import java.util.*;

public class Functions {
    public static <T,S> Function<T,S> constant(S wynik)throws GenericFunctionsException{
        Function funkcja= new Function<T,S>() {
            @Override
            public int arity() {
                return 0;
            }

            @Override
            public S compute(List<? extends T> args) throws GenericFunctionsException {
                if(args==null || !args.isEmpty())
                    throw new GenericFunctionsException();
                return wynik;
            }
        };
        return funkcja;

    }

    public static <T extends S,S> Function<T,S> proj(int n, int k)throws GenericFunctionsException{
        Function funkcja= new Function<T,S>(){
            @Override
            public int arity() throws GenericFunctionsException {
                if(n<=0 || k<0 || k>n)
                    throw new GenericFunctionsException();
                return n;
            }

            @Override
            public S compute(List<? extends T> args) throws GenericFunctionsException {
                if(args==null)
                    throw new GenericFunctionsException();
                if(args.size()!=n)
                    throw new GenericFunctionsException();
                if(args.get(k)==null)
                    throw new GenericFunctionsException();
                return args.get(k);
            }
        };
        return funkcja;

    }

    public static <T,S,R> Function<R,S> compose(final  Function<? super T,? extends S> outer, final List<? extends Function<? super R,? extends T>> inner )throws GenericFunctionsException {
        Function funkcja= new Function<R,S>() { // ??

            @Override
            public int arity() throws GenericFunctionsException {
                if(outer.arity()!=inner.size())
                    throw new GenericFunctionsException();
                if(inner.isEmpty())
                    return 0;
                if(inner.contains(null))
                    throw new GenericFunctionsException();
                int checkArity=-1;
                for(Function<? super R,? extends T> f : inner){
                    if(checkArity==-1)
                        checkArity=f.arity();
                    if(f.arity()!=checkArity)
                        throw new GenericFunctionsException();
                }
                return checkArity;
            }

            @Override
            public Object compute(List args) throws GenericFunctionsException { // tu cos z S
                if(outer.arity()!=inner.size())
                    throw new GenericFunctionsException();
               // ArrayList<T> l=new ArrayList();
                ArrayList l=new ArrayList();
                for(Function<? super R,? extends T> f : inner){
                    l.add(f.compute(args));
                }
                return outer.compute(l);
            }
        };
        return funkcja;
    }


}