Append every array element to the previous array elements inside of a loop

$tmp = array();
$new = array();
for($i = 0; $i < count($split); $i++)
  {
    $tmp[] = $split[$i];
    $new[] = implode(' ',$tmp);
  }

Shorter code, reverse order:

$new = array();
for($i = count($split); $i >= 0; $i--)
  {
    $new[] = implode(' ',$split);
    array_pop($split);
  }

Which of course is not a problem according to array_reverse()

You can do this:

$str = "a nice and sunny day today";
$split = explode(' ', $str);

$newList = array();
// Non-empty string?
if($str) {
    // Add the first element
    $newList[] = $split[0];
    for($i = 1; $i < count($split); $i++) {
        // New element gets appended with previous
        $newList[] = $newList[$i-1] . " " . $split[$i];
    }
}

This is more efficient than executing implode every time, since we're only concatenating the current and previous string.

There's one more bit of inefficiency though - we're calling count every time. Lets not do that.

$newList[] = $split[0]
for($i = 1, $len = count($split); $i < $len; $i++) {
    // New element gets appended with previous
    $newList[] = $newList[$i-1] . " " . $split[$i];
}

<?php
$str = "1 2 3";
$split = explode(' ', $str);
/* 
now $split is array('1','2','3')

Need to convert it to: array('1','1 2','1 2 3')
*/
$n = count($split);
$output = array();
for ($i = 0; $i < $n; ++$i)
{
    $output[$i] = "";
    for ($j = 0; $j <= $i; ++$j)
    {
        $output[$i] .= $split[$j];
        if ($j != $i)
        {
            $output[$i] .= " ";
        }
    }
}

var_dump($output);

output:

array(3) {
  [0]=>
  string(1) "1"
  [1]=>
  string(3) "1 2"
  [2]=>
  string(5) "1 2 3"
}

Just build the string in a loop and add to your array.

$str = "a nice and sunny day today";
$split = explode(' ', $str);
$final_array = array();

$i = 0;
$string = '';
$spacer = '';
for ($i = 0; $i < count($split); $i++) {
    $string .= $spacer . $split[$i];
    $final_array[] = $string;
    $spacer = ' ';
}

You can use array_map() with a callback function to achieve this:

$result = array_filter(array_map(function($k) use($split) { 
    return implode(' ', array_slice($split, 0, $k)); 
}, array_keys($split)));

print_r(array_values($result));

Output:

Array
(
    [0] => a
    [1] => a nice
    [2] => a nice and
    [3] => a nice and sunny
    [4] => a nice and sunny day
)

Demo.

I lean, direct solution should not be using more than one loop or more than one function call (after exploding, of course).

I'll demonstrate a functional-style solution with array_map(). The static declaration allows a value to be retained for access during subsequent iterations.

Code: (Demo) (Uglier version)

var_export(
    array_map(
        function ($word) {
            static $last;                            // declare persistent variable in scope
            $word = ($last ? "$last " : '') . $word; // prepend previous word(s)
            return $last = $word;                    // update $last and return $word (which is identical to $last)
        },
        explode(' ', $str)
    )
);

Or as shown in my other answer: (Demo)

var_export(
    array_map(
        function ($word) {
            static $last;
            return ltrim($last .= " $word");
        },
        explode(' ', $str)
    )
);