%%% Computing mortgage payments
%%% (taken from S. Michaylov's Ph.D. dissertation)
%%% Author: Roberto Virga

%% load the constraint solvers
%use inequality/rationals.

%% equality
== : rational -> rational -> type.  %infix none 1000 ==.

id : X == X.

%% mortgage payments
mortgage : rational -> rational -> rational -> rational -> rational -> type.

%% P = principal, T = no. of months
%% I = annual interest rate,
%% MP = monthly payments, B = balance

m0 : mortgage P T I MP B
       <- T > 0
       <- 1 >= T
       <- MI == T * P * I * 1/1200
       <- B == P + MI - (T * MP).
m1 : mortgage P T I MP B
       <- T > 1
       <- MI == P * I * 1/1200
       <- mortgage (P + MI - MP) (T - 1) I MP B.