System F with Constraint Types

System F is a type system that can be seen as both a proof system for second-order propositional logic and as a polymorphic programming language. In this work we explore several extensions of System F by types which express subtyping constraints. These systems include terms which represent proofs of subtyping relationships between types. Given a proof that one type is a subtype of another, one may use a coercion term constructor to coerce terms from the first type to the second. The ability to manipulate type constraints as first-class entities gives these systems a lot of expressive power, including the ability to encode generalized algebraic data types and intensional type analysis. The main contributions of this work are in the formulation of constraint types and a proof of strong normalization for an extension of System F with constraint types.

Constraint-based Mining of Frequent Arrangements of Temporal Intervals

The problem of discovering frequent arrangements of temporal intervals is studied. It is assumed that the database consists of sequences of events, where an event occurs during a time-interval. The goal is to mine temporal arrangements of event intervals that appear frequently in the database. The motivation of this work is the observation that in practice most events are not instantaneous but occur over a period of time and different events may occur concurrently. Thus, there are many practical applications that require mining such temporal correlations between intervals including the linguistic analysis of annotated data from American Sign Language as well as network and biological data. Two efficient methods to find frequent arrangements of temporal intervals are described; the first one is tree-based and uses depth first search to mine the set of frequent arrangements, whereas the second one is prefix-based. The above methods apply efficient pruning techniques that include a set of constraints consisting of regular expressions and gap constraints that add user-controlled focus into the mining process. Moreover, based on the extracted patterns a standard method for mining association rules is employed that applies different interestingness measures to evaluate the significance of the discovered patterns and rules. The performance of the proposed algorithms is evaluated and compared with other approaches on real (American Sign Language annotations and network data) and large synthetic datasets.