A practical lambda-calculator is a normal-order evaluator for the untyped lambda-calculus, extended with convenient commands and shortcuts to make programming in it more productive. Shortcuts are distinguished constants that represent terms. Commands define new shortcuts, activate tracing of all reductions, compare terms modulo alpha-conversion, print all defined shortcuts and evaluation flags, etc. Terms to evaluate and commands are entered at a read-eval-print-loop (REPL) "prompt" or "included" from a file by a special command. A Haskell branch is an embedding of the lambda calculator (as a domain-specific language) into Haskell. The calculator can be used interactively within Hugs or GHCi.
ACL2 is a mathematical logic, programming language, and mechanical theorem prover based on the applicative subset of Common Lisp. It is an "industrial-strength" version of the NQTHM or Boyer/Moore theorem prover, and has been used for the formal verification of commercial microprocessors, the Java Virtual Machine, interesting algorithms, and so forth.
ASCIIMathML is a script that converts calculator-style ASCII math notation (and many LaTeX formulas) to Presentation MathML while your Web page loads. It works with HTML and XHTML files in Mozilla/Firefox/Netscape 7+ browsers, as well as in Internet Explorer 6 with MathPlayer. For example, the solutions for the equation 'ax^2+bx+c=0' are expressed in the HTML file as '(-b +- sqrt(b^2 - 4ac))/(2a)', and display as nicely formatted MathML. The script can be easily used in wikiservers and blogs, as a rudimentary MathML editor (with instant preview), and to preview math formulas as they are typed into a Web page input area.
The ATLAS (Automatically Tuned Linear Algebra Software) project is an ongoing research effort focusing on applying empirical techniques in order to provide portable performance. It provides C and Fortran77 interfaces to a portably efficient BLAS implementation, as well as a few routines from LAPACK.
Apophenia is an open statistical library. It provides functions on the same level as those of the typical stats package (such as OLS, probit, or singular value decomposition) but doesn't tie the user to an ad hoc language or environment. The core functions are written in C, but a Python interface is included. It supports SQLite and MySQL databases, exponentially expanding the upper limit to manageable data sets. Since the library is significantly faster than most stats packages, computationally-intensive procedures like maximum likelihood estimation and Monte Carlo routines are easy to implement.
The Atropos (formerly AVNMP) Toolkit allows experimentation with predictive capability inside a network while the network is operating: this might be best described as 'in vitro' prediction experimentation. Its purpose is to facilitate experimentation towards addressing a severe limitation in state-of-the-art network management: current management techniques are reactive. The toolkit is an active application that executes in real time within a network that has an overlay active network. Active networking provides a framework in which executable code within data packets executes upon intermediate network nodes. The Atropos Toolkit provides the infrastructure to develop and inject numerous, small, interacting network component models in support of network prediction. Research results in Complexity Theory using Atropos can be found in the DARPA-funded GE Fault Tolerant Networking Project.
AutoAbacus is a powerful equation solving library that finds solutions to equation sets. Equations are passed to AutoAbacus as text, and the program attempts to find a solution that satisfies all constraints. The equations can be linear or polynomial, and can include arbitrary functions. By profiling the types of equations in the system and their dependencies on each other, AutoAbacus uses appropriate solution methods to solve individual subsets of equations. Applications range from use in a business rules engine to solving engineering equation systems.
Benojt is a fast and flexible explorer for various types of fractals. It can render escape-time fractals like Mandelbrot/Julia style fractals, Newton fractals, Lyapunov fractals, and two dimensional attractors/strange attractors. Due to its modular design, single components like iterators, renderers, and colorings can be replaced, making it easy to experiment with individual aspects of fractal creation. New iterators can be created at runtime by typing a fractal fomula which is compiled and loaded automatically.