A Monad for Randomized Algorithms

Building inference algorithms from monad transformers

We show how to decompose popular inference algorithms into a set of simple, reusable building blocks corresponding to monad transformers. We define a collection of such building blocks and implement them in Haskell producing a library for constructing inference algorithms in a modular fashion. We are also working towards formalizing those concepts as monadic denotational semantics for inference...

New Algorithms for Finding Monad Patterns in DNA Sequences

In this paper, we present two new algorithms for discovering monad patterns in DNA sequences. Monad patterns are of the form (l,d)k, where l is the length of the pattern, d is the maximum number of mismatches allowed, and k is the minimum number of times the pattern is repeated in the given sample. The time-complexity of some of the best known algorithms to date is O(ntlσ), where t is the numbe...

A Semi-monad for Semi-structured Data

This document proposes an algebra for XML Query. The algebra has been submitted to the W3C XML Query Working Group. A novel feature of the algebra is the use of regular-expression types, similar in power to DTDs or XML Schemas, and closely related to Hasoya and Pierce’s work on Xduce. The iteration construct is based on the notion of a monad, and involves novel typing rules not encountered else...

A Monad Measure Space for Logarithmic Density

We provide a framework for proofs of structural theorems about sets with positive Banach logarithmic density. For example, we prove that if A ⊆ N has positive Banach logarithmic density, then A contains an approximate geometric progression of any length. We also prove that if A,B ⊆ N have positive Banach logarithmic density, then there are arbitrarily long intervals whose gaps on A·B are multip...

A Hoare Logic for the State Monad