Expand execution docs (#7158)

## Summary

This PR extends the execution flow docs, both on the website and in the
codebase itself. The general points I've tried to clear up are:
1. How are things called and how all types interact.
2. "Where should feature X go" which has been a pain point in the past
3. Tried to have some docs for more types, even if its just a pointer to
some other type.

Signed-off-by: Adam Gutglick <adam@spiraldb.com>

Author: AdamGS

docs/developer-guide/internals/execution.md

@@ -1,9 +1,9 @@
 # Execution
 
-Vortex defers computation wherever possible. When an expression is applied to an array, the
-result is not computed immediately. Instead, a `ScalarFnArray` is constructed that captures the
-operation and its inputs as a new array node. The actual computation happens later, when the
-array is materialized -- either by a scan, a query engine, or an explicit `execute()` call.
+Vortex defers computation wherever possible. Instead of immediately materializing intermediate
+results, it represents them as arrays that still describe work to be done, such as `FilterArray`
+and [`ScalarFnArray`](../../concepts/expressions.md). The actual computation happens later, when
+the array is materialized -- either by a scan, a query engine, or an explicit `execute()` call.
 
 ## Why Defer
 
@@ -32,19 +32,201 @@ pub trait Executable: Sized {
 }
 ```
 
-The `ExecutionCtx` carries the session and provides access to registered encodings during
-execution. Arrays can be executed into different target types:
+The `ExecutionCtx` carries the session and accumulates a trace of execution steps for debugging.
+Arrays can be executed into different target types:
 
 - **`Canonical`** -- fully materializes the array into its canonical form.
 - **`Columnar`** -- like `Canonical`, but with a variant for constant arrays to avoid
   unnecessary expansion.
 - **Specific array types** (`PrimitiveArray`, `BoolArray`, `StructArray`, etc.) -- executes
   to canonical form and unwraps to the expected type, panicking if the dtype does not match.
 
+## Constant Short-Circuiting
+
+Executing to `Columnar` rather than `Canonical` enables an important optimization: if the
+array is constant (a scalar repeated to a given length), execution returns the `ConstantArray`
+directly rather than expanding it. This avoids allocating and filling a buffer with repeated
+values.
+
+```rust
+pub enum Columnar {
+    Canonical(Canonical),
+    Constant(ConstantArray),
+}
+```
+
+Almost all compute functions can make use of constant input values, and many query engines
+support constant vectors directly, avoiding unnecessary expansion.
+
+## Execution Overview
+
+The `execute_until<M: Matcher>` method on `ArrayRef` drives execution. The scheduler is
+iterative: it rewrites and executes arrays in small steps until the current array matches the
+requested target form.
+
+At a high level, each iteration works like this:
+
+1. `optimize(current)` runs metadata-only rewrites to fixpoint:
+   `reduce` lets an array simplify itself, and `reduce_parent` lets a child rewrite its parent.
+2. If optimization does not finish execution, each child gets a chance to `execute_parent`,
+   meaning "execute my parent's operation using my representation".
+3. If no child can do that, the array's own `execute` method returns the next `ExecutionStep`.
+
+This keeps execution iterative rather than recursive, and it gives optimization rules another
+chance to fire after every structural or computational step.
+
+## The Four Layers
+
+The execution model has four layers, but they are not all invoked in the same way. Layers 1 and
+2 make up `optimize`, which runs to fixpoint before and after execution steps. Layers 3 and 4
+run only after optimization has stalled.
+
+```
+execute_until(root):
+  current = optimize(root)             # Layers 1-2 to fixpoint
+
+  loop:
+    if current matches target:
+      return / reattach to parent
+
+    Layer 3: try execute_parent on each child
+      if one succeeds:
+        current = optimize(result)
+        continue
+
+    Layer 4: call execute(current)
+      ExecuteChild(i, pred) -> focus child[i], then optimize
+      Done                  -> current = optimize(result)
+```
+
+### Layer 1: `reduce` -- self-rewrite rules
+
+An encoding applies `ArrayReduceRule` rules to itself. These are structural simplifications
+that look only at the array's own metadata and children types, not buffer contents.
+
+Examples:
+- A `FilterArray` with an all-true mask reduces to its child.
+- A `FilterArray` with an all-false mask reduces to an empty canonical array.
+- A `ScalarFnArray` whose children are all constants evaluates once and returns a `ConstantArray`.
+
+### Layer 2: `reduce_parent` -- child-driven rewrite rules
+
+Each child is given the opportunity to rewrite its parent via `ArrayParentReduceRule`. The child
+matches on the parent's type via a `Matcher` and can return a replacement. This is still
+metadata-only.
+
+Examples:
+- A `FilterArray` child of another `FilterArray` merges the two masks into one.
+- A `PrimitiveArray` inside a `MaskedArray` absorbs the mask into its own validity field.
+- A `DictArray` child of a `ScalarFnArray` pushes the scalar function into the dictionary
+  values, applying the function to `N` unique values instead of `M >> N` total rows.
+- A `RunEndArray` child of a `ScalarFnArray` pushes the function into the run values.
+
+### Layer 3: `execute_parent` -- parent kernels
+
+Each child is given the opportunity to execute its parent in a fused manner via
+`ExecuteParentKernel`. Unlike reduce rules, parent kernels may read buffers and perform real
+computation.
+
+An encoding declares its parent kernels in a `ParentKernelSet`, specifying which parent types
+each kernel handles via a `Matcher`:
+
+```rust
+pub trait ExecuteParentKernel<V: VTable> {
+    type Parent: Matcher;  // which parent types this kernel handles
+
+    fn execute_parent(
+        &self,
+        array: &V::Array,                          // the child
+        parent: <Self::Parent as Matcher>::Match<'_>, // the matched parent
+        child_idx: usize,
+        ctx: &mut ExecutionCtx,
+    ) -> VortexResult<Option<ArrayRef>>;
+}
+```
+
+Examples:
+- A `RunEndArray` child of a `SliceArray` performs a binary search on the run ends to produce a
+  new `RunEndArray` with adjusted offsets, or a `ConstantArray` if the slice falls within a
+  single run.
+- A `PrimitiveArray` child of a `FilterArray` applies the filter mask directly over its buffer,
+  producing a filtered `PrimitiveArray` in one pass.
+
+### Layer 4: `execute` -- the encoding's own decode step
+
+If no reduce rule or parent kernel handled the array, the encoding's `VTable::execute` method
+is called. This is the encoding's chance to decode itself one step closer to canonical form.
+
+Instead of recursively executing children inline, `execute` returns an `ExecutionResult`
+containing an `ExecutionStep` that tells the scheduler what to do next:
+
+```rust
+pub enum ExecutionStep {
+    /// Ask the scheduler to execute child[idx] until it matches the predicate,
+    /// then replace the child and re-enter execution for this array.
+    ExecuteChild(usize, DonePredicate),
+
+    /// Execution is complete. The array in the ExecutionResult is the result.
+    Done,
+}
+```
+
+## The Execution Loop
+
+The full `execute_until<M: Matcher>` loop uses an explicit work stack to manage
+parent-child relationships without recursion:
+
+```
+execute_until<M>(root):
+  stack = []
+  current = optimize(root)
+
+  loop:
+    ┌─────────────────────────────────────────────────────┐
+    │ Is current "done"?                                  │
+    │   (matches M if at root, or matches the stack       │
+    │    frame's DonePredicate if inside a child)         │
+    ├──────────────────────┬──────────────────────────────┘
+    │ yes                  │ no
+    │                      │
+    │  stack empty?        │  Already canonical?
+    │  ├─ yes → return     │  ├─ yes → pop stack (can't make more progress)
+    │  └─ no  → pop frame, │  └─ no  → continue to execution steps
+    │     replace child,   │
+    │     optimize, loop   │
+    │                      ▼
+    │         ┌────────────────────────────────────┐
+    │         │  Try execute_parent on each child  │
+    │         │  (Layer 3 parent kernels)          │
+    │         ├────────┬───────────────────────────┘
+    │         │ Some   │ None
+    │         │        │
+    │         │        ▼
+    │         │  ┌─────────────────────────────────┐
+    │         │  │  Call execute (Layer 4)         │
+    │         │  │  Returns ExecutionResult        │
+    │         │  ├────────┬────────────────────────┘
+    │         │  │        │
+    │         │  │  ExecuteChild(i, pred)?
+    │         │  │  ├─ yes → push (array, i, pred)
+    │         │  │  │        current = child[i]
+    │         │  │  │        optimize, loop
+    │         │  │  └─ Done → current = result
+    │         │  │            loop
+    │         │  │
+    │         ▼  ▼
+    │    optimize result, loop
+    └──────────────────────────
+```
+
+Note that `optimize` runs after every transformation. This is what enables cross-step
+optimizations: after a child is decoded, new `reduce_parent` rules may now match that were
+previously blocked.
+
 ## Incremental Execution
 
 Execution is incremental: each call to `execute` moves the array one step closer to canonical
-form, not necessarily all the way. This gives each child the opportunity to optimize before the 
+form, not necessarily all the way. This gives each child the opportunity to optimize before the
 next iteration of execution.
 
 For example, consider a `DictArray` whose codes are a sliced `RunEndArray`. Dict-RLE is a common
@@ -60,59 +242,82 @@ If execution jumped straight to canonicalizing the dict's children, it would exp
 codes through the slice, missing the Dict-RLE optimization entirely. Incremental execution
 avoids this:
 
-1. First iteration: the slice executes and returns a new `RunEndArray` whose offsets have been binary searched.
+1. First iteration: the slice `execute_parent` (parent kernel on RunEnd for Slice) performs a
+   binary search on run ends, returning a new `RunEndArray` with adjusted offsets.
 
 2. Second iteration: the `RunEndArray` codes child now matches the Dict-RLE pattern. Its
    `execute_parent` provides a fused kernel that expands runs while performing dictionary
    lookups in a single pass, returning the canonical array directly.
 
-The execution loop runs until the array is canonical or constant:
-
-1. **Child optimization** -- each child is given the opportunity to optimize its parent's
-   execution by calling `execute_parent` on the child's vtable. If a child can handle the
-   parent more efficiently, it returns the result directly.
-
-2. **Incremental execution** -- if no child provides an optimized path, the array's own
-   `execute` vtable method is called. This executes children one step and returns a new
-   array that is closer to canonical form, or executes the array itself.
-
-## Constant Short-Circuiting
+## Walkthrough: Executing a RunEnd-Encoded Array
 
-Executing to `Columnar` rather than `Canonical` enables an important optimization: if the
-array is constant (a scalar repeated to a given length), execution returns the `ConstantArray`
-directly rather than expanding it. This avoids allocating and filling a buffer with repeated
-values.
+To make the execution flow concrete, here is a step-by-step trace of executing a
+`RunEndArray` to `Canonical`:
 
-```rust
-pub enum Columnar {
-    Canonical(Canonical),
-    Constant(ConstantArray),
-}
+```
+Input:  RunEndArray { ends: [3, 7, 10], values: [A, B, C], len: 10 }
+Goal:   Canonical (PrimitiveArray or similar)
+
+Iteration 1:
+  reduce?         → None (no self-rewrite rules match)
+  reduce_parent?  → None (no parent, this is root)
+  execute_parent? → None (no parent)
+  execute         → ends are not Primitive yet?
+                    ExecuteChild(0, Primitive::matches)
+                    Stack: [(RunEnd, child_idx=0, Primitive::matches)]
+                    Focus on: ends
+
+Iteration 2:
+  Current: ends array
+  Already Primitive? → yes, done.
+  Pop stack → replace child 0 in RunEnd, optimize.
+
+Iteration 3:
+  reduce?         → None
+  reduce_parent?  → None
+  execute_parent? → None
+  execute         → values are not Canonical yet?
+                    ExecuteChild(1, AnyCanonical::matches)
+                    Stack: [(RunEnd, child_idx=1, AnyCanonical::matches)]
+                    Focus on: values
+
+Iteration 4:
+  Current: values array
+  Already Canonical? → yes, done.
+  Pop stack → replace child 1 in RunEnd, optimize.
+
+Iteration 5:
+  reduce?         → None
+  reduce_parent?  → None
+  execute_parent? → None
+  execute         → all children ready, decode runs:
+                    [A, A, A, B, B, B, B, C, C, C]
+                    Done → return PrimitiveArray
+
+→ Result: PrimitiveArray [A, A, A, B, B, B, B, C, C, C]
 ```
 
-Almost all compute functions can make use of constant input values, and many query engines support constant vectors
-avoiding unnecessary expansion.
-
-## ScalarFnArray
+## Implementing an Encoding: Where Does My Logic Go?
 
-A `ScalarFnArray` holds a scalar function (the operation to perform), a list of child arrays
-(the inputs), and the expected output dtype and length. It is itself a valid Vortex array and
-can be nested, sliced, and passed through the same APIs as any other array.
+When adding a new encoding or optimizing an existing one, the key question is whether the
+transformation needs to read buffer data:
 
-When an expression like `{x: $, y: $ + 1}` is applied to a bit-packed integer array, the
-result is a tree of `ScalarFnArray` nodes rather than a materialized struct:
+| If you need to... | Put it in | Example |
+|-------------------|-----------|---------|
+| Rewrite the array by looking only at its own structure | `reduce` (Layer 1) | `FilterArray` removes itself when the mask is all true |
+| Rewrite the parent by looking at your type and the parent's structure | `reduce_parent` (Layer 2) | `DictArray` pushes a scalar function into its values |
+| Execute the parent's operation using your compressed representation | `execute_parent` / parent kernel (Layer 3) | `PrimitiveArray` applies a filter mask directly over its buffer |
+| Decode yourself toward canonical form | `execute` (Layer 4) | `RunEndArray` expands runs into a `PrimitiveArray` |
 
-```
-scalar_fn(struct.pack):
-  children:
-    - bitpacked(...)                    # x: passed through unchanged
-    - scalar_fn(binary.add):            # y: deferred addition
-        children:
-          - bitpacked(...)              #    original array
-          - constant(1)                 #    literal 1
-```
+Rules of thumb:
 
-Nothing is computed until the tree is executed.
+- Prefer `reduce` over `execute` when possible. Reduce rules are cheaper because they are
+  metadata-only and run before any buffers are touched.
+- Parent rules and parent kernels enable the "child sees parent" pattern. A child encoding often
+  knows how to handle its parent's operation more efficiently than the parent knows how to handle
+  the child.
+- Treat `execute` as the fallback. If no reduce rule or parent kernel applies, the encoding
+  decodes itself and uses `ExecuteChild` to request child execution when needed.
 
 ## Future Work
 

uv.lock

@@ -1,6 +1,13 @@
 // SPDX-License-Identifier: Apache-2.0
 // SPDX-FileCopyrightText: Copyright the Vortex contributors
 
+//! Reduce and execute adaptors for filter operations.
+//!
+//! Encodings that know how to filter themselves implement [`FilterReduce`] (metadata-only)
+//! or [`FilterKernel`] (buffer-reading). The adaptors [`FilterReduceAdaptor`] and
+//! [`FilterExecuteAdaptor`] bridge these into the execution model as
+//! [`ArrayParentReduceRule`] and [`ExecuteParentKernel`] respectively.
+
 use vortex_error::VortexResult;
 use vortex_mask::Mask;
 
@@ -70,6 +77,7 @@ fn precondition<V: VTable>(array: &V::Array, mask: &Mask) -> Option<ArrayRef> {
     None
 }
 
+/// Adaptor that wraps a [`FilterReduce`] impl as an [`ArrayParentReduceRule`].
 #[derive(Default, Debug)]
 pub struct FilterReduceAdaptor<V>(pub V);
 
@@ -93,6 +101,7 @@ where
     }
 }
 
+/// Adaptor that wraps a [`FilterKernel`] impl as an [`ExecuteParentKernel`].
 #[derive(Default, Debug)]
 pub struct FilterExecuteAdaptor<V>(pub V);