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The easy parallel algorithm specification language

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# EzPSL

The easy parallel algorithm specification language.

This is a small, imperative, untyped, pseudocode-like language for describing simple parallel algorithms. The language "compiles" to TLA+ so that it can be exhaustively checked.

## Getting Started

There are no binary distributions. You will need to install the Stack build system and compile this tool from source:

git clone https://github.com/Calvin-L/ezpsl.git
cd ezpsl
stack build
stack test # optional!
cp stack exec -- which ezpsl .


Usage:

./ezpsl FILE


If the file is a .tla file, then the tool looks for a line of the form \* #include FILE.ezs and replaces that line with the compiled TLA+ code. If a compilation was previously done, then the old compilation is replaced with the new one.

If the file is a .ezs file, then the tool prints the compiled TLA+ code on standard out.

You can use the -o OUT option to control where the output gets written, regardless of the input file extension.

For instance, to compile the Test example, run:

./ezpsl examples/Test.ezs


Or, to update the Test TLA+ module, run:

./ezpsl examples/Test.tla


## The Language

Example file:

\* ----------------
\* Global variables

var v1 := 2;
var v2 \in {3, 4};

\* ----------------
\* Procedures

proc helper(x) {
var tmp := x + 1;
return tmp;
}

@entry
proc main() {
v1 := call helper(v2);
}


Comments begin with \* and are completely ignored by the tool.

All global variables must be listed before any procedures, and local variables within a procedure must be declared first, before any statements in the procedure. Variables must be initialized. They can either be initialized with an exact value using := or nondeterministically (as an arbitrary element of a set using \in or as an arbitrary subset of a set using \subseteq).

Procedures may be listed in any order.

Each procedure may have zero or more annotations. Annotations may be listed in any order.

• The @entry annotation indicates that a procedure is an "entry point", where threads may start execution. There must be one or more @entry procedures.
• The @can_restart annotation indicates that a process can crash and restart at any yield or await point, or after terminating. This annotation has no effect unless the procedure is also marked with @entry.

Expressions: a subset of TLA+ including integers and records. Additionally, the special constant self refers to the current thread ID. EzPSL also has a different set-comprehension syntax than TLA+. For example:

• { f[x] : x <- S, x > 0 } - find all positive elements of S and construct a set by applying f to each one.

The TLA+ comprehensions {x \in S : P} and {e : x \in S} are not supported, since they can be expressed using the general set-comprehension primitive.

Statements:

• x := e; - assignment
• pick x \in set : predicate; - nondeterministic choice. You may omit the : predicate part, in which case the predicate defaults to TRUE. If the set is empty or if no element matches the predicate, then the process hangs. You can use \subseteq instead of \in as a shorter way to write pick x \in SUBSET set;.
• if (e) { s } else { s } - if-then-else
• while (e) { s } - looping
• either { s } or { s } - nondeterministic branching
• skip; - no-op
• yield; - pause the current thread and allow others to run
• await e; - wait for a condition to become true. There is an implied yield before each await.
• assert e; - assert that the expression is true
• call p(arg, arg, ...); - call a procedure and ignore its return value
• x := call p(arg, arg, ...); - call a procedure and save its return value. Note that expressions are side-effect free; you can only call other procedures using a call statement.
• return e; - return a value. If the expression is omitted (return;), then a special undefined constant gets returned.

## Details About the TLA+ Output

EzPSL's TLA+ output always requires that your specification EXTENDS the following built-in modules:

• Sequences (for modeling the call stack)
• Integers (for comparing sequence lengths)
• TLC (for constructing maps using the :> and @@ operators, and for the Permutations operator)

The generated TLA+ declares the following constants:

• PROC_calls for each @entry procedure, where PROC is the procedure name. During model checking, each of these should be a set of model values used as process IDs.
• _Undefined, a special token that is used for a number of purposes. During model checking, it should be set to a unique model value.

The generated TLA+ declares the following variables:

• One variable for each global var in the code, with the exact same names
• A number of internal variables whose names begin with underscores:
• _pc (a stack of program counter values for each process)
• _frames (a stack of "call frames" for each process, containing local variables)
• _globalsScratch (the actor's scratch space for globals between yield points)
• _ret (the most recently returned value for each process)
• _actor (the thread that is currently acting, or _Undefined if any thread may act)

The generated TLA+ declares the following operators:

• Init (the initial state predicate)
• Next (the next action predicate)
• symmetry (a symmetry set consisting of all process IDs)
• vars (a tuple of all declared variables, including internal variables)
• NoAssertionFailures (an invariant stating that no process fails an assert)
• Any number of helper operators whose names are prefixed with underscores.

NOTE: The generated TLA+ system uses one step per statement, meaning that a logically atomic block of code goes through multiple TLA+ states. However, the global variables only change when a process yields or terminates. Between yield points, processes use a private snapshot of the global variables and all changes are applied simultaneously when the process yields or terminates.

If you are curious for more details about the TLA+ output, look through the compiled TLA+ output in the examples folder.

## Specifying Correctness Properties

### No Assertion Failures

The compiled TLA+ code always contains an invariant definition named NoAssertionFailures asserting that no process has failed an assert statement. You can tell TLC to check NoAssertionFailures as an invariant to find assertion failures.

### Global Invariants

To write a global invariant, place the invariant's definition after the compiled output. Even if a process makes multiple changes to the global variables between yield points, the global variables are only modified when the process yields. Therefore, your invariant will never "see" intermediate states between yield points.

### Refinement

Refinement works the same way as global invariants. See examples/Refinement.tla for an example.

EzPSL generates TLA+ that supports deadlock checking. Deadlock checking is enabled by default in TLC.

## Comparison to PlusCal

EzPSL is similar to PlusCal, another simple imperative language that can be compiled to TLA+ for model checking.

There are a few ways in which EzPSL is better than PlusCal:

• EzPSL allows larger atomic blocks. PlusCal programs use labels to delimit atomic blocks, while EzPSL programs use yield statements. However, PlusCal requires labels in many places, while EzPSL allows any number of statements---including nonterminating loops---between yield statements. This can lead to shorter model checking times.
• EzPSL allows return values from procedures. While PlusCal can model return values, it is awkward to do so. EzPSL includes them as a first-class primitive. This can make some programs shorter and easier to read.

There are also ways in which PlusCal is better than EzPSL:

• EzPSL produces longer error traces. To support larger atomic blocks, EzPSL produces longer error traces than PlusCal when model checking finds a violation. Sometimes this is an advantage; the longer error traces include more information about what the program did. However, usually this is a disadvantage; the longer error traces take more time to understand.
• EzPSL is not built into the TLA+ toolbox. To use EzPSL you will need to use this command-line tool, which can be awkward and is likely to slow down your workflow.
• EzPSL has no way to specify fairness. As a result, EzPSL is not suitable for specifying or checking liveness properties. PlusCal supports fairness annotations on processes.

The easy parallel algorithm specification language

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