Concrete mathematics: a foundation for computer science
Concrete mathematics: a foundation for computer science
Algorithm 755: ADOL-C: a package for the automatic differentiation of algorithms written in C/C++
ACM Transactions on Mathematical Software (TOMS)
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 differentiation of computer programs
ICFP '98 Proceedings of the third ACM SIGPLAN international conference on Functional programming
Recipes for adjoint code construction
ACM Transactions on Mathematical Software (TOMS)
Functional Programming and Mathematical Objects
FPLE '95 Proceedings of the First International Symposium on Functional Programming Languages in Education
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Computational Divided Differencing and Divided-Difference Arithmetics
Higher-Order and Symbolic Computation
Functional Approach to Texture Generation
PADL '02 Proceedings of the 4th International Symposium on Practical Aspects of Declarative Languages
Functional automatic differentiation with dirac impulses
ICFP '03 Proceedings of the eighth ACM SIGPLAN international conference on Functional programming
Teaching of image synthesis in functional style
Proceedings of the 2005 workshop on Functional and declarative programming in education
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)
Towards an Implementation of a Computer Algebra System in a Functional Language
Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
On the implementation of automatic differentiation tools
Higher-Order and Symbolic Computation
Nesting forward-mode AD in a functional framework
Higher-Order and Symbolic Computation
Using Structural Recursion for Corecursion
Types for Proofs and Programs
Proceedings of the 14th ACM SIGPLAN international conference on Functional programming
ACM Transactions on Mathematical Software (TOMS)
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We present a purely functional implementation of the computational differentiation tools—the well known numeric (i.e., not symbolic) techniques which permit one to compute point-wise derivatives of functions defined by computer programs economically and exactly (with machine precision). We show how the use of lazy evaluation permits a transparent and elegant construction of the entire infinite tower of derivatives of higher order for any expressions present in the program. The formalism may be useful in various problems of scientific computing which often demand a hard and ungracious human preprocessing before writing the final code. Some concrete examples are given.