/*
 
  part1.rex (for cs60 hw1, S09)

  Name:
  
  Comments to the graders:




*/  


// Note the /* slash-star ... star-slash */ multi-line comments, used above
// Rex also has single-line comments, like this one! 

// examples: fac (factorial), rev (reverse), and rmv1 (remove one element)

// fun: fac( n )
//  in: n, a nonnegative integer
// out: the factorial of n as a floating-point value
undef(fac);                        // redefines it each time...

fac( 0 ) => 1.0;                   // base case 
fac( n ) => n * fac( n-1 );        // recursive case

test( fac(0),    1.0 );
test( fac(5),    120.0 );






// fun: rev( L )
//  in: L, a list
// out: a list with the same top-level elements in reverse order
undef(rev);

rev( [] ) => [];                    // base case
rev( [f|R] ) => RR = rev(R),        // recursive call, RR is "Reverse of R"
                append( RR, [f] );  // get f to the end


// it would be equivalent to write
// rev( [f|R] ) => append( rev(R), [f] );
// either would be OK.

test( rev([]),          [] );
test( rev([1,2,3]),     [3,2,1] );
test( rev([[1,2,3]]),   [[1,2,3]] );  // only one element!







// fun: rmv1( e, L )
//  in: e, an element; L, a list
// out: a list like L with the first top-level e removed, if any
undef( rmv1 );

rmv1( e, [] ) => [];                // base case
rmv1( e, [e|R] ) => R;              // removing e from [e|R]
rmv1( e, [f|R] ) => [f|rmv1(e,R)];  // recursive call, keeping f


test( rmv1( 42, [] ),               [] );
test( rmv1( 42, [1,2,42,42] ),      [1,2,42] );
test( rmv1( 42, [1,2,[42]] ),       [1,2,[42]] ); // not if nested









// an example start-of-function comment for problem 1
// feel free to copy and alter this for the other functions, as well

//  pr: #1
// fun: pwr(b,p)
//  in: b - numeric base, p - nonnegative integer power
// out: b**p (floating point!)
undef( pwr );