H γλώσσα CPN ML

1. Δηλώσεις

3

Colour Sets

Unitcolset name = unit [with new_unit];

ex:colset U = unit; >>> 1`()

colset E = unit with e; >>> 1`e

4

Colour Sets

Booleancolset name = bool [with (new_false, new_true)];

ex:colset B = bool; >>> 1`true

colset B2 = bool with (no, yes); >>> 1`yes

Operationsnot, andalso, orelse

5

Colour Sets

Integercolset name = int [with int-exp1..int-exp2];

ex:colset I = int ; >>> 1`36 colset I2 = int with 0..9; >>> 1`7

Operations~(neg), +, -, *, div, mod, abs, Int.min(i1,i2), Int.max(i1,i2)

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Colour SetsStrings

colset name = string [with string-exp1..string-exp2 [and int-exp1..int-exp2] ];

ex:colset lowerstring = string with “a” .. “z” and 1..3;“abc”, “xy” >>> OK “AbC”, “abcd” NOT OK

Operationss1^s2, String.size s, substring(s, i, len), explode s, implode l

(length)

7

Colour SetsEnumerated

colset name = with id0 | id1 | … | idn;

ex:colset dwarfs = Dopey | Doc | Sleepy | Bashful | Happy

| Grumpy | Sneezy;

8

Colour SetsIndex

colset name = index id with int1..int2;

ex:colset STUDENT = index student with 1..11;>>> 1`student(1) .. 1`student(11)

9

Compound Colour SetsProduct

colset name = product name1 * name2 * ... * namen;

ex:colset COUPLES = product MEN * WOMEN;>>> 1`(Bob, Mary)

Operations#i Extract element i of tuple_ Omit element - ex. (Bob,_) - Not allowed in

CPN

10

Compound Colour SetsRecord

colset name = record id1:name1 * id2:name2 * ... * idn:namen;

ex:colset ID = record n:NAME, s:SURNAME, a:AGE;>>> 1`{n=“Bob”, s=“Smith”, a=29}

Operations#idi rec Extract element idi of record rec (ex: #s rec)… Omit element (not allowed in CPN)

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Compound Colour SetsList

colset name = list name0 [with int1..int2];

ex:colset MyList = list INT with 1..3;>>> 1`[3, 8, 54]

OperationsMany; see:http://wiki.daimi.au.dk/cpntools-help/list_colour_sets.wiki

12

Compound Colour SetsUnion

colset name = union id1[:name1] + id2[:name2] + ... + idn[:namen];

ex:colset Digit = int with 0..9;colset MyUnion = union NUM:Digit + NONE;>>> 1`NUM(4) NOT VALID: 1`NUM(13)

1`NONE 1`NONE(a)1`NUM 4 1`NUM

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Compound Colour SetsSubset

colset name = subset name0 by subset-function;

colset name = subset name0 with subset-list;

ex:fun even i = ((i mod 2) = 0);colset evenInt = subset INT by even;

colset int2to4 = subset INT with [2,3,4];

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Compound Colour SetsAlias

colset name = name0;

ex:colset Naturals = POSINT;

15

Variables & Constants

var id1[, id2, …, idn]: name;

val id = exp;

ex:

var x: int;

val maxtries = 5;

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Reference Variables

globref id = exp;

ex:

globref i = 10;

Operations:!a contents of the r.v. a

a:=b assign value b to r.v. a

ref b reference constructor

inc a/dec a in-/decrement value of int r.v. a

17

Functions

fun id pat1 = exp1

id pat2 = exp2

...

id patn = expn;

ex:fun isPos(x) = (x>0);fun diff(x,y) = (x<>y);fun Divide(x,y) = (x div y) Divide(_,0) = error;

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Local Declarations

let

val pat1=exp1

val pat2=exp2

…

val patn=expn

in

exp

end;

letfactor=5;

inmult(num, factor);

end;

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Control Structures

• if boolexp then exp1 else exp2

• case exp ofpat1 => exp1

pat2 => exp2

…

patn => expn;

2. Multisets

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Constructor

It is the ` character. NOT ‘!

Syntax: i`c

ex: 3`true

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Operations

empty constant; empty multiset== equality<><> inequality>> greater than (>>= ..or equal to)<< lesser than (<<= ..or equal to)++ addition-- subtraction** scalar multiplication

23

Operations

size ms sizerandom ms return random colourcf(c, ms) appearances of c in msfilter p ms filter ms by predicate pext_col f ms takes i1`c1++…++in`cn and returns

i1`f(c1)++…++in`f(cn)ext_ms f ms takes i1`c1++…++in`cn and returns

i1*f(c1)++…++in*f(cn)ms_to_col ms returns the element in ms (size

ms=1)

3. Inscriptions

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Place Inscriptions

Name

Colour set

[Initial Marking[@+Delay]]

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Place Inscriptions

Start

INT

1`0 ++ 1`1 ++ 1`21`0++1`1++1`2 3

27

Place Inscriptions

Start

INT

(1`0 ++ 1`1 ++ 1`2)@+31`0@3++1`1@3++1`2@3 3

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Transition Inscriptions

Name

[Guard] [Delay]

[Code]

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Transition Inscriptions

Even

m>0 @+2

input(m)output(n,b)let val even = (m mod 2)=0in (m+1,even)end;

Number Resultm

n

bINT BOOL

3

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Arc Inscriptions

EvenNumber Resultm bINT BOOL

31`3

1

m is bound to 3

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Arc Inscriptions

EvenNumber Resultm bINT BOOL

1`3++1`5

1`3++1`5

2

m is free (3 or 5)

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Arc Inscriptions

EvenNumber Resultm b@+2INT BOOL

1`3++1`5

1`3++1`5

2

Arc delay:Output arc has a delay of 2

33

Arc Inscriptions

EvenNumber Resultm@+2 bINT BOOL

(1`3++1`5)@+6

1`3@6++1`5@6

2

Preemtpying time stamps (on input arcs):“Even” can use tokens from “Number”

at time 4 (before their time stamp would allow)

34

Arc Inscriptions

EvenNumber Resultm if even mthen 1`trueelse 1`false

INT BOOL

1`3++1`5

1`3++1`5

2

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Arc Inscriptions

Arc inscriptions can’t:

• contain I/O or use commands

• Update or use reference variables

• Use the random function

but CPN Tools does not check this!

36

CPN ML Manual

http://wiki.daimi.au.dk/cpntools-help/

cpn_ml.wiki?cmd=get&anchor=CPN+ML

or

http://wiki.daimi.au.dk/cpntools-help

and follow “CPN ML”