Semantics of Writer

[re-xyr]

Writer is probably the strangest "classical" effect, in the sense that it is both mutable (tell) and scoped (listen and pass).

This means we have 3 distinct semantics for listen:

• tell in listen appends to main accumulator immediately;
• tell in listen appends to an alternative accumulator that is later "merged" into the main one. On error, the merge still happens.
• Same as above, but on error, the merge never happens.

And 2 distinct semantics for pass:

• tell in pass appends to an alternative accumulator and later merged into the main one. On error, the merge still happens.
• Same as above, but on error, the merge never happens.

If we make censor a primitive operation on its own rights, then it has 2 semantics:

• Same with the mtl definition, inheriting whatever the semantics pass has.
• Same with eff, apply the transformation function on each individual output. Modulo errors, this coincides with the mtl definition only when the the transformation is a homomorphism.