# Inner product of two vectors.
# 
# Creates two vectors of length n, with elements 0 through n-1.
# Returns their inner product, which will be
# 
#     n^3/3 + n^2/2 + n/6

main (n)
  innerProduct (makeVector (n, (λ (i) i)),
                makeVector (n, (λ (i) i)),
                n);

# Given two vectors of length n, returns their inner product.

innerProduct (v1, v2, n)
  if n > 0
    then vref (v1, n-1) * vref (v2, n-1) + innerProduct (v1, v2, n - 1)
    else 0;

################################################################
#
# Abstract data type of vectors.
#
# Representation:
#     A vector is a finite function from valid indexes to values.
#
# With that representation, there is no way to extract the size
# of a vector.
#
################################################################

# Returns the vector of size n whose elements are obtained
# by calling f on the valid indexes.

makeVector (n, f) f;                # pretty simple, really

# Returns element i of the vector.

vref (v, i) v (i)