% Symbolic differentiation over explicit expression terms.
%
% The source derivative example uses Prolog operators such as `+`, `*`, `^`, and
% cut.  Eyepl keeps expressions as ordinary terms: `add/2`, `mul/2`, `pow/2`,
% `log/1`, and so on.  The result is intentionally unsimplified so the rule that
% produced each part remains visible.

query(derivative_result(X0, X1)).

expr(square, mul(var(x), var(x))).
expr(linear_plus_const, add(var(x), const(3))).
expr(product, mul(add(var(x), const(1)), mul(add(pow(var(x), 2), const(2)), add(pow(var(x), 3), const(3))))).
expr(nested_log, log(log(var(x)))).

d(const(_c), _x, const(0)).
d(var(X), X, const(1)).
d(var(Y), X, const(0)) :-
  neq(X, Y).
d(add(U, V), X, add(Du, Dv)) :-
  d(U, X, Du),
  d(V, X, Dv).
d(sub(U, V), X, sub(Du, Dv)) :-
  d(U, X, Du),
  d(V, X, Dv).
d(mul(U, V), X, add(mul(Du, V), mul(U, Dv))) :-
  d(U, X, Du),
  d(V, X, Dv).
d(divide(U, V), X, divide(sub(mul(Du, V), mul(U, Dv)), pow(V, 2))) :-
  d(U, X, Du),
  d(V, X, Dv).
d(pow(U, N), X, mul(mul(const(N), pow(U, N1)), Du)) :-
  sub(N, 1, N1),
  d(U, X, Du).
d(log(U), X, divide(Du, U)) :-
  d(U, X, Du).

derivative_result(Name, Derivative) :-
  expr(Name, Expr),
  d(Expr, x, Derivative).