set x 1; expr (exp(1/pow($x,2)))/pow($x,2)Which for x=0.5,1.0,2.0 evaluates to: 218.392600133, 2.71828182846 and 0.321006354172 . Now we may want to break that equation down into principal arithmetical operations (by hand in this case), and see it like this:using bwise blocks (the value in the mon block isn't for the same computation). Doing that in a straightforward way gives the above graph, to which I added the input entry and output monitor, where feeding the chain with the same values gives: 218.392600132 , 2.71828182846 and 0.321006354173 correct except the very last digit, which probably comes from the difference between the explicit evaluation order in bwise compared to the internal evaluation, or simply because I didn't include all the relevant digits in the passing of bwise arguments.For analysis of the network, bwise has various functions, for instance to get all blocks left of the last block, let us say

**fr**, we can use

net_allleft fr epo fr rec sq1 sq2and get all subnetwork block names returned. The procedure net_funct returns only the 'leaf' nodes of the tree from the left (input) side of the fr block:

(Tcl) 143 % net_funct fr Entry1And after we remove or detach the entry block:

(Tcl) 144 % net_funct fr rec sq2Now what's the point of 'functional' in this context? Basically, that a block has no memory, and that there is one outcome, which depends on the arguments to the overall function, and the decomposition doesn't matter, assuming it is done right. Then the computation order can be thought to be governed by the availability of the input data for each block: as soon as all data is available, the block can be 'fired', which is what bwises' 'net_funprop' works like, and it is provable that each block needs to get fired only once.Of course once the function (de-) composition tree has been established, it is possible to do obvious enough simplifications, mainly by reusing intermediate results, or by first reordering and reformulating and then outcome reuse, such as the two square operations could be reduced to one.

TV

*(feb 1 2005)*I'll be doing a 'lecture' (entry level) about functional programming / basic functional analysis at fosdem 2005, see [1] .Maybe I'll use this example: Bwise traffic lights with challenges. Also maxima is interesting in that picture like in Bwise blocks using exec maxima because then we could combine maxima mathematical manipulations in a functional way.