Relation domains (#627)

* relation draft

* adjusted size attribute pages to include relation

* add reflexive attributes

* add symmetric type attributes

* adding other attributes

* add notebook

docs/bits/attribute/L_Euclidean.md

@@ -0,0 +1,7 @@
+# Euclidean
+
+A relation is Euclidean if ```a``` is related to ```b``` and ```c```, then ```b``` is related to ```c```.
+
+See this demonstrated [here](https://github.com/conjure-cp/conjure/blob/main/docs/notebooks/RelationDomains.ipynb).
+Read more about this property [here](https://en.wikipedia.org/wiki/Euclidean_relation).
+

docs/bits/attribute/L_aSymmetric.md

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+# aSymmetric
+
+An asymmetric relation is a relation where if ```a``` is related to ```b```, then ```b``` is not related to ```a```.
+
+See this demonstrated [here](https://github.com/conjure-cp/conjure/blob/main/docs/notebooks/RelationDomains.ipynb).
+Read more about this property [here](https://en.wikipedia.org/wiki/Asymmetric_relation).

docs/bits/attribute/L_antiSymmetric.md

@@ -0,0 +1,8 @@
+# antiSymmetric
+
+A relation is anti symmetric that for every ```a``` related to ```b```, where ```a != b```, ```b``` is not related to ```a```.
+
+Essentially, if ```a``` is related to ```b``` and ```b``` is related to ```a```, then  ```a = b```.
+
+See this demonstrated [here](https://github.com/conjure-cp/conjure/blob/main/docs/notebooks/RelationDomains.ipynb).
+Read more about this property [here](https://en.wikipedia.org/wiki/Antisymmetric_relation).

docs/bits/attribute/L_connex.md

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+# connex 
+
+A connected relation is a relation where all elements in either domain are related (in one direction or the other).
+
+See this demonstrated [here](https://github.com/conjure-cp/conjure/blob/main/docs/notebooks/RelationDomains.ipynb).
+Read more about this property [here](https://en.wikipedia.org/wiki/Connected_relation).

docs/bits/attribute/L_coreflexive.md

@@ -0,0 +1,7 @@
+# coreflexive
+
+When used with relation domains, ensures that if ```x``` is related to ```y```, then ```x = y```.
+This means elements of domains are only mapped to themselves.
+
+See this demonstrated [here](https://github.com/conjure-cp/conjure/blob/main/docs/notebooks/RelationDomains.ipynb).
+Read more about this property [here](https://en.wikipedia.org/wiki/Reflexive_relation).

docs/bits/attribute/L_equivalence.md

@@ -0,0 +1,6 @@
+# equivalence
+
+An equivalence relation is a relation that is [reflexive](https://github.com/conjure-cp/conjure/blob/main/docs/bits/attribute/L_reflexive.md), [symmetric](https://github.com/conjure-cp/conjure/blob/main/docs/bits/attribute/L_symmetric.md), and [transitive](https://github.com/conjure-cp/conjure/blob/main/docs/bits/attribute/L_transitive.md).
+
+See this demonstrated [here](https://github.com/conjure-cp/conjure/blob/main/docs/notebooks/RelationDomains.ipynb).
+Read more about this property [here](https://en.wikipedia.org/wiki/Equivalence_relation).

docs/bits/attribute/L_irreflexive.md

@@ -0,0 +1,6 @@
+# irreflexive
+
+When used with relation domains, produces solutions where elements of one domain are not related to themselves. 
+
+See this demonstrated [here](https://github.com/conjure-cp/conjure/blob/main/docs/notebooks/RelationDomains.ipynb).
+Read more about this property [here](https://en.wikipedia.org/wiki/Reflexive_relation).

docs/bits/attribute/L_maxSize.md

@@ -3,5 +3,7 @@
 Takes an integer parameter, n.
 
 When used with a function domain will limit the solutions to functions that contains at most n mappings.
+When used with a relation domain will produce solutions that have up to n tuples.
 
-See it demonstrated [here](https://github.com/conjure-cp/conjure/blob/main/docs/notebooks/functionDemonstration.ipynb).
+See it demonstrated on function domains [here](https://github.com/conjure-cp/conjure/blob/main/docs/notebooks/functionDemonstration.ipynb).
+See it demonstrated on relation domains [here](https://github.com/conjure-cp/conjure/blob/main/docs/notebooks/RelationDomains.ipynb)

docs/bits/attribute/L_minSize.md

@@ -3,5 +3,7 @@
 Takes an integer parameter, n.
 
 When used with a function domain will limit the solutions to functions that contains at least n mappings.
+When used with a relation domain will produce solutions with at least n tuples.
 
-See it demonstrated [here](https://github.com/conjure-cp/conjure/blob/main/docs/notebooks/functionDemonstration.ipynb).
+See it demonstrated on function domains [here](https://github.com/conjure-cp/conjure/blob/main/docs/notebooks/functionDemonstration.ipynb).
+See it demonstrated on relation domains [here](https://github.com/conjure-cp/conjure/blob/main/docs/notebooks/RelationDomains.ipynb)

docs/bits/attribute/L_partialOrder.md

@@ -0,0 +1,6 @@
+# partialOrder
+
+A relation that has a partial order is a relation that is [reflexive](https://github.com/conjure-cp/conjure/blob/main/docs/bits/attribute/L_reflexive.md), [antiSymmetric](https://github.com/conjure-cp/conjure/blob/main/docs/bits/attribute/L_antiSymmetric.md), and [transitive](https://github.com/conjure-cp/conjure/blob/main/docs/bits/attribute/L_transitive.md).
+
+See this demonstrated [here](https://github.com/conjure-cp/conjure/blob/main/docs/notebooks/RelationDomains.ipynb).
+Read more about this property [here](https://en.wikipedia.org/wiki/Partially_ordered_set).

docs/bits/attribute/L_reflexive.md

@@ -0,0 +1,6 @@
+# reflexive 
+
+When used with relation domains produces solutions where every element in one domain is related to itself.
+
+See this demonstrated [here](https://github.com/conjure-cp/conjure/blob/main/docs/notebooks/RelationDomains.ipynb).
+Read more about this property [here](https://en.wikipedia.org/wiki/Reflexive_relation).

docs/bits/attribute/L_serial.md

@@ -0,0 +1,6 @@
+# serial
+
+A serial relation expresses the relationship between an element of a sequence and it's successor.
+
+See this demonstrated [here](https://github.com/conjure-cp/conjure/blob/main/docs/notebooks/RelationDomains.ipynb).
+Read more about this property [here](https://en.wikipedia.org/wiki/Serial_relation).

docs/bits/attribute/L_size.md

@@ -3,5 +3,7 @@
 Takes an integer parameter, n. 
 
 When used with a function domain will limit the solutions to functions that contain n mappings.
+When used with a relation domain will produce solutions with n tuples.
 
-See it demonstrated [here](https://github.com/conjure-cp/conjure/blob/main/docs/notebooks/functionDemonstration.ipynb).
+See it demonstrated on function domains [here](https://github.com/conjure-cp/conjure/blob/main/docs/notebooks/functionDemonstration.ipynb).
+See it demonstrated on relation domains [here](https://github.com/conjure-cp/conjure/blob/main/docs/notebooks/RelationDomains.ipynb)

docs/bits/attribute/L_symmetric.md

@@ -0,0 +1,6 @@
+# symmetric
+
+A relation is symmetric if when ```a``` is related to  ```b```,```b``` is also related to ```a```.
+
+See this demonstrated [here](https://github.com/conjure-cp/conjure/blob/main/docs/notebooks/RelationDomains.ipynb).
+Read more about this property [here](https://en.wikipedia.org/wiki/Symmetric_relation).

docs/bits/attribute/L_total.md

@@ -1,5 +1,7 @@
 # total
 
 When used with a function domain will only return solutions that have mappings for every element in the defined set.
+When used with a relation domain, ensure that each element of the first domain is related to an element of the second domain.
 
-See it demonstrated [here](https://github.com/conjure-cp/conjure/blob/main/docs/notebooks/functionDemonstration.ipynb).
+See it demonstrated on function domains [here](https://github.com/conjure-cp/conjure/blob/main/docs/notebooks/functionDemonstration.ipynb).
+See it demonstrated on relation domains [here](https://github.com/conjure-cp/conjure/blob/main/docs/notebooks/RelationDomains.ipynb).

docs/bits/attribute/L_transitive.md

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+# transitive
+
+A relation is transitive if ```a``` is related to ```b```, and ```b``` is related to ```c```, then ```a``` is also related to ```c```.
+
+See this demonstrated [here](https://github.com/conjure-cp/conjure/blob/main/docs/notebooks/RelationDomains.ipynb).
+Read more about this property [here](https://en.wikipedia.org/wiki/Transitive_relation).

docs/bits/keyword/letting_domain.md

@@ -22,7 +22,7 @@ Types of domains:
 - [multi-set](...)
 - [function](https://github.com/conjure-cp/conjure/blob/main/docs/bits/type/function.md)
 - [sequence](...)
-- [relation](...)
+- [relation](https://github.com/conjure-cp/conjure/blob/main/docs/bits/type/L_relation.md)
 - [partition](...)
 
 

docs/bits/type/L_relation.md

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+# relation
+
+A list of pairs of elements of given domains that are related to each other.
+
+Defined by 
+``` 
+relation (optional attributes) of (domain1 * domain2 * ...)
+```
+
+They can be explicitly defined using tuples (of the same type) as
+```
+letting R be relation((1,1,0),(1,0,1),(0,1,1))
+```
+
+Relations have two groups of attributes
+1. cardinality related
+    - [size](https://github.com/conjure-cp/conjure/blob/main/docs/bits/attribute/L_size.md)
+    - [minSize](https://github.com/conjure-cp/conjure/blob/main/docs/bits/attribute/L_maxSize.md)
+    - [maxSize](https://github.com/conjure-cp/conjure/blob/main/docs/bits/attribute/L_minSize.md)
+2. Binary Relation (only on relations that contain 2 identical domains)
+    - [reflexive](https://github.com/conjure-cp/conjure/blob/main/docs/bits/attribute/L_reflexive.md)
+    - [irreflexive](https://github.com/conjure-cp/conjure/blob/main/docs/bits/attribute/L_irreflexive.md)
+    - [coreflexive](https://github.com/conjure-cp/conjure/blob/main/docs/bits/attribute/L_coreflexive.md)
+    - [symmetric](https://github.com/conjure-cp/conjure/blob/main/docs/bits/attribute/L_symmetric.md)
+    - [antiSymmetric](https://github.com/conjure-cp/conjure/blob/main/docs/bits/attribute/L_antiSymmetric.md)
+    - [aSymmetric](https://github.com/conjure-cp/conjure/blob/main/docs/bits/attribute/L_aSymmetric.md)
+    - [transitive](https://github.com/conjure-cp/conjure/blob/main/docs/bits/attribute/L_transitive.md)
+    - [total](https://github.com/conjure-cp/conjure/blob/main/docs/bits/attribute/L_total.md)
+    - [connex](https://github.com/conjure-cp/conjure/blob/main/docs/bits/attribute/L_connex.md)
+    - [Euclidean](https://github.com/conjure-cp/conjure/blob/main/docs/bits/attribute/L_Euclidean.md)
+    - [serial](https://github.com/conjure-cp/conjure/blob/main/docs/bits/attribute/L_serial.md)
+    - [equivalence](https://github.com/conjure-cp/conjure/blob/main/docs/bits/attribute/L_equivalence.md)
+    - [partialOrder](https://github.com/conjure-cp/conjure/blob/main/docs/bits/attribute/L_partialOrder.md)
+
+See this demonstrated [here](https://github.com/conjure-cp/conjure/blob/main/docs/notebooks/RelationDomains.ipynb).