If one looks at the 3 platform triples, one can see that they overlap such that one could put them together into a chain like:
```
(native, native, native, foreign, foreign)
```

If one imagines the saturating self references at the end being replaced with infinite stages, and then overlays those platform triples, one ends up with the infinite tuple:
```
(native..., native, native, native, foreign, foreign, foreign...)
```
One can then imagine any sequence of platforms such that there are bootstrap stages with their 3 platforms determined by "sliding a window" that is the 3 tuple through the sequence. This was the original model for bootstrapping. Without a target platform (assume a better world where all compilers are multi-target and all standard libraries are built in their own derivation), this is sufficient. Conversely if one wishes to cross compile "faster", with a "Canadian Cross" bootstrapping stage where `build != host != target`, more bootstrapping stages are needed since no sliding window provides the pesky `pkgsBuildTarget` package set since it skips the Canadian cross stage's "host".


::: {.note}
It is much better to refer to `buildPackages` than `targetPackages`, or more broadly package sets that do not mention “target”. There are three reasons for this.

First, it is because bootstrapping stages do not have a unique `targetPackages`. For example a `(x86-linux, x86-linux, arm-linux)` and `(x86-linux, x86-linux, x86-windows)` package set both have a `(x86-linux, x86-linux, x86-linux)` package set. Because there is no canonical `targetPackages` for such a native (`build == host == target`) package set, we set their `targetPackages`

Second, it is because this is a frequent source of hard-to-follow "infinite recursions" / cycles. When only package sets that don't mention target are used, the package set forms a directed acyclic graph. This means that all cycles that exist are confined to one stage. This means they are a lot smaller, and easier to follow in the code or a backtrace. It also means they are present in native and cross builds alike, and so more likely to be caught by CI and other users.

Thirdly, it is because everything target-mentioning only exists to accommodate compilers with lousy build systems that insist on the compiler itself and standard library being built together. Of course that is bad because bigger derivations means longer rebuilds. It is also problematic because it tends to make the standard libraries less like other libraries than they could be, complicating code and build systems alike. Because of the other problems, and because of these innate disadvantages, compilers ought to be packaged another way where possible.
:::

::: {.note}
If one explores Nixpkgs, they will see derivations with names like `gccCross`. Such `*Cross` derivations is a holdover from before we properly distinguished between the host and target platforms—the derivation with “Cross” in the name covered the `build = host != target` case, while the other covered the `host = target`, with build platform the same or not based on whether one was using its `.__spliced.buildHost` or `.__spliced.hostTarget`.
:::