4 ms·

Mappings that admit inverses are bijections. An isomorphism is a special kind of bijection in which, if two things have some relationship before the mapping, th

Mappings that admit inverses are bijections. An isomorphism is a special kind of bijection in which, if two things have some relationship before the mapping, they have some other relationship after the mapping. e.g. if a*b = c, then ln(a)+ln(b) = ln(c) EDIT The isomorphism is the mapping from x to ln(x); the two things before the mapping are a and b; their relationship before the mapping is that their product is c; the two things after the mapping are ln(a) and ln(b); and their new relationship is that their sum is ln(c). In this example, it's not just "some other relationship" after the mapping, but involves c, also mapped.

jdoliner 9y ago
Right, particularly they're homomorphisms that admit inverses. I confused myself into thinking that the fact that they admit an inverse implies that they're structure preserving but that obviously isn't true. Still I don't see anything here that doesn't basically apply to running the same code on client and server. Since the entire point is that you are preserving structure, Go is supposed to have exactly the same semantics on client and server.
- hyperpallium 9y ago
  Yep. But as others have said, it's not really isomorphism in a mathematical sense. The article defines "Isomorphic web applications" as "where the web server and the web browser (the client), may share all, or some parts of the web application code." Just, "same shape" on both sides. If it was identical code, I would (mathematically) call it an identity (which, to be fair, is an isomorphism). But it's not identical; they transpile go to js ("GopherJS - A compiler from Go to JavaScript"). This compilation itself is arguably an isomorphic mapping, with the same code doing equivalent things on both sides. e.g. equivalent assignments between equivalent variables. Two problems with this interpretation (1) a transpiler doesn't have to be isomorphic (e.g. could use different idioms); (2) that's not really the aspect they're referring to.

jdoliner 9y ago

Right, particularly they're homomorphisms that admit inverses. I confused myself into thinking that the fact that they admit an inverse implies that they're structure preserving but that obviously isn't true. Still I don't see anything here that doesn't basically apply to running the same code on client and server. Since the entire point is that you are preserving structure, Go is supposed to have exactly the same semantics on client and server.

hyperpallium 9y ago
Yep. But as others have said, it's not really isomorphism in a mathematical sense. The article defines "Isomorphic web applications" as "where the web server and the web browser (the client), may share all, or some parts of the web application code." Just, "same shape" on both sides. If it was identical code, I would (mathematically) call it an identity (which, to be fair, is an isomorphism). But it's not identical; they transpile go to js ("GopherJS - A compiler from Go to JavaScript"). This compilation itself is arguably an isomorphic mapping, with the same code doing equivalent things on both sides. e.g. equivalent assignments between equivalent variables. Two problems with this interpretation (1) a transpiler doesn't have to be isomorphic (e.g. could use different idioms); (2) that's not really the aspect they're referring to.