Matrix - Matrix product

The following Pei program specifies a matrix-matrix product. The idea is to copy the values of the original matrices A and B wherever needed to compute all the products at a time. Hence, the values of A and B are spread in a 3-dimensional space. Once the products are computed, all of these products belonging to a same segment along the k axis have be added. This summation phase is done accordingly to the definition of C, in the same way as the prefix-sum. The result is R, that is the plane k=n-1 that contains the final sums.

                       <MatMult> : (A,B) -> R
                       {
                         A = aligna :: A0
                         B = alignb :: B0
                         A3 = A0 <| spreadj
                         B3 = B0 <| spreadi
                         P  = mult |> (A3 /&/ B3)
                         C = (P <| first) /&/ add |> (P /&/ C <| pre)
                         R = C <| last
                      }          
                      aligna  = \(i,j,k) |(0<=i<n && j=0 && 0<=k<n).(i,k)
                      alignb  = \(i,j,k) |(i=0 && 0<=j<n && 0<=k<n).(k,j)
                      spreadj = \(i,j,k)|(0<=i<n && 0<=j<n && 0<=k<n).(i,0,k)
                      spreadi = \(i,j,k)|(0<=i<n && 0<=j<n && 0<=k<n).(0,j,k)
                      pre     = \(i,j,k)|(0<=i<n && 0<=j<n && 0<k<n).(i,j,k-1)
                      first   = \(i,j,k)|(0<=i<n && 0<=j<n && k=0)
                      last    = \(i,j,k)|(0<=i<n && 0<=j<n && k=n-1)
                      mult    = \(a;b).(a*b)
                      add     = \(a;b).(a+b)

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