62,289 research outputs found
Uniform Proofs of Normalisation and Approximation for Intersection Types
We present intersection type systems in the style of sequent calculus,
modifying the systems that Valentini introduced to prove normalisation
properties without using the reducibility method. Our systems are more natural
than Valentini's ones and equivalent to the usual natural deduction style
systems. We prove the characterisation theorems of strong and weak
normalisation through the proposed systems, and, moreover, the approximation
theorem by means of direct inductive arguments. This provides in a uniform way
proofs of the normalisation and approximation theorems via type systems in
sequent calculus style.Comment: In Proceedings ITRS 2014, arXiv:1503.0437
The Algebraic Intersection Type Unification Problem
The algebraic intersection type unification problem is an important component
in proof search related to several natural decision problems in intersection
type systems. It is unknown and remains open whether the algebraic intersection
type unification problem is decidable. We give the first nontrivial lower bound
for the problem by showing (our main result) that it is exponential time hard.
Furthermore, we show that this holds even under rank 1 solutions (substitutions
whose codomains are restricted to contain rank 1 types). In addition, we
provide a fixed-parameter intractability result for intersection type matching
(one-sided unification), which is known to be NP-complete.
We place the algebraic intersection type unification problem in the context
of unification theory. The equational theory of intersection types can be
presented as an algebraic theory with an ACI (associative, commutative, and
idempotent) operator (intersection type) combined with distributivity
properties with respect to a second operator (function type). Although the
problem is algebraically natural and interesting, it appears to occupy a
hitherto unstudied place in the theory of unification, and our investigation of
the problem suggests that new methods are required to understand the problem.
Thus, for the lower bound proof, we were not able to reduce from known results
in ACI-unification theory and use game-theoretic methods for two-player tiling
games
An efficient decomposition approach for surgical planning
This talk presents an efficient decomposition approach to surgical planning. Given a set of surgical waiting lists (one for each discipline) and an operating theater, the problem is to decide the room-to-discipline assignment for the next planning period (Master Surgical Schedule), and the surgical cases to be performed (Surgical Case Assignment), with the objective of optimizing a score related to priority and current waiting time of the cases. While in general MSS and SCA may be concurrently found by solving a complex integer programming problem, we propose an effective decomposition algorithm which does not require expensive or sophisticated computational resources, and is therefore suitable for implementation in any real-life setting.
Our decomposition approach consists in first producing a number of subsets of surgical cases for each discipline (potential OR sessions), and select a subset of them. The surgical cases in the selected potential sessions are then discarded, and only the structure of the MSS is retained. A detailed surgical case assignment is then devised filling the MSS obtained with cases from the waiting lists, via an exact optimization model.
The quality of the plan obtained is assessed by comparing it with the plan obtained by solving the exact integrated formulation for MSS and SCA. Nine different scenarios are considered, for various operating theater sizes and management policies. The results on instances concerning a medium-size hospital show that the decomposition method produces comparable solutions with the exact method in much smaller computation time
Straddling the intersection
Music technology straddles the intersection between art and science and presents those who choose to work within its sphere with many practical challenges as well as creative possibilities. The paper focuses on four main areas: secondary education, higher education, practice and research and finally collaboration. The paper emphasises the importance of collaboration in tackling the challenges of interdisciplinarity and in influencing future technological developments
Characterisation of Strongly Normalising lambda-mu-Terms
We provide a characterisation of strongly normalising terms of the
lambda-mu-calculus by means of a type system that uses intersection and product
types. The presence of the latter and a restricted use of the type omega enable
us to represent the particular notion of continuation used in the literature
for the definition of semantics for the lambda-mu-calculus. This makes it
possible to lift the well-known characterisation property for
strongly-normalising lambda-terms - that uses intersection types - to the
lambda-mu-calculus. From this result an alternative proof of strong
normalisation for terms typeable in Parigot's propositional logical system
follows, by means of an interpretation of that system into ours.Comment: In Proceedings ITRS 2012, arXiv:1307.784
Inhabitation for Non-idempotent Intersection Types
The inhabitation problem for intersection types in the lambda-calculus is
known to be undecidable. We study the problem in the case of non-idempotent
intersection, considering several type assignment systems, which characterize
the solvable or the strongly normalizing lambda-terms. We prove the
decidability of the inhabitation problem for all the systems considered, by
providing sound and complete inhabitation algorithms for them
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