1	import Base
2	import ../math/pow2.bend as P2
3	import ./types/dynamic_array.bend as E
4	
5	# Growable, bounds-checked array over native Base.Array.
6	# DynArray<&2, T> is the existing Data API; DynArray<T> stores owning Type
7	# elements through the _owned API below. See docs/DYNAMIC_ARRAY_OWNERSHIP.md.
8	#
9	# Representation: DA{limit, depth, cap, length, slots} with cap = 2^depth kept
10	# in the record (recomputing 2^depth per operation would make every push,
11	# capacity and reserve cost O(depth)). `slots` is a Base.Array of
12	# 2^depth slots. ALeaf/ANode is the LOGICAL model the checker reasons about;
13	# stock Bend 2.0.16 lowers a Base.Array to one indexed memory block, and
14	# get/set/swap compile to a `blk_at` index computation plus a direct
15	# `blk_read`/`blk_write` (docs/C_EQUIVALENCE.md). Slots [0, length)
16	# hold Some{x}; the rest hold None. Capacity is 2^depth. `limit` (<= 31) caps
17	# depth, so every capacity is representable as the U32 size Base computes, and
18	# every index passed to Base is < 2^depth <= 2^31 (so Base's masking is the
19	# identity). Out-of-range indices never reach Base.
20	#
21	# Errors return the state unchanged (see docs/API.md):
22	#   get/set out of range -> IndexOutOfRange; pop on empty -> EmptyArray;
23	#   push/reserve beyond 2^limit -> CapacityExceeded.
24	# Cost (n = length, c = capacity): get/set/push/pop are one indexed load or
25	# store into the block (no tree descent in the native lowering), growth O(c)
26	# (a fresh half is allocated and the merged block copied, like a C realloc),
27	# reserve O(target capacity), clear O(c), to_list O(c).
28	
29	type DynArray<a, -T: Kind(a)> is Type:
30	  DA{limit: Nat, depth: Nat, cap: Nat, length: Nat, slots: Array<Maybe<a, T>>}
31	
32	def max_depth() -> Nat:
33	  31n
34	
35	# 2^d (structural doubling; Base Nat.pow is avoided, see docs/VALIDATION.md).
36	def pow2(d: Nat) -> Nat:
37	  match d:
38	    case 0n:
39	      1n
40	    case 1n+p:
41	      Nat.double(pow2(p))
42	
43	def empty_slots(-T: Data, +depth: Nat) -> Array<Maybe<&2, T>>:
44	  Array.new(Maybe<&2, T>, depth, None{})
45	
46	def new(-T: Data) -> DynArray<&2, T>:
47	  DA{max_depth(), 0n, 1n, 0n, empty_slots(T, 0n)}
48	
49	# Depth limit min(k, 31). (Written with an explicit match: Base Nat.min is a
50	# Bool.pick over shared arguments, which miscompiled at runtime; docs/VALIDATION.md.)
51	def clamp_limit(k: Nat, small: Bool) -> Nat:
52	  match small:
53	    case True{}:
54	      k
55	    case False{}:
56	      max_depth()
57	
58	# Same as new, with capacity bounded by 2^min(k, 31).
59	def with_limit(-T: Data, +k: Nat) -> DynArray<&2, T>:
60	  DA{clamp_limit(k, Nat.is_lt(k, max_depth())), 0n, 1n, 0n, empty_slots(T, 0n)}
61	
62	def length(-T: Data, da: DynArray<&2, T>) -> DynArray<&2, T> & Nat:
63	  DA{limit, depth, cap, +len, arr} = da
64	  (DA{limit, depth, cap, len, arr}, len)
65	
66	def capacity(-T: Data, da: DynArray<&2, T>) -> DynArray<&2, T> & Nat:
67	  DA{limit, depth, +cap, len, arr} = da
68	  (DA{limit, depth, cap, len, arr}, cap)
69	
70	def slot_result(-T: Data, slot: Maybe<&2, T>) -> Result<&2, &2, E.Error, T>:
71	  match slot:
72	    case None{}:
73	      Fail{E.IndexOutOfRange{}}
74	    case Some{x}:
75	      Done{x}
76	
77	# ---- get ----
78	
79	def get_found(-T: Data, limit: Nat, depth: Nat, +cap: Nat, len: Nat, r: Array<Maybe<&2, T>> & Maybe<&2, T>) -> DynArray<&2, T> & Result<&2, &2, E.Error, T>:
80	  (arr, slot) = r
81	  (DA{limit, depth, cap, len, arr}, slot_result(T, slot))
82	
83	def get_checked(-T: Data, limit: Nat, depth: Nat, +cap: Nat, len: Nat, arr: Array<Maybe<&2, T>>, i: Nat, ok: Bool) -> DynArray<&2, T> & Result<&2, &2, E.Error, T>:
84	  match ok:
85	    case True{}:
86	      get_found(T, limit, depth, cap, len, Array.get(Maybe<&2, T>, arr, U32.from_nat(i)))
87	    case False{}:
88	      (DA{limit, depth, cap, len, arr}, Fail{E.IndexOutOfRange{}})
89	
90	def get(-T: Data, da: DynArray<&2, T>, +i: Nat) -> DynArray<&2, T> & Result<&2, &2, E.Error, T>:
91	  DA{limit, depth, cap, +len, arr} = da
92	  get_checked(T, limit, depth, cap, len, arr, i, Nat.is_lt(i, len))
93	
94	# ---- set ----
95	
96	def set_checked(-T: Data, limit: Nat, depth: Nat, +cap: Nat, len: Nat, arr: Array<Maybe<&2, T>>, i: Nat, v: T, ok: Bool) -> DynArray<&2, T> & Result<&2, &2, E.Error, Unit>:
97	  match ok:
98	    case True{}:
99	      (DA{limit, depth, cap, len, Array.set(Maybe<&2, T>, arr, U32.from_nat(i), Some{v})}, Done{Unit{}})
100	    case False{}:
101	      (DA{limit, depth, cap, len, arr}, Fail{E.IndexOutOfRange{}})
102	
103	def set(-T: Data, da: DynArray<&2, T>, +i: Nat, v: T) -> DynArray<&2, T> & Result<&2, &2, E.Error, Unit>:
104	  DA{limit, depth, cap, +len, arr} = da
105	  set_checked(T, limit, depth, cap, len, arr, i, v, Nat.is_lt(i, len))
106	
107	# ---- growth ----
108	
109	# Doubling: the old tree becomes the left half of a tree one level deeper.
110	def grown(-T: Data, +depth: Nat, arr: Array<Maybe<&2, T>>) -> Array<Maybe<&2, T>>:
111	  ANode{arr, empty_slots(T, depth)}
112	
113	def push_room(-T: Data, limit: Nat, +depth: Nat, +cap: Nat, +len: Nat, arr: Array<Maybe<&2, T>>, v: T, room: Bool, grow: Bool) -> DynArray<&2, T> & Result<&2, &2, E.Error, Unit>:
114	  match room grow:
115	    case True{} _:
116	      (DA{limit, depth, cap, 1n+len, Array.set(Maybe<&2, T>, arr, U32.from_nat(len), Some{v})}, Done{Unit{}})
117	    case False{} True{}:
118	      (DA{limit, 1n+depth, Nat.double(cap), 1n+len, Array.set(Maybe<&2, T>, grown(T, depth, arr), U32.from_nat(len), Some{v})}, Done{Unit{}})
119	    case False{} False{}:
120	      (DA{limit, depth, cap, len, arr}, Fail{E.CapacityExceeded{}})
121	
122	def push(-T: Data, da: DynArray<&2, T>, v: T) -> DynArray<&2, T> & Result<&2, &2, E.Error, Unit>:
123	  DA{+limit, +depth, +cap, +len, arr} = da
124	  push_room(T, limit, depth, cap, len, arr, v, Nat.is_lt(len, cap), Nat.is_lt(depth, limit))
125	
126	# ---- pop ----
127	
128	def pop_found(-T: Data, limit: Nat, depth: Nat, +cap: Nat, m: Nat, r: Array<Maybe<&2, T>> & Maybe<&2, T>) -> DynArray<&2, T> & Result<&2, &2, E.Error, T>:
129	  (arr, old) = r
130	  (DA{limit, depth, cap, m, arr}, slot_result(T, old))
131	
132	def pop_len(-T: Data, limit: Nat, depth: Nat, +cap: Nat, len: Nat, arr: Array<Maybe<&2, T>>) -> DynArray<&2, T> & Result<&2, &2, E.Error, T>:
133	  match len:
134	    case 0n:
135	      (DA{limit, depth, cap, 0n, arr}, Fail{E.EmptyArray{}})
136	    case 1n+ +m:
137	      pop_found(T, limit, depth, cap, m, Array.swap(Maybe<&2, T>, arr, U32.from_nat(m), None{}))
138	
139	def pop(-T: Data, da: DynArray<&2, T>) -> DynArray<&2, T> & Result<&2, &2, E.Error, T>:
140	  DA{limit, depth, cap, len, arr} = da
141	  pop_len(T, limit, depth, cap, len, arr)
142	
143	# ---- reserve ----
144	
145	def grow_if(-T: Data, limit: Nat, +depth: Nat, +cap: Nat, len: Nat, arr: Array<Maybe<&2, T>>, fits: Bool) -> DynArray<&2, T>:
146	  match fits:
147	    case True{}:
148	      DA{limit, depth, cap, len, arr}
149	    case False{}:
150	      DA{limit, 1n+depth, Nat.double(cap), len, grown(T, depth, arr)}
151	
152	def grow_step(-T: Data, +n: Nat, st: DynArray<&2, T>) -> DynArray<&2, T>:
153	  DA{limit, +depth, +cap, len, arr} = st
154	  grow_if(T, limit, depth, cap, len, arr, Nat.is_le(n, cap))
155	
156	# Doubles until n fits; `fuel` = limit - depth bounds the number of doublings.
157	def grow_until(-T: Data, fuel: Nat, +n: Nat, st: DynArray<&2, T>) -> DynArray<&2, T>:
158	  match fuel:
159	    case 0n:
160	      st
161	    case 1n+f:
162	      grow_until(T, f, n, grow_step(T, n, st))
163	
164	# The feasibility test (n <= 2^limit) is only reached when the cached capacity
165	# does not already suffice: computing 2^limit is O(limit) and reserve is
166	# otherwise O(1).
167	def reserve_room(-T: Data, +limit: Nat, +depth: Nat, +cap: Nat, len: Nat, arr: Array<Maybe<&2, T>>, +n: Nat, feasible: Bool) -> DynArray<&2, T> & Result<&2, &2, E.Error, Unit>:
168	  match feasible:
169	    case True{}:
170	      (grow_until(T, Nat.sub(limit, depth), n, DA{limit, depth, cap, len, arr}), Done{Unit{}})
171	    case False{}:
172	      (DA{limit, depth, cap, len, arr}, Fail{E.CapacityExceeded{}})
173	
174	def reserve_checked(-T: Data, +limit: Nat, +depth: Nat, +cap: Nat, len: Nat, arr: Array<Maybe<&2, T>>, +n: Nat, fits: Bool) -> DynArray<&2, T> & Result<&2, &2, E.Error, Unit>:
175	  match fits:
176	    case True{}:
177	      (DA{limit, depth, cap, len, arr}, Done{Unit{}})
178	    case False{}:
179	      reserve_room(T, limit, depth, cap, len, arr, n, Nat.is_le(n, pow2(limit)))
180	
181	# Ensures capacity >= n (new capacity: least 2^k >= n with k >= depth).
182	def reserve(-T: Data, da: DynArray<&2, T>, +n: Nat) -> DynArray<&2, T> & Result<&2, &2, E.Error, Unit>:
183	  DA{+limit, +depth, +cap, len, arr} = da
184	  reserve_checked(T, limit, depth, cap, len, arr, n, Nat.is_le(n, cap))
185	
186	# ---- clear / to_list ----
187	
188	# Keeps the capacity; all slots become None.
189	def clear(-T: Data, da: DynArray<&2, T>) -> DynArray<&2, T>:
190	  DA{limit, +depth, +cap, len, arr} = da
191	  DA{limit, depth, cap, 0n, empty_slots(T, depth)}
192	
193	# to_list walks the occupied slots BY INDEX, newest first, and conses them:
194	# the walk gives the array back, so nothing is cloned, and a `Base.Array` is
195	# never matched structurally (that destroys the flat representation, see
196	# docs/VALIDATION.md).
197	def cons_some(-T: Data, x: Maybe<&2, T>, acc: List<&2, T>) -> List<&2, T>:
198	  match x:
199	    case None{}:
200	      acc
201	    case Some{v}:
202	      Con{v, acc}
203	
204	def dec1(n: Nat) -> Nat:
205	  match n:
206	    case 0n:
207	      0n
208	    case 1n+p:
209	      p
210	
211	# k slots are still to be read, the last of them first: the pair `r` is slot
212	# k - 1, already read.
213	def tl_go(k: Nat, -T: Data, acc: List<&2, T>, r: Array<Maybe<&2, T>> & Maybe<&2, T>) -> Array<Maybe<&2, T>> & List<&2, T>:
214	  match k r:
215	    case 0n Tuple{a, x}:
216	      (a, acc)
217	    case 1n+ +m Tuple{a, x}:
218	      tl_go(m, T, cons_some(T, x, acc), Array.get(Maybe<&2, T>, a, U32.from_nat(dec1(m))))
219	
220	def tl_done(-T: Data, limit: Nat, depth: Nat, +cap: Nat, +len: Nat, r: Array<Maybe<&2, T>> & List<&2, T>) -> DynArray<&2, T> & List<&2, T>:
221	  (a, xs) = r
222	  (DA{limit, depth, cap, len, a}, xs)
223	
224	def tl_start(-T: Data, limit: Nat, depth: Nat, +cap: Nat, len: Nat, arr: Array<Maybe<&2, T>>) -> DynArray<&2, T> & List<&2, T>:
225	  match len:
226	    case 0n:
227	      (DA{limit, depth, cap, 0n, arr}, Nil{})
228	    case 1n+ +m:
229	      tl_done(T, limit, depth, cap, 1n+m, tl_go(1n+m, T, Nil{}, Array.get(Maybe<&2, T>, arr, U32.from_nat(m))))
230	
231	def to_list(-T: Data, da: DynArray<&2, T>) -> DynArray<&2, T> & List<&2, T>:
232	  DA{limit, depth, +cap, len, arr} = da
233	  tl_start(T, limit, depth, cap, len, arr)
234	
235	# ---- operation traces ----
236	
237	def obs_nat(-T: Data, r: DynArray<&2, T> & Nat) -> DynArray<&2, T> & E.Obs<T>:
238	  (d, n) = r
239	  (d, E.ONat{n})
240	
241	def obs_item(-T: Data, r: DynArray<&2, T> & Result<&2, &2, E.Error, T>) -> DynArray<&2, T> & E.Obs<T>:
242	  (d, x) = r
243	  (d, E.OItem{x})
244	
245	def obs_unit(-T: Data, r: DynArray<&2, T> & Result<&2, &2, E.Error, Unit>) -> DynArray<&2, T> & E.Obs<T>:
246	  (d, x) = r
247	  (d, E.OUnit{x})
248	
249	def obs_list(-T: Data, r: DynArray<&2, T> & List<&2, T>) -> DynArray<&2, T> & E.Obs<T>:
250	  (d, xs) = r
251	  (d, E.OList{xs})
252	
253	def step(-T: Data, da: DynArray<&2, T>, op: E.Op<T>) -> DynArray<&2, T> & E.Obs<T>:
254	  match op:
255	    case E.Length{}:
256	      obs_nat(T, length(T, da))
257	    case E.Capacity{}:
258	      obs_nat(T, capacity(T, da))
259	    case E.Get{i}:
260	      obs_item(T, get(T, da, i))
261	    case E.Set{i, v}:
262	      obs_unit(T, set(T, da, i, v))
263	    case E.Push{v}:
264	      obs_unit(T, push(T, da, v))
265	    case E.Pop{}:
266	      obs_item(T, pop(T, da))
267	    case E.Reserve{n}:
268	      obs_unit(T, reserve(T, da, n))
269	    case E.Clear{}:
270	      (clear(T, da), E.OUnit{Done{Unit{}}})
271	    case E.ToList{}:
272	      obs_list(T, to_list(T, da))
273	
274	def record(-T: Data, acc: List<&2, E.Obs<T>>, r: DynArray<&2, T> & E.Obs<T>) -> DynArray<&2, T> & List<&2, E.Obs<T>>:
275	  (da, o) = r
276	  (da, Con{o, acc})
277	
278	def step_acc(-T: Data, op: E.Op<T>, st: DynArray<&2, T> & List<&2, E.Obs<T>>) -> DynArray<&2, T> & List<&2, E.Obs<T>>:
279	  (da, acc) = st
280	  record(T, acc, step(T, da, op))
281	
282	# Runs ops left to right; observations are accumulated newest-first.
283	def run_acc(-T: Data, ops: List<&2, E.Op<T>>, st: DynArray<&2, T> & List<&2, E.Obs<T>>) -> DynArray<&2, T> & List<&2, E.Obs<T>>:
284	  match ops:
285	    case Nil{}:
286	      st
287	    case Con{op, rest}:
288	      run_acc(T, rest, step_acc(T, op, st))
289	
290	def finish(-T: Data, st: DynArray<&2, T> & List<&2, E.Obs<T>>) -> DynArray<&2, T> & List<&2, E.Obs<T>>:
291	  (da, acc) = st
292	  (da, List.reverse(&2, E.Obs<T>, acc))
293	
294	# Final state and the observation of every operation, in order.
295	def run(-T: Data, ops: List<&2, E.Op<T>>, da: DynArray<&2, T>) -> DynArray<&2, T> & List<&2, E.Obs<T>>:
296	  finish(T, run_acc(T, ops, (da, Nil{})))
297	
298	# ---- executable specializations at a closed element type ----
299	#
300	# Bend 2.0.16's native C backend miscompiles Base.Array operations whose
301	# element type is still open (an erased `-T` parameter): `Array.new` at a bare
302	# type variable is rejected outright ("an open Array element type"), and
303	# `Array.get`/`Array.set`/`Array.swap`/`Array.clone` under `Maybe<&2, T>`
304	# silently read back wrong data for any element that is not a machine
305	# immediate. See docs/VALIDATION.md and tests/runtime_defects/.
306	#
307	# The definitions above stay parametric, so their proofs are universal in T.
308	# The `*_at` definitions below are template specializations: `~T` is a
309	# compile-time parameter, so every Base.Array call is compiled at a closed
310	# element type. They are the entry points used by tests and benchmarks, and
311	# proofs/dynamic_array/closed.bend proves each of them equal to the
312	# parametric definition at its instance, so every law above transfers.
313	#
314	# Only the definitions that (transitively) reach a Base.Array call need a
315	# specialization; the purely structural helpers are shared.
316	
317	def empty_slots_at(~T: Data, +depth: Nat) -> Array<Maybe<&2, T>>:
318	  Array.new(Maybe<&2, T>, depth, None{})
319	
320	def new_at(~T: Data) -> DynArray<&2, T>:
321	  DA{max_depth(), 0n, 1n, 0n, empty_slots_at(~T, 0n)}
322	
323	def with_limit_at(~T: Data, +k: Nat) -> DynArray<&2, T>:
324	  DA{clamp_limit(k, Nat.is_lt(k, max_depth())), 0n, 1n, 0n, empty_slots_at(~T, 0n)}
325	
326	# Keep the element type specialized through the returned payload. Calling the
327	# erased generic get_found here boxes composite Data on every indexed read.
328	def get_found_at(~T: Data, limit: Nat, depth: Nat, cap: Nat, len: Nat, r: Array<Maybe<&2, T>> & Maybe<&2, T>) -> DynArray<&2, T> & Result<&2, &2, E.Error, T>:
329	  match r:
330	    case Tuple{arr, None{}}:
331	      (DA{limit, depth, cap, len, arr}, Fail{E.IndexOutOfRange{}})
332	    case Tuple{arr, Some{x}}:
333	      (DA{limit, depth, cap, len, arr}, Done{x})
334	
335	def get_checked_at(~T: Data, limit: Nat, depth: Nat, +cap: Nat, len: Nat, arr: Array<Maybe<&2, T>>, i: Nat, ok: Bool) -> DynArray<&2, T> & Result<&2, &2, E.Error, T>:
336	  match ok:
337	    case True{}:
338	      get_found_at(~T, limit, depth, cap, len, Array.get(Maybe<&2, T>, arr, U32.from_nat(i)))
339	    case False{}:
340	      (DA{limit, depth, cap, len, arr}, Fail{E.IndexOutOfRange{}})
341	
342	def get_at(~T: Data, da: DynArray<&2, T>, +i: Nat) -> DynArray<&2, T> & Result<&2, &2, E.Error, T>:
343	  DA{limit, depth, cap, +len, arr} = da
344	  get_checked_at(~T, limit, depth, cap, len, arr, i, Nat.is_lt(i, len))
345	
346	def set_checked_at(~T: Data, limit: Nat, depth: Nat, +cap: Nat, len: Nat, arr: Array<Maybe<&2, T>>, i: Nat, v: T, ok: Bool) -> DynArray<&2, T> & Result<&2, &2, E.Error, Unit>:
347	  match ok:
348	    case True{}:
349	      (DA{limit, depth, cap, len, Array.set(Maybe<&2, T>, arr, U32.from_nat(i), Some{v})}, Done{Unit{}})
350	    case False{}:
351	      (DA{limit, depth, cap, len, arr}, Fail{E.IndexOutOfRange{}})
352	
353	def set_at(~T: Data, da: DynArray<&2, T>, +i: Nat, v: T) -> DynArray<&2, T> & Result<&2, &2, E.Error, Unit>:
354	  DA{limit, depth, cap, +len, arr} = da
355	  set_checked_at(~T, limit, depth, cap, len, arr, i, v, Nat.is_lt(i, len))
356	
357	def grown_at(~T: Data, +depth: Nat, arr: Array<Maybe<&2, T>>) -> Array<Maybe<&2, T>>:
358	  ANode{arr, empty_slots_at(~T, depth)}
359	
360	def push_room_at(~T: Data, limit: Nat, +depth: Nat, +cap: Nat, +len: Nat, arr: Array<Maybe<&2, T>>, v: T, room: Bool, grow: Bool) -> DynArray<&2, T> & Result<&2, &2, E.Error, Unit>:
361	  match room grow:
362	    case True{} _:
363	      (DA{limit, depth, cap, 1n+len, Array.set(Maybe<&2, T>, arr, U32.from_nat(len), Some{v})}, Done{Unit{}})
364	    case False{} True{}:
365	      (DA{limit, 1n+depth, Nat.double(cap), 1n+len, Array.set(Maybe<&2, T>, grown_at(~T, depth, arr), U32.from_nat(len), Some{v})}, Done{Unit{}})
366	    case False{} False{}:
367	      (DA{limit, depth, cap, len, arr}, Fail{E.CapacityExceeded{}})
368	
369	def push_at(~T: Data, da: DynArray<&2, T>, v: T) -> DynArray<&2, T> & Result<&2, &2, E.Error, Unit>:
370	  DA{+limit, +depth, +cap, +len, arr} = da
371	  push_room_at(~T, limit, depth, cap, len, arr, v, Nat.is_lt(len, cap), Nat.is_lt(depth, limit))
372	
373	def pop_len_at(~T: Data, limit: Nat, depth: Nat, +cap: Nat, len: Nat, arr: Array<Maybe<&2, T>>) -> DynArray<&2, T> & Result<&2, &2, E.Error, T>:
374	  match len:
375	    case 0n:
376	      (DA{limit, depth, cap, 0n, arr}, Fail{E.EmptyArray{}})
377	    case 1n+ +m:
378	      pop_found(T, limit, depth, cap, m, Array.swap(Maybe<&2, T>, arr, U32.from_nat(m), None{}))
379	
380	def pop_at(~T: Data, da: DynArray<&2, T>) -> DynArray<&2, T> & Result<&2, &2, E.Error, T>:
381	  DA{limit, depth, cap, len, arr} = da
382	  pop_len_at(~T, limit, depth, cap, len, arr)
383	
384	def grow_if_at(~T: Data, limit: Nat, +depth: Nat, +cap: Nat, len: Nat, arr: Array<Maybe<&2, T>>, fits: Bool) -> DynArray<&2, T>:
385	  match fits:
386	    case True{}:
387	      DA{limit, depth, cap, len, arr}
388	    case False{}:
389	      DA{limit, 1n+depth, Nat.double(cap), len, grown_at(~T, depth, arr)}
390	
391	def grow_step_at(~T: Data, +n: Nat, st: DynArray<&2, T>) -> DynArray<&2, T>:
392	  DA{limit, +depth, +cap, len, arr} = st
393	  grow_if_at(~T, limit, depth, cap, len, arr, Nat.is_le(n, cap))
394	
395	def grow_until_at(~T: Data, fuel: Nat, +n: Nat, st: DynArray<&2, T>) -> DynArray<&2, T>:
396	  match fuel:
397	    case 0n:
398	      st
399	    case 1n+f:
400	      grow_until_at(~T, f, n, grow_step_at(~T, n, st))
401	
402	# The feasibility test (n <= 2^limit) is only reached when the cached capacity
403	# does not already suffice: computing 2^limit is O(limit) and reserve is
404	# otherwise O(1).
405	def reserve_room_at(~T: Data, +limit: Nat, +depth: Nat, +cap: Nat, len: Nat, arr: Array<Maybe<&2, T>>, +n: Nat, feasible: Bool) -> DynArray<&2, T> & Result<&2, &2, E.Error, Unit>:
406	  match feasible:
407	    case True{}:
408	      (grow_until_at(~T, Nat.sub(limit, depth), n, DA{limit, depth, cap, len, arr}), Done{Unit{}})
409	    case False{}:
410	      (DA{limit, depth, cap, len, arr}, Fail{E.CapacityExceeded{}})
411	
412	def reserve_checked_at(~T: Data, +limit: Nat, +depth: Nat, +cap: Nat, len: Nat, arr: Array<Maybe<&2, T>>, +n: Nat, fits: Bool) -> DynArray<&2, T> & Result<&2, &2, E.Error, Unit>:
413	  match fits:
414	    case True{}:
415	      (DA{limit, depth, cap, len, arr}, Done{Unit{}})
416	    case False{}:
417	      reserve_room_at(~T, limit, depth, cap, len, arr, n, Nat.is_le(n, P2.pow2t(limit)))
418	
419	def reserve_at(~T: Data, da: DynArray<&2, T>, +n: Nat) -> DynArray<&2, T> & Result<&2, &2, E.Error, Unit>:
420	  DA{+limit, +depth, +cap, len, arr} = da
421	  reserve_checked_at(~T, limit, depth, cap, len, arr, n, Nat.is_le(n, cap))
422	
423	# The executable clear allocates the fresh all-None block, exactly as the
424	# parametric `clear` does and exactly as benchmarks/native/dynamic_array.c
425	# rewrites the slots: the capacity is kept and every slot is empty again.
426	# (An "already empty, keep the block" fast path was tried in iteration 0011
427	# and removed in 0013: it only pays off when a benchmark clears the same
428	# empty array over and over, and it made the clear rows unmeasurable because
429	# the calibration then compares a no-op against the reference's real work.)
430	def clear_at(~T: Data, da: DynArray<&2, T>) -> DynArray<&2, T>:
431	  DA{+limit, +depth, +cap, len, arr} = da
432	  DA{limit, depth, cap, 0n, empty_slots_at(~T, depth)}
433	
434	# The executable to_list is the same indexed walk, compiled at a closed
435	# element type; proofs/dynamic_array/closed.bend proves the two agree.
436	def tl_go_at(~T: Data, k: Nat, acc: List<&2, T>, r: Array<Maybe<&2, T>> & Maybe<&2, T>) -> Array<Maybe<&2, T>> & List<&2, T>:
437	  match k r:
438	    case 0n Tuple{a, x}:
439	      (a, acc)
440	    case 1n+ +m Tuple{a, x}:
441	      tl_go_at(~T, m, cons_some(T, x, acc), Array.get(Maybe<&2, T>, a, U32.from_nat(dec1(m))))
442	
443	def tl_start_at(~T: Data, limit: Nat, depth: Nat, +cap: Nat, len: Nat, arr: Array<Maybe<&2, T>>) -> DynArray<&2, T> & List<&2, T>:
444	  match len:
445	    case 0n:
446	      (DA{limit, depth, cap, 0n, arr}, Nil{})
447	    case 1n+ +m:
448	      tl_done(T, limit, depth, cap, 1n+m, tl_go_at(~T, 1n+m, Nil{}, Array.get(Maybe<&2, T>, arr, U32.from_nat(m))))
449	
450	def to_list_at(~T: Data, da: DynArray<&2, T>) -> DynArray<&2, T> & List<&2, T>:
451	  DA{limit, depth, +cap, len, arr} = da
452	  tl_start_at(~T, limit, depth, cap, len, arr)
453	
454	def step_at(~T: Data, da: DynArray<&2, T>, op: E.Op<T>) -> DynArray<&2, T> & E.Obs<T>:
455	  match op:
456	    case E.Length{}:
457	      obs_nat(T, length(T, da))
458	    case E.Capacity{}:
459	      obs_nat(T, capacity(T, da))
460	    case E.Get{i}:
461	      obs_item(T, get_at(~T, da, i))
462	    case E.Set{i, v}:
463	      obs_unit(T, set_at(~T, da, i, v))
464	    case E.Push{v}:
465	      obs_unit(T, push_at(~T, da, v))
466	    case E.Pop{}:
467	      obs_item(T, pop_at(~T, da))
468	    case E.Reserve{n}:
469	      obs_unit(T, reserve_at(~T, da, n))
470	    case E.Clear{}:
471	      (clear_at(~T, da), E.OUnit{Done{Unit{}}})
472	    case E.ToList{}:
473	      obs_list(T, to_list_at(~T, da))
474	
475	def step_acc_at(~T: Data, op: E.Op<T>, st: DynArray<&2, T> & List<&2, E.Obs<T>>) -> DynArray<&2, T> & List<&2, E.Obs<T>>:
476	  (da, acc) = st
477	  record(T, acc, step_at(~T, da, op))
478	
479	def run_acc_at(~T: Data, ops: List<&2, E.Op<T>>, st: DynArray<&2, T> & List<&2, E.Obs<T>>) -> DynArray<&2, T> & List<&2, E.Obs<T>>:
480	  match ops:
481	    case Nil{}:
482	      st
483	    case Con{op, rest}:
484	      run_acc_at(~T, rest, step_acc_at(~T, op, st))
485	
486	def run_at(~T: Data, ops: List<&2, E.Op<T>>, da: DynArray<&2, T>) -> DynArray<&2, T> & List<&2, E.Obs<T>>:
487	  finish(T, run_acc_at(~T, ops, (da, Nil{})))
488	
489	# ---- owning elements (Type) ----
490	# Same DA representation and native Base.Array storage. No operation copies T.
491	# Data clients keep their existing get/to_list API at quantity &2. Owning
492	# clients use quantity &1 and move values with pop/swap/update/into_list.
493	# A failed push or swap returns the supplied value in E.Rejected.
494	
495	# Stock Array.new requires Data. This fresh-empty initializer is O(c log c)
496	# in the native backend because ANode merges blocks; see ownership docs.
497	def empty_owned(~T: Type, depth: Nat) -> Array<Maybe<&1, T>>:
498	  match depth:
499	    case 0n:
500	      ALeaf{None{}}
501	    case 1n+ +p:
502	      ANode{empty_owned(~T, p), empty_owned(~T, p)}
503	
504	def new_owned(~T: Type) -> DynArray<&1, T>:
505	  DA{max_depth(), 0n, 1n, 0n, empty_owned(~T, 0n)}
506	
507	def with_limit_owned(~T: Type, +k: Nat) -> DynArray<&1, T>:
508	  DA{clamp_limit(k, Nat.is_lt(k, max_depth())), 0n, 1n, 0n, empty_owned(~T, 0n)}
509	
510	def length_owned(~T: Type, da: DynArray<&1, T>) -> DynArray<&1, T> & Nat:
511	  DA{limit, depth, cap, +len, arr} = da
512	  (DA{limit, depth, cap, len, arr}, len)
513	
514	def capacity_owned(~T: Type, da: DynArray<&1, T>) -> DynArray<&1, T> & Nat:
515	  DA{limit, depth, +cap, len, arr} = da
516	  (DA{limit, depth, cap, len, arr}, cap)
517	
518	def grown_owned(~T: Type, +depth: Nat, arr: Array<Maybe<&1, T>>) -> Array<Maybe<&1, T>>:
519	  ANode{arr, empty_owned(~T, depth)}
520	
521	def push_room_owned(~T: Type, limit: Nat, +depth: Nat, +cap: Nat, +len: Nat, arr: Array<Maybe<&1, T>>, v: T, room: Bool, grow: Bool) -> DynArray<&1, T> & Result<&1, &2, E.Rejected<T>, Unit>:
522	  match room grow:
523	    case True{} _:
524	      (DA{limit, depth, cap, 1n+len, Array.set(Maybe<&1, T>, arr, U32.from_nat(len), Some{v})}, Done{Unit{}})
525	    case False{} True{}:
526	      (DA{limit, 1n+depth, Nat.double(cap), 1n+len, Array.set(Maybe<&1, T>, grown_owned(~T, depth, arr), U32.from_nat(len), Some{v})}, Done{Unit{}})
527	    case False{} False{}:
528	      (DA{limit, depth, cap, len, arr}, Fail{E.Rejected{E.CapacityExceeded{}, v}})
529	
530	def push_owned(~T: Type, da: DynArray<&1, T>, v: T) -> DynArray<&1, T> & Result<&1, &2, E.Rejected<T>, Unit>:
531	  DA{+limit, +depth, +cap, +len, arr} = da
532	  push_room_owned(~T, limit, depth, cap, len, arr, v, Nat.is_lt(len, cap), Nat.is_lt(depth, limit))
533	
534	def owned_result(~T: Type, slot: Maybe<&1, T>) -> Result<&2, &1, E.Error, T>:
535	  match slot:
536	    case None{}:
537	      Fail{E.IndexOutOfRange{}}
538	    case Some{x}:
539	      Done{x}
540	
541	def pop_found_owned(~T: Type, limit: Nat, depth: Nat, cap: Nat, n: Nat, r: Array<Maybe<&1, T>> & Maybe<&1, T>) -> DynArray<&1, T> & Result<&2, &1, E.Error, T>:
542	  (arr, old) = r
543	  (DA{limit, depth, cap, n, arr}, owned_result(~T, old))
544	
545	def pop_len_owned(~T: Type, limit: Nat, depth: Nat, cap: Nat, len: Nat, arr: Array<Maybe<&1, T>>) -> DynArray<&1, T> & Result<&2, &1, E.Error, T>:
546	  match len:
547	    case 0n:
548	      (DA{limit, depth, cap, 0n, arr}, Fail{E.EmptyArray{}})
549	    case 1n+ +n:
550	      pop_found_owned(~T, limit, depth, cap, n, Array.swap(Maybe<&1, T>, arr, U32.from_nat(n), None{}))
551	
552	def pop_owned(~T: Type, da: DynArray<&1, T>) -> DynArray<&1, T> & Result<&2, &1, E.Error, T>:
553	  DA{limit, depth, cap, len, arr} = da
554	  pop_len_owned(~T, limit, depth, cap, len, arr)
555	
556	# The result on success is the previous value. Invalid indices return v.
557	# None can occur only in an invalid externally constructed DA representation.
558	def swap_found_owned(~T: Type, limit: Nat, depth: Nat, cap: Nat, len: Nat, r: Array<Maybe<&1, T>> & Maybe<&1, T>) -> DynArray<&1, T> & Result<&1, &1, E.Rejected<T>, Maybe<&1, T>>:
559	  (arr, old) = r
560	  (DA{limit, depth, cap, len, arr}, Done{old})
561	
562	def swap_checked_owned(~T: Type, limit: Nat, depth: Nat, cap: Nat, len: Nat, arr: Array<Maybe<&1, T>>, i: Nat, v: T, ok: Bool) -> DynArray<&1, T> & Result<&1, &1, E.Rejected<T>, Maybe<&1, T>>:
563	  match ok:
564	    case True{}:
565	      swap_found_owned(~T, limit, depth, cap, len, Array.swap(Maybe<&1, T>, arr, U32.from_nat(i), Some{v}))
566	    case False{}:
567	      (DA{limit, depth, cap, len, arr}, Fail{E.Rejected{E.IndexOutOfRange{}, v}})
568	
569	def swap_owned(~T: Type, da: DynArray<&1, T>, +i: Nat, v: T) -> DynArray<&1, T> & Result<&1, &1, E.Rejected<T>, Maybe<&1, T>>:
570	  DA{limit, depth, cap, +len, arr} = da
571	  swap_checked_owned(~T, limit, depth, cap, len, arr, i, v, Nat.is_lt(i, len))
572	
573	def set_done_owned(~T: Type, r: DynArray<T> & Result<&1, &1, E.Rejected<T>, Maybe<T>>) -> DynArray<T> & Result<&1, &2, E.Rejected<T>, Unit>:
574	  match r:
575	    case Tuple{da, Done{old}}:
576	      (da, Done{Unit{}})
577	    case Tuple{da, Fail{rejected}}:
578	      (da, Fail{rejected})
579	
580	# Replace and release the previous element. Use swap_owned to retain it.
581	def set_owned(~T: Type, da: DynArray<T>, i: Nat, value: T) -> DynArray<T> & Result<&1, &2, E.Rejected<T>, Unit>:
582	  set_done_owned(~T, swap_owned(~T, da, i, value))
583	
584	# Scoped ownership: f receives the element and must return a replacement.
585	# No placeholder escapes the call. f is not called for an invalid index.
586	def update_put_owned(~T: Type, ~R: Type, limit: Nat, depth: Nat, cap: Nat, len: Nat, arr: Array<Maybe<&1, T>>, i: Nat, r: T & R) -> DynArray<&1, T> & Result<&2, &1, E.Error, R>:
587	  (value, result) = r
588	  (DA{limit, depth, cap, len, Array.set(Maybe<&1, T>, arr, U32.from_nat(i), Some{value})}, Done{result})
589	
590	def update_found_owned(~T: Type, ~R: Type, limit: Nat, depth: Nat, cap: Nat, len: Nat, i: Nat, f: T -> T & R, r: Array<Maybe<&1, T>> & Maybe<&1, T>) -> DynArray<&1, T> & Result<&2, &1, E.Error, R>:
591	  match r:
592	    case Tuple{arr, None{}}:
593	      (DA{limit, depth, cap, len, arr}, Fail{E.IndexOutOfRange{}})
594	    case Tuple{arr, Some{x}}:
595	      update_put_owned(~T, ~R, limit, depth, cap, len, arr, i, f(x))
596	
597	def update_checked_owned(~T: Type, ~R: Type, limit: Nat, depth: Nat, cap: Nat, len: Nat, arr: Array<Maybe<&1, T>>, +i: Nat, f: T -> T & R, ok: Bool) -> DynArray<&1, T> & Result<&2, &1, E.Error, R>:
598	  match ok:
599	    case False{}:
600	      (DA{limit, depth, cap, len, arr}, Fail{E.IndexOutOfRange{}})
601	    case True{}:
602	      update_found_owned(~T, ~R, limit, depth, cap, len, i, f, Array.swap(Maybe<&1, T>, arr, U32.from_nat(i), None{}))
603	
604	def update_owned(~T: Type, ~R: Type, da: DynArray<&1, T>, +i: Nat, f: T -> T & R) -> DynArray<&1, T> & Result<&2, &1, E.Error, R>:
605	  DA{limit, depth, cap, +len, arr} = da
606	  update_checked_owned(~T, ~R, limit, depth, cap, len, arr, i, f, Nat.is_lt(i, len))
607	
608	def grow_if_owned(~T: Type, limit: Nat, +depth: Nat, +cap: Nat, len: Nat, arr: Array<Maybe<&1, T>>, fits: Bool) -> DynArray<&1, T>:
609	  match fits:
610	    case True{}:
611	      DA{limit, depth, cap, len, arr}
612	    case False{}:
613	      DA{limit, 1n+depth, Nat.double(cap), len, grown_owned(~T, depth, arr)}
614	
615	def grow_step_owned(~T: Type, +n: Nat, st: DynArray<&1, T>) -> DynArray<&1, T>:
616	  DA{limit, +depth, +cap, len, arr} = st
617	  grow_if_owned(~T, limit, depth, cap, len, arr, Nat.is_le(n, cap))
618	
619	def grow_until_owned(~T: Type, fuel: Nat, +n: Nat, st: DynArray<&1, T>) -> DynArray<&1, T>:
620	  match fuel:
621	    case 0n:
622	      st
623	    case 1n+f:
624	      grow_until_owned(~T, f, n, grow_step_owned(~T, n, st))
625	
626	def reserve_room_owned(~T: Type, +limit: Nat, +depth: Nat, cap: Nat, len: Nat, arr: Array<Maybe<&1, T>>, +n: Nat, feasible: Bool) -> DynArray<&1, T> & Result<&2, &2, E.Error, Unit>:
627	  match feasible:
628	    case False{}:
629	      (DA{limit, depth, cap, len, arr}, Fail{E.CapacityExceeded{}})
630	    case True{}:
631	      (grow_until_owned(~T, Nat.sub(limit, depth), n, DA{limit, depth, cap, len, arr}), Done{Unit{}})
632	
633	def reserve_checked_owned(~T: Type, +limit: Nat, depth: Nat, cap: Nat, len: Nat, arr: Array<Maybe<&1, T>>, +n: Nat, fits: Bool) -> DynArray<&1, T> & Result<&2, &2, E.Error, Unit>:
634	  match fits:
635	    case True{}:
636	      (DA{limit, depth, cap, len, arr}, Done{Unit{}})
637	    case False{}:
638	      reserve_room_owned(~T, limit, depth, cap, len, arr, n, Nat.is_le(n, pow2(limit)))
639	
640	def reserve_owned(~T: Type, da: DynArray<&1, T>, +n: Nat) -> DynArray<&1, T> & Result<&2, &2, E.Error, Unit>:
641	  DA{+limit, depth, +cap, len, arr} = da
642	  reserve_checked_owned(~T, limit, depth, cap, len, arr, n, Nat.is_le(n, cap))
643	
644	def clear_owned(~T: Type, da: DynArray<&1, T>) -> DynArray<&1, T>:
645	  DA{limit, +depth, cap, len, arr} = da
646	  DA{limit, depth, cap, 0n, empty_owned(~T, depth)}
647	
648	def cons_owned(~T: Type, x: Maybe<&1, T>, acc: List<&1, T>) -> List<&1, T>:
649	  match x:
650	    case None{}:
651	      acc
652	    case Some{v}:
653	      Con{v, acc}
654	
655	def drain_go_owned(~T: Type, k: Nat, acc: List<&1, T>, r: Array<Maybe<&1, T>> & Maybe<&1, T>) -> List<&1, T>:
656	  match k r:
657	    case 0n Tuple{arr, x}:
658	      cons_owned(~T, x, acc)
659	    case 1n+ +m Tuple{arr, x}:
660	      drain_go_owned(~T, m, cons_owned(~T, x, acc), Array.swap(Maybe<&1, T>, arr, U32.from_nat(m), None{}))
661	
662	def drain_len_owned(~T: Type, len: Nat, arr: Array<Maybe<&1, T>>) -> List<&1, T>:
663	  match len:
664	    case 0n:
665	      Nil{}
666	    case 1n+ +m:
667	      drain_go_owned(~T, m, Nil{}, Array.swap(Maybe<&1, T>, arr, U32.from_nat(m), None{}))
668	
669	# Consumes the container; values move into the returned list, in order.
670	def into_list_owned(~T: Type, da: DynArray<&1, T>) -> List<&1, T>:
671	  DA{limit, depth, cap, len, arr} = da
672	  drain_len_owned(~T, len, arr)
673	
674	# Copyable-element exchange, used by indexed collection storage. The previous
675	# value is returned and all other slots remain unchanged. Like set_at, an
676	# invalid index leaves the array unchanged and reports IndexOutOfRange.
677	def swap_checked_at(~T: Data, limit: Nat, depth: Nat, cap: Nat, len: Nat, arr: Array<Maybe<&2, T>>, i: Nat, v: T, ok: Bool) -> DynArray<&2, T> & Result<&2, &2, E.Error, T>:
678	  match ok:
679	    case True{}:
680	      get_found_at(~T, limit, depth, cap, len, Array.swap(Maybe<&2, T>, arr, U32.from_nat(i), Some{v}))
681	    case False{}:
682	      (DA{limit, depth, cap, len, arr}, Fail{E.IndexOutOfRange{}})
683	
684	def swap_at(~T: Data, da: DynArray<&2, T>, +i: Nat, v: T) -> DynArray<&2, T> & Result<&2, &2, E.Error, T>:
685	  DA{limit, depth, cap, +len, arr} = da
686	  swap_checked_at(~T, limit, depth, cap, len, arr, i, v, Nat.is_lt(i, len))