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Records in TLA+ are special kinds of functions that have the following properties:

  • The domain of a record contains only strings.
  • The domain of a record is finite.

That is it in pure TLA+. Essentially, TLA+ is following the duck-typing principle for records: Any function over strings can be also treated as a record, and vice versa, a record is also a function. So you can use all function operators on records too.

Construction. TLA+ provides you with a convenient syntax for constructing records. For instance, the following example shows how to construct a record that has two fields: Field "a" is assigned value 2, and field "b" is assigned value TRUE.

  [ a |-> 2, b |-> TRUE ]

Similar to the function set [S -> T], there is a record set constructor:

  [ name: { "Alice", "Bob" }, year_of_birth: 1900..2000 ]

The expression in the above example constructs a set of records that have: the name field set to either "Alice" or "Bob", and the year_of_birth field set to an integer from 1900 to 2000.

Application. TLA+ provides you with a shorthand operator for accessing a record field by following C-style struct-member notation. For example:


This is essentially syntax sugar for r["myField"].

Immutability. As records are special kinds of functions, records are immutable.

Types. In contrast to pure TLA+ and TLC, the Apalache model checker distinguishes between general functions and records. When Apalache processes a record constructor, it assigns the record type to the result. This record type carries the information about the names of the record fields and their types. Similarly, Apalache assigns the type of a set of records, when it processes a record set constructor. See the Apalache ADR002 on types.

Owing to the type information, records are translated into SMT more efficiently by Apalache than the general functions.

Every record is assigned a type in Apalache. For instance, the record [name |-> "A", a |-> 3] has the type { name: Str, a: Int }. In contrast to TLC, the type checker statically flags an error, if a spec is trying to access a non-existent field. Consider the following example:

--------------------------- MODULE TestUnsafeRecord ---------------------------
\* the record in R has the type { name: Str, a: Int}
R == [name |-> "A", a |-> 3]

\* the type checker will report a type error in UnsafeAccess
UnsafeAccess == R.b

If we run the type checker, it will immediately find unsafe record access:

$ apalache-mc typecheck TestUnsafeRecord.tla
[TestUnsafeRecord.tla:6:17-6:19]: Cannot apply R() to the argument "b" in R()["b"]

Sometimes, record types can get tricky, when operators in a spec only have partial type information. For example, consider operator GetX:

----------------------------- MODULE TestGetX ---------------------------------
GetX(r) == r.x

If we run the type checker, it will complain about not being able to infer the type of r:

$ apalache-mc typecheck TestGetX.tla
[TestGetX.tla:2:12-2:14]: Cannot apply r to the argument "x" in r["x"].

The reason is simple: The type checker could not decide, whether r was a record or a function. Even if we knew that r was a record, what type should it have? Luckily, the Apalache type checker supports Row polymorphism. Hence, we can specify the type of r as follows:

--------------------- MODULE TestGetXWithRows ---------------------------------
\* @type: { x: a, b } => a;
GetX(r) == r.x

In the type annotation, we are saying that r is a record that has the field x of some type a (which we don't know), and the rest of the record does not matter. This matches our intuition about the behavior of GetX. This time the type checker does not complain:

$ apalache-mc typecheck TestGetXWithRows.tla
Type checker [OK]

In untyped TLA+, it is common to mix records of different shapes into sets. For instance, see how the variable msgs is updated in Paxos. It is not possible to do so with records in Apalache. To address this pattern, Apalache supports Variants.


In the Python examples, we are using the package frozendict, to produce an immutable dictionary.

Record constructor

Notation: [ field_1 |-> e_1, ..., field_n |-> e_n]

LaTeX notation: rec-ctor

Arguments: An even number of arguments: field names and field values, interleaved. At least one field is expected. Note that field names are TLA+ identifiers, not strings.

Apalache type: (a_1, ..., a_n) => { field_1: a_1, ..., field_n: a_n }, for some types a_1, ..., a_n.

Effect: The record constructor returns a function r that is constructed as follows:

  • set DOMAIN r to { field_1, ..., field_n },
  • set r[field_i] to the value of e_i for i \in 1..n.

Determinism: Deterministic.

Errors: No errors.

Example in TLA+:

  [ name |-> "Printer", port |-> 631 ]
    \* A record that has two fields:
    \* field "name" that is equal to "Printer", and field "port" that is equal to 631.

Example in Python:

>>> { "name": "Printer", "port": 631 }
{'name': 'Printer', 'port': 631}

Record set constructor

Notation: [ field_1: S_1, ..., field_n: S_n]

LaTeX notation: recset-ctor

Arguments: An even number of arguments: field names and field values, interleaved. At least one field is expected. Note that field names are TLA+ identifiers, not strings.

Apalache type: (Set(a_1), ..., Set(a_n)) => Set({ field_1: a_1, ..., field_n: a_n }), for some types a_1, ..., a_n.

Effect: The record set constructor [ field_1: S_1, ..., field_n: S_n] is syntax sugar for the set comprehension:

{ [ field_1 |-> e_1, ..., field_n |-> e_n]: e_1 \in S_1, ..., e_n \in S_n }

Determinism: Deterministic.

Errors: The arguments S_1, ..., S_n must be sets. If they are not sets, the result is undefined in pure TLA+. TLC raises a model checking error. Apalache flags a static type error.

TLC raises a model checking error, whenever one of the sets S_1, ..., S_n is infinite. Apalache can handle infinite records sets in some cases, when one record is picked with \E r \in [ field_1: S_1, ..., field_n: S_n].

Example in TLA+:

  [ name: { "A", "B", "C" }, port: 1..65535 ]
    \* A set of records. Each has two fields:
    \* field "name" that has the value from the set { "A", "B", "C" }, and
    \* field "port" that has the value from the set 1..65535.

Example in Python: TLA+ functions are immutable, so we are using frozendict:

  frozenset({ frozendict({ "name": n, "port": p })
                for n in { "A", "B", "C" } for p in range(1, 65535 + 1) })

Access by field name

Notation: r.field_i

LaTeX notation: r.field_i

Arguments: Two arguments: a record and a field name (as an identifier).

Apalache type: { field_i: a, b } => b, for some types a and b (technically, b is a row that captures the other fields).

Note that r.field_i is just a syntax sugar for r["field_i"] in TLA+. Hence, if the Apalache type checker cannot choose between r being a record or a function, the type checker fails with a type error. In this case, you have to type-annotate the definition that contains r.

Effect: As records are also functions, this operator works as r["field_i"].

Apalache treats records as values of a record type. In comparison to the general function application r["field"], the operator r.field is handled much more efficiently in Apalache. Due to the use of types, Apalache can extract the respective field when translating the access expression into SMT.

Determinism: Deterministic.

Example in TLA+:

  LET r == [ name |-> "Printer", port |-> 631 ] IN    \* "Printer"

Example in Python:

>>> r = { "name": "Printer", "port": 631 }
>>> r["name"]