------------------------------ 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.
=============================================================================