mmadt-monad.groovy

person[name:str~a,age:int~b]{*}~c   =>[id] 
 |                                  <=[=mongo][get,users]
 |                                            [is,[get,name][eq,a]]
 |                                            [map,[name:[get,'first'][plus,[get,'last']],
 |                                                  age:2019-[get,'dob']]]
 |
 |-[-rule]([dedup]|[order]) => [id] | [count] => 100
 |-[-path][put,'c',c]
 |-[-loop][is,[get,i][a,repeat]][incr]
 |-[-akka][is,[get,remote]][put,c,akka[ip:127.0.0.1,port:2222]]
 |-[-sack][fold,real => [mult,b]]
 |-[-ring]([mult,[one]]  => [id] | 
           [plus,[zero]] => [id] |
           [one]         => person[name:'',age:0])

An object is structurally defined with ~x serving as global variables while an instance is being referenced.

=> ("map to" operator) there is no prescribed computation. In principle, => should be the remaining instructions in the program (pop off the stack, execute, and go).

<= ("map from" operator) there is a functor from the mongo model to the "social model". note that a structurally equivalent record is created in the mongo space and is what is ultimately returned by <=. Thus, there is a homomorphism between these two algebraically isolated environments.

|- ("monadic feature" operator) these are monadic state features (computational metadata). These will not be specified off datatypes, but off a monad-type perhaps.? these are the Traverser<S> features in TP3, but fully specified within mm-ADT.

[-rule]: a "first to fire" [inst] => [inst] listing (one particular rewrite engine. people can write their own). | is the binary operator for [choose]
[-path]: the current location of the traverser is stored in its path history. (only necessary if path data is being used by the query)
[-loop]: loop metadata associated with `[repeat]` (only necessary if the query uses loops)
[-akka]: serialization and network metadata necessary for distributed message passing with Akka. (only necessary if the processor is Akka)
[-sack]: a monoidal function that maintains a running sum of the ages of the people encountered.
[-ring]: like [-rule], instruction rewrites that respect the ring axioms.

[-] instructions represent features of the monad. ("object-oriented methods" programmable in mm-ADT)
[=] instructions represent exogenous model mappings. (embeddings/homomorphisms/projections/transformations/couplings/etc.)
[ ] instructions represent endogenous model mappings. (endomorphisms, i.e. moving through the current model.)