1	# Retry policy: a shared attempt budget, an operation deadline, bounded backoff, and a circuit breaker.
2	# All times are ms on one monotonic clock. The caller reads the clock; these defs are pure.
3	import Base
4	
5	# left: attempts the whole operation may still start, the first one included. Nested layers share one Budget.
6	# deadline: no attempt starts at or after this time. None: no deadline.
7	type Budget is Data:
8	  Budget{left: Nat, deadline: Maybe<&2, Nat>}
9	
10	type Deny is Data:
11	  DenyLate{}
12	  DenySpent{}
13	  DenyOpen{}
14	
15	type Gate is Data:
16	  GateGo{}
17	  GateNo{why: Deny}
18	
19	# threshold: failures in a row, each inside window ms of the newest, that open the circuit. cooldown: ms it stays open.
20	# probes: attempts allowed at once while half-open.
21	type Circuit is Data:
22	  Circuit{threshold: Nat, window: Nat, cooldown: Nat, probes: Nat}
23	
24	# Closed: the failures since the last success that are still inside the window, newest first.
25	# Open: no attempt before until. Half: probes in flight.
26	type State is Data:
27	  CircuitClosed{fails: List<&2, Nat>}
28	  CircuitOpen{until: Nat}
29	  CircuitHalf{busy: Nat}
30	
31	type Breaker is Data:
32	  BreakerOff{}
33	  BreakerOn{circuit: Circuit, state: State}
34	
35	# Settled: a success. Failed: a failure that another try would repeat. Rejected: the caller is at fault (such as
36	# a 4xx), so another try would repeat it, and it is not the target's failure. Unsafe: a transient failure of a
37	# request that must not repeat. Transient: another try can help; after is the server's wait in ms.
38	type Outcome is Data:
39	  Settled{}
40	  Failed{}
41	  Rejected{}
42	  Unsafe{}
43	  Transient{after: Maybe<&2, Nat>}
44	
45	# attempts: tries in one layer, the first one included. base: the first backoff in ms. cap: the longest wait in ms.
46	# deadline: ms from the start of the operation to its deadline. None: no deadline.
47	type Policy is Data:
48	  Policy{attempts: Nat, base: Nat, cap: U32, deadline: Maybe<&2, Nat>}
49	
50	type Plan is Data:
51	  PlanStop{}
52	  PlanWait{ms: Nat}
53	
54	# ---- budget
55	
56	def Budget.new(+attempts: Nat, +now: Nat, ms: Maybe<&2, Nat>) -> Budget:
57	  match ms:
58	    case None{}:
59	      Budget{attempts, None{}}
60	    case Some{m}:
61	      Budget{attempts, Some{Nat.add(now, m)}}
62	
63	def Budget.late(+now: Nat, d: Maybe<&2, Nat>) -> Bool:
64	  match d:
65	    case None{}:
66	      False{}
67	    case Some{t}:
68	      Nat.is_le(t, now)
69	
70	# ---- circuit
71	
72	# The failure times still inside the window: now < t + window. Newest first, so the first old time ends the list.
73	def prune(+now: Nat, +window: Nat, fs: List<&2, Nat>) -> List<&2, Nat>:
74	  match fs:
75	    case Nil{}:
76	      Nil{}
77	    case Con{+t, rest}:
78	      Bool.pick(List<&2, Nat>, Nat.is_lt(now, Nat.add(t, window)), Con{t, prune(now, window, rest)}, Nil{})
79	
80	def Circuit.probes(c: Circuit) -> Nat:
81	  Circuit{t, w, cd, p} = c
82	  p
83	
84	def Circuit.cooldown(c: Circuit) -> Nat:
85	  Circuit{t, w, cd, p} = c
86	  cd
87	
88	def half.admit(go: Bool, +k: Nat) -> State & Bool:
89	  match go:
90	    case True{}:
91	      (CircuitHalf{1n+k}, True{})
92	    case False{}:
93	      (CircuitHalf{k}, False{})
94	
95	def open.admit(early: Bool, +p: Nat, +u: Nat) -> State & Bool:
96	  match early:
97	    case True{}:
98	      (CircuitOpen{u}, False{})
99	    case False{}:
100	      half.admit(Nat.is_lt(0n, p), 0n)
101	
102	# Closed admits. Open admits nothing before until; at or after until it turns half-open and admits a probe.
103	# Half-open admits while fewer than probes are in flight.
104	def State.admit(+c: Circuit, s: State, +now: Nat) -> State & Bool:
105	  match s:
106	    case CircuitClosed{fs}:
107	      (CircuitClosed{fs}, True{})
108	    case CircuitOpen{+u}:
109	      open.admit(Nat.is_lt(now, u), Circuit.probes(c), u)
110	    case CircuitHalf{+k}:
111	      half.admit(Nat.is_lt(k, Circuit.probes(c)), k)
112	
113	def closed.trip(under: Bool, fs: List<&2, Nat>, +until: Nat) -> State:
114	  match under:
115	    case True{}:
116	      CircuitClosed{fs}
117	    case False{}:
118	      CircuitOpen{until}
119	
120	def closed.fail(+c: Circuit, fs: List<&2, Nat>, +now: Nat) -> State:
121	  Circuit{+t, +w, +cd, p} = c
122	  +kept = {Con{now, prune(now, w, fs)} : List<&2, Nat>}
123	  closed.trip(Nat.is_lt(List.length(&2, Nat, kept), t), kept, Nat.add(now, cd))
124	
125	# A closed success clears the failures. A closed failure opens the circuit when the window then holds threshold
126	# failures. A half-open success closes it; a half-open failure opens it again for cooldown. An attempt that ends
127	# while open changes nothing.
128	def State.done(+c: Circuit, s: State, +now: Nat, failed: Bool) -> State:
129	  match s:
130	    case CircuitClosed{fs}:
131	      match failed:
132	        case False{}:
133	          CircuitClosed{Nil{}}
134	        case True{}:
135	          closed.fail(c, fs, now)
136	    case CircuitOpen{u}:
137	      CircuitOpen{u}
138	    case CircuitHalf{k}:
139	      match failed:
140	        case False{}:
141	          CircuitClosed{Nil{}}
142	        case True{}:
143	          CircuitOpen{Nat.add(now, Circuit.cooldown(c))}
144	
145	def Breaker.new(c: Circuit) -> Breaker:
146	  BreakerOn{c, CircuitClosed{Nil{}}}
147	
148	def Breaker.on(+c: Circuit, x: State & Bool) -> Breaker & Bool:
149	  (s, ok) = x
150	  (BreakerOn{c, s}, ok)
151	
152	def Breaker.admit(br: Breaker, +now: Nat) -> Breaker & Bool:
153	  match br:
154	    case BreakerOff{}:
155	      (BreakerOff{}, True{})
156	    case BreakerOn{+c, s}:
157	      Breaker.on(c, State.admit(c, s, now))
158	
159	def Breaker.done(br: Breaker, +now: Nat, failed: Bool) -> Breaker:
160	  match br:
161	    case BreakerOff{}:
162	      BreakerOff{}
163	    case BreakerOn{+c, s}:
164	      BreakerOn{c, State.done(c, s, now, failed)}
165	
166	# ---- admission
167	
168	def admit.ok(ok: Bool, br: Breaker, +p: Nat, d: Maybe<&2, Nat>) -> Breaker & Budget & Gate:
169	  match ok:
170	    case True{}:
171	      (br, Budget{p, d}, GateGo{})
172	    case False{}:
173	      (br, Budget{1n+p, d}, GateNo{DenyOpen{}})
174	
175	def admit.breaker(x: Breaker & Bool, +p: Nat, d: Maybe<&2, Nat>) -> Breaker & Budget & Gate:
176	  (br, ok) = x
177	  admit.ok(ok, br, p, d)
178	
179	def admit.late(late: Bool, br: Breaker, left: Nat, d: Maybe<&2, Nat>, +now: Nat) -> Breaker & Budget & Gate:
180	  match late:
181	    case True{}:
182	      (br, Budget{left, d}, GateNo{DenyLate{}})
183	    case False{}:
184	      match left:
185	        case 0n:
186	          (br, Budget{0n, d}, GateNo{DenySpent{}})
187	        case 1n+p:
188	          admit.breaker(Breaker.admit(br, now), p, d)
189	
190	# Ask to start one attempt at now. The deadline is checked first, then the budget, then the breaker.
191	# Only GateGo takes one attempt from the budget.
192	def admit(br: Breaker, b: Budget, +now: Nat) -> Breaker & Budget & Gate:
193	  Budget{left, +d} = b
194	  admit.late(Budget.late(now, d), br, left, d, now)
195	
196	# ---- backoff
197	
198	# min(cap, base * 2^n), doubled one step at a time, so no step passes cap.
199	def delay(n: Nat, +base: Nat, +cap: Nat) -> Nat:
200	  match n:
201	    case 0n:
202	      Nat.min(base, cap)
203	    case 1n+p:
204	      +d = delay(p, base, cap)
205	      Nat.min(Nat.add(d, d), cap)
206	
207	# Equal jitter: d / 2, plus r mod (d / 2 + 1). The wait is in [d / 2, d] for every r.
208	def jitter(+d: Nat, +r: Nat) -> Nat:
209	  +h = Nat.div(d, 2n)
210	  Nat.add(h, Nat.mod(r, 1n+h))
211	
212	# The wait before retry n (0 first): the server's wait when it gave one, else the jittered backoff. At most cap.
213	def wait(after: Maybe<&2, Nat>, p: Policy, +n: Nat, +r: Nat) -> Nat:
214	  match after:
215	    case None{}:
216	      Policy{a, +base, +cap, d} = p
217	      jitter(delay(n, base, U32.to_nat(cap)), r)
218	    case Some{+ms}:
219	      Policy{a, base, +cap, d} = p
220	      Nat.min(ms, U32.to_nat(cap))
221	
222	def plan.left(left: Nat, +w: Nat, d: Maybe<&2, Nat>, +now: Nat) -> Plan:
223	  match left:
224	    case 0n:
225	      PlanStop{}
226	    case 1n+k:
227	      Bool.pick(Plan, Budget.late(Nat.add(now, w), d), PlanStop{}, PlanWait{w})
228	
229	def plan.at(+w: Nat, b: Budget, +now: Nat) -> Plan:
230	  Budget{left, d} = b
231	  plan.left(left, w, d, now)
232	
233	# After an attempt ends at now: stop, or wait ms and then ask admit again. Settled, Failed, Rejected, and Unsafe always stop.
234	# A transient outcome stops when the budget is spent or the wait would reach the deadline.
235	def plan(o: Outcome, p: Policy, b: Budget, +n: Nat, +now: Nat, +r: Nat) -> Plan:
236	  match o:
237	    case Settled{}:
238	      PlanStop{}
239	    case Failed{}:
240	      PlanStop{}
241	    case Rejected{}:
242	      PlanStop{}
243	    case Unsafe{}:
244	      PlanStop{}
245	    case Transient{after}:
246	      plan.at(wait(after, p, n, r), b, now)
247	
248	# Failed, Unsafe, and Transient count as failures for the breaker. Settled and Rejected do not.
249	def failed(o: Outcome) -> Bool:
250	  match o:
251	    case Settled{}:
252	      False{}
253	    case Failed{}:
254	      True{}
255	    case Rejected{}:
256	      False{}
257	    case Unsafe{}:
258	      True{}
259	    case Transient{after}:
260	      True{}