/* 
**	The train Problem solution in Euclid
**              This program attempts to solve the automated
**              train driver program for a smooth ride (for
**              the passengers) and better consumption (for
**              the company).
**
**      Solving this type of problems in Euclid takes these few steps:
**              1. Think of the properties that describe the problem
**              2. Give their initial values, their relations to
**                 each other and any other values known
**              3. Describe any explicit and more complicated relations
**                 through predicates.
**              4. Relax and watch the system find the solution
**	Use constraints to describe the quantities of the system
**	and logic to show when constraints are applicable.
**
**		(C) Copyright K J Dryllerakis 1993-1995 
**		ALL RIGHTS RESERVED
**	$Id: train.eu,v 1.2 1995/03/24 12:48:06 kd Exp kd $
*/

solve(A,T1,T2,Tf,D,Umax,Acc):-
	initial_data(U,A,D,Acc,Umax,Tf,S) ,
	acceleration_f(0,Tf,A,D,S,Acc,Umax,0,T1,T2,Tf) ,
	T1 = T2,		/* We did not reach the Umax */
	U@T1=Umax.


solve(A,T1,T2,Tf,D,Umax,Acc):-
	initial_data(U,A,D,Acc,Umax,Tf,S) ,
	acceleration_f(0,Tf,A,D,S,Acc,Umax,0,T1,T2,Tf),
	T1 \= T2.


initial_data(U,A,D,Acc,Umax,Tf,S):-
	functions([U,A,S]) , 
	reals([D,Acc,Umax,Tf]),
	U@0=0 , U@Tf=0 , U=integral(A) , continuous(U) ,
	S@0=0 , S@Tf=D , S=integral(U) , continuous(S).

acceleration_f(0,Tf,FF,D,S,Acc,Umax,0,T1,T2,Tf):-
	functions([F1,F2]) ,
	F1={[cc(0,T1):(Acc)//X]} , 
	T1>0 ,
	S@T1 > D/2,
	F2=F1#{[oc(T1,T2):0//X]}, 
	T1 < T2,
	FF=F2 # {[oc(T2,Tf):(-Acc)//X]},
	T2 <Tf.

acceleration_f(0,Tf,FF,D,S,Acc,Umax,0,T1,T2,Tf):-
	functions([F1]) ,
	F1={[cc(0,T1):(Acc)//X]} , 
	T1>0 ,
	S@T1 <= D/2,
	T1=T2, 
	FF=F1 # {[oc(T2,Tf):(-Acc)//X]},
	T2 <Tf.