Concrete mathematics: a foundation for computer science
Concrete mathematics: a foundation for computer science
SIAM Journal on Scientific Computing
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Generating power of lazy semantics
Theoretical Computer Science - Special volume on computer algebra
Functional Programming and Mathematical Objects
FPLE '95 Proceedings of the First International Symposium on Functional Programming Languages in Education
Functional Differentiation of Computer Programs
Higher-Order and Symbolic Computation
Scientific Computation and Functional Programming
Computing in Science and Engineering
Computational Divided Differencing and Divided-Difference Arithmetics
Higher-Order and Symbolic Computation
Polygonizing Implicit Surfaces in a Purely Functional Way
IFL '00 Selected Papers from the 12th International Workshop on Implementation of Functional Languages
Lazy multivariate higher-order forward-mode AD
Proceedings of the 34th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Reverse-mode AD in a functional framework: Lambda the ultimate backpropagator
ACM Transactions on Programming Languages and Systems (TOPLAS)
Nesting forward-mode AD in a functional framework
Higher-Order and Symbolic Computation
PADL'10 Proceedings of the 12th international conference on Practical Aspects of Declarative Languages
| Hi-index | 0.00 |
We present two purely functional implementations of the computational differentiation tools -- the well known numeric (not symbolic!) techniques which permit to compute pointwise derivatives of functions defined by computer programs economically and exactly. We show how the co-recursive (lazy) algorithm formulation permits to construct in a transparent and elegant manner the entire infinite tower of derivatives of higher order for any expressions present in the program, and we present a purely functional variant of the reverse (or adjoint) mode of computational differentiation, using a chain of delayed evaluations represented by closures. Some concrete applications are also discussed.