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