2.1 Getting from 𝑎 to 𝑏

Resource interpretation

See also linear logic in nLab § As a logic of resource availability and Linear logic § The resource interpretation.

Constructivist interpretation

If we aren’t using up resources (that is, we can either copy or reuse them) then we’re really dealing with constructive mathematics (see Constructivism (philosophy of mathematics)). At the core of this philosophy is Intuitionism and Heyting algebras, which are join-semilattice.

Are you using Ubuntu and planning on a software upgrade? See software recommendation - How to visually display dependencies of a package? for the excellent debtree package. The dependency trees you’ll get from it show you how to construct a package. Let’s start from their example:

Notice we have a join-semilattice. In this example, a package like coreutils can be thought of as a function (compilation) taking a (hidden/implied in this drawing) source code input, along with all its binary library dependencies. This is similar to (2.1) above, but with the drawing flipped horizontally.