lean4-htt/doc/examples/NFM2022/nfm8.lean
Mario Carneiro 4f664fb3b5
feat: improve @[deprecated] attr (#3968)
Complement to #3967 , adds a `(since := "<date>")` field to
`@[deprecated]` so that metaprogramming code has access to the
deprecation date for e.g. bulk removals. Also adds `@[deprecated
"deprecation message"]` to optionally replace the default text
"`{declName}` has been deprecated, use `{newName}` instead".
2024-04-23 17:00:32 +00:00

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Text

/- Well-founded recursion -/
def ack : Nat → Nat → Nat
| 0, y => y+1
| x+1, 0 => ack x 1
| x+1, y+1 => ack x (ack (x+1) y)
termination_by x y => (x, y)
def sum (a : Array Int) : Int :=
let rec go (i : Nat) :=
if _ : i < a.size then
a[i] + go (i+1)
else
0
termination_by a.size - i
go 0
set_option pp.proofs true
#print sum.go
/-
def sum.go : Array Int → Nat → Int :=
fun a =>
WellFounded.fix (sum.go.proof_1 a) fun i a_1 =>
if h : i < Array.size a then Array.getOp a i + a_1 (i + 1) (sum.go.proof_2 a i h) else 0
-/