mirror of
https://github.com/leanprover/lean4.git
synced 2026-03-17 18:34:06 +00:00
08eb78a5b2
This PR sets up the new integrated test/bench suite. It then migrates all benchmarks and some related tests to the new suite. There's also some documentation and some linting. For now, a lot of the old tests are left alone so this PR doesn't become even larger than it already is. Eventually, all tests should be migrated to the new suite though so there isn't a confusing mix of two systems.
45 lines
1.4 KiB
Lean4
45 lines
1.4 KiB
Lean4
inductive InfTree.{u} (α : Type u)
|
||
| leaf : α → InfTree α
|
||
| node : (Nat → InfTree α) → InfTree α
|
||
|
||
open InfTree
|
||
|
||
def szn.{u} {α : Type u} (n : Nat) : InfTree α → InfTree α → Nat
|
||
| leaf a, t2 => 1
|
||
| node c, leaf b => 0
|
||
| node c, node d => szn n (c n) (d n)
|
||
|
||
universe u
|
||
|
||
theorem ex1 {α : Type u} (n : Nat) (c : Nat → InfTree α) (d : Nat → InfTree α) : szn n (node c) (node d) = szn n (c n) (d n) :=
|
||
rfl
|
||
|
||
inductive BTree (α : Type u)
|
||
| leaf : α → BTree α
|
||
| node : (Bool → Bool → BTree α) → BTree α
|
||
|
||
def BTree.sz {α : Type u} : BTree α → Nat
|
||
| leaf a => 1
|
||
| node c => sz (c true true) + sz (c true false) + sz (c false true) + sz (c false false) + 1
|
||
|
||
theorem ex2 {α : Type u} (c : Bool → Bool → BTree α) : (BTree.node c).sz = (c true true).sz + (c true false).sz + (c false true).sz + (c false false).sz + 1 :=
|
||
rfl
|
||
|
||
inductive L (α : Type u)
|
||
| nil : L α
|
||
| cons : (Unit → α) → (Unit → L α) → L α
|
||
|
||
def L.append {α} : L α → L α → L α
|
||
| nil, bs => bs
|
||
| cons a as, bs => cons a (fun _ => append (as ()) bs)
|
||
|
||
theorem L.appendNil {α} : (as : L α) → append as nil = as
|
||
| nil => rfl
|
||
| cons a as =>
|
||
show cons a (fun _ => append (as ()) nil) = cons a as from
|
||
have ih : append (as ()) nil = as () := appendNil $ as ()
|
||
have thunkAux : (fun _ => as ()) = as := funext fun x => by
|
||
cases x
|
||
exact rfl
|
||
by rw [ih, thunkAux]
|