> It does seem to rhyme with how function calls work under the hood.

You're just overindexing on the fact that block "arguments" are called "arguments". In SSA with block arguments, you can pass data to a block without passing it as an argument. The arguments are just a way of expressing Phis.

And in Phi/Upsilon, this is valid:

    MyBlock:
        X = Whatever(...)
        Upsilon(X, ^Y)
        Y = Phi()

Note how I'm using an upsilon to set the shadow variable of a Phi that's in the same block. You can't do that with block arguments.

These things just aren't the same at all. Saying that they are the same just shows that you don't get it.

> When people say equivalent, it is usually not in the mathematical sense, which would be meaningless here because all forms are turing complete anyway.

But they're not equivalent even in a mathematical sense.

> Take equivalent as--similarity that helps you understand A given you know B, and perhaps some of the wisdom from B translates to A.

If you want to understand these things, then focus on how they are so very different rather than brain damaging yourself into thinking they are similar

> You're just overindexing on the fact that block "arguments" are called "arguments"

But that's what it is. Briefly stated, your "upsilon" is just picking the 'actual' argument for the 'formal' parameter in a matching "phi". That's exactly what a function call does, and this holds even though you've intentionally decoupled the "upsilon" and "phi" nodes from any control-flow "jump" construct.

> Note how I'm using an upsilon to set the shadow variable of a Phi that's in the same block. You can't do that with block arguments.

Classically, the phi node would sit at the top of a block anyway, and this arrangement helps significantly in computing dominator set properties, renaming and use-def chains etc. etc. Giving up that property makes everything more awkward, including proofs of correctness for transformations, minimality, etc.

> But that's what it is. Briefly stated, your "upsilon" is just picking the 'actual' argument for the 'formal' parameter in a matching "phi". That's exactly what a function call does, and this holds even though you've intentionally decoupled the "upsilon" and "phi" nodes from any control-flow "jump" construct.

By that argument, every store instruction is an "argument". And basic block arguments and lambda calculus are equivalent to people storing and loading to memory willy nilly.

As I said before, these equivalence claims are so nonsensical because if you take the arguments to their limits, you end up with all languages being equivalent to one another

> Classically, the phi node would sit at the top of a block anyway, and this arrangement helps significantly in computing dominator set properties, renaming and use-def chains etc. etc. Giving up that property makes everything more awkward, including proofs of correctness for transformations, minimality, etc.

All of those things that Phi-at-top-of-blocks works with also work in the Phi/Upsilon world