What is TLA+ Version 2? [show]
TLA+ Version 2, here called TLA+2 for short, is the current version of TLA+. TLA+ now means TLA+2. The previous version is referred to here as TLA+1. This page contains a brief description of how TLA+2 differs from TLA+1, which is the language described in the book Specifying Systems.
Features for Writing Specifications [show]
Recursive Operator DefinitionsA RECURSIVE statement allows you to define operators recursively, including the use of mutual recursion. For example, here's a silly way to define both fact1(n) and fact2(n) to equal n factorial, for any natural number n:
RECURSIVE fact1(_), fact2(_) fact1(n) == IF n = 0 THEN 1 ELSE n*fact2(n-1) fact2(n) == IF n = 0 THEN 1 ELSE n*fact1(n-1)
LAMBDA ExpressionsTLA+ allows you to define a higher-order operator that takes an operator as an argument. In TLA+1, you could use only the name of an operator that has already been defined or declared as such an argument. TLA+2 allows the use of a LAMBDA expression as the argument. For example, if F is an operator that takes as its argument an operator with two arguments, then you can write the expression
LET Id(a, b) == a + 2*b IN F(Id)In TLA+2, you can write this as
F(LAMBDA a, b : a + 2*b)You can also use a LAMBDA expression to substitute for an operator in the WITH clause of an INSTANCE statement.
Writing Proofs [show]
The major new feature of TLA+2 is the introduction of constructs for writing proofs. A checker for these proofs is being built as part of a project at the Microsoft Research–Inria Joint Centre. It does not yet handle temporal-logic reasoning, but it can check most other parts of a proof.
The language supports hierarchically structured proofs. The paper How to Write a Proof describes the basic hierarchical proof style and explains why it is much better than the way mathematicians and computer scientists now write proofs. The TLA+2 documentation describes the language features for writing structured proofs. The TLAPS project page contains a brief tutorial on writing TLA+ proofs.
Other Changes [show]
Other than introducing a few new keywords that can no longer be used as identifiers, there are two changes in TLA+2 that may make a TLA+ specification no longer legal. The first is the handling of instantiated infix operators. In TLA+1, if you wrote
Foo(x) == INSTANCE Mand module M defines the infix operator ++, then you had to write a weird expression like
a Foo(42)!++ bto use the instantiated operator. In TLA+2, this is written Foo(42)!++(a,b).
The second change is that certain operators can no longer be used to instantiate operator parameters in a constant module. You're unlikely to encounter it. However, if you get an error message of the form
Error in instantiating module '...': A non-Leibniz operator substituted for '...'.then you should read Section 5.2 in the TLA+2 Preliminary Guide for an explanation.
All current documentation written since 2008 describes TLA+2. That include the TLA+ Video Course and the TLA+ Hyperbook. Here is some more detailed documentation: