go/types, types2: use type nest to detect type cycles (fix validType)

validType was using a global type info map to detect invalid recursive
types, which was incorrect. Instead, change the algorithm as follows:

- Rather than using a "seen" (or typeInfo) map which is cumbersome to
  update correctly, use the stack of embedding types (the type nest)
  to check whether a type is embedded within itself, directly or
  indirectly.

- Use Identical for type comparisons which correctly considers identity
  of instantiated generic types.

- As before, maintain the full path of types leading to a cycle. But
  unlike before, track the named types rather than their objects, for
  a smaller slice ([]*Named rather than []Object), and convert to an
  object list only when needed for error reporting.

- As an optimization, keep track of valid *Named types (Checker.valids).
  This prevents pathological cases from consuming excessive computation
  time.

- Add clarifying comments and document invariants.

Based on earlier insights by David Chase (see also CL 408818).

Fixes #52698.

Change-Id: I5e4598c58afcf4ab987a426c5c4b7b28bdfcf5ea
Reviewed-on: https://go-review.googlesource.com/c/go/+/409694
Reviewed-by: Robert Findley <rfindley@google.com>
Run-TryBot: Robert Griesemer <gri@google.com>
Reviewed-by: David Chase <drchase@google.com>
TryBot-Result: Gopher Robot <gobot@golang.org>

src/cmd/compile/internal/types2/check.go

@@ -98,7 +98,7 @@ type Checker struct {
 	nextID  uint64                 // unique Id for type parameters (first valid Id is 1)
 	objMap  map[Object]*declInfo   // maps package-level objects and (non-interface) methods to declaration info
 	impMap  map[importKey]*Package // maps (import path, source directory) to (complete or fake) package
-	infoMap map[*Named]typeInfo    // maps named types to their associated type info (for cycle detection)
+	valids  instanceLookup         // valid *Named (incl. instantiated) types per the validType check
 
 	// pkgPathMap maps package names to the set of distinct import paths we've
 	// seen for that name, anywhere in the import graph. It is used for
@@ -241,7 +241,6 @@ func NewChecker(conf *Config, pkg *Package, info *Info) *Checker {
 		version: version,
 		objMap:  make(map[Object]*declInfo),
 		impMap:  make(map[importKey]*Package),
-		infoMap: make(map[*Named]typeInfo),
 	}
 }
 

src/cmd/compile/internal/types2/testdata/fixedbugs/issue52698.go

@@ -0,0 +1,62 @@
+// Copyright 2022 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package p
+
+// correctness check: ensure that cycles through generic instantiations are detected
+type T[P any] struct {
+	_ P
+}
+
+type S /* ERROR illegal cycle */ struct {
+	_ T[S]
+}
+
+// simplified test 1
+
+var _ A1[A1[string]]
+
+type A1[P any] struct {
+	_ B1[P]
+}
+
+type B1[P any] struct {
+	_ P
+}
+
+// simplified test 2
+var _ B2[A2]
+
+type A2 struct {
+	_ B2[string]
+}
+
+type B2[P any] struct {
+	_ C2[P]
+}
+
+type C2[P any] struct {
+	_ P
+}
+
+// test case from issue
+type T23 interface {
+	~struct {
+		Field0 T13[T15]
+	}
+}
+
+type T1[P1 interface {
+}] struct {
+	Field2 P1
+}
+
+type T13[P2 interface {
+}] struct {
+	Field2 T1[P2]
+}
+
+type T15 struct {
+	Field0 T13[string]
+}

src/cmd/compile/internal/types2/validtype.go

@@ -5,29 +5,24 @@
 package types2
 
 // validType verifies that the given type does not "expand" indefinitely
-// producing a cycle in the type graph. Cycles are detected by marking
+// producing a cycle in the type graph.
-// defined types.
 // (Cycles involving alias types, as in "type A = [10]A" are detected
 // earlier, via the objDecl cycle detection mechanism.)
 func (check *Checker) validType(typ *Named) {
-	check.validType0(typ, nil, nil)
+	check.validType0(typ, nil, nil, nil)
 }
 
-type typeInfo uint
-
 // validType0 checks if the given type is valid. If typ is a type parameter
 // its value is looked up in the provided environment. The environment is
 // nil if typ is not part of (the RHS of) an instantiated type, in that case
 // any type parameter encountered must be from an enclosing function and can
-// be ignored. The path is the list of type names that lead to the current typ.
+// be ignored. The nest list describes the stack (the "nest in memory") of
-func (check *Checker) validType0(typ Type, env *tparamEnv, path []Object) typeInfo {
+// types which contain (or embed in the case of interfaces) other types. For
-	const (
+// instance, a struct named S which contains a field of named type F contains
-		unknown typeInfo = iota
+// (the memory of) F in S, leading to the nest S->F. If a type appears in its
-		marked
+// own nest (say S->F->S) we have an invalid recursive type. The path list is
-		valid
+// the full path of named types in a cycle, it is only needed for error reporting.
-		invalid
+func (check *Checker) validType0(typ Type, env *tparamEnv, nest, path []*Named) bool {
-	)
-
 	switch t := typ.(type) {
 	case nil:
 		// We should never see a nil type but be conservative and panic
@@ -37,60 +32,79 @@ func (check *Checker) validType0(typ Type, env *tparamEnv, path []Object) typeIn
 		}
 
 	case *Array:
-		return check.validType0(t.elem, env, path)
+		return check.validType0(t.elem, env, nest, path)
 
 	case *Struct:
 		for _, f := range t.fields {
-			if check.validType0(f.typ, env, path) == invalid {
+			if !check.validType0(f.typ, env, nest, path) {
-				return invalid
+				return false
 			}
 		}
 
 	case *Union:
 		for _, t := range t.terms {
-			if check.validType0(t.typ, env, path) == invalid {
+			if !check.validType0(t.typ, env, nest, path) {
-				return invalid
+				return false
 			}
 		}
 
 	case *Interface:
 		for _, etyp := range t.embeddeds {
-			if check.validType0(etyp, env, path) == invalid {
+			if !check.validType0(etyp, env, nest, path) {
-				return invalid
+				return false
 			}
 		}
 
 	case *Named:
+		// Exit early if we already know t is valid.
+		// This is purely an optimization but it prevents excessive computation
+		// times in pathological cases such as testdata/fixedbugs/issue6977.go.
+		// (Note: The valids map could also be allocated locally, once for each
+		// validType call.)
+		if check.valids.lookup(t) != nil {
+			break
+		}
+
 		// Don't report a 2nd error if we already know the type is invalid
 		// (e.g., if a cycle was detected earlier, via under).
 		// Note: ensure that t.orig is fully resolved by calling Underlying().
 		if t.Underlying() == Typ[Invalid] {
-			check.infoMap[t] = invalid
+			return false
-			return invalid
 		}
 
-		switch check.infoMap[t] {
+		// If the current type t is also found in nest, (the memory of) t is
-		case unknown:
+		// embedded in itself, indicating an invalid recursive type.
-			check.infoMap[t] = marked
+		for _, e := range nest {
-			check.infoMap[t] = check.validType0(t.Origin().fromRHS, env.push(t), append(path, t.obj))
+			if Identical(e, t) {
-		case marked:
+				// t cannot be in an imported package otherwise that package
-			// We have seen type t before and thus must have a cycle.
+				// would have reported a type cycle and couldn't have been
-			check.infoMap[t] = invalid
+				// imported in the first place.
-			// t cannot be in an imported package otherwise that package
+				assert(t.obj.pkg == check.pkg)
-			// would have reported a type cycle and couldn't have been
+				t.underlying = Typ[Invalid] // t is in the current package (no race possibility)
-			// imported in the first place.
+				// Find the starting point of the cycle and report it.
-			assert(t.obj.pkg == check.pkg)
+				// Because each type in nest must also appear in path (see invariant below),
-			t.underlying = Typ[Invalid] // t is in the current package (no race possibility)
+				// type t must be in path since it was found in nest. But not every type in path
-			// Find the starting point of the cycle and report it.
+				// is in nest. Specifically t may appear in path with an earlier index than the
-			for i, tn := range path {
+				// index of t in nest. Search again.
-				if tn == t.obj {
+				for start, p := range path {
-					check.cycleError(path[i:])
+					if Identical(p, t) {
-					return invalid
+						check.cycleError(makeObjList(path[start:]))
+						return false
+					}
 				}
+				panic("cycle start not found")
 			}
-			panic("cycle start not found")
 		}
-		return check.infoMap[t]
+
+		// No cycle was found. Check the RHS of t.
+		// Every type added to nest is also added to path; thus every type that is in nest
+		// must also be in path (invariant). But not every type in path is in nest, since
+		// nest may be pruned (see below, *TypeParam case).
+		if !check.validType0(t.Origin().fromRHS, env.push(t), append(nest, t), append(path, t)) {
+			return false
+		}
+
+		check.valids.add(t) // t is valid
 
 	case *TypeParam:
 		// A type parameter stands for the type (argument) it was instantiated with.
@@ -98,13 +112,29 @@ func (check *Checker) validType0(typ Type, env *tparamEnv, path []Object) typeIn
 		if env != nil {
 			if targ := env.tmap[t]; targ != nil {
 				// Type arguments found in targ must be looked
-				// up in the enclosing environment env.link.
+				// up in the enclosing environment env.link. The
-				return check.validType0(targ, env.link, path)
+				// type argument must be valid in the enclosing
+				// type (where the current type was instantiated),
+				// hence we must check targ's validity in the type
+				// nest excluding the current (instantiated) type
+				// (see the example at the end of this file).
+				// For error reporting we keep the full path.
+				return check.validType0(targ, env.link, nest[:len(nest)-1], path)
 			}
 		}
 	}
 
-	return valid
+	return true
+}
+
+// makeObjList returns the list of type name objects for the given
+// list of named types.
+func makeObjList(tlist []*Named) []Object {
+	olist := make([]Object, len(tlist))
+	for i, t := range tlist {
+		olist[i] = t.obj
+	}
+	return olist
 }
 
 // A tparamEnv provides the environment for looking up the type arguments
@@ -146,3 +176,93 @@ func (env *tparamEnv) push(typ *Named) *tparamEnv {
 // same information should be available via the path:
 // We should be able to just walk the path backwards
 // and find the type arguments in the instance objects.
+
+// Here is an example illustrating why we need to exclude the
+// instantiated type from nest when evaluating the validity of
+// a type parameter. Given the declarations
+//
+//   var _ A[A[string]]
+//
+//   type A[P any] struct { _ B[P] }
+//   type B[P any] struct { _ P }
+//
+// we want to determine if the type A[A[string]] is valid.
+// We start evaluating A[A[string]] outside any type nest:
+//
+//   A[A[string]]
+//         nest =
+//         path =
+//
+// The RHS of A is now evaluated in the A[A[string]] nest:
+//
+//   struct{_ B[P₁]}
+//         nest = A[A[string]]
+//         path = A[A[string]]
+//
+// The struct has a single field of type B[P₁] with which
+// we continue:
+//
+//   B[P₁]
+//         nest = A[A[string]]
+//         path = A[A[string]]
+//
+//   struct{_ P₂}
+//         nest = A[A[string]]->B[P]
+//         path = A[A[string]]->B[P]
+//
+// Eventutally we reach the type parameter P of type B (P₂):
+//
+//   P₂
+//         nest = A[A[string]]->B[P]
+//         path = A[A[string]]->B[P]
+//
+// The type argument for P of B is the type parameter P of A (P₁).
+// It must be evaluated in the type nest that existed when B was
+// instantiated:
+//
+//   P₁
+//         nest = A[A[string]]        <== type nest at B's instantiation time
+//         path = A[A[string]]->B[P]
+//
+// If we'd use the current nest it would correspond to the path
+// which will be wrong as we will see shortly. P's type argument
+// is A[string], which again must be evaluated in the type nest
+// that existed when A was instantiated with A[string]. That type
+// nest is empty:
+//
+//   A[string]
+//         nest =                     <== type nest at A's instantiation time
+//         path = A[A[string]]->B[P]
+//
+// Evaluation then proceeds as before for A[string]:
+//
+//   struct{_ B[P₁]}
+//         nest = A[string]
+//         path = A[A[string]]->B[P]->A[string]
+//
+// Now we reach B[P] again. If we had not adjusted nest, it would
+// correspond to path, and we would find B[P] in nest, indicating
+// a cycle, which would clearly be wrong since there's no cycle in
+// A[string]:
+//
+//   B[P₁]
+//         nest = A[string]
+//         path = A[A[string]]->B[P]->A[string]  <== path contains B[P]!
+//
+// But because we use the correct type nest, evaluation proceeds without
+// errors and we get the evaluation sequence:
+//
+//   struct{_ P₂}
+//         nest = A[string]->B[P]
+//         path = A[A[string]]->B[P]->A[string]->B[P]
+//   P₂
+//         nest = A[string]->B[P]
+//         path = A[A[string]]->B[P]->A[string]->B[P]
+//   P₁
+//         nest = A[string]
+//         path = A[A[string]]->B[P]->A[string]->B[P]
+//   string
+//         nest =
+//         path = A[A[string]]->B[P]->A[string]->B[P]
+//
+// At this point we're done and A[A[string]] and is valid.

src/go/types/check.go

@@ -105,7 +105,7 @@ type Checker struct {
 	nextID  uint64                 // unique Id for type parameters (first valid Id is 1)
 	objMap  map[Object]*declInfo   // maps package-level objects and (non-interface) methods to declaration info
 	impMap  map[importKey]*Package // maps (import path, source directory) to (complete or fake) package
-	infoMap map[*Named]typeInfo    // maps named types to their associated type info (for cycle detection)
+	valids  instanceLookup         // valid *Named (incl. instantiated) types per the validType check
 
 	// pkgPathMap maps package names to the set of distinct import paths we've
 	// seen for that name, anywhere in the import graph. It is used for
@@ -249,7 +249,6 @@ func NewChecker(conf *Config, fset *token.FileSet, pkg *Package, info *Info) *Ch
 		version: version,
 		objMap:  make(map[Object]*declInfo),
 		impMap:  make(map[importKey]*Package),
-		infoMap: make(map[*Named]typeInfo),
 	}
 }
 

src/go/types/testdata/fixedbugs/issue52698.go

@@ -0,0 +1,50 @@
+// Copyright 2022 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package p
+
+// sanity check
+type T[P any] struct {
+	_ P
+}
+
+type S /* ERROR illegal cycle */ struct {
+	_ T[S]
+}
+
+// simplified test
+var _ B[A]
+
+type A struct {
+	_ B[string]
+}
+
+type B[P any] struct {
+	_ C[P]
+}
+
+type C[P any] struct {
+	_ P
+}
+
+// test case from issue
+type T23 interface {
+	~struct {
+		Field0 T13[T15]
+	}
+}
+
+type T1[P1 interface {
+}] struct {
+	Field2 P1
+}
+
+type T13[P2 interface {
+}] struct {
+	Field2 T1[P2]
+}
+
+type T15 struct {
+	Field0 T13[string]
+}

src/go/types/validtype.go

@@ -5,29 +5,24 @@
 package types
 
 // validType verifies that the given type does not "expand" indefinitely
-// producing a cycle in the type graph. Cycles are detected by marking
+// producing a cycle in the type graph.
-// defined types.
 // (Cycles involving alias types, as in "type A = [10]A" are detected
 // earlier, via the objDecl cycle detection mechanism.)
 func (check *Checker) validType(typ *Named) {
-	check.validType0(typ, nil, nil)
+	check.validType0(typ, nil, nil, nil)
 }
 
-type typeInfo uint
-
 // validType0 checks if the given type is valid. If typ is a type parameter
 // its value is looked up in the provided environment. The environment is
 // nil if typ is not part of (the RHS of) an instantiated type, in that case
 // any type parameter encountered must be from an enclosing function and can
-// be ignored. The path is the list of type names that lead to the current typ.
+// be ignored. The nest list describes the stack (the "nest in memory") of
-func (check *Checker) validType0(typ Type, env *tparamEnv, path []Object) typeInfo {
+// types which contain (or embed in the case of interfaces) other types. For
-	const (
+// instance, a struct named S which contains a field of named type F contains
-		unknown typeInfo = iota
+// (the memory of) F in S, leading to the nest S->F. If a type appears in its
-		marked
+// own nest (say S->F->S) we have an invalid recursive type. The path list is
-		valid
+// the full path of named types in a cycle, it is only needed for error reporting.
-		invalid
+func (check *Checker) validType0(typ Type, env *tparamEnv, nest, path []*Named) bool {
-	)
-
 	switch t := typ.(type) {
 	case nil:
 		// We should never see a nil type but be conservative and panic
@@ -37,59 +32,79 @@ func (check *Checker) validType0(typ Type, env *tparamEnv, path []Object) typeIn
 		}
 
 	case *Array:
-		return check.validType0(t.elem, env, path)
+		return check.validType0(t.elem, env, nest, path)
 
 	case *Struct:
 		for _, f := range t.fields {
-			if check.validType0(f.typ, env, path) == invalid {
+			if !check.validType0(f.typ, env, nest, path) {
-				return invalid
+				return false
 			}
 		}
 
 	case *Union:
 		for _, t := range t.terms {
-			if check.validType0(t.typ, env, path) == invalid {
+			if !check.validType0(t.typ, env, nest, path) {
-				return invalid
+				return false
 			}
 		}
 
 	case *Interface:
 		for _, etyp := range t.embeddeds {
-			if check.validType0(etyp, env, path) == invalid {
+			if !check.validType0(etyp, env, nest, path) {
-				return invalid
+				return false
 			}
 		}
 
 	case *Named:
-		// Don't report a 2nd error if we already know the type is invalid
+		// Exit early if we already know t is valid.
-		// Note: ensure that t.orig is fully resolved by calling Underlying().
+		// This is purely an optimization but it prevents excessive computation
-		if t.Underlying() == Typ[Invalid] {
+		// times in pathological cases such as testdata/fixedbugs/issue6977.go.
-			check.infoMap[t] = invalid
+		// (Note: The valids map could also be allocated locally, once for each
-			return invalid
+		// validType call.)
+		if check.valids.lookup(t) != nil {
+			break
 		}
 
-		switch check.infoMap[t] {
+		// Don't report a 2nd error if we already know the type is invalid
-		case unknown:
+		// (e.g., if a cycle was detected earlier, via under).
-			check.infoMap[t] = marked
+		// Note: ensure that t.orig is fully resolved by calling Underlying().
-			check.infoMap[t] = check.validType0(t.Origin().fromRHS, env.push(t), append(path, t.obj))
+		if t.Underlying() == Typ[Invalid] {
-		case marked:
+			return false
-			// We have seen type t before and thus must have a cycle.
-			check.infoMap[t] = invalid
-			// t cannot be in an imported package otherwise that package
-			// would have reported a type cycle and couldn't have been
-			// imported in the first place.
-			assert(t.obj.pkg == check.pkg)
-			t.underlying = Typ[Invalid] // t is in the current package (no race possibility)
-			// Find the starting point of the cycle and report it.
-			for i, tn := range path {
-				if tn == t.obj {
-					check.cycleError(path[i:])
-					return invalid
-				}
-			}
-			panic("cycle start not found")
 		}
-		return check.infoMap[t]
+
+		// If the current type t is also found in nest, (the memory of) t is
+		// embedded in itself, indicating an invalid recursive type.
+		for _, e := range nest {
+			if Identical(e, t) {
+				// t cannot be in an imported package otherwise that package
+				// would have reported a type cycle and couldn't have been
+				// imported in the first place.
+				assert(t.obj.pkg == check.pkg)
+				t.underlying = Typ[Invalid] // t is in the current package (no race possibility)
+				// Find the starting point of the cycle and report it.
+				// Because each type in nest must also appear in path (see invariant below),
+				// type t must be in path since it was found in nest. But not every type in path
+				// is in nest. Specifically t may appear in path with an earlier index than the
+				// index of t in nest. Search again.
+				for start, p := range path {
+					if Identical(p, t) {
+						check.cycleError(makeObjList(path[start:]))
+						return false
+					}
+				}
+				panic("cycle start not found")
+			}
+		}
+
+		// No cycle was found. Check the RHS of t.
+		// Every type added to nest is also added to path; thus every type that is in nest
+		// must also be in path (invariant). But not every type in path is in nest, since
+		// nest may be pruned (see below, *TypeParam case).
+		if !check.validType0(t.Origin().fromRHS, env.push(t), append(nest, t), append(path, t)) {
+			return false
+		}
+
+		check.valids.add(t) // t is valid
 
 	case *TypeParam:
 		// A type parameter stands for the type (argument) it was instantiated with.
@@ -97,13 +112,29 @@ func (check *Checker) validType0(typ Type, env *tparamEnv, path []Object) typeIn
 		if env != nil {
 			if targ := env.tmap[t]; targ != nil {
 				// Type arguments found in targ must be looked
-				// up in the enclosing environment env.link.
+				// up in the enclosing environment env.link. The
-				return check.validType0(targ, env.link, path)
+				// type argument must be valid in the enclosing
+				// type (where the current type was instantiated),
+				// hence we must check targ's validity in the type
+				// nest excluding the current (instantiated) type
+				// (see the example at the end of this file).
+				// For error reporting we keep the full path.
+				return check.validType0(targ, env.link, nest[:len(nest)-1], path)
 			}
 		}
 	}
 
-	return valid
+	return true
+}
+
+// makeObjList returns the list of type name objects for the given
+// list of named types.
+func makeObjList(tlist []*Named) []Object {
+	olist := make([]Object, len(tlist))
+	for i, t := range tlist {
+		olist[i] = t.obj
+	}
+	return olist
 }
 
 // A tparamEnv provides the environment for looking up the type arguments
@@ -145,3 +176,93 @@ func (env *tparamEnv) push(typ *Named) *tparamEnv {
 // same information should be available via the path:
 // We should be able to just walk the path backwards
 // and find the type arguments in the instance objects.
+
+// Here is an example illustrating why we need to exclude the
+// instantiated type from nest when evaluating the validity of
+// a type parameter. Given the declarations
+//
+//   var _ A[A[string]]
+//
+//   type A[P any] struct { _ B[P] }
+//   type B[P any] struct { _ P }
+//
+// we want to determine if the type A[A[string]] is valid.
+// We start evaluating A[A[string]] outside any type nest:
+//
+//   A[A[string]]
+//         nest =
+//         path =
+//
+// The RHS of A is now evaluated in the A[A[string]] nest:
+//
+//   struct{_ B[P₁]}
+//         nest = A[A[string]]
+//         path = A[A[string]]
+//
+// The struct has a single field of type B[P₁] with which
+// we continue:
+//
+//   B[P₁]
+//         nest = A[A[string]]
+//         path = A[A[string]]
+//
+//   struct{_ P₂}
+//         nest = A[A[string]]->B[P]
+//         path = A[A[string]]->B[P]
+//
+// Eventutally we reach the type parameter P of type B (P₂):
+//
+//   P₂
+//         nest = A[A[string]]->B[P]
+//         path = A[A[string]]->B[P]
+//
+// The type argument for P of B is the type parameter P of A (P₁).
+// It must be evaluated in the type nest that existed when B was
+// instantiated:
+//
+//   P₁
+//         nest = A[A[string]]        <== type nest at B's instantiation time
+//         path = A[A[string]]->B[P]
+//
+// If we'd use the current nest it would correspond to the path
+// which will be wrong as we will see shortly. P's type argument
+// is A[string], which again must be evaluated in the type nest
+// that existed when A was instantiated with A[string]. That type
+// nest is empty:
+//
+//   A[string]
+//         nest =                     <== type nest at A's instantiation time
+//         path = A[A[string]]->B[P]
+//
+// Evaluation then proceeds as before for A[string]:
+//
+//   struct{_ B[P₁]}
+//         nest = A[string]
+//         path = A[A[string]]->B[P]->A[string]
+//
+// Now we reach B[P] again. If we had not adjusted nest, it would
+// correspond to path, and we would find B[P] in nest, indicating
+// a cycle, which would clearly be wrong since there's no cycle in
+// A[string]:
+//
+//   B[P₁]
+//         nest = A[string]
+//         path = A[A[string]]->B[P]->A[string]  <== path contains B[P]!
+//
+// But because we use the correct type nest, evaluation proceeds without
+// errors and we get the evaluation sequence:
+//
+//   struct{_ P₂}
+//         nest = A[string]->B[P]
+//         path = A[A[string]]->B[P]->A[string]->B[P]
+//   P₂
+//         nest = A[string]->B[P]
+//         path = A[A[string]]->B[P]->A[string]->B[P]
+//   P₁
+//         nest = A[string]
+//         path = A[A[string]]->B[P]->A[string]->B[P]
+//   string
+//         nest =
+//         path = A[A[string]]->B[P]->A[string]->B[P]
+//
+// At this point we're done and A[A[string]] and is valid.