mapping functions in solidity

Question

I'm wondering if it's possible to map functions in a map in solidity, something like:

mapping (uint256=> function) function_map;
f(){
    do something;
}
function_map[1] = f;

Answer 1

While you can't store the function as a type, you can store the bytes4 representation and then invoke through call().

pragma solidity ^0.4.20;

contract Test {
    uint public _val;

    mapping(uint => bytes4) _methodToInvoke;

    function Test() public {
        _methodToInvoke[1] = bytes4(keccak256("incrementBy1()"));
        _methodToInvoke[2] = bytes4(keccak256("incrementBy2()"));
    }

    function incrementBy1() public {
        _val++;
    }

    function incrementBy2() public {
        _val += 2;
    }

    function invoke(uint idx) public returns (bool) {
        return this.call(_methodToInvoke[idx]);
    }
}

Answer 2

As you can read in the ethereum solidity documentation: Mapping in ethereum solidity

Mappings are only allowed for state variables (or as storage reference types in internal functions).

So the answer is no. (so far)