(* 15-814 Fall 2025 *)
(* Lec 19: Linear Functional Programming *)

type nat[k] = +{'zero : 1, 'succ : <nat[k]>}

type list[m k] = +{'nil : 1, 'cons : <nat[k]> * <list[m k]>}

mode U structural :> A L
mode A affine :> L
mode L linear

decl append (l1 : list[L L]) (l2 : list[L L]) : list[L L]
defn append l1 l2 = match l1 with
     | 'nil () => l2
     | 'cons (<x>, <xs>) => 'cons (<x>, <append xs l2>)

decl length (l : list[L A]) : nat[L]
defn length l = match l with
     | 'nil () => 'zero ()
     | 'cons (<x>, <xs>) => 'succ <length xs>

decl map (f : [U] up[L] (nat[L] -> nat[L])) (l : list[L L]) : list[L L]
defn map f l = match l with
     | 'nil () => 'nil ()
     | 'cons (<x>, <xs>) => 'cons (<f.force x>, <map f xs>)