How does one obtain the type of the value that an AST represents?

I’m trying to write the following:

import scala.reflect.runtime.universe._

val value: Tree = /* some AST */
val tpe = typeOf(value)    // This should be the result type of the AST.
                           // This is pseudocode. What should
                           // actually go on this line?
q"""
type U = $tpe
val v: U = $value
"""

I need to capture the type of the value represented by the AST value in tpe and assign it to U. How does one do this?

Edit: Giving a type annotation for value and matching on it via quasiquotes isn't an option here. The use case is a Shapeless extensible record, which has complicated types such as String with labelled.KeyTag[1, String] :: Long with labelled.KeyTag[three, Long] :: HNil for something like val ls = (1 ->> "two") :: ("three" ->> 4L) :: HNil. Also, the value AST is programmatically generated and not a literal.

Get a ToolBox, use it to typecheck value, and ask the annotated tree for its type.

import scala.runtime.reflect.currentMirror
val toolbox = currentMirror.mkToolBox()
val tpe = TypeTree(toolbox.typecheck(value).tpe)

The code you've written states you're doing this at runtime. The use case you've stated in your comment makes it seem like you're in a compile-time macro. In that case, use the similar typecheck method in your Context. It won't typecheck otherwise; the value would be a Tree from the wrong Universe, representing the fact that the new compiler instance made by ToolBox operates in the context of the current program (which happens to be a compiler), while the reflection represented by the Context is all about the future context of the code manipulated by the containing compiler.