lean2/tests/lean/slow/tactic1.lean

33 lines
1.3 KiB
Text
Raw Normal View History

Definition double {A : Type} (f : A -> A) : A -> A := fun x, f (f x).
Definition big {A : Type} (f : A -> A) : A -> A := (double (double (double (double (double (double (double f))))))).
(**
-- Tactic for trying to prove goal using Reflexivity, Congruence and available assumptions
local congr_tac = REPEAT(ORELSE(apply_tac("Refl"), apply_tac("Congr"), assumption_tac))
-- Create an eager tactic that only tries to prove goal after unfolding everything
eager_tac = THEN(-- unfold homogeneous equality
TRY(unfold_tac("eq")),
-- keep unfolding defintions above and beta-reducing
REPEAT(unfold_tac .. REPEAT(beta_tac)),
congr_tac)
-- The 'lazy' version tries first to prove without unfolding anything
lazy_tac = ORELSE(THEN(TRY(unfold_tac("eq")), congr_tac, now_tac),
eager_tac)
**)
Theorem T1 (a b : Int) (f : Int -> Int) (H : a = b) : (big f a) = (big f b).
apply eager_tac.
done.
Theorem T2 (a b : Int) (f : Int -> Int) (H : a = b) : (big f a) = (big f b).
apply lazy_tac.
done.
Theorem T3 (a b : Int) (f : Int -> Int) (H : a = b) : (big f a) = ((double (double (double (double (double (double (double f))))))) b).
apply lazy_tac.
done.