Have assertEqual support alpha equivalence

[ngeiswei]

Describe the bug Probably not a bug, but it would be very convenient if assertEqual and assertEqualToResult could support alpha-equivalence. Either it could be the default (maybe undesirable though), or new assert operators, such as assertAlphaEqual and assertAlphaEqualToResult could be added.

To Reproduce Steps to reproduce the behavior:

1. Run the following MeTTa script

   (= (foo) (R $x $y))
   !(assertEqual (foo) (R $x $y))

2. See output

Expected behavior If assertEqual supported alpha-equivalence it would output [()].

Actual behavior Instead it outputs

[(Error (assertEqual (foo) (R $x $y)) 
Expected: [(R $x $y)]
Got: [(R $x#31 $y#32)]
Missed result: (R $x $y))]

Additional context

• MeTTa version: 0.2.0+ga57bb5b2.d20240718
• I suppose it's better to add assertAlphaEqual and assertAlphaEqualToResult than relaxing the behavior of assertEqual. Such addition could be at the Rust level or at the MeTTa level. Note that I have already implemented an alpha-equivalence MeTTa function here https://github.com/ngeiswei/chaining/blob/97923a18f3c6138f2eaf697e89ca9500e219e729/experimental/converters/calculi-converter.metta#L311-L327. However it is slow and I wonder if it would be actually easier to implement at the Rust level. If you think implementing it at the MeTTa level is fine, I'm happy to take care of it.

[vsbogd]

We have a Rust function which checks two atoms for being alpha-equivalent: https://github.com/trueagi-io/hyperon-experimental/blob/9c126b107f8a5c4ea95db33f7c805e70692d8e9c/lib/src/atom/matcher.rs#L1253 Thus it is not a problem to add couple new operations actually.

[ngeiswei]

Awesome, would you do it? Or would you rather have me do it? I'll be a bit slower but it should be within my reach.

[ngeiswei]

Also, there are at least two ways to do it:

1. Expose atoms_are_equivalent to MeTTa, then implement assertAlphaEqual in MeTTa (add it in stdlib.metta I suppose).
2. Implement assertAlphaEqual in Rust, exposed to MeTTa.

Even if we go with 2, I think it would be useful to expose atoms_are_equivalent to MeTTa. I did find it useful in my own code, and I assume the Rust implementation is far more efficient than my MeTTa implementation.

[ngeiswei]

Also, how would you name in MeTTa

• atoms_are_equivalent. I have used =alpha in my code for instance.
• assertEqual up to alpha-equivalence? I had thought of assertAlphaEqual but they are other possibilities like assertEquivalent, etc.

[ngeiswei]

Also, a different issue that I'm bringing only because we are discussing names. I don't understand the name assertEqualToResult. Didn't you mean assertEqualToResults, ending with an s? But anyway, that certainly is for another issue.