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2021-06-08 01:02:21 <blankhart> when this paper (https://dl.acm.org/doi/10.1145/3371121) says that "guessing the right answer is typical of declarative type systems" what precisely is meant by "guess"?
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2021-06-08 01:04:30 merijn joins (~merijn@83-160-49-249.ip.xs4all.nl)
2021-06-08 01:04:30 <blankhart> the paper is talking about guessing in recursive binding groups and adding kinds to a context before looking at the related declarations
2021-06-08 01:06:32 <cdsmith> Yes, I suppose it just means that the declarative specification of the type system cannot be interpreted as an algorithm, or used as an implementation, because you need to know what the kinds are before you can evaluate the claims there.
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2021-06-08 01:07:35 <blankhart> is the point that in "algorithmic type systems" a unification variable is used but in a declarative system the kind is "guessed" in the sense of being solved by whatever algorithm implements the system?
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2021-06-08 01:11:15 <cdsmith> I'm not sure of the details here, sorry. Maybe someone else can help more!
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2021-06-08 01:15:59 <ski> blankhart : i think "guess" means that there's no way to order the premises, viewed as (calls to) relations that compute outputs from inputs, in such a way that every (meta-)variable is output before it needs to be input (considering the inputs of the conclusion relation as "initial inputs", and the corresponding outputs as "final outputs")
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2021-06-08 01:19:38 <blankhart> so, for starters, we don't mean "guess" in the sense of something that might be wrong. it is more like, we consult an oracle that tells us what the answer would be if we had a constraint solving algorithm?
2021-06-08 01:20:14 <cdsmith> Yes, "consult an oracle" sounds like exactly what they mean.
2021-06-08 01:20:23 <ski> i believe that's the idea, yes
2021-06-08 01:21:08 <blankhart> thanks both
2021-06-08 01:21:28 <ski> (having some knowledge of logic programming is relevant here)
2021-06-08 01:22:52 <blankhart> well haskell is declarative, so i was trying to think of an analogy with mutually recursive let bindings, but couldn't really get one that i would describe as involving "guessing"
2021-06-08 01:24:23 <ski> well, the "declarative" in "declarative typing rules" isn't really related to the one in "declarative programming paradigm"
2021-06-08 01:25:14 <cdsmith> Well, in some sense recursive let bindings present a similar issue, in that there could be multiple values that satisfy the system of equations. But we also have an algorithmic interpretation involving least fixed points in the definedness order. So that's the sense in which Haskell is more "algorithmic" and not purely "declarative" in the paper's usage of the words.
2021-06-08 01:26:13 <ski> yes, recursive `let' also needs "guessing" in the same sense
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2021-06-08 01:27:32 <blankhart> that was the missing piece thank you
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2021-06-08 01:30:43 <ski> (btw, i think i've heard the term "guess" even used in situations like e.g. the typing rule for function application, in that there's a (meta-)variable that occurs in the premises, that doesn't appear in the conclusion, and so, if you're attempting to build a typing derivation tree, from the root, you'd have to "guess" the argument type, when coming to an application. this corresponds to viewing all
2021-06-08 01:30:49 <ski> (judgement) relation parameters as "input". however, at least in a typing (as opposed to a more general derivation, or logic programming, context) context, i think it's common to consider them as having both input and output parameters. cf. bidirectional type checking)
2021-06-08 01:31:58 <ski> (for comparision, for deductive databases, all parameters would be considered "output", as the derivation tree is built bottom-up (rather than top-down), from the leaves/facts (rather than from the root/goal))
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2021-06-08 01:37:08 <blankhart> algorithmically interpreted as call by need, call by value, call by...both
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2021-06-08 01:39:59 <blankhart> so the point of a "syntax-directed
2021-06-08 01:40:02 <ski> hm ?
2021-06-08 01:40:23 <blankhart> " declarative specification is that it is also algorithmic in that there is no need to guess?
2021-06-08 01:40:45 <ski> not sure of a relation to the call-by-* stuff
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2021-06-08 01:43:03 <ski> blankhart : i'd say it's not that simple. i think syntax-directed would mean that there's only one (or maybe at most a few ?) rules to consider / choose from, given the term (or whatever one is syntax-directed wrt) as an input. but there could still be other (meta-)variables that would need to be "guessed", in the application of the selected rule
2021-06-08 01:44:02 ski . o O ( attribute grammars )
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2021-06-08 01:52:27 <blankhart> thank you ski i will think more about that
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