So I've been testing out serialising a query to the AST representation, it looks like there's a slight bug when referencing params (serializing them is fine). So this works:
query().params({param1: 3}).filter((d, $) => d.colA}).toAST()
but including the param in any expression fails:
query().params({param1: 3}).filter((d, $) => d.colA / $.param1 }).toAST()

Presumably all verbs that boil down to an ExprObject exhibit the same problem.

Calling aq.internal.parse directly with a fake table in opt works:

const fakeTable = {
  params: () => ({param1: 3}),
  column: () => true
}
const compiledAst = aq.internal.parse({expr: `(d, $) => d.colA < $.param1`, {table: fakeTable, ast: true})

I suspect we just need to pass down the query context in query.js, as a fourth parameter to toAST in verb.js, and tweak getParams to pull in params from opt.table or opt.query.