## Adapton: Composable, Demand-Driven Incremental Computation

by Clayton Mentzer and Matt Hammer cmentzer at ccs dot neu dot edu

Adapton is a library for demand driven incremental computation and dynamic programming The library provides drop-in replacement forms for defining Racket functions that memoize their results and record their computation graphs. In addition, it provides tools for leveraging articulation points to improve performance of algorithms on large inputs and the tools to mutate those inputs.

(require adapton) | package: Adapton |

### 1` `Example: Fibonacci

A typical example of a dynamic programming problem is computing the Fibonacci numbers, whose simplest implementation involves a heavy amount of duplicated computation. By simply defining the function with define/memo, previously computed answers are cached, avoiding the duplicated computation.

calling a funciton defined with define/memo returns a node, which is a structure that contains a thunk. Nodes are one of the two types of articulation points in Adapton, the other being cells. We’ll get to Cells in a moment. Forcing a node will force the thunk contained within that node, and also perform a number of steps to keep track of relationships between articulation points.

each recursive call to fib will also return a node, which means we need to force that node before we can use it. Each node created is placed into a global level hash-table called "*memo-table*". Then, each time a node is created we can check if it exists in memo-table already, and use its cached result.

(define (fib n) (if (<= n 1) 1 (+ (fib (- n 1)) (fib (- n 2))))) graphing is OFF

> (time (fib 35)) cpu time: 206 real time: 206 gc time: 0

14930352

> (define/memo (fib n) (if (<= n 1) 1 (+ (force (fib (- n 1))) (force (fib (- n 2)))))) define/memo: undefined;

cannot reference an identifier before its definition

in module: top-level

The other kind of articulation point in Adapton is a cell. Cells are structures that contain a mutable box for atomic data. The difference between cells and nodes is that a cell will never have any successors (that is, the data contained in a cell will never force another articulation point). We use cells to contain our input data, so that when a node forces a cell to get the atomic data out of it, that cell is flagged as a successor to that node, and we say that the node is dependent upon that cell.

We use these dependencies to build a Directed Computation Graph (DCG), which is a model of the control flow of the program. When the data contained within a cell is mutated, we can determine based on the DCG which nodes have been invalidated (dirtied), and recomputing only those nodes will correct our now invalid result.

This allows us to only re-compute a fraction of the computations that we originally performed to achieve a new correct result. The merge-sort example in the adapton library uses cells liberally.

### 2` `Forms

Just like the function definition forms in PLT Scheme, the formals list of a memoized function may be a single identifier, a proper list of identifiers, or an improper list of identifiers.

formals | = | id | ||

| | () | |||

| | (id . formals) |