Rational deconstruction of rational reconstruction

A Rational Deconstruction of Landin's SECD Machine

Landin’s SECD machine was the first abstract machine for the λ-calculus viewed as a programming language. Both theoretically as a model of computation and practically as an idealized implementation, it has set the tone for the subsequent development of abstract machines for functional programming languages. However, and even though variants of the SECD machine have been presented, derived, and ...

A Rational Deconstruction of Landin's J Operator

Landin’s J operator was the first control operator for functional languages. It was specified with an extension of the SECD machine, which was the first abstract machine for functional languages. We present a family of compositional evaluation functions corresponding to this extension of the SECD machine, using a series of elementary transformations (transformation into continuation-passing sty...

Protos - a Rational Reconstruction

Eecient Rational Number Reconstruction

The paper presents an eecient algorithm for reconstructing a rational number from its residue modulo a given integer. The algorithm is based on a double-digit version of Lehmer's multi-precision extended Euclidean algorithm. While asymptotic complexity remains quadratic in the length of the input, experiments with an implementation show that for small inputs the new algorithm is more than 3 tim...

Efficient Rational Number Reconstruction