{{x,y},{x,z}}{{w,x},{w,z},{x,y}}
Iterated map on functions
Something like {{x,y},{x,z}} is a word in a free monoid
Every concrete hyperedge is a generator; rule gives equivalences between words [[ as a schema ]]
Operator algebra without nesting
{{x,y},{x,z}}{{w,x},{w,z},{x,y}}

lambdas

Needs matching; not an ordinary lambda
​
{{x_,y_},{x_,z_}}Module[{w},{{w,x},{w,z},{x,y}}]
Deploy an armada of lambdas:
{{0,5},{1,2},{3,2},{4,1}}
​
Treat the list as curried
Function[{e,f},Function[{c,d},Function[{a,b},XXXX]]][l[l[l[l[XXXXX]]]]]
Possibly using parametrized types to do matches

category theory

[[f endofunctor on the powerset of ]]
[[equipped with a morphism on the category Set]]
Object is set of possible hyperedges;
In[]:=
Tuples[Range[3],2]
Out[]=
{{1,1},{1,2},{1,3},{2,1},{2,2},{2,3},{3,1},{3,2},{3,3}}
In[]:=
Subsets[%]
Out[]=
This object is a set of sets....
Morphism maps one set onto another
Can I enumerate models with category theory??

[More]

Rule application is associative

Concatenation of strings has associativity
Concatenation of hypergraphs has associativity and commutativity [ identity element is empty hypergraph ]
(Not clear what rule application means...)
Commutative monoid
​
{f[a,b],f[c,d],XXXXX}