pbpath

pbpath

pbpath lets you address any value inside a protobuf message using a compact, human-readable string path. Given a .proto schema and a message descriptor you can parse a path string, then traverse a live message to extract the values at that location — including fan-out across repeated fields via wildcards, ranges, and Python-style slices.

For hot paths that evaluate multiple paths against many messages of the same type, the Plan API compiles paths into a trie-based execution plan that traverses shared prefixes only once.

For a deep dive into the internal object model, trie structure, expression system, and performance recommendations, see the Architecture Guide.

Core API

// Parse a path string against a message descriptor.
path, err := pbpath.ParsePath(md, "device.geo.country")

// Walk the path through a concrete message to collect values at every step.
// PathValues returns a slice — one Values per matching branch when the path
// contains wildcards, ranges, or slices.
results, err := pbpath.PathValues(path, msg)

// For a scalar path (no fan-out) there is exactly one result.
last := results[0].Index(-1)
fmt.Println(last.Value.String()) // e.g. "US"

PathValues

func PathValues(p Path, m proto.Message, opts ...PathOption) ([]Values, error)

PathValues walks the given Path through message m and returns every matching Values branch. When the path contains fan-out steps — ListWildcardStep, ListRangeStep, or a ListIndexStep with a negative index — the function produces one Values per matching element. Nested fan-out steps produce the cartesian product of all matches.

Each Values carries:

• Path — the concrete path taken (wildcards/ranges are replaced with the actual ListIndex of each element).
• Values — the protoreflect.Value at every step along that path.

Options

Option	Effect
Strict()	Return an error when a negative index or range bound resolves out-of-bounds. Without it, out-of-range accesses are silently clamped or the branch is skipped.

Values helpers

// Index returns the (step, value) pair at position i (supports negative indices).
pair := vals.Index(-1)   // last step+value
pair.Step                // the Step
pair.Value               // the protoreflect.Value

// ListIndices returns the concrete list indices visited along the path.
indices := vals.ListIndices() // e.g. [0, 2] for repeats[0].inner[2]

// String returns a human-readable "path = value" representation.
fmt.Println(vals.String())
// (pkg.Msg).items[0].name = "widget"

Multi-Path Plan API

When you need to extract several values from every message in a stream, the Plan API avoids redundant work by sharing traversal across paths with common prefixes.

Quick Start

// Compile once.
plan, err := pbpath.NewPlan(md,
    pbpath.PlanPath("device.geo.country",       pbpath.Alias("country")),
    pbpath.PlanPath("device.geo.city",           pbpath.Alias("city")),
    pbpath.PlanPath("imp[*].id",                 pbpath.Alias("imp_id")),
    pbpath.PlanPath("imp[*].pmp.deals[*].id",    pbpath.Alias("deal_id")),
    pbpath.PlanPath("imp[0:3].banner.w",         pbpath.StrictPath()),
)
if err != nil {
    log.Fatal(err)
}

// Evaluate many times.
for _, msg := range messages {
    results, err := plan.Eval(msg)
    if err != nil {
        log.Fatal(err)
    }
    // results[0] = country  (1 branch)
    // results[1] = city     (1 branch)
    // results[2] = imp_id   (N branches, one per impression)
    // results[3] = deal_id  (N×M branches, impressions × deals)
    // results[4] = banner.w (up to 3 branches, strict)
}

plan.Eval returns [][]Values — one []Values slot per path, in the order the paths were provided to NewPlan. Each slot may contain multiple Values branches when the path fans out via wildcards, ranges, or slices.

NewPlan

func NewPlan(md protoreflect.MessageDescriptor, paths ...PlanPathSpec) (*Plan, error)

Compiles path strings against md, builds a trie of shared prefixes, and returns an immutable Plan. All parse errors are bundled into a single returned error. The Plan is safe for concurrent use by multiple goroutines.

PlanPath and PlanOption

func PlanPath(path string, opts ...PlanOption) PlanPathSpec

Pairs a raw path string with per-path options. Available options:

Option	Effect
Alias(name)	Give the entry a human-readable name (returned by Plan.Entries). Defaults to the raw path string.
StrictPath()	Return an error from Eval if any range or index on this path was clamped due to the list being shorter than the bound.

Plan.Eval

func (p *Plan) Eval(m proto.Message) ([][]Values, error)

Traverses m along all compiled paths simultaneously. Paths sharing a prefix are walked once through the shared segment, then forked. Returns [][]Values indexed by entry position.

The Eval method always traverses leniently — out-of-bounds indices and range bounds are clamped or skipped rather than returning errors. If a path was compiled with StrictPath(), the clamped flag is checked at the leaf and an error is returned only for that path.

Plan.Entries

func (p *Plan) Entries() []PlanEntry

Returns metadata for each compiled path:

type PlanEntry struct {
    Name string   // alias or raw path string
    Path Path     // the compiled Path
}

Useful for mapping result slots to output column names.

for i, e := range plan.Entries() {
    fmt.Printf("slot %d: name=%s  path=%s\n", i, e.Name, e.Path)
}

PathValuesMulti (Convenience)

func PathValuesMulti(
    md protoreflect.MessageDescriptor,
    m proto.Message,
    paths ...PlanPathSpec,
) ([][]Values, error)

One-shot wrapper that compiles a Plan and immediately evaluates it. Handy for tests and one-off extractions. For repeated evaluation of the same paths against many messages, prefer NewPlan + Plan.Eval.

results, err := pbpath.PathValuesMulti(md, msg,
    pbpath.PlanPath("nested.stringfield", pbpath.Alias("greeting")),
    pbpath.PlanPath("repeats[*].nested.stringfield"),
)

Trie-Based Shared-Prefix Optimization

Paths are inserted into a trie keyed by step equality. Two steps are merged when they have the same kind and kind-specific parameters:

Step kind	Equality criterion
FieldAccessStep	Same field number
ListIndexStep	Same index (including negatives)
MapIndexStep	Same key value
ListWildcardStep	Always equal
ListRangeStep	Same start, end, step, and omitted flags
AnyExpandStep	Same message full name

Different step types on the same field (e.g. imp[*] vs imp[0:3]) fork into separate trie branches — they produce independent fan-out groups.

Path String Syntax

A path string is a dot-separated chain of field names, optionally prefixed by an explicit root and suffixed with index, map-key, wildcard, range, or slice accessors.

Grammar

path         = [ root ] { accessor }
root         = "(" full_message_name ")"
accessor     = field_access | index_access
field_access = "." field_name
index_access = "[" key "]"
key          = integer | string_literal | "true" | "false"
             | "*"                           ← wildcard
             | [ start ] ":" [ end ]         ← range
             | [ start ] ":" [ end ] ":" [ step ]  ← slice

Obtaining the Message Descriptor

ParsePath requires a protoreflect.MessageDescriptor. You can get one from:

• Generated code – (*pb.MyMessage)(nil).ProtoReflect().Descriptor()
• Dynamic descriptors – via protodesc.NewFile from a FileDescriptorProto
• protocompile / buf – parse .proto files at runtime

Protobuf Editions

pbpath operates entirely on protoreflect descriptors, so it works with proto2, proto3, and Protobuf Editions (Edition 2023+) without any changes. Editions features are resolved by the protobuf runtime before pbpath sees the descriptors.

Identifying the Root Message

Every path implicitly starts at a root message – the outermost message type whose descriptor you pass to ParsePath.

Given this .proto file:

// file: BidRequest.proto
package bidrequest;

message BidRequestEvent {
  string id = 1;
  DeviceEvent device = 3;
  repeated ImpressionEvent imp = 4;
  // ...
}

The root message is BidRequestEvent. You may write the root explicitly or omit it:

Path string	Equivalent explicit form
id	(bidrequest.BidRequestEvent).id
device.ip	(bidrequest.BidRequestEvent).device.ip

The explicit (package.MessageName) form is optional and only required when you want to be unambiguous in documentation or tooling.

Field Access

Use the text name of the field (the snake_case name from the .proto file), separated by dots:

field_name
parent.child
parent.child.grandchild

Field names correspond exactly to the names in your .proto definition. For example, given:

message DeviceEvent {
  string ip = 3;
  GeoEvent geo = 4;

  message GeoEvent {
    string country = 4;
    string city = 6;
  }
}

Goal	Path
Device IP	device.ip
Geo country	device.geo.country
Geo city	device.geo.city

Repeated Field (List) Indexing

Append [index] after a repeated field name, where index is an integer. Zero-based, and negative indices are allowed (resolved at traversal time relative to the list length: -1 is the last element, -2 is second-to-last, etc.).

repeated_field[0]     // first element
repeated_field[-1]    // last element
repeated_field[-2]    // second-to-last element

Index literals may be decimal, octal (0-prefixed), or hex (0x-prefixed):

Literal	Decimal value
0	0
12	12
0x1F	31
010	8 (octal)

Map Field Indexing

Append [key] after a map field, where the key literal matches the map's key type:

Map key type	Syntax	Example
string	["value"] or ['value']	strkeymap["hello"]
bool	true / false	boolkeymap[true]
int32 / int64	signed integer	int32keymap[-6]
uint32 / uint64	unsigned integer	uint64keymap[0xffffffffffffffff]

String keys support the same escape sequences as protobuf text format (\n, \t, \", \\, hex \xHH, unicode \uHHHH / \UHHHHHHHH, and octal \ooo).

After indexing a map you can continue traversing into the value type:

strkeymap["mykey"].stringfield

Wildcards, Ranges, and Slices

These step types cause PathValues to fan out, producing one result per matching element. They may only be applied to repeated (list) fields; using them on a map field is a parse error.

Wildcard — [*] or [:] or [::]

Selects every element in the list:

repeats[*]              // all elements
repeats[:]              // same (normalizes to [*])
repeats[::]             // same (normalizes to [*])

Range — [start:end]

Selects a half-open range of elements [start, end) with stride 1. Both start and end may be negative:

repeats[0:3]            // elements 0, 1, 2
repeats[1:3]            // elements 1, 2
repeats[-3:-1]          // 3rd-to-last through 2nd-to-last
repeats[2:]             // element 2 through the end
repeats[:2]             // elements 0, 1

Slice — [start:end:step] (Python semantics)

Full Python-style slice with an explicit stride/step. Any of start, end, and step may be omitted — omitted bounds default based on the step sign:

When step > 0	Default start	Default end
omitted start	0 (beginning)	—
omitted end	—	len (past the end)

When step < 0	Default start	Default end
omitted start	len - 1 (last)	—
omitted end	—	before index 0

repeats[::2]            // every other element: 0, 2, 4, …
repeats[1::2]           // odd-indexed: 1, 3, 5, …
repeats[::-1]           // all elements in reverse
repeats[3:0:-1]         // elements 3, 2, 1 (reverse, half-open)
repeats[-1::-1]         // reverse from last element
repeats[0:10:3]         // elements 0, 3, 6, 9
repeats[:3:2]           // elements 0, 2

A step of 0 is always a parse error ([::0]).

Chaining Steps

Steps can be freely chained. After a field access you can index, after an index you can access a field, and so on:

field.subfield[0].deeper_field["key"].leaf
repeats[*].nested.stringfield
repeats[::2].nested.int32repeats[0]

Fan-Out and Nested Fan-Outs

When a path contains one or more wildcard, range, or slice steps, PathValues fans out and returns multiple Values — one per matching list element. When multiple fan-out steps appear in a single path the result is the cartesian product of all expansions.

Single Fan-Out

Given a message with repeats = [A, B, C]:

path, _ := pbpath.ParsePath(md, "repeats[*].nested.stringfield")
results, _ := pbpath.PathValues(path, msg)

// results has 3 entries:
// [0] → (pkg.Test).repeats[0].nested.stringfield = "alpha"
// [1] → (pkg.Test).repeats[1].nested.stringfield = "beta"
// [2] → (pkg.Test).repeats[2].nested.stringfield = "gamma"

Each result's Path contains the concrete ListIndex (not the wildcard), so you always know exactly which element produced the value.

Nested Fan-Out (Cartesian Product)

Consider a schema where a repeated field contains another repeated field:

message Outer {
  repeated Middle items = 1;
}
message Middle {
  repeated Inner sub = 1;
}
message Inner {
  string value = 1;
}

With items containing two Middle messages, each with three Inner messages:

path, _ := pbpath.ParsePath(md, "items[*].sub[*].value")
results, _ := pbpath.PathValues(path, msg)

This produces 2 × 3 = 6 results — every combination of outer and inner index:

items[0].sub[0].value = "a"
items[0].sub[1].value = "b"
items[0].sub[2].value = "c"
items[1].sub[0].value = "d"
items[1].sub[1].value = "e"
items[1].sub[2].value = "f"

You can use Values.ListIndices() to recover the indices for each level:

for _, r := range results {
    indices := r.ListIndices()
    // indices[0] = items index, indices[1] = sub index
    fmt.Printf("items[%d].sub[%d] = %s\n",
        indices[0], indices[1], r.Index(-1).Value.String())
}

Mixed Fan-Out: Range × Wildcard

Fan-out steps don't all have to be the same kind. You can mix ranges, slices, and wildcards:

// First two items, all their sub-items in reverse
path, _ := pbpath.ParsePath(md, "items[0:2].sub[::-1].value")
results, _ := pbpath.PathValues(path, msg)

If items[0] has 3 subs and items[1] has 2 subs, this produces 5 results:

items[0].sub[2].value   ← reversed
items[0].sub[1].value
items[0].sub[0].value
items[1].sub[1].value   ← reversed
items[1].sub[0].value

Step Constructors (Programmatic API)

Paths can also be built programmatically instead of parsing a string:

p := pbpath.Path{
    pbpath.Root(md),
    pbpath.FieldAccess(repeatsFD),
    pbpath.ListWildcard(),
    pbpath.FieldAccess(nestedFD),
    pbpath.FieldAccess(stringfieldFD),
}
results, err := pbpath.PathValues(p, msg)

Available Constructors

Constructor	Produces	Path Syntax
Root(md)	RootStep	(full.Name)
FieldAccess(fd)	FieldAccessStep	.field
ListIndex(i)	ListIndexStep	[i] (negative OK)
MapIndex(k)	MapIndexStep	[key]
AnyExpand(md)	AnyExpandStep	.(full.Name)
ListWildcard()	ListWildcardStep	[*]
ListRange(start, end)	ListRangeStep	[start:end]
ListRangeFrom(start)	ListRangeStep	[start:]
ListRangeStep3(start, end, step, startOmitted, endOmitted)	ListRangeStep	[start:end:step]

ListRangeStep3 panics if step is 0. Use the startOmitted/endOmitted flags to indicate that a bound should be defaulted at traversal time (matching the behaviour of omitting them in the string syntax).

Examples

Simple Scalar

message BidRequestEvent {
  string id = 1;
  bool throttled = 10;
}

id              → string value of the id field
throttled       → bool value of the throttled field

Nested Messages

message BidRequestEvent {
  DeviceEvent device = 3;
  message DeviceEvent {
    GeoEvent geo = 4;
    DeviceExtEvent ext = 7;
    message GeoEvent { string country = 4; }
    message DeviceExtEvent {
      DoohEvent dooh = 1;
      message DoohEvent { uint32 venuetypeid = 2; }
    }
  }
}

device.geo.country          → the country string
device.ext.dooh.venuetypeid → uint32 venue type id

Repeated Message Elements

message BidRequestEvent {
  repeated ImpressionEvent imp = 4;
  message ImpressionEvent {
    string id = 1;
    BannerEvent banner = 4;
    message BannerEvent { uint32 w = 2; }
  }
}

imp[0].id        → id of the first impression
imp[0].banner.w  → banner width of the first impression
imp[-1].id       → id of the last impression

Repeated Scalars

message BidRequestEvent {
  repeated string cur = 6;
}

cur[0]   → first currency string
cur[-1]  → last currency string

Wildcard over Repeated Messages

path, _ := pbpath.ParsePath(md, "imp[*].id")
results, _ := pbpath.PathValues(path, msg)
// One Values per impression, each ending with that impression's id.
for _, r := range results {
    fmt.Println(r.Index(-1).Value.String())
}

Range: First N Impressions

path, _ := pbpath.ParsePath(md, "imp[0:3].banner.w")
results, _ := pbpath.PathValues(path, msg)
// Up to 3 results (or fewer if imp has < 3 elements).

Slice: Every Other Element in Reverse

path, _ := pbpath.ParsePath(md, "imp[::-2]")
results, _ := pbpath.PathValues(path, msg)
// With 5 impressions → indices 4, 2, 0.

Nested Fan-Out with ListIndices

// All deals across all impressions.
path, _ := pbpath.ParsePath(md, "imp[*].pmp.deals[*].id")
results, _ := pbpath.PathValues(path, msg)

for _, r := range results {
    idx := r.ListIndices() // [imp_index, deal_index]
    fmt.Printf("imp[%d].deal[%d] = %s\n",
        idx[0], idx[1], r.Index(-1).Value.String())
}

Deeply Nested Through Repeated Fields

message ImpressionEvent {
  PrivateMarketplaceEvent pmp = 3;
  message PrivateMarketplaceEvent {
    repeated DealEvent deals = 2;
    message DealEvent {
      string id = 1;
      DealExtEvent ext = 6;
      message DealExtEvent { bool must_bid = 3; }
    }
  }
}

imp[0].pmp.deals[0].id            → deal id
imp[0].pmp.deals[0].ext.must_bid  → must_bid flag on the deal
imp[*].pmp.deals[*].ext.must_bid  → must_bid for every deal in every impression

Map Access

message Test {
  map<string, Nested> strkeymap = 4;
  map<int32, Test>    int32keymap = 6;
  message Nested { string stringfield = 2; }
}

strkeymap["mykey"]              → the Nested message for key "mykey"
strkeymap["mykey"].stringfield  → stringfield inside that Nested message
int32keymap[-6]                 → the Test message for key -6

Self-Referential / Recursive Messages

message Test {
  Nested nested = 1;
  message Nested {
    string stringfield = 2;
    Test nested = 4;        // back-reference to Test
  }
}

nested.stringfield                  → top-level Nested's stringfield
nested.nested.nested.stringfield    → 3 levels deep through the cycle

Complex: Multiple Step Types Combined

Using the testmessage.proto schema with octal and hex literals:

int32keymap[-6].uint64keymap[040000000000].repeats[0].nested.nested.strkeymap["k"].intfield

This path:

1. Indexes int32keymap with key -6
2. On the resulting Test, indexes uint64keymap with key 4294967296 (octal 040000000000)
3. Indexes repeats list at position 0
4. Accesses nested (a Nested message)
5. Accesses nested on that Nested (back to a Test)
6. Indexes strkeymap with string key "k"
7. Reads the intfield scalar

Explicit Root

When you want to be explicit about the message type:

(bidrequest.BidRequestEvent).imp[0].pmp.deals[0].id
(pbpath.testdata.Test).nested.stringfield

The fully-qualified name inside () must exactly match the message descriptor's FullName().

Strict Mode

By default, out-of-bounds indices and range bounds are silently handled:

• A negative index that resolves past the beginning of a list skips that branch (no result is emitted for it).
• Range/slice bounds are clamped to the list length.

PathValues — global strict

Pass Strict() to make any out-of-bounds condition an immediate error:

results, err := pbpath.PathValues(path, msg, pbpath.Strict())
// err is non-nil if any index or bound is out of range.

Plan — per-path strict

With the Plan API, strict checking is per-path via StrictPath(). The traversal itself is always lenient (clamp/skip); the clamped flag is checked at leaf nodes only for strict paths.

plan, _ := pbpath.NewPlan(md,
    pbpath.PlanPath("imp[0:100].id", pbpath.StrictPath()), // errors if clamped
    pbpath.PlanPath("imp[0:100].banner.w"),                    // silently clamped
)
results, err := plan.Eval(msg)
// err is non-nil only if the strict path's bounds were clamped.

This lets you mix lenient and strict paths in the same plan without separate traversals.

Expression Engine

The Plan API supports computed columns through a composable Expr tree. Expressions reference protobuf field paths via PathRef and apply functions to produce derived values — all evaluated inline during plan traversal.

Quick Start

plan, err := pbpath.NewPlan(md, nil,
    // Coalesce: first non-zero value from multiple paths
    pbpath.PlanPath("device_id",
        pbpath.WithExpr(pbpath.FuncCoalesce(
            pbpath.PathRef("user.id"),
            pbpath.PathRef("site.id"),
            pbpath.PathRef("device.ifa"),
        )),
        pbpath.Alias("device_id"),
    ),

    // Conditional: use banner dimensions if present, else video
    pbpath.PlanPath("width",
        pbpath.WithExpr(pbpath.FuncCond(
            pbpath.FuncHas(pbpath.PathRef("imp[0].banner.w")),
            pbpath.PathRef("imp[0].banner.w"),
            pbpath.PathRef("imp[0].video.w"),
        )),
        pbpath.Alias("width"),
    ),

    // Arithmetic: compute a derived value
    pbpath.PlanPath("total",
        pbpath.WithExpr(pbpath.FuncMul(
            pbpath.PathRef("items[0].price"),
            pbpath.PathRef("items[0].qty"),
        )),
        pbpath.Alias("total"),
    ),

    // Default: provide a fallback literal
    pbpath.PlanPath("country",
        pbpath.WithExpr(pbpath.FuncDefault(
            pbpath.PathRef("device.geo.country"),
            protoreflect.ValueOfString("UNKNOWN"),
        )),
        pbpath.Alias("country"),
    ),
)

Available Functions

Category	Functions	Output kind
Control flow	FuncCoalesce, FuncDefault, FuncCond	Same as input
Existence	FuncHas	Bool
Length	FuncLen	Int64
Predicates	FuncEq, FuncNe, FuncLt, FuncLe, FuncGt, FuncGe	Bool
Arithmetic	FuncAdd, FuncSub, FuncMul, FuncDiv, FuncMod	Numeric (auto-promoted)
Math	FuncAbs, FuncCeil, FuncFloor, FuncRound, FuncMin, FuncMax	Preserved
String	FuncUpper, FuncLower, FuncTrim, FuncTrimPrefix, FuncTrimSuffix, FuncConcat	String
Cast	FuncCastInt, FuncCastFloat, FuncCastString	Changed
Timestamp	FuncStrptime, FuncTryStrptime, FuncAge, FuncExtract{Year,Month,Day,Hour,Minute,Second}	Int64
ETL	FuncHash, FuncEpochToDate, FuncDatePart, FuncBucket, FuncMask, FuncCoerce, FuncEnumName	Varies
Aggregates	FuncSum, FuncDistinct, FuncListConcat	Varies

Expressions compose freely — a FuncCond can contain FuncHas as its predicate, PathRef as the then-branch, and FuncDefault as the else-branch. See the Architecture Guide for implementation details.

EvalLeaves — High-Performance Evaluation

Plan.EvalLeaves is the recommended method for hot paths. It returns only leaf values (not the full path/values chain) and reuses pre-allocated scratch buffers, giving near-zero per-call allocations.

// Compile once.
plan, _ := pbpath.NewPlan(md, nil,
    pbpath.PlanPath("device.geo.country", pbpath.Alias("country")),
    pbpath.PlanPath("imp[*].id",          pbpath.Alias("imp_id")),
)

// Evaluate per message — near-zero allocations.
for _, msg := range stream {
    leaves, _ := plan.EvalLeaves(msg)
    country := leaves[0]  // []protoreflect.Value with 1 element
    impIDs  := leaves[1]  // []protoreflect.Value with N elements
}

Method	Allocations	Thread-safe	Returns
Eval(msg)	Full Values chains	✅	[][]Values
EvalLeaves(msg)	Near-zero (scratch reuse)	❌	[][]protoreflect.Value
EvalLeavesConcurrent(msg)	Fresh buffers per call	✅	[][]protoreflect.Value

Running Benchmarks

# Run all pbpath benchmarks
go test -bench=. -benchmem ./proto/pbpath/

# Run Plan evaluation benchmarks
go test -bench='BenchmarkPlan' -benchmem ./proto/pbpath/

# Run with longer duration for stable results
go test -bench='BenchmarkPlan' -benchmem -benchtime=5s -count=3 ./proto/pbpath/

Error Cases

Input	Error
unknown	field not found in message descriptor
int32keymap["foo"]	string key for int32 map
nested.stringfield[0]	indexing a non-repeated field
strkeymap.key	traversing map internal fields
strkeymap["k"]["k2"]	double-indexing (value is not a map)
strkeymap[*]	wildcard not supported on map fields
strkeymap[0:3]	range/slice not supported on map fields
repeats[::0]	step must not be zero
(wrong.Name).id	root name doesn't match descriptor
nested.	trailing dot with no field name
nested 🎉	illegal characters

Slice Quick-Reference

Syntax	Selects	Python equivalent
[*]	all elements	[:]
[:]	all elements	[:]
[::]	all elements	[::]
[0:3]	elements 0, 1, 2	[0:3]
[2:]	from index 2 to end	[2:]
[:2]	elements 0, 1	[:2]
[-2:]	last 2 elements	[-2:]
[-3:-1]	3rd-to-last through 2nd-to-last	[-3:-1]
[::2]	every other (0, 2, 4, …)	[::2]
[1::2]	odd-indexed (1, 3, 5, …)	[1::2]
[::-1]	all in reverse	[::-1]
[3:0:-1]	3, 2, 1	[3:0:-1]
[0:10:3]	0, 3, 6, 9	[0:10:3]
[5:2]	empty (start ≥ end, step=1)	[5:2]
[::0]	error — step must not be 0	[::0] → ValueError