# Write an evaluator based on the grammar from ‹t3/lisp.py›. The
# basic semantic rules are as follows: the first item in a compound
# expression is always an identifier, and the compound expression
# itself is interpreted as a function application.  Evaluation is
# eager, i.e.  innermost applications are evaluated first. Literals
# evaluate to themselves, i.e. ‹3.14› becomes a ‹real› with the
# value ‹3.14›. Only numeric literals are relevant in this homework,
# and all numeric literals represent reals (floats). Besides
# literals, implement the following objects:
#
#  • ‹(vector <real>+)› where <real>+ means 1 or more objects of
#    type ‹real›
#  • ‹(matrix <vector>+)› where each vector is one row, starting
#    from the top
#
# And these operations on them:
#
#  • ‹(+ <vector> <vector>)› vector addition, returns a ‹vector›
#  • ‹(dot <vector> <vector>)› dot product, returns a ‹real›
#  • ‹(cross <vector> <vector>)› cross product, returns a ‹vector›
#  • ‹(+ <matrix> <matrix>)› matrix addition, returns a ‹matrix›
#  • ‹(* <matrix> <matrix>)› matrix multiplication, returns a ‹matrix›
#  • ‹(det <matrix>)› determinant, returns a ‹real›
#  • ‹(solve <matrix>)› solve a system of linear equations, returns
#    a ‹vector›
#
# For ‹solve›, the argument is a matrix of coefficients and the result
# is an assignment of variables -- if there are multiple solutions,
# return a non-zero one.
#
#     system  │ matrix │ written as
#  x + y = 0  │  1  1  │ (matrix (vector 1  1)
#     -y = 0  │  0 -1  │         (vector 0 -1))
#
# Expressions with argument type mismatches (both in object
# constructors and in operations), attempts to construct a matrix
# where the individual vectors (rows) are not of the same length,
# addition of differently-shaped matrices, multiplication of
# incompatible matrices, addition or dot product of different-sized
# vectors, and so on, should evaluate to an ‹error› object. Attempt to
# get a cross product of vectors with dimension other than 3 is an
# ‹error›. Any expression with an ‹error› as an argument is also an
# ‹error›.
#
# The evaluator should be available as ‹evaluate()› and take a string
# for an argument. The result should be an object with methods
# ‹is_real()›, ‹is_vector()›, ‹is_matrix()› and ‹is_error()›.
# Iterating vectors gives reals and iterating matrices gives
# vectors. Both should also support indexing.  ‹float(x)› for
# ‹x.is_real()› should do the right thing.
#
# You can use ‹numpy› in this task (in addition to standard
# modules).