implies ⇒ and equivalent ⇔ operators

[Lakedaemon]

math.js implement the logical operators or, and, not, xor.
Why doesn't it implement "implies" ⇒ and "equivalence" ⇔ ?

Also, is there a way to extend math.js with operators ? with symbols ? (with corresponding eval and toTex callBacks ) ?

[FSMaxB]

For the question about extending mathjs with custom operators, take a look at #467. Currently you would have to modify the parser yourself manually.

The logical operators or, and, not and xor work on boolean values. ⇒ and ⇔ are usually used to express a relation between expression for writing mathematical proofs, I'm not quite sure how they would work as operators in mathjs.

Because mathjs isn't a computer algebra system, comparing expressions would essentially come down to evaluating it and comparing the value. Wouldn't ⇔ be identical to == in this case? And how would ⇒ work? Maybe like this:

⇒	true	false
true	true	false
false	true	true

Not quite sure what you intend those operators to do.

[Lakedaemon]

Thanks for the pointer to #467

I'm trying to implement a (simple) proof checker.
I'm doing (basic) symbolic computations on trees (tree transformations).
comparing expressions is somewhat akin (but not quite) to evaluating it and comparing the value

⇔ is quite identical to == but doesn't expand to TeX with the same symbol and only operates on logical propositions/boolean values
⇒ is implemented as you wrote

At the moment, I use them through math.parse and FunctionNode
It works but the input is quite human unfriendly especially with deeply nested stuff like
imply(A, imply(B, C)) instead of A ⇒ (B ⇒ C) etc...

[FSMaxB]

Implementing these operators seems quite feasible. But ultimately it's @josdejong's decision.

If Jos accepts this the only issue that remains in my opinion, is the choice of the operators. I don't think it is a good idea to introduce unicode operators into mathjs. So maybe <=> and => can be used, I'm not quite sure about that though.

[josdejong]

Interesting discussion, thanks.

Some ideas that crossed my mind:

• Nicest would be to make the parser customizable, allow adding new operators. That would give you the freedom to introduce new operators like <=> and => yourself. I think there is already an open issue for this.
• I agree with Max that it's probably best to create these operators using regular ascii symbols instead of unicode ⇒ and ⇔. But that could depend on your use case of course.
• Until we have support for symbolic computation, I don't see any use for implementing these operators in math.js: you can't do anything with it. Support for symbolic computation has been worked on already but is on the back burner for now.

[Lakedaemon]

Point 1 would be awesome. But I can do without points 1, 2, 3 for the moment (thanks to FunctioNode)
I'll keep experimenting and get back to you if I manage to produce something interesting with math.js and basic symbolic computations