Coupler Chains

[darianboggs]

Coupler Chains

Each Coupler C has an ImportState S_I and an ExportState S_E. I refer to the Fields in those States as Import I and Export Fields E, respectively. Though nothing precludes multiple Fields in the ExportState, I'm considering each ExportState as the value of a mapping M that maps all the Coupler Import Fields to a single Coupler Export Field. Therefore each Coupler can be identified with one or more mappings M₁, M₂, ..., that have the same Import Fields. For the remainder of this document, I will treat each Coupler as a single Export Field Coupler. This generalizes to the case of multiple Export Fields if the state of each Action is independent of the other Action states. Also, though a Coupler can have multiple Actions, for now I consider only Couplers with a single Action. This may not generalize to Couplers with multiple Actions.

All Couplers have a single Export Field, but I divide them into SingleImport Couplers C₁ with a single Import Mapping M₁ and MultiImport C_N Couplers with multiple Imports M_N for the sake of considering the complications introduced by multiple Import Fields. A Coupler with an AccumulatorAction is a SingleImport Coupler. Similarly, a Coupler with an ExpressionAction is a MultiImport Coupler. The case of these two Couplers motivates the analysis below.

Now, I focus on the mappings, M₁ and M_N. Suppose the Export Field of an Expression Coupler C_X is used as the Import Field of an Accumulation Coupler C_A. The mapping application would be a composition:

M_A M_X I₁ I₂ = (M_A M_X) (I₁ I₂)

M I means that M applies to an import field I. Mappings apply right to left. So the composite mapping is M_C = M_A M_X

There are 8 possible chains of mappings (Couplers):

1. M₁ M₁ M₁
2. M₁ M₁ M_N
3. M_N M₁ M₁
4. M_N M₁ M_N
5. M₁ M_N M₁
6. M₁ M_N M_N
7. M_N M_N M₁
8. M_N M_N M_N

(1) is the simplest case with no complications. (2) and (4) are two possible chains for the case of an Expression Mapping followed by an Accumulator Mapping. (3) may be a simple case like (1).

The chaining problem is that if a SimpleImport Coupler comes in the chain immediately after a MulitImport Coupler, the combined Coupler is a MultiImport Coupler. Put another way, a composite mapping M_C = M₁ M_N is in the set of MultiImport mappings M.

[tclune]

Therefore each Coupler can be identified with one or more mappings M1, M2, ..., that have the same Import Fields.

I don't think that sentence follows from the previous ones. Nor do I think it is true, depending on what you mean by "associated".

[tclune]

MA MX I1 I2 = (MA MX) (I1 I2)

Would it not be clearer to join I1 I2 as a tuple: (I1, i2) to make it clear that they cannot be treated as operators. The LHS makes it look like I1 applies to I2. And even the RHS makes it ambiguous.

[tclune]

There are 8 possible chains of mappings (Couplers):

I assume you mean 8 possible chains for 3 couplers?

[tclune]

I cannot follow your analysis of the 8 cases. In particular your description of case 3 - I'm missing something basic.

[tclune]

The chaining problem is that if a SimpleImport Coupler comes in the chain immediately after a MulitImport Coupler, the combined Coupler is a MultiImport Coupler.

Why is that a problem? That seems just a restatement of what we mean to apply a series of mappings in a sequence.

[tclune]

Another issue to keep in mind is that there are (potentially) 2 different use cases for expressions. In ExtData we want to export an expression that involves other export items of the same state. In History we want to import items that are exported from multiple other locations. So the write-up above is more akin to the History use case.