3 files changed, 183 insertions, 0 deletions
diff --git a/formal/tla/README.md b/formal/tla/README.md
new file mode 100644
index 0000000..a80c687
--- /dev/null
+++ b/formal/tla/README.md
@@ -0,0 +1,62 @@
+# TLA+ model check of sleep sort
+
+`SleepSort.tla` is a [TLA+](https://lamport.azurewebsites.net/tla/tla.html)
+model of the concurrent sleep sort in [`sort/sleep.go`](../../sort/sleep.go),
+checked exhaustively by the TLC model checker.
+
+## What this does and does NOT prove
+
+Model checking verifies a **hand-written model**, not the Go source. TLC
+explores *every* reachable state of the model and confirms:
+
+- **`OutputSorted`** (safety) — the collected output is always non-decreasing.
+- **`PermutationWhenDone`** (safety) — the output is a multiset permutation of
+  the input; nothing is dropped, duplicated, or invented.
+- **`Terminates`** (liveness) — the collector eventually receives every value:
+  no deadlock and no value left sleeping forever.
+
+The gap you keep responsibility for: that the model faithfully abstracts
+`sleep.go`. The model represents the sleeps as a discrete clock and the
+unbuffered channel + `WaitGroup` as an urgent single-value rendezvous — see the
+header comment in `SleepSort.tla`.
+
+Sortedness is **not** assumed. It emerges from one rule: time cannot pass while
+a fired-but-unreceived timer waits (`Tick`'s urgency guard). Delete that guard
+and TLC finds an unsorted counterexample — proof the check has teeth.
+
+## Running
+
+Needs Java and `tla2tools.jar` (download once):
+
+```sh
+mkdir -p ~/tools/tlaplus
+curl -fsSL -o ~/tools/tlaplus/tla2tools.jar \
+  https://github.com/tlaplus/tlaplus/releases/latest/download/tla2tools.jar
+```
+
+Then, from the repository root:
+
+```sh
+make verify-model
+```
+
+or directly:
+
+```sh
+java -cp ~/tools/tlaplus/tla2tools.jar tlc2.TLC \
+  -config formal/tla/SleepSort.cfg formal/tla/SleepSort.tla
+```
+
+Expected output ends with:
+
+```
+Model checking completed. No error has been found.
+```
+
+## The input
+
+`SleepSort.cfg` checks the input `<<3, 1, 4, 1, 2>>` (defined as `InputValue`
+in the module, because a `.cfg` cannot hold a sequence literal). It has a
+duplicate and is out of order — enough to exercise ordering, ties, and
+termination. Edit `InputValue` in `SleepSort.tla` to try others; the state space
+stays small because the clock never exceeds the largest input value.
diff --git a/formal/tla/SleepSort.cfg b/formal/tla/SleepSort.cfg
new file mode 100644
index 0000000..6c86d67
--- /dev/null
+++ b/formal/tla/SleepSort.cfg
@@ -0,0 +1,13 @@
+\* TLC configuration for the SleepSort model.
+\* Input is a small multiset with a duplicate (the two 1s) and out-of-order
+\* values -- enough to exercise ordering, ties, and termination exhaustively.
+\* It is defined as InputValue in the module (a .cfg cannot hold a <<..>>).
+CONSTANT Input <- InputValue
+
+SPECIFICATION Spec
+
+INVARIANT TypeOK
+INVARIANT OutputSorted
+INVARIANT PermutationWhenDone
+
+PROPERTY Terminates
diff --git a/formal/tla/SleepSort.tla b/formal/tla/SleepSort.tla
new file mode 100644
index 0000000..45cc0e0
--- /dev/null
+++ b/formal/tla/SleepSort.tla
@@ -0,0 +1,108 @@
+------------------------------ MODULE SleepSort ------------------------------
+(***************************************************************************)
+(* A TLA+ model of the sleep sort in sort/sleep.go.                        *)
+(*                                                                         *)
+(* This verifies a *model*, not the Go source. It abstracts the goroutines *)
+(* + WaitGroup + unbuffered channel of sleep.go into:                      *)
+(*                                                                         *)
+(*   - a global discrete clock (stand-in for wall-clock time / sleeps),    *)
+(*   - one "timer" per input element that fires when the clock reaches     *)
+(*     that element's value (a value-v element sleeps v seconds), and      *)
+(*   - a single collector that receives one fired value at a time          *)
+(*     (an unbuffered channel with one receiver hands off exactly one      *)
+(*     value per rendezvous, with no buffering or reordering).             *)
+(*                                                                         *)
+(* Crucially, sortedness of the output is NOT baked in: it must *emerge*   *)
+(* from the timing mechanism. The only thing that enforces order is Tick's *)
+(* urgency guard (time cannot pass while a fired-but-unreceived timer is    *)
+(* waiting). Remove that guard and TLC finds an unsorted counterexample --  *)
+(* which is exactly what makes this a real check rather than a tautology.   *)
+(***************************************************************************)
+EXTENDS Naturals, Sequences, FiniteSets
+
+CONSTANT Input          \* the values to sort, as a sequence, e.g. <<3, 1, 2>>
+
+\* Concrete value for the model. TLC config files cannot parse a sequence
+\* literal in a "CONSTANT Input = ..." assignment, so SleepSort.cfg overrides the
+\* constant with this operator via "CONSTANT Input <- InputValue".
+InputValue == <<3, 1, 4, 1, 2>>
+
+Idx    == DOMAIN Input
+Values == { Input[i] : i \in Idx }
+
+VARIABLES
+    clock,              \* global time; the sleeps are measured against it
+    sent,               \* sent[i] = TRUE once element i has been received
+    output              \* the values collected so far, in arrival order
+
+vars == <<clock, sent, output>>
+
+\* Multiplicity of value v in a sequence s (compares the two as multisets).
+Count(v, s) == Cardinality({ k \in DOMAIN s : s[k] = v })
+
+TypeOK ==
+    /\ clock \in Nat
+    /\ sent \in [Idx -> BOOLEAN]
+    /\ \A k \in DOMAIN output : output[k] \in Values
+    /\ Len(output) =< Cardinality(Idx)
+
+Init ==
+    /\ clock  = 0
+    /\ sent   = [i \in Idx |-> FALSE]
+    /\ output = << >>
+
+\* Element i's timer has fired (its sleep of Input[i] seconds has elapsed) and
+\* it has not yet been received.
+Ready(i) == /\ ~sent[i]
+            /\ clock >= Input[i]
+
+AllDone == \A i \in Idx : sent[i]
+
+\* The collector receives one ready value (channel rendezvous: exactly one
+\* value transfers, chosen nondeterministically among those currently ready).
+Receive ==
+    /\ \E i \in Idx :
+        /\ Ready(i)
+        /\ sent'   = [sent EXCEPT ![i] = TRUE]
+        /\ output' = Append(output, Input[i])
+    /\ clock' = clock
+
+\* Time advances only when no fired timer is waiting to be received: every
+\* not-yet-received element still has its deadline strictly in the future.
+\* This urgency is what guarantees shorter sleeps deliver before longer ones.
+Tick ==
+    /\ ~AllDone
+    /\ \A i \in Idx : ~sent[i] => clock < Input[i]
+    /\ clock' = clock + 1
+    /\ UNCHANGED <<sent, output>>
+
+\* Once everything has been collected, stutter (models the closed channel /
+\* finished range loop) so termination is not mistaken for a deadlock.
+Done ==
+    /\ AllDone
+    /\ UNCHANGED vars
+
+Next == Receive \/ Tick \/ Done
+
+Spec == Init /\ [][Next]_vars /\ WF_vars(Receive) /\ WF_vars(Tick)
+
+-----------------------------------------------------------------------------
+\* Properties checked by TLC (see SleepSort.cfg).
+
+\* SAFETY: whatever has been collected so far is always non-decreasing.
+IsSorted(s) == \A a, b \in DOMAIN s : a < b => s[a] <= s[b]
+OutputSorted == IsSorted(output)
+
+\* SAFETY: the output never invents or duplicates values, and once finished it
+\* is exactly a permutation (multiset) of the input.
+PermutationWhenDone ==
+    AllDone => \A v \in Values : Count(v, output) = Count(v, Input)
+
+\* LIVENESS: the collector eventually receives every value (no deadlock, no
+\* value left sleeping forever) -- i.e. the algorithm terminates.
+Terminates == <>AllDone
+
+\* Note: the state space is already finite without a constraint -- Tick is
+\* disabled once clock reaches the largest input value, so clock never grows
+\* unbounded and TLC explores every reachable state.
+=============================================================================