binary-search

Binary and exponential searches.

Introduction

This package provides varieties of binary search functions. c.f. Numeric.Search for the examples.

These search function can search for pure and monadic predicates, of type:

pred :: Eq b => a -> b
pred :: (Eq b, Monad m) => a -> m b

The predicates must satisfy that the domain range for any codomain value is continuous; that is, ∀x≦y≦z. pred x == pred z ⇒ pred y == pred x .

For example, we can address the problem of finding the boundary of an upward-closed set of integers, using a combination of exponential and binary searches.

Variants are provided for searching within bounded and unbounded intervals of both Integer and bounded integral types.

The package was created by Ross Paterson, and extended by Takayuki Muranushi, to be used together with SMT solvers.

The Module Structure

• Numeric.Search provides the generic search combinator, to search for pure and monadic predicates.

• Numeric.Search.Bounded , Numeric.Search.Integer , Numeric.Search.Range provides the various specialized searchers, which means less number of function arguments, and easier to use.