A Real Example

• Attempting the First Process
• A Real Example continued

I am now going to construct a very simple process to illustrate the aspects of the Process Language in concrete terms. We first need to setup our universe $\Omega$, which defines the domain of operation.

In this universe, we are in the business of Fruit Smoothies, and our very simple process is that of Blending.

The inputs to this process are a variety of different fruits, as well as a measure of sugar. The output of this process is a blended smoothie, which is decanted into glasses.

We define our Input Space, ${\Phi }_i$ as follows:

$${\Phi }_i=\left\{{\Phi }_i^1,{\Phi }_i^2,\dots ,{\Phi }_i^N\right\}$$

where there are $N$ possible Distinct Input Components to this process. For simplicity, let us say that only apples, bananas, pears, and sugar can be used.

Now, “apples”, “bananas”, etc are not the basis of Input Components to the blend process, no indeed. These are themselves bound to the Output Components of a previous Process.

The Universe, $\Omega$

flowchart LR
0[Apples] ---> 4
1[Bananas] ---> 4
2[Pears] ---> 4
3[Sugar] ---> 4
4[Blender] ---> 5
5[Smoothie]

This is now a complete description of the universe. We have five processes that we call:

• Apples: where the apples come from
• Bananas: where the bananas come from
• Pears: where the pears comes from
• Sugar: where the sugar comes from
• Blender: where the fruit and sugar is blended into smoothies
• Smoothies: where the smoothies go

We also number them accordingly:

• Apples: 0
• Bananas: 1
• Pears: 2
• Sugar: 3
• Blender: 4
• Smoothies: 5

Thus we have our Process Space $P$:

$$P=\left\{P_0,P_1,\dots ,P_5\right\}$$

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Aside: I am now coming to think

$${\Phi }_o=P({\Phi }_i,\Theta )$$

i.e. replace $F$ with $P$, thus making it more than just a Conveyance Function. I changed my mind about this one.

I am also thinking that we just use time $t$ as the locational space. I’m still on for this one.

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