  Semantic parsing has made significant progress, but most current semantic
parsers are extremely slow (CKY-based) and rather primitive in representation.
We introduce three new techniques to tackle these problems. First, we design
the first linear-time incremental shift-reduce-style semantic parsing algorithm
which is more efficient than conventional cubic-time bottom-up semantic
parsers. Second, our parser, being type-driven instead of syntax-driven, uses
type-checking to decide the direction of reduction, which eliminates the need
for a syntactic grammar such as CCG. Third, to fully exploit the power of
type-driven semantic parsing beyond simple types (such as entities and truth
values), we borrow from programming language theory the concepts of subtype
polymorphism and parametric polymorphism to enrich the type system in order to
better guide the parsing. Our system learns very accurate parses in GeoQuery,
Jobs and Atis domains.
