adapton 0.3.31

#![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)
- [Fungi: A typed, functional language for programs that dynamically name their own dependency graphs](https://github.com/Adapton/fungi-lang.rust)
- [IODyn: Adapton collections, for algorithms with dynamic input and output](https://github.com/cuplv/iodyn.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 `cell` names

Behind the scenes, the (editor's) invocation `cell!(123)` uses an
imperative global counter to choose a unique name to hold the number
`123`. After each use, it increments this global counter, ensuring
that each such number is used at most once.

```
# #[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 );
# }
```

## Naming strategy: *Global counter* ###

Using a global counter to name cells, as above, _may_ be appopriate
for the Editor role, but is _never appropriate for the Archivist
role_, since this global counter is too sensitive to global
(often-changing) properties, such as an index into the sequence of all
allocations, globally.

To replace this global counter, we the Archivist may give names
*explicitly*, as shown in various forms, below.


## Explicitly named `cell`s

### Names via Rust "identifiers"

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);
# }
```

### Optional `Name`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 programmer 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 thunk `check` is demanded for 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 programmer 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`) with all of the edges 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::*;
}