save - Saving memoization to disk

I like using memoization (i.e. the construct myFunction[x_]:=myFunction[x]=...) when I have a heavy function that I need to re-evaluate on the same arguments. However, I find it frustrating that each time I quit the kernel(s), all the advantage goes lost.

Is there a way of saving the results? I can think of a very cumbersome way of doing it, such as this block upon defining our function

memo = If[FileExistsQ[FileNameJoin[{Directory[], "memo.mx"}]], Import["memo.mx"], {}];
myFunction[x_] := Module[{value = ...},
AppendTo[memo, "myFunction[" <> ToString[x] <> "]=" <> ToString[value]]; 
Export["memo.mx", Union@memo];

myFunction[x] = value]
Evaluate[ToExpression/@memo];

Is this okay, or is there a better (or even designated) way of doing this?

Answer

Not much different from your approach and maybe not the best/safest approach, but DumpSave helps a bit because at least you don't have to works with strings:

cacheFile = FileNameJoin[{$TemporaryDirectory, "fibonacciCache" <> ".mx"}];
If[FileExistsQ[cacheFile],
 Get[cacheFile],
 fibonacci[1] = 1;

 fibonacci[2] = 1;
 fibonacci[n_Integer] := Module[{},
   fibonacci[n] = fibonacci[n - 1] + fibonacci[n - 2];
   DumpSave[cacheFile, fibonacci];
   fibonacci[n]
   ]
 ]

For example

In[3]:= fibonacci[500] // Timing

Out[3]= {0.562500, \ 1394232245616978801397243828704072839500702565876973072641089629483255\ 71622863290691557658876222521294125}

Now Quit[]-ing and reevaluating the previous cell:

In[3]:= fibonacci[500] // Timing

Out[3]= {0., \ 1394232245616978801397243828704072839500702565876973072641089629483255\ 71622863290691557658876222521294125}