Partial Application is where you can take a multi-argument function and construct a new function by assigning a value to one or more of the leading arguments but not all of them. For example, in Mathcad 15 you could write
| Define a two-parameter function power (same as exponentiation operator) |
power(x,y) := x^y |
| Define function Bin to raise 2 to the power of y by partially applying power to 2 |
Bin := power(2) |
| Evaluate Bin like any other 1-argument function |
Bin(8) = 256 |
Once you get used to how it looks, it's very useful for abbreviating function definitions, particularly so when, say, you have a 3+ argument function with the last two arguments being x & y or i & j and can then set the leading arguments when, say, using it into a 3D plot.
Another example to help make its utility clearer. The built-in function matrix(m,n,f) takes two integers m & n and a two-argument function f(i,j). matrix iterates over the matrix indices i = 0 .. m-1 and j = 0.. n-1, generating a matrix whose elements are f(i,j).
succ(m,i,j) := i + m*j
M(m,n) := matrix(m,n,succ(m))
M(3,3) should create a 3x3 matrix of column-wise successive integers.
If you have programming, it could be done using a local function definition
M(m,n) := matrix(m,n,f(i,j)<-succ(m,i,j))
But I think the latter is less 'succ'inct and harder to read, particularly when there are long names or even expressions for the arguments, or multiple functions in a plot.
Unfortunately, Prime doesn't do it, nor, whilst I'm having a moan, does Prime allow local functions to be recursive; Mathcad 15 provided both these features.
PTC deliberately removed partial application because it confused somebody when they left an argument out of a function <Sigh>. So we have a mathematical application removing a facility that every other programming language and their dogs are busy implementing ...
I think the lack of local recursion is just a specification / programming mistake.
Regardless, I have a number of useful worksheets that are now broken. I could do a lot more with Prime (especially Express) if it had both.
https://en.wikipedia.org/wiki/Partial_application
