Algebraic graphs with class (functional pearl)

FUNCTIONAL PEARL InvertingtheBurrowsWheelertransform

The objective of this pearl is to derive the inverse of the Burrows-Wheeler transform from its specification, using simple equational reasoning. In fact, we derive the inverse of a more general version of the transform, proposed by Schindler.

FUNCTIONAL PEARL Pickler Combinators

The tedium of writing pickling and unpickling functions by hand is relieved using a combinator library similar in spirit to the well-known parser combinators. Picklers for primitive types are combined to support tupling, alternation, recursion, and structure sharing. Code is presented in Haskell; an alternative implementation in ML is discussed.

FUNCTIONAL PEARL LinearlambdacalculusandPTIME-completeness

We give transparent proofs of the PTIME-completeness of two decision problems for terms in the λ-calculus. The first is a reproof of the theorem that type inference for the simplytyped λ-calculus is PTIME-complete. Our proof is interesting because it uses no more than the standard combinators Church knew of some 70 years ago, in which the terms are linear affine – each bound variable occurs at ...

FUNCTIONAL PEARL Linear, Bounded, Functional Pretty-Printing

We present two implementations of Oppen’s pretty-printing algorithm in Haskell that meet the efficiency of Oppen’s imperative solution but have a simpler, clear structure. We start with an implementation that uses lazy evaluation to simulate two co-operating processes. Then we present an implementation that uses higher-order functions for delimited continuations to simulate co-routines with exp...

Functional Pearl: Enumerating the rationals