Derivable Type Classes

Derivable Type Classes

Generi programming allows you to write a fun tion on e, and use it many times at di erent types. A lot of good foundational work on generi programming has been done. The goal of this paper is to propose a pra ti al way of supporting generi programming within the Haskell language, without radi ally hanging the language or its type system. The key idea is to present generi programming as a ri her...

Induction Is Not Derivable in Second Order Dependent Type Theory

Closed Non-derivable Itemsets

Itemset mining typically results in large amounts of redundant itemsets. Several approaches such as closed itemsets, non-derivable itemsets and generators have been suggested for losslessly reducing the amount of itemsets. We propose a new pruning method based on combining techniques for closed and non-derivable itemsets that allows further reductions of itemsets. This reduction is done without...

Left derivable or Jordan left derivable mappings on Banach algebras

‎Let $mathcal{A}$ be a unital Banach algebra‎, ‎$mathcal{M}$ be a left $mathcal{A}$-module‎, ‎and $W$ in $mathcal{Z}(mathcal{A})$ be a left separating point of $mathcal{M}$‎. ‎We show that if $mathcal{M}$ is a unital left $mathcal{A}$-module and $delta$ is a linear mapping from $mathcal{A}$ into $mathcal{M}$‎, ‎then the following four conditions are equivalent‎: ‎(i) $delta$ is a Jordan left de...

Type Reconstruction for Type Classes

We study the type inference problem for a system with type classes as in the functional programming language Haskell. Type classes are an extension of ML-style polymorphism with overloading. We generalize Milner’s work on polymorphism by introducing a separate context constraining the type variables in a typing judgement. This leads to simple type inference systems and algorithms which closely ...