A Type Theory for Incremental Computational Complexity with Control Flow Changes (Technical Appendix)
نویسندگان
چکیده
1 Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Value and expression syntax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3 Context well-formedness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 4 Constraint well-formedness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 5 Well-formedness of types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 6 Mode under type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 7 Upper bound of typing mode and variation annotation . . . . . . . . . . . . . . . 5 8 Force annotation on type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 9 Sorting rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 10 Subtyping rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 11 Expression typing rules, part 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 12 Expression typing rules, part 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 13 Concrete costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 14 Syntax of bi-values and bi-expression . . . . . . . . . . . . . . . . . . . . . . . . . 10 15 Typing rules for bi-values and bi-expressions . . . . . . . . . . . . . . . . . . . . . 11 16 Step-indexed interpretation of types . . . . . . . . . . . . . . . . . . . . . . . . . 12 17 Unary step-indexed interpretation of types . . . . . . . . . . . . . . . . . . . . . . 13 18 L(ee): Left or the original expression. R(ee): Right or the modified expression. . 13 19 Traces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 20 From-scratch evaluation semantics . . . . . . . . . . . . . . . . . . . . . . . . . . 15 21 Change propagation rules part 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 22 Change propagation rules, part 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 23 Target Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
منابع مشابه
Refinement Types for Incremental Computational Complexity (Technical Appendix)
– four new types: type variable X, universal type ∀X : K.τ , type operator abstraction λi :: S.τ and type operator application τ I. – A new kinding judgment Ψ; ∆ ` T :: K that assigns kinds to types – Typing judgment ∆; Φ; Γ ` e :κ τ changes to Ψ; ∆; Φ; Γ ` e :κ τ in which the context Ψ binds the type variables. – The subtyping judgment is changed as follows: Ψ; ∆; Φ |= τ1 v τ2 : K. – Semantics...
متن کاملA Hybrid Framework for Building an Efficient Incremental Intrusion Detection System
In this paper, a boosting-based incremental hybrid intrusion detection system is introduced. This system combines incremental misuse detection and incremental anomaly detection. We use boosting ensemble of weak classifiers to implement misuse intrusion detection system. It can identify new classes types of intrusions that do not exist in the training dataset for incremental misuse detection. As...
متن کاملPOPL: G: Refinement Types for Incremental Computational Complexity
With recent advances, programs can be compiled to efficiently respond to incremental input changes. However, there is no language-level support for reasoning about the time complexity of incremental updates. Motivated by this gap, we present CostIt, a higher-order functional language with a lightweight refinement type system for proving asymptotic bounds on incremental computation time. Type re...
متن کاملIntroduction to Combinatorial Optimization
1. Basic Concepts in Graph Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2. Connectedness and Optimal Trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7 3. Shortest Paths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....
متن کاملDistributed and Cooperative Compressive Sensing Recovery Algorithm for Wireless Sensor Networks with Bi-directional Incremental Topology
Recently, the problem of compressive sensing (CS) has attracted lots of attention in the area of signal processing. So, much of the research in this field is being carried out in this issue. One of the applications where CS could be used is wireless sensor networks (WSNs). The structure of WSNs consists of many low power wireless sensors. This requires that any improved algorithm for this appli...
متن کامل