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tutorial_subsystem

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# SubSystem in Alpha

In this tutorial, we will present how to write structured alpha programs with subsystems, and we will present the associated transformations.

### Syntax of Use Equation (without extension domain)

Let us assume that we want to compute the mean of the values of a vector. It is feasible through the following Alpha system:

affine mean {N | N>0}
input
float A {k | 0<=k<N};
output
float C {|};
local
float temp {|};
let
temp = reduce(+, [k], A[k]);
C = temp / N;
.


However, let us assume that you already have another Alpha system which computes the sum of the elements of a vector. It is possible to use this affine system (instead of rewriting its equation in the main system), by calling it through a “use equation”:

affine sum {P| P>0}	// Computes the sum of the elements of a vector of size P
input
float vect {i | 0<=i<P };
output
float Res;
let
Res = reduce(+, [k], vect[k]);
.

affine mean {N | N>0}
input
float A {k | 0<=k<N};
output
float C {|};
local
float temp {|};
let
use sum[N] (A) returns (temp);		// Compute "temp" using the system "sum"
C = temp / N;
.


The system “mean” is calling the system “sum” (which is called a subsystem). The subsystem is called with the parameter “N” and the input “A”. After doing its computation, the result of “sum” will be stored inside the local variable “temp”.

In general, the syntax of a use equation is the following:

use subsystem_name[list of parameters] (list of input expressions) returns (list of output variables);


If your subsystem have several parameters/inputs/outputs, you have to provide them in the order in which they are declared.

(incoming)

### Transformations involving subsystems

(incoming, after the previous incoming)