Tail recursion through universal invariants

Tail Recursion Through Universal Invariants

Tail recursive constructions suggest a new semantics for datatypes, which allows a direct match between speciications and tail recursive programs. The semantics focusses on loops, their xpoints, invariants and convergence. Convergent models of the natural numbers and lists are examined in detail, and, under very mild conditions, are shown to be equivalent to the corresponding initial algebra mo...

Inductive Invariants for Nested Recursion

We show that certain input-output relations, termed inductive invariants are of central importance for termination proofs of algorithms defined by nested recursion. Inductive invariants can be used to enhance the standard recdef definition package in Isabelle/HOL. We also offer a formalized theory in higher-order logic that incorporates inductive invariants and that can be used as an alternativ...

Inductive Invariants for Nested Recursion

Tail Recursion without Space Leaks

The G-machine (Johnsson, 1987; Peyton Jones, 1987) is a compiled graph reduction machine for lazy functional languages. The G-machine compiler contains many optimisations to improve performance. One set of such optimisations is designed to improve the performance of tail recursive functions. Unfortunately the abstract machine is subject to a space leak—objects are unnecessarily preserved by the...

The Universal Kolyvagin Recursion Implies the Kolyvagin Recursion

Let Uz be the universal norm distribution and M a fixed power of prime p, by using the double complex method employed by Anderson, we study the universal Kolyvagin recursion occurred in the canonical basis in the cohomology group H(Gz ,Uz/MUz). We furthermore show that the universal Kolyvagin recursion implies the Kolyvagin recursion in the theory of Euler systems. One certainly hopes this coul...