selt - SE-MMC model checkerPart of Tina Toolbox for analysis of Petri nets and Time Petri nets.

Synopsis

Description

Options

Muse Se-mmc Language And Commands

Examples

See Also

Authors

muse[-help]

musektzfile [-f formula | formfile] [-prelude mmcfile]

[-q | -v] [-b | -c | -s] [-wp n]

[outfile] [errorfile]

muse model-checks state-event modal mu-calculus (MMC) formulas on a kripke transition system given in ktz format.

If some formula is specified (by flag -f or by providing formfile), then the result of evaluation of the formula is printed according to the output mode and verbosity flags, and muse exits.

If no formula file is specified, then muse starts an interactive session, evaluating commands entered by the user on standard input (see "muse se-mmc language and commands" below).

- help Recalls options.

Ktz input:

ktzfile The kripke transition system on which formula are model-checked, in ktz format (extension .ktz).

-wp (0|1|2) This flag removes (0), preserves (1), or forces at each state (2) the temporal divergence property possibly present in the kts file (see tina’s -wp flag for details).

MMC input:

-f formula Passes to muse the formula to be verified.

formfile Specifies a file holding the formulas to be verified. Must have extension .mmc

-prelude mmcfile Specifies a file containing muse commands to be evaluated on entry, before any formula provided by -f, by formfile, or interactively. This flag is useful to load SE-MMC libraries. mmcfile must have extension .mmc.

Verbosity level:

-v prints banner and evaluation times for MMC commands (default).

-q No banner nor times are printed. This flag is useful for batch operation.

Output mode flags:

-b When evaluating a state (resp. event) formula, prints its truth value for state (resp. transition) numbered 0.

-c When evaluating a state (resp. event) formula, prints the number of states (resp. transitions) satisfying the formula.

-s When evaluating a state (resp. event) formula, prints the set of states (resp. transitions) satisfying the formula. States (resp. transitions) are numberred in their order of occurrence in the ktz file.

Other flags:

-S scnfile When a formula evaluates to FALSE, writes a counter example in .scn format of in file scnfile (creating the file if it does not exist, and overwriting it otherwise). This flag is useful to replay counter examples in the nd stepper when modelchecking an existing ktz description and a description of the net the .ktz file describes the behavior of is available (see "interacting with the nd stepper" below).

Output destination:

outfile Where results are written.

Errors destination:

errorfile Where error messages are written. By default, errors are printed on standard error.

- A identifier is either:

Any place or transition identifier allowed in .net or .ndr descriptions, that is: any sequence of letters, digits, underscores "_" and primes "’", or any sequence of characters enclosed in braces in which "{", "}" (except the outer ones) and "\" are prefixed by "\"

Any sequence of symbols from the list ~ ‘ ! @ # $ % ^ & * - + = : ? | / < > [ ];

A qualified identifier: an identifier prefixed by S., E. or L.

e.g. hello, _p4’_, 123, >=<, or {variable x45}, are legal identifiers.

- The commands are: op, infix, prefix, forget, verb, output, source, quit, assert. Command names may not be used as operator or variable names.

- When analyzing identifiers, the scanner advances as right as possible. So, in a juxtaposition of identifiers, two symbolic or two alphanumeric unbraced identifiers, or e.g. an alphanumeric identifier and a command name, must be separated by a space. But no space is necessary between identifiers of different kinds or between a parenthesis (or ";") and an identifier.

- justaposition bind tighter than infixes and associate to the left, infixes and prefixes associate to the right. That is, if f is a 3-ary operator in functional notation, A, B, -, are prefixes, and /\, \/, are infixes:

A p1 => B - p3 /\ f u v w parses as (A p1) => ((B (- p3)) /\ (f u v wp)) f - B p1 (f p0 p1 (p4 /\ p5)) \/ f u v w parses as (f (- B p1) (f p0 p1 (p4 /\ p5))) \/ (f u v w)and f - B p1 f p0 p1 p4 \/ f u v w parses as (f (- B p1) f p0 p1 p4) \/ (f u v w) which is ill-typed

- infixes have precedence in 0..5 (see below). Infixes with higher precedence bind tighter than those with lower precedence.

It is made up of (pushed in that order):

- The atomic state and event propositions. They have the names captured in the .ktz file, i.e. those of the places and transitions of the Petri net if the .ktz file was generated by tina.

- Then, the logic and arithmetic primitives, constituted of:

constants: T (true), F (false), div (temporal divergence property), sub (partially defined state or transition)prefixes: - (logic negation), ~ (arithmetic negation), operators <f>_ and [f]_, for each formula f modal operators <f> and [f], ‘ (followed by an integer, designating a state or transition by its rank in the ktz input file), the MEC4 primitives src, tgt, rsrc, rtgt

infixes: => (implies), <=> (equivalent), of precedence 1 /\ (and), \/ (or), of precedence 2 <=, >=, =, le, lt, ge, gt, of precedence 3 +, of precedence 4 *, of precedence 5

- Then the user defined operators.Since the syntactic classes of atomic state propositions, atomic event propositions, logic primitives, integer, and user defined operators, overlap, we must have some way of disambiguating identifiers. For this:

- unqualified identifiers are bound to the command with than name, if any, or otherwise to the last pushed environment entry with that name.

- identifiers qualified by S (e.g. S.p1) are bound to the atomic state proposition with that name with the qualifier removed (e.g. p1);

- identifiers qualified by E (e.g. E.t1) are bound to the atomic event proposition with that name with the qualifier removed (e.g. t1);

- identifiers qualified by L (e.g. L./\) are bound to the logic primitive with that name with the qualifier removed (e.g. /\);

So, atomic propositions (found in the ktz file) sharing their name with some atomic propositions in a different group (state or event) or with some command (e.g. op), or some logical primitive (e.g. -), or the name of which is an integer (e.g. 3), must be referred to in formulas by their qualified form (e.g. S.op, E.-, or S.3);

The modalities of the mu-calculus are derived from the MEC4 primitives, as follows. They benefit however of a specific concrete syntax:

<p>q stands for src (p /\ rtgt q)

[p]q stands for -<p>(-q)Modal mu-calculus makes use of fixpoint expressions:

- Minimal fixpoint expressions make use of keywords "min" or "mu", followed by the bound variable and a bar separating the variable from the body of the expression, as in "min x | p <q>x".

- Maximal fixpoints makes use of keywords "max" or "nu".

Note: muse does not perform yet any polarity checks on fixpoint expressions, this check is left to the user’s responsability. Hence termination of evaluation is not guaranteed (ill-formed expressions may diverge).

(more derived notations to come)

Identifiers declared infix (binary logic primitives or user defined operators declared by "infix") must be used in infix notation;

Identifiers declared prefix (unary logic primitives or user defined operators declared by "prefix") must be used in prefix notation (in a juxtaposition of identifiers, prefix operators associate with the right expression);

Other operators or primitives accessed by their qualified names must be used in functional notation. E.g. if a1, a2, a3 are parenthesized expressions, and f has arity 3, then:

a1 /\ a2 and L./\ a1 a2 are legal (and equivalent) but a1 L./\ a2 is ill-typedf - a1 a2 a3 is legal (parses as ((f (- a1)) a2) a3) but f L.- a1 a2 a3 T is ill-typed (parses as (((f L.-) a1) a2) a3)

Commands must terminate with ";". In formula files, the final ";" may be omitted (EOF plays that role). The effects of commands are as follows ("exp" is any ltl expression, x, y, f, xi are identifiers):

exp; evaluates MMC expression exp; The result of evaluation of the last expression is always bound to identifier "it";assert exp "whentrue" "whenfalse"; in bool output mode, evaluates exp then prints string whentrue (resp. whenfalse) if exp holds (resp. does not) instead of the default message TRUE (resp. FALSE). Equivalent to exp in other modes.

op f x1 ... xn = exp; declares an operator f or arity n (n >= 0), to be used in functional notation;

infix [n] x f y = exp; declares a binary operator f in infix notation. n is an optional integer in 0..5 specifying precedence.

prefix f x = exp; declares a unary operator f in prefix notation;

forget f1 ... fn; Removed items names f1 ... fn from the environment, and their fixity information;

source [file | "file"]; reads at toplevel the contents of file. The file name is optionally surrounded by string quotes (this is necessary if the name includes spaces);

verb [true | false | debug]; verbosity level. Tne initial setting follows from the command line flags -v | -q (default -v);

true (default): prints the banner, prompts, results of commands, and evaluation times;

false: just prints the results of evaluation of LTL expressions (useful in batch mode);

debug: may print extra information (mainly for developper);

output [bool | card | set]; specify effects and results of evaluations of MMC expressions. The command line flags -b, -c, -s, specifie the initial setting (default -c);

If the expression evaluated is a state (resp. transition) expression:

bool: evaluation returns the truth value (TRUE or FALSE) of the expression at state 0 (resp. transition 0);

card (default): evaluation returns the number of states (resp. transitions) satisfying the expression;

set: evaluation returns the set of states (resp. transitions) satisfying the expression;

which exp; Like exp; but overrides the default output option by "set";

card exp; Like exp; but overrides the default output option by "card";

quit leaves selt (also ^D on Unix targets).

p1; (eqv. p1 lt 0 p gt 0) - p1; (eqv. p1 = 0) p1 /\ p2 >= 2; (eqv. p1 /\ (p2 >= 2)) op x > y = x >= y + 1; (declares arithmetic operator >, in infix form) p1+p2; (eqv. p1+p2 >= 0, eqv. p1 \/ p2) p1+p2 > p3; p1*p2 = 0; infix y follows x = [] (x => <>y); (declares logical operator "follows:, in infix form) (t3 \/ p5) follows (t1 /\ p1>=p2); (eqv. [] ((t1 /\ (p1>=p2)) => <> (t3 \/ p5)));

muse abp.ktz -b -f "[] (t1 => <> t3)" -q -b muse abp.ktz

nd(n), tina(n), sift(n), tedd(n), plan(n), struct(n), ktzio(n), ndrio(n), selt(n), pathto(n), play(n), formats(n)

Bernard Berthomieu LAAS/CNRS, 2000-2012, Bernard.Berthomieu@laas.fr

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