_content/blog: add post on type construction and cycle detection

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Change-Id: I4d4c840d37b3d66c2d0a95cf8dbd4a5d381e52cd
Reviewed-on: https://go-review.googlesource.com/c/website/+/756180
Reviewed-by: Austin Clements <austin@google.com>
Reviewed-by: Robert Griesemer <gri@google.com>
Auto-Submit: Mark Freeman <markfreeman@google.com>
LUCI-TryBot-Result: Go LUCI <golang-scoped@luci-project-accounts.iam.gserviceaccount.com>

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diff --git a/_content/blog/type-construction-and-cycle-detection.md b/_content/blog/type-construction-and-cycle-detection.md
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+---
+title: Type Construction and Cycle Detection
+date: 2026-03-24
+by:
+- Mark Freeman
+summary: Go 1.26 simplifies type construction and enhances cycle detection for certain kinds of recursive types.
+template: true
+---
+
+Go's static typing is an important part of why Go is a good fit for production
+systems that have to be robust and reliable. When a Go package is compiled, it
+is first parsed—meaning that the Go source code within that package is converted
+into an abstract syntax tree (or AST). This AST is then passed to the Go
+*type checker*.
+
+In this blog post, we'll dive into a part of the type checker we significantly
+improved in Go 1.26. How does this change things from a Go user's perspective?
+Unless one is fond of arcane type definitions, there's no observable change
+here. This refinement was intended to reduce corner cases, setting us up for
+future improvements to Go. Also, it's a fun look at something that seems quite
+ordinary to Go programmers, but has some real subtleties hiding within.
+
+But first, what exactly is *type checking*? It's a step in the Go compiler that
+eliminates whole classes of errors at compile time. Specifically, the Go type
+checker verifies that:
+
+1. Types appearing in the AST are valid (for example, a map's key type must be
+   `comparable`).
+2. Operations involving those types (or their values) are valid (for example,
+   one can't add an `int` and a `string`).
+
+To accomplish this, the type checker constructs an internal representation for
+each type it encounters while traversing the AST—a process informally called
+*type construction*.
+
+As we'll soon see, even though Go is known for its simple type system, type
+construction can be deceptively complex in certain corners of the language.
+
+## Type construction
+
+Let’s start by considering a simple pair of type declarations:
+
+```go
+type T []U
+type U *int
+```
+
+When the type checker is invoked, it first encounters the type declaration for
+`T`. Here, the AST records a type definition of a type name `T` and a
+*type expression* `[]U`. `T` is a [defined type](/ref/spec#Types); to represent
+the actual data structure that the type checker uses when constructing defined
+types, we’ll use a `Defined` struct.
+
+The `Defined` struct contains a pointer to the type for the type expression to
+the right of the type name. This `underlying` field is relevant for sourcing the
+type’s [underlying type](/ref/spec#Underlying_types). To help illustrate the
+type checker’s state, let’s see how walking the AST fills in the data
+structures, starting with:
+
+<img style="background-color:#f3f3f3" src="type-construction-and-cycle-detection/01.svg" />
+
+At this point, `T` is *under construction*, indicated by the color yellow. Since
+we haven’t evaluated the type expression `[]U` yet—it’s still black—`underlying`
+points to `nil`, indicated by an open arrow.
+
+When we evaluate `[]U`, the type checker constructs a `Slice` struct, the
+internal data structure used to represent slice types. Similarly to `Defined`,
+it contains a pointer to the element type for the slice. We don’t yet know what
+the name `U` refers to, though we expect it to refer to a type. So, again, this
+pointer is `nil`. We are left with:
+
+<img style="background-color:#f3f3f3" src="type-construction-and-cycle-detection/02.svg" />
+
+By now you might be getting the gist, so we’ll pick up the pace a bit.
+
+To convert the type name `U` to a type, we first locate its declaration. Upon
+seeing that it represents another defined type, we construct a separate
+`Defined` for `U` accordingly. Inspecting the right side of `U`, we see the type
+expression `*int`, which evaluates to a `Pointer` struct, with the base type of
+the pointer being the type expression `int`.
+
+When we evaluate `int`, something special happens: we get back a predeclared
+type. Predeclared types are constructed *before* the type checker even begins
+walking the AST. Since the type for `int` is already constructed, there’s
+nothing for us to do but point to that type.
+
+We now have:
+
+<img style="background-color:#f3f3f3" src="type-construction-and-cycle-detection/03.svg" />
+
+Note that the `Pointer` type is *complete* at this point, indicated by the color
+green. Completeness means that the type’s internal data structure has all of its
+fields populated and any types pointed to by those fields are complete.
+Completeness is an important property of a type because it ensures that
+accessing the internals, or *deconstruction*, of that type is sound: we have all
+the information describing the type.
+
+In the image above, the `Pointer` struct only contains a `base` field, which
+points to `int`. Since `int` has no fields to populate, it’s “vacuously”
+complete, making the type for `*int` complete.
+
+From here, the type checker begins unwinding the stack. Since the type for
+`*int` is complete, we can complete the type for `U`, meaning we can complete
+the type for `[]U`, and so on for `T`. When this process ends, we are left with
+only complete types, as shown below:
+
+<img style="background-color:#f3f3f3" src="type-construction-and-cycle-detection/04.svg" />
+
+The numbering above shows the order in which the types were completed (after the
+`Pointer`). Note that the type on the bottom completed first. Type construction
+is naturally a depth-first process, since completing a type requires its
+dependencies to be completed first.
+
+## Recursive types
+
+With this simple example out of the way, let’s add a bit more nuance. Go’s type
+system also allows us to express recursive types. A typical example is something
+like:
+
+```go
+type Node struct {
+  next *Node
+}
+```
+
+If we reconsider our example from above, we can add a bit of recursion by
+swapping `*int` for `*T` like so:
+
+```go
+type T []U
+type U *T
+```
+
+Now for a trace: let’s start once more with `T`, but skip ahead to illustrate
+the effects of this change. As one might suspect from our previous example, the
+type checker will approach the evaluation of `*T` with the below state:
+
+<img style="background-color:#f3f3f3" src="type-construction-and-cycle-detection/05.svg" />
+
+The question is what to do with the base type for `*T`. We have an idea of what
+`T` is (a `Defined`), but it’s currently being constructed (its `underlying` is
+still `nil`).
+
+We simply point the base type for `*T` to `T`, even though `T` is incomplete:
+
+<img id="example" style="background-color:#f3f3f3" src="type-construction-and-cycle-detection/06.svg" />
+
+We do this assuming that `T` will complete when it finishes construction
+*in the future* (by pointing to a complete type). When that happens, `base` will
+point to a complete type, thus making `*T` complete.
+
+In the meantime, we'll begin heading back up the stack:
+
+<img style="background-color:#f3f3f3" src="type-construction-and-cycle-detection/07.svg" />
+
+When we get back to the top and finish constructing `T`, the “loop” of types
+will close, completing each type in the loop simultaneously:
+
+<img style="background-color:#f3f3f3" src="type-construction-and-cycle-detection/08.svg" />
+
+Before we considered recursive types, evaluating a type expression always
+returned a complete type. That was a convenient property because it meant the
+type checker could always deconstruct (look inside) a type returned from
+evaluation.
+
+But in the [example above](#example), evaluation of `T` returned an *incomplete*
+type, meaning deconstructing `T` is unsound until it completes. Generally
+speaking, recursive types mean that the type checker can no longer assume that
+types returned from evaluation will be complete.
+
+Yet, type checking involves many checks which require deconstructing a type. A
+classic example is confirming that a map key is `comparable`, which requires
+inspecting the `underlying` field. How do we safely interact with incomplete
+types like `T`?
+
+Recall that type completeness is a prerequisite for deconstructing a type. In
+this case, type construction never deconstructs a type, it merely refers to
+types. In other words, type completeness *does not* block type construction
+here.
+
+Because type construction isn't blocked, the type checker can simply delay such
+checks until the end of type checking, when all types are complete (note that
+the checks themselves also do not block type construction). If a type were to
+reveal a type error, it makes no difference when that error is reported during
+type checking—only that it is reported eventually.
+
+With this knowledge in mind, let’s examine a more complex example involving
+values of incomplete types.
+
+## Recursive types and values
+
+Let’s take a brief detour and have a look at Go’s
+[array types](/ref/spec#Array_types). Importantly, array types have a size,
+which is a [constant](/ref/spec#Array_types) that is part of the type. Some
+operations, like the built-in functions `unsafe.Sizeof` and `len` can return
+constants when applied to [certain values](/ref/spec#Package_unsafe) or
+[expressions](/ref/spec#Length_and_capacity), meaning they can appear as array
+sizes. Importantly, the values passed to those functions can be of any type,
+even an incomplete type. We call these *incomplete values*.
+
+Let's consider this example:
+
+```go
+type T [unsafe.Sizeof(T{})]int
+```
+
+In the same way as before, we'll reach a state like the below:
+
+<img style="background-color:#f3f3f3" src="type-construction-and-cycle-detection/09.svg" />
+
+To construct the `Array`, we must calculate its size. From the value expression
+`unsafe.Sizeof(T{})`, that’s the size of `T`. For array types (such as `T`),
+calculating their size requires deconstruction: we need to look inside the type
+to determine the length of the array and size of each element.
+
+In other words, type construction for the `Array` *does* deconstruct `T`,
+meaning the `Array` cannot finish construction (let alone complete) before `T`
+completes. The “loop” trick that we used earlier—where a loop of types
+simultaneously completes as the type starting the loop finishes
+construction—doesn’t work here.
+
+This leaves us in a bind:
+
+* `T` cannot be completed until the `Array` completes.
+* The `Array` cannot be completed until `T` completes.
+* They *cannot* be completed simultaneously (unlike before).
+
+Clearly, this is impossible to satisfy. What is the type checker to do?
+
+### Cycle detection
+
+Fundamentally, code such as this is invalid because the size of `T` cannot be
+determined without knowing the size of `T`, regardless of how the type checker
+operates. This particular instance—cyclic size definition—is part of a class of
+errors called *cycle errors*, which generally involve cyclic definition of Go
+constructs. As another example, consider `type T T`, which is also in this
+class, but for different reasons. The process of finding and reporting cycle
+errors in the course of type checking is called *cycle detection*.
+
+Now, how does cycle detection work for `type T [unsafe.Sizeof(T{})]int`? To
+answer this, let’s look at the inner `T{}`. Because `T{}` is a composite literal
+expression, the type checker knows that its resulting value is of type `T`.
+Because `T` is incomplete, we call the value `T{}` an *incomplete value*.
+
+We must be cautious—operating on an incomplete value is only sound if it doesn’t
+deconstruct the value’s type. For example, `type T [unsafe.Sizeof(new(T))]int`
+*is* sound, since the value `new(T)` (of type `*T`) is never deconstructed—all
+pointers have the same size. To reiterate, it is sound to size an incomplete
+value of type `*T`, but not one of type `T`.
+
+This is because the “pointerness” of `*T` provides enough type information for
+`unsafe.Sizeof`, whereas just `T` does not. In fact, it’s never sound to operate
+on an incomplete value *whose type is a defined type*, because a mere type name
+conveys no (underlying) type information at all.
+
+#### Where to do it
+
+Up to now we’ve focused on `unsafe.Sizeof` directly operating on potentially
+incomplete values. In `type T [unsafe.Sizeof(T{})]`, the call to `unsafe.Sizeof`
+is just the "root" of the array length expression. We can readily imagine the
+incomplete value `T{}` as an operand in some other value expression.
+
+For example, it could be passed to a function (i.e.
+`type T [unsafe.Sizeof(f(T{}))]int`), sliced (i.e.
+`type T [unsafe.Sizeof(T{}[:])]int`), indexed (i.e.
+`type T [unsafe.Sizeof(T{}[0])]int`), etc. All of these are invalid because they
+require deconstructing `T`. For instance, indexing `T`
+[requires checking](/ref/spec#Index_expressions) the underlying type of `T`.
+Because these expressions "consume" potentially incomplete values, let's call
+them *downstreams*. There are many more examples of downstream operators, some
+of which are not syntactically obvious.
+
+Similarly, `T{}` is just one example of an expression that "produces" a
+potentially incomplete value—let's call these kinds of expressions *upstreams*:
+
+<img style="background-color:#f3f3f3" src="type-construction-and-cycle-detection/10.svg" />
+
+Comparatively, there are fewer and more syntactically obvious value expressions
+that might result in incomplete values. Also, it’s rather simple to enumerate
+these cases by inspecting Go’s syntax definition. For these reasons, it'll be
+simpler to implement our cycle detection logic via the upstreams, where
+potentially incomplete values originate. Below are some examples of them:
+
+```go
+
+type T [unsafe.Sizeof(T(42))]int                // conversion
+
+func f() T
+type T [unsafe.Sizeof(f())]int                  // function call
+
+var i interface{}
+type T [unsafe.Sizeof(i.(T))]int                // assertion
+
+type T [unsafe.Sizeof({{raw "<"}}-(make({{raw "<"}}-chan T)))]int   // channel receive
+
+type T [unsafe.Sizeof(make(map[int]T)[42])]int  // map access
+
+type T [unsafe.Sizeof(*new(T))]int              // dereference
+
+// ... and a handful more
+```
+
+For each of these cases, the type checker has extra logic where that particular
+kind of value expression is evaluated. As soon as we know the type of the
+resulting value, we insert a simple test that checks that the type is complete.
+
+For instance, in the conversion example `type T [unsafe.Sizeof(T(42))]int`,
+there is a snippet in the type checker that resembles:
+
+```go
+func callExpr(call *syntax.CallExpr) operand {
+  x := typeOrValue(call.Fun)
+  switch x.mode() {
+  // ... other cases
+  case typeExpr:
+    // T(), meaning it's a conversion
+    T := x.typ()
+    // ... handle the conversion, T *is not* safe to deconstruct
+  }
+}
+```
+
+As soon as we observe that the `CallExpr` is a conversion to `T`, we know that
+the resulting type will be `T` (assuming no preceding errors). Before we pass
+back a value (here, an `operand`) of type `T` to the rest of the type checker,
+we need to check for completeness of `T`:
+
+```go
+func callExpr(call *syntax.CallExpr) operand {
+  x := typeOrValue(call.Fun)
+  switch x.mode() {
+  // ... other cases
+  case typeExpr:
+    // T(), meaning it's a conversion
+    T := x.typ()
++   if !isComplete(T) {
++     reportCycleErr(T)
++     return invalid
++   }
+    // ... handle the conversion, T *is* safe to deconstruct
+  }
+}
+```
+
+Instead of returning an incomplete value, we return a special `invalid` operand,
+which signals that the call expression could not be evaluated. The rest of the
+type checker has special handling for invalid operands. By adding this, we
+prevented incomplete values from “escaping” downstream—both into the rest of the
+type conversion logic and to downstream operators—and instead reported a cycle
+error describing the problem with `T`.
+
+A similar code pattern is used in all other cases, implementing cycle detection
+for incomplete values.
+
+## Conclusion
+
+Systematic cycle detection involving incomplete values is a new addition to the
+type checker. Before Go 1.26, we used a more complex type construction algorithm,
+which involved more bespoke cycle detection that didn’t always work. Our new,
+simpler approach addressed a number of (admittedly esoteric) compiler panics
+(issues [\#75918](/issue/75918), [\#76383](/issue/76383),
+[\#76384](/issue/76384), [\#76478](/issue/76478), and more), resulting in a more
+stable compiler.
+
+As programmers, we’ve become accustomed to features like recursive type
+definitions and sized array types such that we might overlook the nuance of
+their underlying complexity. While this post does skip over some finer details,
+hopefully we’ve conveyed a deeper understanding of (and perhaps appreciation
+for) the problems surrounding type checking in Go.
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