Guarded Command Language

The Guarded Command Language (GCL) is a language defined by Edsger Dijkstra for predicate transformer semantics cite web | last=Dijkstra | first=Edsger W | authorlink=E. W. Dijkstra | url=http://www.cs.utexas.edu/users/EWD/ewd04xx/EWD472.PDF | title=EWD472: Guarded commands, non-determinacy and formal. derivation of programs. | accessdate=August 16 | accessyear=2006] . The language is strictly theoretical, no compilers exist. It combines programming concepts in a compact way, before the program is written in some practical programming language. Its simplicity makes proving the correctness of programs easier, using Hoare logic.

Guarded command

The guarded command is the most important element of the guarded command language. In a guarded command, just as the name says, the command is "guarded". The guard is a proposition, which must be true before the statement is executed. At the start of that statement's execution, one may assume the guard to be true. Also, if the guard is false, the statement will not be executed. The use of guarded commands makes it easier to prove the program meets the specification. The statement is often another guarded command.

Syntax

A guarded command is a statement of the form G $ightarrow$ S, where
* G is a proposition, called the guard
* S is a statement

If G ≡ true, the guarded command may be written simply S.

Semantics

At the moment G is encountered in a calculation, it is evaluated.
* If G is true, execute S
* If G is false, look at the context to decide what to do (in any case, do not execute S)

kip and Abort

Skip and Abort are very simple as well as important statements in the guarded command language. Abort is the undefined instruction: do anything. The abort statement does not even need to terminate. It is used to describe the program when formulating a proof, in which case the proof usually fails. Skip is the empty instruction: do nothing. It is used in the program itself, when the syntax requires a statement, but the programmer does not want the machine to change states.

yntax

skip

abort

emantics

* Skip: do nothing
* Abort: do anything

Assignment

Assigns values to variables.

yntax

v := Eor v0, v1, ... , vn := E0, E1, ... , En

where
* v are program variables
* E are expressions of the same data type as their corresponding variables

Concatenation

Assignments are separated by one semicolon (;)

Selection: "if"

The selection (often called the "conditional statement" or "if statement") is a list of guarded commands, of which one is chosen to execute. If more than one guard is true, one statement is nondeterministically chosen to be executed. If none of the guards are true, the result is undefined. Because at least one of the guards must be true, the empty statement "skip" is often needed.

yntax

if G0 $ightarrow$ S0 [] G1 $ightarrow$ S1 ... [] Gn $ightarrow$ Sn fi

emantics

Upon execution of a selection all guards are evaluated. If none of the guards evaluates to true then execution of the selection aborts, otherwise one of the guards that has the value true is chosen non-deterministically and the corresponding statement is executed. cite | author=Anne Kaldewaij | title=Programming: The Derivation of Algorithms | publisher=Prentice Hall | date=1990]

Examples

imple

In pseudocode::if a < b then c := True:else c := False

In guarded command language: if a < b $ightarrow$ c := true [] a &ge; b $ightarrow$ c := false fi

Use of Skip

In pseudocode::if error = True then x := 0

In guarded command language: if error = true $ightarrow$ x := 0 [] error = false $ightarrow$ skip fi

If the second guard is omitted and error = False, the result is abort.

More guards true

if a &ge; b $ightarrow$ max := a [] b &ge; a $ightarrow$ max := b fi

If a = b, either a or b is chosen as the new value for the maximum, with equal results. However, someone implementing this, may find that one is easier or faster than the other. Since there is no difference to the programmer, he is free to implement either way.

Repetition: "do"

The repetition executes the guarded commands repeatedly until none of the guards are true. Usually there is only one guard.

yntax

do G0 $ightarrow$ S0 [] G1 $ightarrow$ S1 ... [] Gn $ightarrow$ Sn od

emantics

Upon execution of a repetition all guards are evaluated. If all guards evaluate to false then skip is executed. Otherwise one of the guards that has value true is chosen non-deterministically and the corresponding statement is executed after which the repetition is executed again.

Examples

Original Euclidean algorithm

a, b := A, B; do a < b $ightarrow$ b := b - a [] b < a $ightarrow$ a := a - b od

This repetition ends when a = b, in which case a and b hold the greatest common divisor of A and B.

Extended Euclidean algorithm

a, b, x, y, u, v := A, B, 1, 0, 0, 1; do b &ne; 0 $ightarrow$ q, r := a div b, a mod b; a, b, x, y, u, v := b, r, u, v, x - q*u, y - q*v od

This repetition ends when b = 0, in which case the variables hold the solution to Bézout's identity: xA + yB = gcd(A,B) .

Applications

Asynchronous Circuits

Guarded commands are suitable for Quasi Delay Insensitive circuit design because the repetitionallows arbitrary relative delays for the selection of different commands. In this application,a logic gate driving a node "y" in the circuit consists of two guarded commands, as follows:

PullDownGuard $ightarrow$ y := 0 PullUpGuard $ightarrow$ y := 1

"PullDownGuard" and "PullUpGuard" here are functions of the logic gate's inputs,which describe when the gate pulls the output down or up, respectively. Unlike classicalcircuit evaluation models, the repetition for a set of guarded commands (corresponding to an asynchronous circuit) can accurately describe all possible dynamic behaviors of that circuit.Depending on the model one is willing to live with for the electrical circuit elements,additional restrictions on the guarded commands may be necessary for a guarded-command descriptionto be entirely satisfactory. Common restrictions include stability, non-interference, and absenceof self-invalidating commands.cite web | title=Synthesis of Asynchronous VLSI Circuits|last=Martin | first=Alain J | url=http://resolver.caltech.edu/CaltechCSTR:1991.cs-tr-93-28 ]

Model Checking

Guarded commands are used within the Promela programming language, which is used by the SPIN model checker. SPIN verifies correct operation of concurrent software applications.

Other

The Perl module [http://search.cpan.org/perldoc/Commands::Guarded Commands::Guarded] implements a deterministic, rectifying variant on Dijkstra's guarded commands.

References