
|
def foo (n m : Nat) : Nat := foo n (dec2 m) + foo (dec1 n) 100
|
|
termination_by (n, m)
|
|
decreasing_by apply id -- Error
|
|
|
|
end Ex6
|
|
|
|
namespace Ex7
|
|
|
|
-- Incomplete tactic, no termination_by
|
|
-- Shows guess-lex matrix
|
|
def foo (n m : Nat) : Nat := foo n (dec2 m) + foo (dec1 n) 100 -- Error
|
|
decreasing_by apply id
|
|
|
|
end Ex7
|
|
|
|
namespace Ex8
|
|
|
|
-- tactic solving just one goal
|
|
-- unsolved goals
|
|
def foo (n m : Nat) : Nat := foo n (dec2 m) + foo (dec1 n) 100
|
|
termination_by (n, m)
|
|
decreasing_by -- Error
|
|
· simp_wf
|
|
apply Prod.Lex.right
|
|
apply dec2_lt
|
|
|
|
end Ex8
|
|
|
|
namespace Ex9
|
|
|
|
-- Incomplete tactic, no termination_by
|
|
-- Shows guess-lex matrix
|
|
def foo (n m : Nat) : Nat := foo n (dec2 m) + foo (dec1 n) 100 -- Error
|
|
decreasing_by
|
|
· simp_wf
|
|
apply Prod.Lex.right
|
|
apply dec2_lt
|
|
|
|
end Ex9
|
|
|
|
namespace Ex10
|
|
|
|
-- This checks that guess-lex does not run tactics in “recover” mode.
|
|
-- (If it would it would produce the wrong termination order and then we should see errors)
|
|
def foo (n m : Nat) : Nat := foo (n - 1) (dec2 m)
|
|
decreasing_by all_goals
|
|
· simp_wf
|
|
apply dec2_lt
|
|
|
|
end Ex10
|