How can I define a function that can accumulate its parameter?

Question

For example, write a function add:

add[3] return 3

add[4] return 7

add[10] return 17

Answer 1

Module and Function

Possibly the easiest way is to use a unique symbol generated with Module to hold the value:

Module[{x = 0},
 add = x += # &;
]

add[3]
add[4]
add[10]

3
7
17

Or generating such a function:

makeAccumulator[init_: 0] := 
  Module[{x = init},
    x += # &
  ]

add = makeAccumulator[99];

add[3]
add[4]
add[10]

102
106
116

---

DownValues definitions

Another approach is to store the value in a separate rule attached to the same symbol:

add[] = 0;
add[x_] := add[] += x;

add[3]
add[4]
add[10]

3
7
17

Here I used add[] to hold the value but you could use any other pattern you wish. Also, this makes it easy to reset the counter: just do add[] = (* new value *).