Input Area | Output Area | Remarks | Notations |

Input: A dstributed systems consisting of a list of classifications, a list of informorphisms, and a list of constraints.

Output: A universal cover (= core) of the input distributed system.

Remark(1): The cover computed by this cgi is not exactly universal; the intermediate arrow to other covers always does exist but not necessarily unique. However this is not a problem in theory and practice.

Remark(2): 'Atoms' of each classfication are represented by 'sequents' of types due to adjointness of informorphism. Thanks to this fact, the token maps are replaced with that on these atoms, which has made also the algorithm much simpler.

` `` cla([x,y],[a],[a-[x,y]]),cla([x,y],[a],[a-[x,y]]) `

means a classification whose token set iswhich reads`[x,y]`

, type set is`[a]`

, with support relation`[a-[x,y]]`

x supports a, and y supports a.A term

` `` [cla([x,y],[a],[a-[x,y]]),cla([x,y],[a],[a-[x,y]])] `

means a list of two classfications, which are indexed 1 and 2 in order. Note that, in this case, the two classifications are identical as a classification, but are indexed differently, which is necessary for sum operations.`cla([x,y],[a],[a-[x,y]])`

, and`cla([x,y],[a],[a-[x,y]])`

,

A term

` `` im(1,2, [a-a],[x-x]) `

means an informorphism from the classification 1 to the classification 2,
whose token map is [x-x] (identity) and type map is [a-a] (identity).

A sequent` [1:a, 2:b]-[3:c] `

means the set of tokens which supports

typewhere 1,2,3 are indexes of classifications.`1:a`

, and`2:b`

, but not`3:c`

,

The term, ` [[[a]-[],[a]-[]]] `

appearing in the output token area means the set of tokens
as a list [u, v] such that

u supports a (in classification 1), and v supports a (in classification 2).In other words, the tokens set of the core is represented as an idexed sequence of sequents with the same idexing set for given series of classifications.

The term,

` `` [[1:b,1:a,2:a]] `

appearing in the output type area means the set of types.
In this particular case the set is a singleton of the sum type` `` [1:b, 1:a, 2:a] `

.

It is straightforward to recover the token set and the support relation from this conventional representation, which is the reason why neither tokens nor support relation of the core built appear in the output area,