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#![doc(html_logo_url = "https://raw.githubusercontent.com/cuplv/adapton-talk/master/logos/adapton-logo-bonsai.png", html_root_url = "https://docs.rs/adapton/")] /*! Adapton for Rust ================ This Rust implementation embodies the latest implementation [Adapton](http://adapton.org), which offers a foundational, language-based semantics for [general-purpose incremental computation](wikipedia.org/en/Incremental_computing). Programming model -------------------- - The [documentation below](#adapton-programming-model) gives many illustrative examples, with pointers into the other Rust documentation. - The [`engine` module](https://docs.rs/adapton/0/adapton/engine/index.html) gives the core programming interface. Resources --------------- - [Presentations and benchmark results](https://github.com/cuplv/adapton-talk#benchmark-results) - [IODyn: Adapton collections, for algorithms with dynamic input and output](https://github.com/cuplv/iodyn.rust) - [Adapton Lab: Evaluation and testing](https://github.com/cuplv/adapton-lab.rust) Background --------------- Adapton proposes the _demanded computation graph_ (or **DCG**), and a demand-driven _change propagation_ algorithm. Further, it proposes first-class _names_ for identifying cached data structures and computations. For a quick overview of the role of names in incremental computing, we give [background on incremental computing with names](#background-incremental-computing-with-names), below. The following academic papers detail these technical proposals: - **DCG, and change propagation**: [_Adapton: Composable, demand-driven incremental computation_, **PLDI 2014**](http://www.cs.umd.edu/~hammer/adapton/). - **Nominal memoization**: [_Incremental computation with names_, **OOPSLA 2015**](http://arxiv.org/abs/1503.07792). - **Type and effect structures**: The draft [_Typed Adapton: Refinement types for incremental computation with precise names_](https://arxiv.org/abs/1610.00097). Why Rust? ---------- Adapton's first implementations used Python and OCaml; The latest implementation in Rust offers the best performance thus far, since (1) Rust is fast, and (2) [traversal-based garbage collection presents performance challenges for incremental computation](http://dl.acm.org/citation.cfm?doid=1375634.1375642). By liberating Adapton from traversal-based collection, [our empirical results](https://github.com/cuplv/adapton-talk#benchmark-results) are both predictable and scalable. Adapton programming model ========================== **Adapton roles**: Adapton proposes _editor_ and _achivist roles_: - The **Editor role** _creates_ and _mutates_ input, and _demands_ the output of incremental computations in the **Archivist role**. - The **Archivist role** consists of **Adapton thunks**, where each is cached computation that consumes incremental input and produces incremental output. **Examples:** The examples below illustrate these roles, in increasing complexity: - [Start the DCG engine](#start-the-dcg-engine) - [Create incremental cells](#create-incremental-cells) - [Observe `Art`s](#observe-arts) - [Mutate input cells](#mutate-input-cells) - [Demand-driven change propagation](#demand-driven-change-propagation) and [switching](#switching) - [Memoization](#memoization) - [Create thunks](#create-thunks) - [Use `force_map` for more precise dependencies](#use-force_map-for-more-precise-dependencies) - [Nominal memoization](#nominal-memoization) - [Nominal cycles](#nominal-cycles) - [Nominal firewalls](#nominal-firewalls) **Programming primitives:** The following list of primitives covers the core features of the Adapton engine. Each primitive below is meaningful in each of the two, editor and archivist, roles: - **Ref cell allocation**: Mutable input (editor role), and cached data structures that change across runs (archivist role). - [**`cell!`**](https://docs.rs/adapton/0/adapton/macro.cell.html) -- Preferred version - [`let_cell!`](https://docs.rs/adapton/0/adapton/macro.let_cell.html) -- Useful in simple examples - [`engine::cell`](https://docs.rs/adapton/0/adapton/engine/fn.cell.html) -- Engine's raw interface - **Observation** and **demand**: Both editor and archivist role. - [**`get!`**](https://docs.rs/adapton/0/adapton/macro.get.html) -- Preferred version - [`engine::force`](https://docs.rs/adapton/0/adapton/engine/fn.force.html) -- Engine's raw interface - [`engine::force_map`](https://docs.rs/adapton/0/adapton/engine/fn.force_map.html) -- A variant for observations that compose before projections - **Thunk Allocation**: Both editor and archivist role. - Thunk allocation, **_without_ demand**: - [**`thunk!`**](https://docs.rs/adapton/0/adapton/macro.thunk.html) -- Preferred version - [`let_thunk!`](https://docs.rs/adapton/0/adapton/macro.let_thunk.html) -- Useful in simple examples - [`engine::thunk`](https://docs.rs/adapton/0/adapton/engine/fn.thunk.html) -- Engine's raw interface (can be cumbersome) - Thunk allocation, **_with_ demand**: - [**`memo!`**](https://docs.rs/adapton/0/adapton/macro.memo.html) -- Preferred version - [`let_memo!`](https://docs.rs/adapton/0/adapton/macro.let_memo.html) -- Useful in simple examples Start the DCG engine ===================== The call `init_dcg()` below initializes a DCG-based engine, replacing the `Naive` default engine. ``` #[macro_use] extern crate adapton; use adapton::macros::*; use adapton::engine::*; fn main() { manage::init_dcg(); // Put example code below here # let c : Art<usize> = cell!( 123 ); # assert_eq!( get!(c), 123 ); } ``` Create incremental cells ======================== Commonly, the input and intermediate data of Adapton computations consists of named reference `cell`s. A reference `cell` is one variety of `Art`s; another are [`thunk`s](#create-thunks). ## Implicit counter for naming `cell`s `cell!(123)` uses a global counter to choose a unique name to hold `123`. Important note: This _may_ be appopriate for the Editor role, but is _never appropriate for the Archivist role_. ``` # #[macro_use] extern crate adapton; # fn main() { # use adapton::macros::*; # use adapton::engine::*; # manage::init_dcg(); let c : Art<usize> = cell!( 123 ); assert_eq!( get!(c), 123 ); # } ``` Explicitly-named `cell`s ------------------------- Sometimes we name a cell using a Rust identifier. We specify this case using the notation `[ name ]`, which specifies that the cell's name is a string, constructed from the Rust identifer `name`: ``` # #[macro_use] extern crate adapton; # fn main() { # use adapton::macros::*; # use adapton::engine::*; # manage::init_dcg(); let c : Art<usize> = cell!([c] 123); assert_eq!(get!(c), 123); # } ``` Optionally-named `cell`s ------------------------- Most generally, we supply an expression `optional_name` of type `Option<Name>` to specify the name for the `Art`. This `Art` is created by either `cell` or `put`, in the case that `optional_name` is `Some(name)` or `None`, respectively: ``` # #[macro_use] extern crate adapton; # fn main() { # use adapton::macros::*; # use adapton::engine::*; # manage::init_dcg(); let n : Name = name_of_str(stringify!(c)); let c : Art<usize> = cell!([Some(n)]? 123); assert_eq!(get!(c), 123); let c = cell!([None]? 123); assert_eq!(get!(c), 123); # } ``` Observe `Art`s ====================== The macro `get!` is sugar for `engine::force!`, with reference introduction operation `&`: ``` # #[macro_use] extern crate adapton; # fn main() { # use adapton::macros::*; # use adapton::engine::*; # manage::init_dcg(); let c : Art<usize> = cell!(123); assert_eq!( get!(c), force(&c) ); # } ``` Since the type `Art<T>` classifies both `cell`s and [`thunk`s](#create-thunks), the operations `force` and `get!` can be used interchangeably on `Art<T>`s that arise as `cell`s or `thunk`s. Mutate input cells ========================= One may mutate cells explicitly, or _implicitly_, which is common in Nominal Adapton. The editor (implicitly or explicitly) mutates cells that hold input and they re-demand the output of the archivist's computations. During change propagation, the archivist mutates cells with implicit mutation. **Implicit mutation uses nominal allocation**: By allocating a cell with the same name, one may _overwrite_ cells with new content: ``` # #[macro_use] extern crate adapton; # fn main() { # use adapton::macros::*; # use adapton::engine::*; # manage::init_dcg(); let n : Name = name_of_str(stringify!(c)); let c : Art<usize> = cell!([Some(n.clone())]? 123); assert_eq!(get!(c), 123); // Implicit mutation (re-use cell by name `n`): let d : Art<usize> = cell!([Some(n)]? 321); assert_eq!(d, c); assert_eq!(get!(c), 321); assert_eq!(get!(d), 321); # } ``` **No names implies no effects**: Using `None` to allocate cells always **gives distinct cells, with no overwriting: ``` # #[macro_use] extern crate adapton; # fn main() { # use adapton::macros::*; # use adapton::engine::*; # manage::init_dcg(); let c = cell!([None]? 123); let d = cell!([None]? 321); assert_eq!(get!(c), 123); assert_eq!(get!(d), 321); # } ``` **Explicit mutation, via `set`**: If one wants mutation to be totally explicit, one may use `set`: ``` # #[macro_use] extern crate adapton; # fn main() { # use adapton::macros::*; # use adapton::engine::*; # manage::init_dcg(); let n : Name = name_of_str(stringify!(c)); let c : Art<usize> = cell!([Some(n)]? 123); assert_eq!(get!(c), 123); // Explicit mutation (overwrites cell `c`): set(&c, 321); assert_eq!(get!(c), 321); # } ``` Demand-driven change propagation ================================= The example below demonstrates _demand-driven change propagation_, which is unique to Adapton's DCG, and its approach to incremental computation. The example DCG below consists of two kinds of nodes: - [Cells](#create-incremental-cells) consist of data that changes over time, including (but not limited to) incremental input. - [Thunks](#create-thunks) consist of computations whose observations and results are cached in the DCG. The simple example below uses two mutable input cells, `num` and `den`, whose values are used by an intermediate subcomputation `div` that divides the numerator in `num` by the denominator in `den`, and a thunk `check` that first checks whether the denominator is zero (returning zero if so) and if non-zero, returns the value of the division: ``` # #[macro_use] extern crate adapton; # fn main() { # use adapton::macros::*; # use adapton::engine::*; # manage::init_dcg(); # // Two mutable inputs, for numerator and denominator of division let num = cell!(42); let den = cell!(2); // In Rust, cloning is explicit: let den2 = den.clone(); // clone _global reference_ to cell. let den3 = den.clone(); // clone _global reference_ to cell, again. // Two subcomputations: The division, and a check thunk with a conditional expression let div = thunk![ get!(num) / get!(den) ]; let check = thunk![ if get!(den2) == 0 { None } else { Some(get!(div)) } ]; # } ``` After allocating `num`, `den` and `check`, the editor changes `den` and observes `check`, inducing the following change propagation behavior. In sum, _whether_ `div` runs is based on _demand_ from the Editor (of the output of `check`), _and_ the value of input cell `den`, via the condition in `check`: 1. When the editor demands thunk `check` the first time, Adapton executes the condition, and cell `den` holds `2`, which is non-zero. Hence, the `else` branch executes `get!(div)`, which demands the output of the division, `21`. 2. After this first observation of `check`, the editor changes cell `den` to `0`, and re-demands the output of thunk `check`. In response, Adapton's change propagation algorithm first re-executes the condition (not the division), and the condition branches to the `then` branch, resulting in `None`; in particular, it does _not_ re-demand the `div` node, though this node still exists in the DCG. 3. Next, the programmer changes `den` back to its original value, `2`, and re-demands the output of `check`. In response, change propagation re-executes the condition, which re-demands the output of `div`. Change propagation attempts to "clean" the `div` node before re-executing it. To do so, it compares its _last observations_ of `num` and `den` to their current values, of `42` and `2`, respectively. In so doing, it finds that these earlier observations match the current values. Consequently, it _reuses_ the output of the division (`21`) _without_ having to re-execute the division. ``` # #[macro_use] extern crate adapton; # fn main() { # use adapton::macros::*; # use adapton::engine::*; # manage::init_dcg(); # # // Two mutable inputs, for numerator and denominator of division # let num = cell!(42); # let den = cell!(2); # # // In Rust, cloning is explicit: # let den2 = den.clone(); // clone _global reference_ to cell. # let den3 = den.clone(); // clone _global reference_ to cell, again. # # // Two subcomputations: The division, and a check thunk with a conditional expression # let div = thunk![ get!(num) / get!(den) ]; # let check = thunk![ if get!(den2) == 0 { None } else { Some(get!(div)) } ]; # // Observe output of `check` while we change the input `den` // Editor Step 1: (Explained in detail, below) assert_eq!(get!(check), Some(21)); // Editor Step 2: (Explained in detail, below) set(&den3, 0); assert_eq!(get!(check), None); // Editor Step 3: (Explained in detail, below) set(&den3, 2); assert_eq!(get!(check), Some(21)); // division is reused # } ``` [Slides with illustrations](https://github.com/cuplv/adapton-talk/blob/master/adapton-example--div-by-zero/) of the graph structure and the code side-by-side may help: **Editor Step 1** <img src="https://raw.githubusercontent.com/cuplv/adapton-talk/master/adapton-example--div-by-zero/Adapton_Avoiddivbyzero_10.png" alt="Slide-10" style="width: 800px;"/> **Editor Steps 2 and 3** <img src="https://raw.githubusercontent.com/cuplv/adapton-talk/master/adapton-example--div-by-zero/Adapton_Avoiddivbyzero_12.png" alt="Slide_12" style="width: 200px;"/> <img src="https://raw.githubusercontent.com/cuplv/adapton-talk/master/adapton-example--div-by-zero/Adapton_Avoiddivbyzero_16.png" alt="Slide_16" style="width: 200px;"/> <img src="https://raw.githubusercontent.com/cuplv/adapton-talk/master/adapton-example--div-by-zero/Adapton_Avoiddivbyzero_17.png" alt="Slide-17" style="width: 200px;"/> <img src="https://raw.githubusercontent.com/cuplv/adapton-talk/master/adapton-example--div-by-zero/Adapton_Avoiddivbyzero_23.png" alt="Slide-23" style="width: 200px;"/> [Full-sized slides](https://github.com/cuplv/adapton-talk/blob/master/adapton-example--div-by-zero/) In sum, _whether_ `div` runs is based on _demand_ from the Editor (of `check`), _and_ the value of input `den`. The reuse of `div` illustrates the _switching pattern_, which is unique to Adapton's approach to incremental computation. Switching ----------- In the [academic literature on Adapton](http://matthewhammer.org/adapton/), we refer to the three-step pattern of change propagation illustrated above as _switching_: 1. [The demand of `div` switches from being present (in step 1)](https://github.com/cuplv/adapton-talk/tree/master/adapton-example--div-by-zero#initial-graph-after-initial-demand-due-to-1st-get), 2. [to absent (in step 2)](https://github.com/cuplv/adapton-talk/tree/master/adapton-example--div-by-zero#updated-graph-after-first-cleaning-phase-due-to-2nd-get), 3. [to present (in step 3)](https://github.com/cuplv/adapton-talk/tree/master/adapton-example--div-by-zero#updated-graph-after-second-cleaning-phase-due-to-3rd-get). Past work on self-adjusting computation does not support the switching pattern directly: Because of its change propagation semantics, it would "forget" the division in step 2, and rerun it _from-scratch_ in step 3. Furthermore, some other change propagation algorithms base their re-execution schedule on "node height" (of the graph's topological ordering). These algorithms may also have undesirable behavior. In particular, they may re-execute the division `div` in step 2, though it is not presently in demand. For an example, see [this gist](https://gist.github.com/khooyp/98abc0e64dc296deaa48). Memoization ============ Memoization provides a mechanism for caching the results of subcomputations; it is a crtical feature of Adapton's approach to incremental computation. In Adapton, each _memoization point_ has three ingredients: - A function expression (of type `Fn`) - Zero or more arguments. Each argument type must have an implementation for the traits `Eq + Clone + Hash + Debug`. The traits `Eq` and `Clone` are both critical to Adapton's caching and change propagation engine. The trait `Hash` is required when Adapton's naming strategy is _structural_ (e.g., where function names are based on the hashes of their arguments). The trait `Debug` is useful for debugging, and reflection. - An optional _name_, which identifies the function call for reuse later. - When this optional name is `None`, the memoization point may be treated in one of two ways: either as just an ordinary, uncached function call, or as a cached function call that is identified _structurally_, by its function pointer and arguments. Adapton permits structural subcomputations via the engine's [structural](https://docs.rs/adapton/0/adapton/engine/fn.structural.html) function. - When this is `Some(name)`, the memoization point uses `name` to identify the work performed by the function call, and its result. Critically, in future incremental runs, it is possible for `name` to associate with different functions and/or argument values. Each memoization point yields two results: - A [thunk](#create-thunks) articulation, of type `Art<Res>`, where `Res` is the result type of the function expression. - A result value of type `Res`, which is also cached at the articulation. Optional name version ---------------------- The following form is preferred: `memo!( [ optional_name ]? fnexp ; lab1 : arg1, ..., labk : argk )` It accepts an optional name, of type `Option<Name>`, and an arbitrary function expression `fnexp` (closure or function pointer). Like the other forms, it requires that the programmer label each argument. Example ------- ``` # #[macro_use] extern crate adapton; # fn main() { # use adapton::macros::*; # use adapton::engine::*; # manage::init_dcg(); let (t,z) : (Art<usize>, usize) = memo!([Some(name_unit())]? |x:usize,y:usize|{ if x > y { x } else { y }}; x:10, y:20 ); assert_eq!(z, 20); # } ``` [More examples of `memo!` macro](https://docs.rs/adapton/0/adapton/macro.memo.html#memoization) Create thunks =============== **Thunks** consist of suspended computations whose observations, allocations and results are cached in the DCG, when `force`d. Each thunk has type `Art<Res>`, where `Res` is the return type of the thunk's suspended computation. Each [_memoization point_](#memoization) is merely a _forced thunk_. We can also create thunks without demanding them. The following form is preferred: `thunk!( [ optional_name ]? fnexp ; lab1 : arg1, ..., labk : argk )` It accepts an optional name, of type `Option<Name>`, and an arbitrary function expression `fnexp` (closure or function pointer). Like the other forms, it requires that the programmer label each argument. Example ------- ``` # #[macro_use] extern crate adapton; # fn main() { # use adapton::macros::*; # use adapton::engine::*; # manage::init_dcg(); let t : Art<usize> = thunk!([ Some(name_unit()) ]? |x:usize,y:usize|{ if x > y { x } else { y }}; x:10, y:20 ); assert_eq!(get!(t), 20); # } ``` [More examples of `thunk!` macro](https://docs.rs/adapton/0/adapton/macro.thunk.html#thunks) Use `force_map` for more precise dependencies ============================================== Suppose that we want to project only one field of type `A` from a pair within an `Art<(A,B)>`. If the field of type `B` changes, our observation of the `A` field will not be affected. Below, we show that using `force_map` prunes the dirtying phase of change propagation. Doing so means that computations that would otherwise be dirty and cleaned via re-execution are never diritied in the first place. We show a simple example of projecting a pair. To observe this fact, this test traces the engine, counts the number of dirtying steps, and ensures that this count is zero, as expected. ``` # #[macro_use] extern crate adapton; # fn main() { # use adapton::macros::*; # use adapton::engine::*; # use adapton::reflect; # manage::init_dcg(); # // Trace the behavior of change propagation; ensure dirtying works as expected reflect::dcg_reflect_begin(); let pair = cell!((1234, 5678)); let pair1 = pair.clone(); let t = thunk![{ // Project the first component of pair: let fst = force_map(&pair, |_,x| x.0); fst + 100 }]; // The output is `1234 + 100` = `1334` assert_eq!(get!(t), 1334); // Update the second component of the pair; the first is still 1234 set(&pair1, (1234, 8765)); // The output is still `1234 + 100` = `1334` assert_eq!(get!(t), 1334); // Assert that nothing was dirtied (due to using `force_map`) let traces = reflect::dcg_reflect_end(); let counts = reflect::trace::trace_count(&traces, None); assert_eq!(counts.dirty.0, 0); assert_eq!(counts.dirty.1, 0); # } ``` Nominal memoization ========================= Adapton offers **nominal memoization**, which uses first-class _names_ (each of type `Name`) to identify cached computations and data. ``` # #[macro_use] extern crate adapton; # fn main() { # use adapton::macros::*; # use adapton::engine::*; # use adapton::reflect; # # // create an empty DCG (demanded computation graph) # manage::init_dcg(); # fn sum(x:usize, y:usize) -> usize { x + y } // create a memo entry, named `a`, that remembers that `sum(42,43) = 85` let res1 : usize = get!(thunk!([a] sum; x:42, y:43)); # } ``` Behind the scenes, the name `a` controls how and when the Adapton engine _overwrites_ the cached computation of `sum`. As such, names permit patterns of programmatic _cache eviction_. The macro `memo!` relies on programmer-supplied variable names in its macro expansion of these call sites, shown as `x` and `y` in the uses above. These can be chosen arbitrarily: So long as these symbols are distinct from one another, they can be _any_ symbols, and need not actually match the formal argument names. **Example as Editor role** For a simple illustration, we memoize several function calls to `sum` with different names and arguments. In real applications, the memoized function typically performs more work than summing two machine words. :) ``` # #[macro_use] extern crate adapton; # fn main() { # use adapton::macros::*; # use adapton::engine::*; # use adapton::reflect; # manage::init_dcg(); # fn sum(x:usize, y:usize) -> usize { # x + y # } # // Optional: Traces what the engine does below (for diagnostics, testing, illustration) reflect::dcg_reflect_begin(); // create a memo entry, named `a`, that remembers that `sum(42,43) = 85` let res1 : usize = get!(thunk!([a] sum; x:42, y:43)); // same name `a`, same arguments (42, 43), Adapton reuses cached result let res2 : usize = get!(thunk!([a] sum; x:42, y:43)); // different name `b`, same arguments (42, 43), Adapton re-computes `sum` for `b` let res3 : usize = get!(thunk!([b] sum; x:42, y:43)); // same name `b`, different arguments, editor overwrites thunk `b` with new args let res4 : usize = get!(thunk!([b] sum; x:55, y:66)); # } ``` Below we confirm the following facts: - The Editor: - allocated two thunks (`a` and `b`), - allocated one thunk without changing it (`a`, with the same arguments) - allocated one thunk by changing it (`b`, with different arguments) - The Archivist allocated nothing. ``` # #[macro_use] extern crate adapton; # fn main() { # use adapton::macros::*; # use adapton::engine::*; # use adapton::reflect; # # // create an empty DCG (demanded computation graph) # manage::init_dcg(); # # // a simple function (memoized below for illustration purposes; # // probably actually not worth it!) # fn sum(x:usize, y:usize) -> usize { # x + y # } # # // Optional: Traces what the engine does below (for diagnostics, testing, illustration) # reflect::dcg_reflect_begin(); # # // create a memo entry, named `a`, that remembers that `sum(42,43) = 85` # let res1 : usize = get!(thunk!([a] sum; x:42, y:43)); # # // same name `a`, same arguments (42, 43) => reuse cached result # let res2 : usize = get!(thunk!([a] sum; x:42, y:43)); # # // different name `b`, same arguments (42, 43) => recomputes `sum` for `b` # let res3 : usize = get!(thunk!([b] sum; x:42, y:43)); # # // same name `b`, different arguments; *overwrite* `b` with new args & result # let res4 : usize = get!(thunk!([b] sum; x:55, y:66)); # // Optional: Assert what happened above, in terms of analytical counts let traces = reflect::dcg_reflect_end(); let counts = reflect::trace::trace_count(&traces, None); // Editor allocated two thunks (`a` and `b`) assert_eq!(counts.alloc_fresh.0, 2); // Editor allocated one thunk without changing it (`a`, with same args) assert_eq!(counts.alloc_nochange.0, 1); // Editor allocated one thunk by changing it (`b`, different args) assert_eq!(counts.alloc_change.0, 1); // Archivist allocated nothing assert_eq!(counts.alloc_fresh.1, 0); # drop((res1,res2,res3,res4)); # } ``` Nominal Cycles =================== In many settings, we explore structures that contain cycles, and it is useful to use Adapton's DCG mechanism to detect such cycles. Example problem: Recursive computation over a directed graph --------------------------------------------------------------- As a tiny example, consider the following graph, defined as a table of adjacencies: ``` // Node | Adjacency pair // | (two outgoing edges to other nodes): // -----+------------------------------------- // 0 | (1, 0) // 1 | (2, 3) // 2 | (3, 0) // 3 | (3, 1) // 4 | (2, 5) // 5 | (5, 4) ``` This is a small arbitrary directed graph, and it has several cycles (e.g., `0 --> 0`, `3 --> 3`, `0 --> 1 --> 2 --> 0`). It also has distinct strongly-connected components (SCCs), e.g., the one involving `0` versus the one involving `4`. **Problem statement:** Suppose that we wish to explore this graph, to build a list (or `Vec`) of all of the nodes that it contains. **Desired solution program:** Consider the simple (naive) recursive exploration logic, defined as `explore_rec` below. The problems with this logic are that 1. **Repeated work**: `explore_rec` re-explores some sub-graphs multiple times, and 2. **Divergence**: `explore_rec` diverges on graphs with cycles. To address the first problem, we can leverage the DCG, which performs function caching. To address the second problem, the algorithm needs a mechanism to detect cycles. In terms of DCG evaluation, we can detect a cycle if we can remember and check whether we are "currently" visiting the node (on the recursive call stack) before we evaluate a node recursively. Regardless of how we detect the cycle, we wish to do something different (other than recur). ### DCG cycles: Detection and valuation Rather than implement this cycle-detection mechanism directly, we can use Adapton's DCG, which operates behind the scenes. Specifically, we can use the engine operation [`force_cycle`](https://docs.rs/adapton/0/adapton/engine/fn.force_cycle.html) to specify a "cycle value" for the result of a thunk `t` when `t` is forcing itself, or when `t` is forcing another thunk `s` that transitively forces `t`. In either case, the force operation that forms the cycle in the DCG evaluates to this programmer-specified cycle value, rather than diverging, or using the cached value at the thunk, which generally is not sound (e.g., it may be stale, from a prior run). ### Example cycle valuation Notice that in `explore` below, we use `get!(_, vec![])` on `at` and `bt` instead of `get!(_)`. This macro uses `force_cycle` in its expansion. The empty vector gives the cycle value for when this force forms a cycle in the DCG. ``` # #[macro_use] extern crate adapton; # fn main() { # use adapton::macros::*; # use adapton::engine::*; // Define the graph, following the table above fn adjs (n:usize) -> (usize, usize) { match n { 0 => (1, 0), 1 => (2, 3), 2 => (3, 0), 3 => (3, 1), 4 => (2, 5), 5 => (5, 4), _ => unimplemented!() } } // This version will diverge on all of the cycles (e.g., 3 --> 3) #[warn(unconditional_recursion)] fn explore_rec(cur_n:usize) -> Vec<usize> { let (a,b) = adjs(cur_n); let mut av = explore_rec(a); let mut bv = explore_rec(b); let mut res = vec![cur_n]; res.append(&mut av); res.append(&mut bv); res } // This version will not diverge; it gives an empty vector value // as "cycle output" when it performs each `get!`. Hence, when // Adapton detects a cycle, it will not re-force this thunk // cyclicly, but rather return this predetermined "cycle output" // value. For non-cyclic calls, the `get!` ignores this value, and // works in the usual way. fn explore(cur_n:usize) -> Vec<usize> { let (a,b) = adjs(cur_n); let at = explore_thunk(a); let bt = explore_thunk(b); let mut av = get!(at, vec![]); let mut bv = get!(bt, vec![]); let mut res = vec![cur_n]; res.append(&mut av); res.append(&mut bv); res } fn explore_thunk(cur_n:usize) -> Art<Vec<usize>> { thunk!([Some(name_of_usize(cur_n))]? explore ; n:cur_n) } adapton::engine::manage::init_dcg(); assert_eq!(get!(explore_thunk(0)), vec![0,1,2,3,3]) # } ``` Nominal Firewalls =================== Nominal firewalls use nominal allocation to dirty the DCG incrementally, _while change propagation cleans it_. In some situations (Run 2, below), these firewalls prevent dirtying from cascading, leading to finer-grained dependency tracking, and more incremental reuse. Thanks to [@nikomatsakis](https://github.com/nikomatsakis) for suggesting the term "firewall" in this context. First, consider this graph, as Rust code (graph picture below): Example: nominal firewall ------------------------- ``` # #[macro_use] extern crate adapton; # fn main() { # use adapton::macros::*; # use adapton::engine::*; fn demand_graph(a: Art<i32>) -> String { let_memo!{ d =(f)= { let a = a.clone(); let_memo!{ b =(g)={ let x = get!(a); cell!([b] x * x) }; c =(h)={ format!("{:?}", get!(b)) }; c }}; d } } # drop(demand_graph) } ``` The use of `let_memo!` is [convenient sugar](#let_memo-example) for `thunk!` and `force`. This code induces DCGs with the following structure: ``` /* +---- Legend ------------------+ cell a | [ 2 ] ref cell holding 2 | [ 2 ] "Nominal | (g) thunk named 'g' | ^ firewall" | ----> force/observe edge | | force | | --->> allocation edge | | 2 \|/ +------------------------------+ | ` | g allocs b cell g forces b When cell a changes, g is dirty, h is not; | to hold 4 b observes 4 in this sense, cell b _firewalls_ h from g: (g)------------->>[ 4 ]<--------------(h) <~~ note that h does not observe cell a, or g. ^ ^ | f forces g | f forces h, | g returns cell b | returns String "4" | | (f)------------------------------------+ ^ | force f, | returns String "4" | (demand_graph(a)) */ ``` In this graph, the ref cell `b` acts as the "firewall". Below, we show a particular input change for cell `a` where a subcomputation `h` is never dirtied nor cleaned by change propagation (input change 2 to -2). We show another change to the same input where this subcomputation `h` *is* _eventually_ dirtied and cleaned by Adapton, though not immediately (input change -2 to 3). Here's the Rust code for generating this DCG, and these changes to its input cell, named `"a"`: ``` # #[macro_use] extern crate adapton; # fn main() { # use adapton::macros::*; # use adapton::engine::*; # # fn demand_graph(a: Art<i32>) -> String { # let_memo!{ # d =(f)= { # let a = a.clone(); # let_memo!{ b =(g)={ let x = get!(a); cell!([b] x * x) }; # c =(h)={ format!("{:?}", get!(b)) }; # c }}; # d } # } # # manage::init_dcg(); # // 1. Initialize input cell "a" to hold 2, and do the computation illustrated above: assert_eq!(demand_graph(let_cell!{a = 2; a}), "4".to_string()); // 2. Change input cell "a" to hold -2, and do the computation illustrated above: assert_eq!(demand_graph(let_cell!{a = -2; a}), "4".to_string()); // 3. Change input cell "a" to hold 3, and do the computation illustrated above: assert_eq!(demand_graph(let_cell!{a = 3; a}), "9".to_string()); # } ``` **Run 1.** In the first computation, the input cell `a` holds 2, and the final result is `"4"`. **Run 2.** When the input cell `a` changes, e.g., from 2 to -2, thunks `f` and `g` are dirtied. Thunk `g` is dirty because it observes the changed input. Thunk `f` is dirty because it demanded (observed) the output of thunk `g` in the extent of its own computation. _Importantly, thunk `h` is *not* immediately dirtied when cell `a` changes._ In a sense, cell `a` is an indirect ("transitive") input to thunk `h`. This fact may suggest that when cell `a` is changed from 2 to -2, we should dirty thunk `h` immediately. However, thunk `h` is related to this input only by reading ref cell `b`. Rather, when the editor re-demands thunk `f`, Adapton will necessarily perform a cleaning process (aka, "change propagation"), re-executing `g`, its immediate dependent, which is dirty. Since thunk `g` merely squares its input, and 2 and -2 both square to 4, the output of thunk `g` will not change in this case. Consequently, the observers of cell `b`, which holds this output, will not be dirtied or re-executed. In this case, thunk `h` is this observer. In situations like these, Adapton's dirtying + cleaning algorithms do not dirty nor clean thunk `h`. In sum, under this change, after `f` is re-demanded, the cleaning process will first re-execute `g`, the immediate observer of cell `a`. Thunk `g` will again allocate cell `b` to hold 4, the same value as before. It also yields this same cell pointer (to cell `b`). Consequently, thunk `f` is not re-executed, and is cleaned. Meanwhile, the outgoing (dependency) edges thunk of `h` are never dirtied. Effectively, the work of `h` is reused from cache as well. Alternatively, if we had placed the code for `format!("{:?}",get!(b))` in thunk `f`, Adapton _would_ have re-executed this step when `a` changes from `2` to `-2`: It would be dirtied when `a` changes, since it directly observes `g`, which directly observes cell `a`. **Run 3.** For some other change, e.g., from 2 to 3, thunk `h` would _eventually_ _will be_ - dirtied, when `f` redemands `g`, which will overwrite cell `b` with `9`, - and cleaned, when `f` re-demands `h`, which will `format!` a new `String` of `"9"`. `let_memo!` example ---------------------------- The [use of `let_memo!` macro above](#example-nominal-firewall) expands as follows: ``` # #[macro_use] extern crate adapton; # fn main() { # use adapton::macros::*; # use adapton::engine::*; fn demand_graph__mid_macro_expansion(a: Art<i32>) -> String { let f = thunk!([f]{ let a = a.clone(); let g = thunk!([g]{ let x = get!(a); cell!([b] x * x) }); let b = force(&g); let h = thunk!([h]{ let x = get!(b); format!("{:?}", x) }); let c = force(&h); c }); let d = force(&f); d }; # } ``` Incremental sequences ======================== A _level tree_ consists of a binary tree with levels that decrease monotonically along each path to its leaves. Here, we implement incremental level trees by including `Name`s and `Art`s in the tree structure, with two additional constructors for the recursive type, `Rec<X>`: ``` # #[macro_use] extern crate adapton; # fn main() { # use adapton::macros::*; # use adapton::engine::*; use std::fmt::Debug; use std::hash::Hash; #[derive(Clone,PartialEq,Eq,Debug,Hash)] enum Rec<X> { Bin(BinCons<X>), Leaf(LeafCons<X>), Name(NameCons<X>), Art(Art<Rec<X>>), } #[derive(Clone,PartialEq,Eq,Debug,Hash)] struct LeafCons<X> { elms:Vec<X>, } #[derive(Clone,PartialEq,Eq,Debug,Hash)] struct BinCons<X> { level: u32, recl:Box<Rec<X>>, recr:Box<Rec<X>> } #[derive(Clone,PartialEq,Eq,Debug,Hash)] struct NameCons<X> { level:u32, name:Name, rec:Box<Rec<X>>, } # } ``` Example: Nominal memoization and recursion -------------------------------------------- **Introduction forms:** ``` # #[macro_use] extern crate adapton; # fn main() { # # use std::fmt::Debug; # use std::hash::{Hash}; # use adapton::macros::*; # use adapton::engine::*; # # #[derive(Clone,PartialEq,Eq,Debug,Hash)] # struct BinCons<X> { # level: u32, # recl:Box<Rec<X>>, # recr:Box<Rec<X>> # } # #[derive(Clone,PartialEq,Eq,Debug,Hash)] # struct NameCons<X> { # level:u32, # name:Name, # rec:Box<Rec<X>>, # } # #[derive(Clone,PartialEq,Eq,Debug,Hash)] # struct LeafCons<X> { # elms:Vec<X>, # } # #[derive(Clone,PartialEq,Eq,Debug,Hash)] # enum Rec<X> { # Leaf(LeafCons<X>), # Bin(BinCons<X>), # Name(NameCons<X>), # Art(Art<Rec<X>>), # } impl<X:'static+Clone+PartialEq+Eq+Debug+Hash> Rec<X> { pub fn leaf(xs:Vec<X>) -> Self { Rec::Leaf(LeafCons{elms:xs}) } pub fn bin(lev:u32, l:Self, r:Self) -> Self { Rec::Bin(BinCons{level:lev,recl:Box::new(l),recr:Box::new(r)}) } pub fn name(lev:u32, n:Name, r:Self) -> Self { Rec::Name(NameCons{level:lev,name:n, rec:Box::new(r)}) } fn art(a:Art<Rec<X>>) -> Self { Rec::Art(a) } # } # } ``` **Elimination forms:** Folds use `memo!` to create and `force` `thunks`: ``` # #[macro_use] extern crate adapton; # fn main() { # # use std::fmt::Debug; # use std::hash::{Hash}; # use adapton::macros::*; # use adapton::engine::*; # # #[derive(Clone,PartialEq,Eq,Debug,Hash)] # struct BinCons<X> { # level: u32, # recl:Box<Rec<X>>, # recr:Box<Rec<X>> # } # #[derive(Clone,PartialEq,Eq,Debug,Hash)] # struct NameCons<X> { # level:u32, # name:Name, # rec:Box<Rec<X>>, # } # #[derive(Clone,PartialEq,Eq,Debug,Hash)] # struct LeafCons<X> { # elms:Vec<X>, # } # #[derive(Clone,PartialEq,Eq,Debug,Hash)] # enum Rec<X> { # Leaf(LeafCons<X>), # Bin(BinCons<X>), # Name(NameCons<X>), # Art(Art<Rec<X>>), # } # impl<X:'static+Clone+PartialEq+Eq+Debug+Hash> # Rec<X> # { # pub fn leaf(xs:Vec<X>) -> Self { # Rec::Leaf(LeafCons{elms:xs}) # } # pub fn bin(lev:u32, l:Self, r:Self) -> Self { # Rec::Bin(BinCons{level:lev,recl:Box::new(l),recr:Box::new(r)}) # } # pub fn name(lev:u32, n:Name, r:Self) -> Self { # Rec::Name(NameCons{level:lev,name:n, rec:Box::new(r)}) # } # fn art(a:Art<Rec<X>>) -> Self { # Rec::Art(a) # } # pub fn fold_monoid<B:'static+Clone+PartialEq+Eq+Debug+Hash> (t:Rec<X>, z:X, b:B, bin:fn(B,X,X)->X, art:fn(Art<X>,X)->X) -> X { fn m_leaf<B:Clone,X>(m:(B,fn(B,X,X)->X,X), elms:Vec<X>) -> X { # let mut x = m.2; # for elm in elms { # x = m.1(m.0.clone(), x, elm) # }; # x // ... } fn m_bin<B,X>(_n:Option<Name>, m:(B,fn(B,X,X)->X,X), _lev:u32, l:X, r:X) -> X { m.1(m.0, l, r) } Self::fold_up_namebin::<(B,fn(B,X,X)->X,X), (B,fn(B,X,X)->X,X),X> (t, (b.clone(),bin,z.clone()), m_leaf, None, (b,bin,z), m_bin, art) } fn fold_up_namebin <L:'static+Clone+PartialEq+Eq+Debug+Hash, B:'static+Clone+PartialEq+Eq+Debug+Hash, R:'static+Clone+PartialEq+Eq+Debug+Hash> (t:Rec<X>, l:L, leaf:fn(L,Vec<X>)->R, n:Option<Name>, b:B, namebin:fn(Option<Name>,B,u32,R,R)->R, art:fn(Art<R>,R)->R) -> R { match t { Rec::Art(a) => Self::fold_up_namebin(get!(a), l, leaf, n, b, namebin, art), Rec::Leaf(leafcons) => leaf(l, leafcons.elms), Rec::Bin(bincons) => { let (n1,n2) = forko!(n.clone()); let r1 = memo!([n1]? Self::fold_up_namebin; t:*bincons.recl, l:l.clone(), leaf:leaf, n:None, b:b.clone(), namebin:namebin, art:art); let r1 = art(r1.0,r1.1); let r2 = memo!([n2]? Self::fold_up_namebin; t:*bincons.recr, l:l.clone(), leaf:leaf, n:None, b:b.clone(), namebin:namebin, art:art); let r2 = art(r2.0,r2.1); namebin(n, b, bincons.level, r1, r2) } Rec::Name(namecons) => { Self::fold_up_namebin( *namecons.rec, l, leaf, Some(namecons.name), b, namebin, art ) } } } # }} ``` Background: Incremental Computing with Names ============================================= We explain the role of names in incremental computing. ## Pointer locations in incremental computing Suppose that we have a program that we wish to run repeatedly on similar (but changing) inputs, and that this program constructs a dynamic data structure as output. To cache this computation, including its output, we generally require caching some of its function calls, their results, and whatever allocations are relevant to represent these results, including the final output structure. Furthermore, to quickly test for input and output changes (in `O(1)` time per "change") we would like to _store allocate_ input and output, and use allocated _pointer locations_ (globally-unique "names") to compare structures, giving a cheap, conservative approximation of structural equality. ## Deterministic allocation The first role of explicit names for incremental computing concerns _deterministic pointer allocation_, which permits us to give a meaningful definition to _cached_ allocation. To understand this role, consider these two evaluation rules: ``` // l ∉ dom(σ) n ∉ dom(σ) // ---------------------------- :: alloc_1 ------------------------------- :: alloc_2 // σ; cell(v) ⇓ σ{l↦v}; ref l σ; cell[n](v) ⇓ σ{n↦v}; ref n ``` Each rule is of the judgement form `σ1; e ⇓ σ2; v`, where `σ1` and `σ2` are stores that map pointers to thunks and values, and `e` is an expression to evaluate, and `v` is its valuation. The left rule is conventional: it allocates a value `v` at a store location `l`; because the program does not determine `l`, the implementor of this rule has the freedom to choose `l` any way that they wish. Consequently, this program is not deterministic, and not a function. Hence, it is not immediately obvious what it means to _cache_ this kind of dynamic allocation using a technique like _function caching_, or techniques based on it. To address this question, the programmer can determine a name `n` for the value `v` as in the right rule. The point of this version is to expose the naming choice directly to the programmer. ### Structural names In some systems, the programmer chooses this name as the hash value of value `v`. This naming style is often called "hash-consing". We refer to it as _structural naming_, since by using it, the name of each ref cell reflects the _entire structure_ of that cell's content. (Structural hashing approach is closely related to Merkle trees, the basis for revision-control systems like `git`.) ### Independent names By contrast, in a _nominal_ incremental system, the programmer generally chooses `n` to be related to the _evaluation context of using `v`_, and often, to be _independent_ of the value `v` itself. We give one example of such a naming strategy below. ## Nominal independence Names augment programs to permit memoization and change propagation to exploit independence among dynamic dependencies. Specifically, the name value `n` is (generally) unrelated to the content value `v`. In many incremental applications, its role is analogous to that of location `l` in the left rule, where `l` is only related to `v` by the final store. When pointer name `n` is independent of pointer content `v`, we say this name, via the store, affords the program _nominal independence_. Suppose that in a subsequent incremental run, value `v` changes to `v2` at name `n`. The pointer name `n` localizes this change, preventing any larger structure that contains cell `n` from itself having a changed identity. By contrast, consider the case of structural naming, which lacks nominal indirection: by virtue of being determined by the value `v`, the allocated name `n` must change to `n2` when `v` changes to `v2`. Structural naming is deterministic, but lacks nominal independence, by definition. ## Simple example of nominal independence The independence afforded by nominal indirection is critical in many incremental programs. As a simple illustrative example, consider `rev`, which recursively reverses a list that, after being reversed, undergoes incremental insertions and removals. ``` // rev : List -> List -> List // rev l r = match l with // | Nil => r // | Cons(h,t) => // memo(rev !t (Cons(h,r))) ``` The function `rev` reverses a list of `Cons` cells, using an accumulator value `r`. To incrementalize the code for `rev`, in the `Cons` case, we memoize the recursive call to `rev`, which involves matching its arguments with those of cached calls. Problematically, if we do not introduce any indirection for it, the accumulator `Cons(h,r)` will contain any incremental changes to head value `h`, as well as any changes in the prefix of the input list (now reversed in the previous accumulator value `r`). This is a problem for memoization because, without indirection in this accumulator list, such changes will repeatedly prevent us from `memo`-matching the recursive call. Consequently, change propagation will re-evaluate all the calls that follow the position of an insertion or removal: This change is recorded in the accumulator, which has changed structurally. To address this issue, which is an example of a general pattern (c.f. the output accumulators of quicksort and quickhull), past researchers suggest that we introduce nominal `cell`s into the accumulator, each allocated with a name associated with their corresponding input `Cons` cell. In place of "names", prior work variously used the terms _(allocation) keys_~\cite{AcarThesis,Hammer08,AcarLeyWild09} and _indices_~\cite{Acar06,Acar06ML}, but the core idea is the same. ``` // | Cons(n,h,t) => // let rr = ref[n](r) in // memo(rev !t (Cons(h,rr))) ``` In this updated version, each name `n` localizes any change to the accumulator argument `r` via nominal indirection. When and if a later part of the program consumes the output in ref cell `rr`, the system will process any changes associated with this accumulator; they may be relevant later, but they are not _directly_ relevant for reversing the tail `!t` in cell `t`: The body of `rev` never inspects `r`, it merely uses it to construct its output, for the `Nil` base case. In summary, this example illustrate a general principle: Nominal indirection augments programs to permit memoization and change propagation to exploit dynamic independence. Specifically, we exploit the independence of the steps that reverse the pointers of a linked list. */ //#![feature(associated_consts)] #![feature(box_patterns)] #![feature(box_syntax)] #![crate_name = "adapton"] #![crate_type = "lib"] extern crate core; #[macro_use] pub mod macros ; pub mod engine ; pub mod catalog ; pub mod parse_val; pub mod reflect; mod adapton { pub use super::*; }