# memoize -- record results of function evaluation for future use

## Description

memoize f -- produces, from a function f, a new function that behaves the same as f, but remembers previous answers to be provided the next time the same arguments are presented.

 i1 : fib = n -> if n <= 1 then 1 else fib(n-1) + fib(n-2) o1 = fib o1 : FunctionClosure i2 : time fib 28 -- used 6.29081 seconds o2 = 514229 i3 : fib = memoize fib o3 = fib o3 : FunctionClosure i4 : time fib 28 -- used 0.000211753 seconds o4 = 514229 i5 : time fib 28 -- used 4.602e-6 seconds o5 = 514229

An optional second argument to memoize provides a list of initial values, each of the form x => v, where v is the value to be provided for the argument x.

The function memoize operates by constructing a MutableHashTable, in which the arguments are used as keys for accessing the return value of the function. This mutable hash table can be obtained using the function memoizeValues, as follows.

 i6 : peek memoizeValues fib o6 = MutableHashTable{0 => 1 } 1 => 1 2 => 2 3 => 3 4 => 5 5 => 8 6 => 13 7 => 21 8 => 34 9 => 55 10 => 89 11 => 144 12 => 233 13 => 377 14 => 610 15 => 987 16 => 1597 17 => 2584 18 => 4181 19 => 6765 20 => 10946 21 => 17711 22 => 28657 23 => 46368 24 => 75025 25 => 121393 26 => 196418 27 => 317811 28 => 514229

That hash table can be replaced by an empty one with the function memoizeClear.

 i7 : memoizeClear fib i8 : peek memoizeValues fib o8 = MutableHashTable{}

Warning: the new function created by memoize will save references to all arguments and values it encounters, and this will often prevent those arguments and values from being garbage-collected as soon as they might have been. If the arguments are implemented as mutable hash tables (modules, matrices and rings are implemented this way) then a viable strategy is to stash computed results in the arguments themselves. See also CacheTable.

## Ways to use memoize :

• "memoize(Function)"
• "memoize(Function,List)"

## For the programmer

The object memoize is .