General Tips

General small things for writing better specs.

Both TLA+ and PlusCal

Use ASSUME

Every CONSTANT should have an ASSUME to communicate what values are expected of the constant. For model values, it usually suffices to make the ASSUME say it’s not part of a set. To say something is a certain data type, compare it to the empty value of that type. If it’s not that type TLC will crash the ASSUME, which serves the same purpose as it legitimiately failing.

CONSTANT Threads, NULL
ASSUME Threads # {}
ASSUME NULL \notin Threads

From this it’s clear that Threads is a set and NULL is not a thread.

Model tagged unions with structs

TLC can’t have a set of strings and integers. If you need that, you can instead use structs with a type and val field.

{
 [type |-> "int", val |-> 1],
 [type |-> "str", val |-> "1"] \* ok
}

Decompose functions of structs

I often see people encode variables that are functions of structures:

VARIABLE state
WorkerState == [queue: Seq(Msg), online: BOOLEAN]
Types ==
  state \in [Worker -> WorkerState]

\* ...

This more closely matches how we do things in programming languages. It’s harder to work with in TLA+, though, because you can only update a variable once per step. So if you want to both online and queue in one step, you have to do them in the same expression. ie you can’t write

Label:
  state[w].online = FALSE;
  state[w].queue = <<>>;

It’s easier to instead break the variable into two other variables, like this:

VARIABLES worker_queue, worker_online

Types ==
  /\ worker_queue \in [Worker -> Seq(Msg)]
  /\ worker_online \in [Worker -> BOOLEAN]

\* ...

Then you can update worker_queue and worker_online separately.

The downsides of this are 1) when working in pure TLA+, your UNCHANGED statements get a bit more cluttered, and 2) it’s a little further from what your implementation will look like. But the upsides are enough to make it worth it.

In general, I mostly use structures for immutable values, like the bodies of messages.

Separate Safety and Liveness Models

Since liveness properties take a lot longer to check (and can’t use symmetry sets), I use a separate model for just checking liveness properties, which uses smaller constants.

Use the extra space in a module

All modules have to take the form

::

* top area —- MODULE name —- * actual module ==== * bottom area

Everything in the top space and the bottom space is ignored. I like using the bottom area as a “scratch space” and put various TLA+ code there. I use the top area to write more about the problem domain and requirements we’re trying to model, as well as information about the spec itself.

More recently I’ve been experimenting with putting configuration data in the top area, which I then target with scripts. I used that to generate a lot of the spec diffs for this guide.

THEOREM

TLA+ has a THEOREM keyword, which ostensibly declares the properties of the spec:

THEOREM Spec => []TypeInvariant

This doesn’t do anything to the model checker, but it can be useful for documenting the properties of your system.

TypeInvariants and ModelInvariants

We’ve used TypeInvariants a lot already. They’re a good invariant for any system, and it’s good to always cover all of your variables in TypeInvariants. As a principle, I like the TypeInvariant to only cover the possible values of a variable, as opposed to the legitimate values. IE if two sets of numbers have to be disjoint, I’d split that into two invariants:

TypeInvariant ==
  /\ set1 \subseteq Int
  /\ set2 \subseteq Int

SetsAreDisjoint ==
  /\ set1 \intersect set2 = {}

I wouldn’t put SetsAreDisjoint into my TypeInvariant because I see that more as a “correctness” property of the system instead of just a bounds-check.

Model invariants are like TypeInvariants, except that they used to check the state space is finite. For example:

CONSTANTS MinInt, MaxInt
ASSUME {MinInt, MaxInt} \subseteq Int

ModelInt == MinInt .. MaxInt
ModelInvariant ==
  /\ set1 \subseteq ModelInt
  /\ set2 \subseteq ModelInt

Then you can write your spec to satisfy ModelInvariant, or at a state constraint to your model runs.

PlusCal

Use macros

Macros are your main form of statement reuse in PlusCal.

While loops considered harmful

A while loop creates a new state for every loop iteration, adding a lot of concurrency and state-space explosion to your spec. Sometimes this is what you want, when say reading from a queue. But I often see beginners use while loops to do computations, like this:

Double:
  while i <= Len(seq) do
    seq[i] := seq[i] * 2;
    i := i + 1;
  end while;

Instead, reassign the entire sequence in one step:

Double:
  seq := [i \in 1..Len(seq) |-> seq[i] * 2];

State sweeping

Discussed here.

TLA+

Managing UNCHANGED

If you have a lot of variables, Everything must be defined statements get unweildy quickly. Fortunately, you can group variables as sequences and then use UNCHANGED on a sequence of groups.

VARIABLE worker_queue, worker_online
VARIABLE topic_subscribers, topic_id

worker_state == <<worker_queue, worker_online>>
topic_state == <<topic_subscribers, topic_id>>

SomeAction ==
  /\ x' = x + 1
  /\ UNCHANGED <<worker_state, topic_state>>

Helper Actions

It’s okay to split the next-state relations across multiple actions. One thing I do a lot is write a helper to update pc:

Trans(agent, a, b) ==
  /\ pc[agent] = a
  /\ pc' = [pc EXCEPT ![agent] = b]

Then I can write Trans(agent, "state1", "state2") inside another action.

@

In a function update, @ refers to the old value.

\* Verbose
f' = [f EXCEPT ![1][2].a = f[1][2].a + 1]

\* Clean
f' = [f EXCEPT ![1][2].a = @ + 1]

Parameterize your actions

Instead of

Add ==
  \E w \in Worker: s' = s \union {w}

Remove ==
  \E w \in Worker: s' = s \ {w}

Next == Add \/ Remove

Write

Add(w) == s' = s \union {w}
Remove(w) == s' = s \ {w}

Next ==
  \E w \in Worker:
    \/ Add(w)
    \/ Remove(w)

Move the \E to the bottom layer and pass a value into your actions. This is better because it lets you reuse the same value in multiple actions. Say you want to log every worker that’s added or removed. You can’t easily do this in the first version of the spec, but in the second you could write

Log(w) == log' = Append(log, w)

Next ==
  \E w \in Worker:
    /\ \/ Add(w)
       \/ Remove(w)
    /\ Log(w)

Refactor with Action Properties

If we’re simplifying an action, we want to make sure that our simplification doesn’t change it.

OldAction(user) ==
  seq' = seq \o <<user>>

NewAction(user) ==
  seq' = Append(seq, user)

We can check that by adding an action property that checks the two are equivalent:

RefactorProp == [][
  \A u \in User:
    OldAction(user) <=> NewAction(user)
]_vars

If we’re trying to expand an action, then we only care that NewAction does a superset of the things OldAction does. In that case, we can loosen our requirements by using => instead of <=>.