The type SCGMorphism is the type of SafeCompositionGraphs morphisms.

It is just like a CGMorphism, we also store the maximum number of cycles.

Return the label of a SafeCompositionGraph generator.

A SafeCompositionGraph is a graph with a composition law such that the free category generated by the graph quotiented out by the composition law gives a FiniteCategory. It has a maximum number of composition for loops.

SafeCompositionGraph is private, use the smart constructors safeCompositionGraph or unsafeSafeCompositionGraph to instantiate one.

The generating graph of the safe composition graph.

The composition law of the safe composition graph.

The maximum number of times a cycle can be composed with itself.

Smart constructor of SafeCompositionGraph.

If the SafeCompositionGraph constructed is valid, returns Right the composition graph, otherwise returns Left a FiniteCategoryError.

Unsafe constructor of SafeCompositionGraph for performance purposes. It does not check the structure of the SafeCompositionGraph.

Use this constructor only if the SafeCompositionGraph is necessarily well formed.

Read a .scg string to create a SafeCompositionGraph.

A .scg string follows the following rules :

0. Every character of a line following a "#" character are ignored.
1. Each line defines either an object, a morphism or a composition law entry.
2. The following strings are reserved : " -","-> "," = ", "<ID>", "<SRC>", "<SRC>", "<TGT>", "</TGT>", " => "
3. To define an object, write a line containing its name.
4. To define an arrow, the syntax "source_object -name_of_morphism-> target_object" is used, where "source_object", "target_object" and "name_of_morphism" should be replaced.
4. 1. If an object mentionned in an arrow does not exist, it is created.
4. 2. The spaces are important.
5. To define a composition law entry, the syntax "source_object1 -name_of_first_morphism-> middle_object -name_of_second_morphism-> target_object1 = source_object2 -name_of_composite_morphism-> target_object2" is used, where "source_object1", "name_of_first_morphism", "middle_object", "name_of_second_morphism", "target_object1", "source_object2", "name_of_composite_morphism", "target_object2" should be replaced.
5. 1 If an object mentionned does not exist, it is created.
5. 2 If a morphism mentionned does not exist, it is created.
5. 3 You can use the tag <ID/> in order to map a morphism to an identity.
6. The first line of the should be a number, this number determines the maximum number of cycles.

Unsafe version of readSCGString which does not check the structure of the resulting SafeCompositionGraph.

Read a .scg file to create a SafeCompositionGraph.

A .scg file follows the following rules :

0. Every character of a line following a "#" character are ignored.
1. Each line defines either an object, a morphism or a composition law entry.
2. The following strings are reserved : " -","-> "," = ", "<ID>", "<SRC>", "<SRC>", "<TGT>", "</TGT>", " => "
3. To define an object, write a line containing its name.
4. To define an arrow, the syntax "source_object -name_of_morphism-> target_object" is used, where "source_object", "target_object" and "name_of_morphism" should be replaced.
4. 1. If an object mentionned in an arrow does not exist, it is created.
4. 2. The spaces are important.
5. To define a composition law entry, the syntax "source_object1 -name_of_first_morphism-> middle_object -name_of_second_morphism-> target_object1 = source_object2 -name_of_composite_morphism-> target_object2" is used, where "source_object1", "name_of_first_morphism", "middle_object", "name_of_second_morphism", "target_object1", "source_object2", "name_of_composite_morphism", "target_object2" should be replaced.
5. 1 If an object mentionned does not exist, it is created.
5. 2 If a morphism mentionned does not exist, it is created.
5. 3 You can use the tag <ID/> in order to map a morphism to an identity.
6. The first line of the should be a number, this number determines the maximum number of cycles.

Unsafe version of readSCGFile which does not check the structure of the resulting SafeCompositionGraph.

Transform a CompositionGraph into a SafeCompositionGraph given a maximum number of loops.

Transform a SafeCompositionGraph into a CompositionGraph.

Transform a composition graph into a string following the .scg convention.

Saves a safe composition graph into a file located at a given path.

Unsafe version of readCGDString which does not check the structure of the resulting Diagram.

Read a .scgd string and returns a diagram. A .scgd string obeys the following rules :

1. There is a line "<SRC>" and a line "</SRC>".
1. 1 Between these two lines, the source composition graph is defined as in a scg file.
2. There is a line "<TGT>" and a line "</TGT>".
2. 1 Between these two lines, the target composition graph is defined as in a scg file.
3. Outside of the two previously described sections, you can declare the maps between objects and morphisms.
3. 1 You map an object to another with the following syntax : "object1 => object2".
3. 2 You map a morphism to another with the following syntax : "objSrc1 -arrowSrc1-> objSrc2 => objTgt1 -arrowTgt1-> objTgt2".
4. You don't have to (and you shouldn't) specify maps from identities, nor maps from composite arrows.

Unsafe version readSCGDFile which does not check the structure of the resulting Diagram.

Read a .scgd file and returns a diagram. A .scgd file obeys the following rules :

1. There is a line "<SRC>" and a line "</SRC>".
1. 1 Between these two lines, the source composition graph is defined as in a scg file.
2. There is a line "<TGT>" and a line "</TGT>".
2. 1 Between these two lines, the target composition graph is defined as in a scg file.
3. Outside of the two previously described sections, you can declare the maps between objects and morphisms.
3. 1 You map an object to another with the following syntax : "object1 => object2".
3. 2 You map a morphism to another with the following syntax : "objSrc1 -arrowSrc1-> objSrc2 => objTgt1 -arrowTgt1-> objTgt2".
4. You don't have to (and you shouldn't) specify maps from identities, nor maps from composite arrows.

Transform a safe composition graph diagram into a string following the .scgd convention.

Saves a safe composition graph diagram into a file located at a given path.

Generates a random CompositionGraph and transforms it into a SafeCompositionGraph (see constructRandomCompositionGraph).

Creates a random safe composition graph with default random values.

The number of arrows will be in the interval [1, 20].

The max number of loops is set to 100 as it is almost impossible to have a greater number of loops with monoidification attempts.

Constructs two random safe composition graphs and choose a random diagram between the two.

The max number of loops is set to 100 as it is almost impossible to have a greater number of loops with monoidification attempts.