Macro COSY Notation

To shorten some otherwise lengthy expressions in the following rules, we adopt the convention:

Syntax of General COSY Macro Notation

Context-Sensitive Restrictions:

Crest1:

If the upperbound and lowerbound of dimensions of the collective names are integers then the upperbound has to be greater than or equal to their corresponding implicit or explicit lowerbound.

Crest2:

An array identifier may occur only once in collectivisors.

Crest3:

Each replicator without range variables must specify a non-empty range for its index.

Irest1:

Identifiers for replicator indices and range variables should be distinct from any identifiers used for simple events. Identifiers for replicator indices and range variables should also be distinct.

Irest2:

Replicator index variables are only defined inside the [ ] of the replicators with which they are associated. In the scope of a replicator index variable no other replicator index variable having the same name is permitted.

BRrest:

The range of the bodyreplicator indices should be non-empty.

Rrest1.1:

For every replicator if inc is an integer then .

Rrest1.2:

For every concatenator and bodyreplicator if in, fi, inc are integers then .

Rrest1.3:

For every imbricator, if in, fi, inc are integers then .

Rrest2:

The replicators should generate indexed events permitted by the corresponding collectivisors.

Drest1:

For every distributor , msequence must contain at least one slice event.

Drest2.1:

If both range and dim are blank then the number of sections generated by the rightmost distributable (current) dimension must be the same for all slice events occurring in msequence.

Drest2.2:

If range is blank, dim=j and j is an integer, then the number of sections generated by jth dimension must be the same for all slice events occurring in msequence and having the jth dimension distributable.

Drest3:

Inside a k-nested distributor there must be at least one slice event with k distributable dimensions, and no array slices with more than k distributable dimensions.

Drest4:

If dim=j then every slice event with maximal number of distributable dimensions must have the jth dimension as a distributable dimension.

Drest5.1:

If , dim is blank and , , are integers, then , and must be smaller than or equal to the number of sections generated by the rightmost distributable (current) dimension of any slice event occurring in msequence.

Drest5.2:

If , , , dim=j and , , , j are integers, then , and must be smaller than or equal to the number of sections generated by the jth dimension of any slice event occurring in msequence which has the jth dimension distributable.