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== Examples from programming == | == Examples from programming == | ||
Let's consider possible "side effects" of a function A → B. It might... | Let's consider possible "side effects" of a function A → B. It might... | ||
* < | * <mark>throw an error of type Err</mark> instead of actually returning a result of type B. | ||
* < | * <mark>return some "log" data</mark> alongside its result of type B. | ||
* < | * <mark>depend on / read some "environment" data</mark> in order to produce a result of type B. | ||
One way a programming language can encode this is using '''monads'''. Basically, we say we have functions of types like | One way a programming language can encode this is using '''monads'''. Basically, we say we have functions of types like | ||
* A → < | * A → <mark>Either Err</mark> B | ||
* A → < | * A → <mark>Writer Log</mark> B | ||
* A → < | * A → <mark>Reader Env</mark> B | ||
and we rely on some way to ''compose'' these functions, while ''propagating'' their effects. | and we rely on some way to ''compose'' these functions, while ''propagating'' their effects. | ||
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== In syntax == | == In syntax == | ||
It turns out that we can extend this concept to syntax. For example, consider a [[noun phrase]] with an apposition, like ''Mary, a linguist''. This seems to be essentially (syntactically) an entity of type ''e'' that also wants to "write" a presupposition like "Mary is a linguist" to some environment. So, we say that it is an entity ''e'' in an effectful context ''W'', and we write this as the subtree having type ''W e''. | It turns out that we can extend this concept to syntax. For example, consider a [[noun phrase]] with an apposition, like ''Mary, a linguist''. This seems to be essentially (syntactically) an entity of type ''e'' that also wants to "write" a presupposition like "Mary is a linguist" to some environment. So, we say that it is an entity ''e'' in an effectful context ''<mark>W</mark>'', and we write this as the subtree having type ''<mark>W</mark> e''. | ||
When we move up the tree to a bigger constituent like '' | When we move up the tree to a bigger constituent like ''John saw Mary, a linguist'', we want to keep this effectful context and "lift" the rest of the sentence, ''John saw'' (of type ''e → t''), into it. We first turn ''e → t'' into ''<mark>W</mark> (e → t)'' and then compose this with our ''<mark>W</mark> e'' to get a ''<mark>W</mark> t''. | ||
Similarly, a pronoun like ''her'' can be considered to be an entity ''e'' in an effectful "reader" context that provides a value for the binding: its type is ''<mark>R</mark> e''. This, again, might compose the same way to form a larger constituent like ''John saw her'', of type ''<mark>R</mark> t''. | |||
When we compose the meaning of two effectful constituents, we have to pick a way to combine the contexts. For example, ''John saw Mary, a linguist'' might have type ''R (W t)'' or type ''W (R t)''. It depends on which effect we ''lift'' "into" the other effect before combining them. | |||
Eventually, we arrive at a denoted sentence wrapped in a list of effects (presuppositions, bindings, focus…) gathered from everywhere in the sentence. | Eventually, we arrive at a denoted sentence wrapped in a list of effects (presuppositions, bindings, focus…) gathered from everywhere in the sentence. | ||
When parsing English, the freedom you have in deciding how to combine effects accounts for syntactic ambiguity. In an effectful version of [[Kuna]], we'd have a handful of rules saying exactly how effects combine, and this would answer questions about [[scope]]. | |||
== See also == | == See also == | ||
* [https://simoncharlow.com/esslli/ Effectful composition in natural language semantics], slides by Dylan Bumford and Simon Charlow. | * [https://simoncharlow.com/esslli/ Effectful composition in natural language semantics], slides by Dylan Bumford and Simon Charlow. | ||
* https://ncatlab.org/nlab/show/monad+%28in+linguistics%29 | * https://ncatlab.org/nlab/show/monad+%28in+linguistics%29 | ||