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Javier Neira Sanchez
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Regarding 'Adverbs'

In word-based functional concatenative languages, it isn't difficult to express that a word is mapped over a sequence. Some expression of the form:
        [ foo ] each

should be sufficient. Unfortunately, use of brackets for quotation becomes surprisingly noisy and difficult to read in practice, i.e. once we have sentences of more than a few words.

J and K languages have an interesting concept of 'adverbs', which modify how a word is applied without explicitly reifying the word. Applied to languages like Factor or AO, adverbs could greatly reduce noise and improve parsimony. I propose we steal this nice feature of J and K and adapt it to concatenative languages.

To realize adverbs in a concatenative, word-based PL requires representing adverbs within the structure of the word, i.e. such that we can modify the word without quoting it. I propose use of a suffix. We might imagine that:


should have the same behavior as `[ foo ] each`, but without any requirement to define `foo⋆` explicitly. This technique should be composable and concatenative, such that `foo⋆⋆` has the behavior of `[ [ foo ] each ] each` - thereby operating on each element of a matrix. 

(Sadly, even in 2014 not all readers will correctly render unicode. If you're not seeing stars (U+22C6), this post might not make full sense.) 

We could further formalize this behavior, and support user-defined adverbs, while sticking aggressively to the concatenative philosophy. For example, we might systematically rewrite `foo⋆⋆` as:

        [ foo ] \⋆ \⋆ inline

Here, `inline` is a trivial combinator such that `∀foo . [ foo ] inline = foo`. Though... this particular semantics is less-than-ideal because it allows adverb `\⋆` access to the full stack. The type for an adverb should be  `(x→y)→(x'→y')` - i.e. a context-free function from verb to verb. So the actual rewrite might be a little bit more involved.

At least one important requirement remains to be addressed:  I need a systematic way to parse `foo⋆⋆` into a word with two adverbs! Why not `[ foo ] \⋆⋆ inline` or `[ f ] \o \o \⋆ \⋆ inline`? 

The obvious answer, I think, is to reserve a few characters and introduce some disambiguating syntactic structure for parsing words. For example, I could use a backslash like `foo\⋆\⋆`. But, IMO, that is aesthetically unpleasing and risks aggregating the same syntactic noise I'm hoping to avoid in the first place. I could use an invisible character (e.g. U+2060) but that would only succeed in confusing readers of code.

Can we do better?

In a few conversations regarding adverbs, my strong impression was that we don't need many of them - that just a few can go a very long way. If this is true, then perhaps we could restrict to one character per adverb. That restriction appeals both to parsimony and my aesthetic sense. So we could have `foo\⋆⋆` - not too bad.

Perhaps, then, we could make adverbs separable from their use, i.e. such that `\⋆⋆` can be understood separately from its use on 'foo'. This will make it easier to refactor code using adverbs. Also, rewriting then becomes much more incremental. Perhaps:

        foo\⋆⋆ = [ foo ] \⋆⋆ inline = [ foo ] \⋆ \⋆ inline

Potential roles for adverbs include:

* collection-oriented operations (map/each, fold)
* minor data shuffling - e.g. flipped arguments
* quotation of a single word
* partial application and currying
* deep application - dip, zippers
* exponentiation, bi, tri, etc.

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Haskell y sus mónadas, con un breve trasfondo matemático que nunca deja de ser necesario.

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