src

graph.go (24684B)

---

 // Copyright 2021 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 vta
 
 import (
 	"fmt"
 	"go/token"
 	"go/types"
 	"iter"
 
 	"golang.org/x/tools/go/ssa"
 	"golang.org/x/tools/go/types/typeutil"
 	"golang.org/x/tools/internal/typeparams"
 )
 
 // node interface for VTA nodes.
 type node interface {
 	Type() types.Type
 	String() string
 }
 
 // constant node for VTA.
 type constant struct {
 	typ types.Type
 }
 
 func (c constant) Type() types.Type {
 	return c.typ
 }
 
 func (c constant) String() string {
 	return fmt.Sprintf("Constant(%v)", c.Type())
 }
 
 // pointer node for VTA.
 type pointer struct {
 	typ *types.Pointer
 }
 
 func (p pointer) Type() types.Type {
 	return p.typ
 }
 
 func (p pointer) String() string {
 	return fmt.Sprintf("Pointer(%v)", p.Type())
 }
 
 // mapKey node for VTA, modeling reachable map key types.
 type mapKey struct {
 	typ types.Type
 }
 
 func (mk mapKey) Type() types.Type {
 	return mk.typ
 }
 
 func (mk mapKey) String() string {
 	return fmt.Sprintf("MapKey(%v)", mk.Type())
 }
 
 // mapValue node for VTA, modeling reachable map value types.
 type mapValue struct {
 	typ types.Type
 }
 
 func (mv mapValue) Type() types.Type {
 	return mv.typ
 }
 
 func (mv mapValue) String() string {
 	return fmt.Sprintf("MapValue(%v)", mv.Type())
 }
 
 // sliceElem node for VTA, modeling reachable slice and array element types.
 type sliceElem struct {
 	typ types.Type
 }
 
 func (s sliceElem) Type() types.Type {
 	return s.typ
 }
 
 func (s sliceElem) String() string {
 	return fmt.Sprintf("Slice([]%v)", s.Type())
 }
 
 // channelElem node for VTA, modeling reachable channel element types.
 type channelElem struct {
 	typ types.Type
 }
 
 func (c channelElem) Type() types.Type {
 	return c.typ
 }
 
 func (c channelElem) String() string {
 	return fmt.Sprintf("Channel(chan %v)", c.Type())
 }
 
 // field node for VTA.
 type field struct {
 	StructType types.Type
 	index      int // index of the field in the struct
 }
 
 func (f field) Type() types.Type {
 	s := typeparams.CoreType(f.StructType).(*types.Struct)
 	return s.Field(f.index).Type()
 }
 
 func (f field) String() string {
 	s := typeparams.CoreType(f.StructType).(*types.Struct)
 	return fmt.Sprintf("Field(%v:%s)", f.StructType, s.Field(f.index).Name())
 }
 
 // global node for VTA.
 type global struct {
 	val *ssa.Global
 }
 
 func (g global) Type() types.Type {
 	return g.val.Type()
 }
 
 func (g global) String() string {
 	return fmt.Sprintf("Global(%s)", g.val.Name())
 }
 
 // local node for VTA modeling local variables
 // and function/method parameters.
 type local struct {
 	val ssa.Value
 }
 
 func (l local) Type() types.Type {
 	return l.val.Type()
 }
 
 func (l local) String() string {
 	return fmt.Sprintf("Local(%s)", l.val.Name())
 }
 
 // indexedLocal node for VTA node. Models indexed locals
 // related to the ssa extract instructions.
 type indexedLocal struct {
 	val   ssa.Value
 	index int
 	typ   types.Type
 }
 
 func (i indexedLocal) Type() types.Type {
 	return i.typ
 }
 
 func (i indexedLocal) String() string {
 	return fmt.Sprintf("Local(%s[%d])", i.val.Name(), i.index)
 }
 
 // function node for VTA.
 type function struct {
 	f *ssa.Function
 }
 
 func (f function) Type() types.Type {
 	return f.f.Type()
 }
 
 func (f function) String() string {
 	return fmt.Sprintf("Function(%s)", f.f.Name())
 }
 
 // resultVar represents the result
 // variable of a function, whether
 // named or not.
 type resultVar struct {
 	f     *ssa.Function
 	index int // valid index into result var tuple
 }
 
 func (o resultVar) Type() types.Type {
 	return o.f.Signature.Results().At(o.index).Type()
 }
 
 func (o resultVar) String() string {
 	v := o.f.Signature.Results().At(o.index)
 	if n := v.Name(); n != "" {
 		return fmt.Sprintf("Return(%s[%s])", o.f.Name(), n)
 	}
 	return fmt.Sprintf("Return(%s[%d])", o.f.Name(), o.index)
 }
 
 // nestedPtrInterface node represents all references and dereferences
 // of locals and globals that have a nested pointer to interface type.
 // We merge such constructs into a single node for simplicity and without
 // much precision sacrifice as such variables are rare in practice. Both
 // a and b would be represented as the same PtrInterface(I) node in:
 //
 //	type I interface
 //	var a ***I
 //	var b **I
 type nestedPtrInterface struct {
 	typ types.Type
 }
 
 func (l nestedPtrInterface) Type() types.Type {
 	return l.typ
 }
 
 func (l nestedPtrInterface) String() string {
 	return fmt.Sprintf("PtrInterface(%v)", l.typ)
 }
 
 // nestedPtrFunction node represents all references and dereferences of locals
 // and globals that have a nested pointer to function type. We merge such
 // constructs into a single node for simplicity and without much precision
 // sacrifice as such variables are rare in practice. Both a and b would be
 // represented as the same PtrFunction(func()) node in:
 //
 //	var a *func()
 //	var b **func()
 type nestedPtrFunction struct {
 	typ types.Type
 }
 
 func (p nestedPtrFunction) Type() types.Type {
 	return p.typ
 }
 
 func (p nestedPtrFunction) String() string {
 	return fmt.Sprintf("PtrFunction(%v)", p.typ)
 }
 
 // panicArg models types of all arguments passed to panic.
 type panicArg struct{}
 
 func (p panicArg) Type() types.Type {
 	return nil
 }
 
 func (p panicArg) String() string {
 	return "Panic"
 }
 
 // recoverReturn models types of all return values of recover().
 type recoverReturn struct{}
 
 func (r recoverReturn) Type() types.Type {
 	return nil
 }
 
 func (r recoverReturn) String() string {
 	return "Recover"
 }
 
 type empty = struct{}
 
 // idx is an index representing a unique node in a vtaGraph.
 type idx int
 
 // vtaGraph remembers for each VTA node the set of its successors.
 // Tailored for VTA, hence does not support singleton (sub)graphs.
 type vtaGraph struct {
 	m    []map[idx]empty // m[i] has the successors for the node with index i.
 	idx  map[node]idx    // idx[n] is the index for the node n.
 	node []node          // node[i] is the node with index i.
 }
 
 func (g *vtaGraph) numNodes() int {
 	return len(g.idx)
 }
 
 func (g *vtaGraph) successors(x idx) iter.Seq[idx] {
 	return func(yield func(y idx) bool) {
 		for y := range g.m[x] {
 			if !yield(y) {
 				return
 			}
 		}
 	}
 }
 
 // addEdge adds an edge x->y to the graph.
 func (g *vtaGraph) addEdge(x, y node) {
 	if g.idx == nil {
 		g.idx = make(map[node]idx)
 	}
 	lookup := func(n node) idx {
 		i, ok := g.idx[n]
 		if !ok {
 			i = idx(len(g.idx))
 			g.m = append(g.m, nil)
 			g.idx[n] = i
 			g.node = append(g.node, n)
 		}
 		return i
 	}
 	a := lookup(x)
 	b := lookup(y)
 	succs := g.m[a]
 	if succs == nil {
 		succs = make(map[idx]empty)
 		g.m[a] = succs
 	}
 	succs[b] = empty{}
 }
 
 // typePropGraph builds a VTA graph for a set of `funcs` and initial
 // `callgraph` needed to establish interprocedural edges. Returns the
 // graph and a map for unique type representatives.
 func typePropGraph(funcs map[*ssa.Function]bool, callees calleesFunc) (*vtaGraph, *typeutil.Map) {
 	b := builder{callees: callees}
 	b.visit(funcs)
 	b.callees = nil // ensure callees is not pinned by pointers to other fields of b.
 	return &b.graph, &b.canon
 }
 
 // Data structure responsible for linearly traversing the
 // code and building a VTA graph.
 type builder struct {
 	graph   vtaGraph
 	callees calleesFunc // initial call graph for creating flows at unresolved call sites.
 
 	// Specialized type map for canonicalization of types.Type.
 	// Semantically equivalent types can have different implementations,
 	// i.e., they are different pointer values. The map allows us to
 	// have one unique representative. The keys are fixed and from the
 	// client perspective they are types. The values in our case are
 	// types too, in particular type representatives. Each value is a
 	// pointer so this map is not expected to take much memory.
 	canon typeutil.Map
 }
 
 func (b *builder) visit(funcs map[*ssa.Function]bool) {
 	// Add the fixed edge Panic -> Recover
 	b.graph.addEdge(panicArg{}, recoverReturn{})
 
 	for f, in := range funcs {
 		if in {
 			b.fun(f)
 		}
 	}
 }
 
 func (b *builder) fun(f *ssa.Function) {
 	for _, bl := range f.Blocks {
 		for _, instr := range bl.Instrs {
 			b.instr(instr)
 		}
 	}
 }
 
 func (b *builder) instr(instr ssa.Instruction) {
 	switch i := instr.(type) {
 	case *ssa.Store:
 		b.addInFlowAliasEdges(b.nodeFromVal(i.Addr), b.nodeFromVal(i.Val))
 	case *ssa.MakeInterface:
 		b.addInFlowEdge(b.nodeFromVal(i.X), b.nodeFromVal(i))
 	case *ssa.MakeClosure:
 		b.closure(i)
 	case *ssa.UnOp:
 		b.unop(i)
 	case *ssa.Phi:
 		b.phi(i)
 	case *ssa.ChangeInterface:
 		// Although in change interface a := A(b) command a and b are
 		// the same object, the only interesting flow happens when A
 		// is an interface. We create flow b -> a, but omit a -> b.
 		// The latter flow is not needed: if a gets assigned concrete
 		// type later on, that cannot be propagated back to b as b
 		// is a separate variable. The a -> b flow can happen when
 		// A is a pointer to interface, but then the command is of
 		// type ChangeType, handled below.
 		b.addInFlowEdge(b.nodeFromVal(i.X), b.nodeFromVal(i))
 	case *ssa.ChangeType:
 		// change type command a := A(b) results in a and b being the
 		// same value. For concrete type A, there is no interesting flow.
 		//
 		// When A is an interface, most interface casts are handled
 		// by the ChangeInterface instruction. The relevant case here is
 		// when converting a pointer to an interface type. This can happen
 		// when the underlying interfaces have the same method set.
 		//
 		//	type I interface{ foo() }
 		//	type J interface{ foo() }
 		//	var b *I
 		//	a := (*J)(b)
 		//
 		// When this happens we add flows between a <--> b.
 		b.addInFlowAliasEdges(b.nodeFromVal(i), b.nodeFromVal(i.X))
 	case *ssa.TypeAssert:
 		b.tassert(i)
 	case *ssa.Extract:
 		b.extract(i)
 	case *ssa.Field:
 		b.field(i)
 	case *ssa.FieldAddr:
 		b.fieldAddr(i)
 	case *ssa.Send:
 		b.send(i)
 	case *ssa.Select:
 		b.selekt(i)
 	case *ssa.Index:
 		b.index(i)
 	case *ssa.IndexAddr:
 		b.indexAddr(i)
 	case *ssa.Lookup:
 		b.lookup(i)
 	case *ssa.MapUpdate:
 		b.mapUpdate(i)
 	case *ssa.Next:
 		b.next(i)
 	case ssa.CallInstruction:
 		b.call(i)
 	case *ssa.Panic:
 		b.panic(i)
 	case *ssa.Return:
 		b.rtrn(i)
 	case *ssa.MakeChan, *ssa.MakeMap, *ssa.MakeSlice, *ssa.BinOp,
 		*ssa.Alloc, *ssa.DebugRef, *ssa.Convert, *ssa.Jump, *ssa.If,
 		*ssa.Slice, *ssa.SliceToArrayPointer, *ssa.Range, *ssa.RunDefers:
 		// No interesting flow here.
 		// Notes on individual instructions:
 		// SliceToArrayPointer: t1 = slice to array pointer *[4]T <- []T (t0)
 		// No interesting flow as sliceArrayElem(t1) == sliceArrayElem(t0).
 		return
 	case *ssa.MultiConvert:
 		b.multiconvert(i)
 	default:
 		panic(fmt.Sprintf("unsupported instruction %v\n", instr))
 	}
 }
 
 func (b *builder) unop(u *ssa.UnOp) {
 	switch u.Op {
 	case token.MUL:
 		// Multiplication operator * is used here as a dereference operator.
 		b.addInFlowAliasEdges(b.nodeFromVal(u), b.nodeFromVal(u.X))
 	case token.ARROW:
 		t := typeparams.CoreType(u.X.Type()).(*types.Chan).Elem()
 		b.addInFlowAliasEdges(b.nodeFromVal(u), channelElem{typ: t})
 	default:
 		// There is no interesting type flow otherwise.
 	}
 }
 
 func (b *builder) phi(p *ssa.Phi) {
 	for _, edge := range p.Edges {
 		b.addInFlowAliasEdges(b.nodeFromVal(p), b.nodeFromVal(edge))
 	}
 }
 
 func (b *builder) tassert(a *ssa.TypeAssert) {
 	if !a.CommaOk {
 		b.addInFlowEdge(b.nodeFromVal(a.X), b.nodeFromVal(a))
 		return
 	}
 	// The case where a is <a.AssertedType, bool> register so there
 	// is a flow from a.X to a[0]. Here, a[0] is represented as an
 	// indexedLocal: an entry into local tuple register a at index 0.
 	tup := a.Type().(*types.Tuple)
 	t := tup.At(0).Type()
 
 	local := indexedLocal{val: a, typ: t, index: 0}
 	b.addInFlowEdge(b.nodeFromVal(a.X), local)
 }
 
 // extract instruction t1 := t2[i] generates flows between t2[i]
 // and t1 where the source is indexed local representing a value
 // from tuple register t2 at index i and the target is t1.
 func (b *builder) extract(e *ssa.Extract) {
 	tup := e.Tuple.Type().(*types.Tuple)
 	t := tup.At(e.Index).Type()
 
 	local := indexedLocal{val: e.Tuple, typ: t, index: e.Index}
 	b.addInFlowAliasEdges(b.nodeFromVal(e), local)
 }
 
 func (b *builder) field(f *ssa.Field) {
 	fnode := field{StructType: f.X.Type(), index: f.Field}
 	b.addInFlowEdge(fnode, b.nodeFromVal(f))
 }
 
 func (b *builder) fieldAddr(f *ssa.FieldAddr) {
 	t := typeparams.CoreType(f.X.Type()).(*types.Pointer).Elem()
 
 	// Since we are getting pointer to a field, make a bidirectional edge.
 	fnode := field{StructType: t, index: f.Field}
 	b.addInFlowEdge(fnode, b.nodeFromVal(f))
 	b.addInFlowEdge(b.nodeFromVal(f), fnode)
 }
 
 func (b *builder) send(s *ssa.Send) {
 	t := typeparams.CoreType(s.Chan.Type()).(*types.Chan).Elem()
 	b.addInFlowAliasEdges(channelElem{typ: t}, b.nodeFromVal(s.X))
 }
 
 // selekt generates flows for select statement
 //
 //	a = select blocking/nonblocking [c_1 <- t_1, c_2 <- t_2, ..., <- o_1, <- o_2, ...]
 //
 // between receiving channel registers c_i and corresponding input register t_i. Further,
 // flows are generated between o_i and a[2 + i]. Note that a is a tuple register of type
 // <int, bool, r_1, r_2, ...> where the type of r_i is the element type of channel o_i.
 func (b *builder) selekt(s *ssa.Select) {
 	recvIndex := 0
 	for _, state := range s.States {
 		t := typeparams.CoreType(state.Chan.Type()).(*types.Chan).Elem()
 
 		if state.Dir == types.SendOnly {
 			b.addInFlowAliasEdges(channelElem{typ: t}, b.nodeFromVal(state.Send))
 		} else {
 			// state.Dir == RecvOnly by definition of select instructions.
 			tupEntry := indexedLocal{val: s, typ: t, index: 2 + recvIndex}
 			b.addInFlowAliasEdges(tupEntry, channelElem{typ: t})
 			recvIndex++
 		}
 	}
 }
 
 // index instruction a := b[c] on slices creates flows between a and
 // SliceElem(t) flow where t is an interface type of c. Arrays and
 // slice elements are both modeled as SliceElem.
 func (b *builder) index(i *ssa.Index) {
 	et := sliceArrayElem(i.X.Type())
 	b.addInFlowAliasEdges(b.nodeFromVal(i), sliceElem{typ: et})
 }
 
 // indexAddr instruction a := &b[c] fetches address of a index
 // into the field so we create bidirectional flow a <-> SliceElem(t)
 // where t is an interface type of c. Arrays and slice elements are
 // both modeled as SliceElem.
 func (b *builder) indexAddr(i *ssa.IndexAddr) {
 	et := sliceArrayElem(i.X.Type())
 	b.addInFlowEdge(sliceElem{typ: et}, b.nodeFromVal(i))
 	b.addInFlowEdge(b.nodeFromVal(i), sliceElem{typ: et})
 }
 
 // lookup handles map query commands a := m[b] where m is of type
 // map[...]V and V is an interface. It creates flows between `a`
 // and MapValue(V).
 func (b *builder) lookup(l *ssa.Lookup) {
 	t, ok := l.X.Type().Underlying().(*types.Map)
 	if !ok {
 		// No interesting flows for string lookups.
 		return
 	}
 
 	if !l.CommaOk {
 		b.addInFlowAliasEdges(b.nodeFromVal(l), mapValue{typ: t.Elem()})
 	} else {
 		i := indexedLocal{val: l, typ: t.Elem(), index: 0}
 		b.addInFlowAliasEdges(i, mapValue{typ: t.Elem()})
 	}
 }
 
 // mapUpdate handles map update commands m[b] = a where m is of type
 // map[K]V and K and V are interfaces. It creates flows between `a`
 // and MapValue(V) as well as between MapKey(K) and `b`.
 func (b *builder) mapUpdate(u *ssa.MapUpdate) {
 	t, ok := u.Map.Type().Underlying().(*types.Map)
 	if !ok {
 		// No interesting flows for string updates.
 		return
 	}
 
 	b.addInFlowAliasEdges(mapKey{typ: t.Key()}, b.nodeFromVal(u.Key))
 	b.addInFlowAliasEdges(mapValue{typ: t.Elem()}, b.nodeFromVal(u.Value))
 }
 
 // next instruction <ok, key, value> := next r, where r
 // is a range over map or string generates flow between
 // key and MapKey as well value and MapValue nodes.
 func (b *builder) next(n *ssa.Next) {
 	if n.IsString {
 		return
 	}
 	tup := n.Type().(*types.Tuple)
 	kt := tup.At(1).Type()
 	vt := tup.At(2).Type()
 
 	b.addInFlowAliasEdges(indexedLocal{val: n, typ: kt, index: 1}, mapKey{typ: kt})
 	b.addInFlowAliasEdges(indexedLocal{val: n, typ: vt, index: 2}, mapValue{typ: vt})
 }
 
 // addInFlowAliasEdges adds an edge r -> l to b.graph if l is a node that can
 // have an inflow, i.e., a node that represents an interface or an unresolved
 // function value. Similarly for the edge l -> r with an additional condition
 // of that l and r can potentially alias.
 func (b *builder) addInFlowAliasEdges(l, r node) {
 	b.addInFlowEdge(r, l)
 
 	if canAlias(l, r) {
 		b.addInFlowEdge(l, r)
 	}
 }
 
 func (b *builder) closure(c *ssa.MakeClosure) {
 	f := c.Fn.(*ssa.Function)
 	b.addInFlowEdge(function{f: f}, b.nodeFromVal(c))
 
 	for i, fv := range f.FreeVars {
 		b.addInFlowAliasEdges(b.nodeFromVal(fv), b.nodeFromVal(c.Bindings[i]))
 	}
 }
 
 // panic creates a flow from arguments to panic instructions to return
 // registers of all recover statements in the program. Introduces a
 // global panic node Panic and
 //  1. for every panic statement p: add p -> Panic
 //  2. for every recover statement r: add Panic -> r (handled in call)
 //
 // TODO(zpavlinovic): improve precision by explicitly modeling how panic
 // values flow from callees to callers and into deferred recover instructions.
 func (b *builder) panic(p *ssa.Panic) {
 	// Panics often have, for instance, strings as arguments which do
 	// not create interesting flows.
 	if !canHaveMethods(p.X.Type()) {
 		return
 	}
 
 	b.addInFlowEdge(b.nodeFromVal(p.X), panicArg{})
 }
 
 // call adds flows between arguments/parameters and return values/registers
 // for both static and dynamic calls, as well as go and defer calls.
 func (b *builder) call(c ssa.CallInstruction) {
 	// When c is r := recover() call register instruction, we add Recover -> r.
 	if bf, ok := c.Common().Value.(*ssa.Builtin); ok && bf.Name() == "recover" {
 		if v, ok := c.(ssa.Value); ok {
 			b.addInFlowEdge(recoverReturn{}, b.nodeFromVal(v))
 		}
 		return
 	}
 
 	for f := range siteCallees(c, b.callees) {
 		addArgumentFlows(b, c, f)
 
 		site, ok := c.(ssa.Value)
 		if !ok {
 			continue // go or defer
 		}
 
 		results := f.Signature.Results()
 		if results.Len() == 1 {
 			// When there is only one return value, the destination register does not
 			// have a tuple type.
 			b.addInFlowEdge(resultVar{f: f, index: 0}, b.nodeFromVal(site))
 		} else {
 			tup := site.Type().(*types.Tuple)
 			for i := 0; i < results.Len(); i++ {
 				local := indexedLocal{val: site, typ: tup.At(i).Type(), index: i}
 				b.addInFlowEdge(resultVar{f: f, index: i}, local)
 			}
 		}
 	}
 }
 
 func addArgumentFlows(b *builder, c ssa.CallInstruction, f *ssa.Function) {
 	// When f has no parameters (including receiver), there is no type
 	// flow here. Also, f's body and parameters might be missing, such
 	// as when vta is used within the golang.org/x/tools/go/analysis
 	// framework (see github.com/golang/go/issues/50670).
 	if len(f.Params) == 0 {
 		return
 	}
 	cc := c.Common()
 	if cc.Method != nil {
 		// In principle we don't add interprocedural flows for receiver
 		// objects. At a call site, the receiver object is interface
 		// while the callee object is concrete. The flow from interface
 		// to concrete type in general does not make sense. The exception
 		// is when the concrete type is a named function type (see #57756).
 		//
 		// The flow other way around would bake in information from the
 		// initial call graph.
 		if isFunction(f.Params[0].Type()) {
 			b.addInFlowEdge(b.nodeFromVal(cc.Value), b.nodeFromVal(f.Params[0]))
 		}
 	}
 
 	offset := 0
 	if cc.Method != nil {
 		offset = 1
 	}
 	for i, v := range cc.Args {
 		// Parameters of f might not be available, as in the case
 		// when vta is used within the golang.org/x/tools/go/analysis
 		// framework (see github.com/golang/go/issues/50670).
 		//
 		// TODO: investigate other cases of missing body and parameters
 		if len(f.Params) <= i+offset {
 			return
 		}
 		b.addInFlowAliasEdges(b.nodeFromVal(f.Params[i+offset]), b.nodeFromVal(v))
 	}
 }
 
 // rtrn creates flow edges from the operands of the return
 // statement to the result variables of the enclosing function.
 func (b *builder) rtrn(r *ssa.Return) {
 	for i, rs := range r.Results {
 		b.addInFlowEdge(b.nodeFromVal(rs), resultVar{f: r.Parent(), index: i})
 	}
 }
 
 func (b *builder) multiconvert(c *ssa.MultiConvert) {
 	// TODO(zpavlinovic): decide what to do on MultiConvert long term.
 	// TODO(zpavlinovic): add unit tests.
 	typeSetOf := func(typ types.Type) []*types.Term {
 		// This is a adaptation of x/exp/typeparams.NormalTerms which x/tools cannot depend on.
 		var terms []*types.Term
 		var err error
 		switch typ := types.Unalias(typ).(type) {
 		case *types.TypeParam:
 			terms, err = typeparams.StructuralTerms(typ)
 		case *types.Union:
 			terms, err = typeparams.UnionTermSet(typ)
 		case *types.Interface:
 			terms, err = typeparams.InterfaceTermSet(typ)
 		default:
 			// Common case.
 			// Specializing the len=1 case to avoid a slice
 			// had no measurable space/time benefit.
 			terms = []*types.Term{types.NewTerm(false, typ)}
 		}
 
 		if err != nil {
 			return nil
 		}
 		return terms
 	}
 	// isValuePreserving returns true if a conversion from ut_src to
 	// ut_dst is value-preserving, i.e. just a change of type.
 	// Precondition: neither argument is a named or alias type.
 	isValuePreserving := func(ut_src, ut_dst types.Type) bool {
 		// Identical underlying types?
 		if types.IdenticalIgnoreTags(ut_dst, ut_src) {
 			return true
 		}
 
 		switch ut_dst.(type) {
 		case *types.Chan:
 			// Conversion between channel types?
 			_, ok := ut_src.(*types.Chan)
 			return ok
 
 		case *types.Pointer:
 			// Conversion between pointers with identical base types?
 			_, ok := ut_src.(*types.Pointer)
 			return ok
 		}
 		return false
 	}
 	dst_terms := typeSetOf(c.Type())
 	src_terms := typeSetOf(c.X.Type())
 	for _, s := range src_terms {
 		us := s.Type().Underlying()
 		for _, d := range dst_terms {
 			ud := d.Type().Underlying()
 			if isValuePreserving(us, ud) {
 				// This is equivalent to a ChangeType.
 				b.addInFlowAliasEdges(b.nodeFromVal(c), b.nodeFromVal(c.X))
 				return
 			}
 			// This is equivalent to either: SliceToArrayPointer,,
 			// SliceToArrayPointer+Deref, Size 0 Array constant, or a Convert.
 		}
 	}
 }
 
 // addInFlowEdge adds s -> d to g if d is node that can have an inflow, i.e., a node
 // that represents an interface or an unresolved function value. Otherwise, there
 // is no interesting type flow so the edge is omitted.
 func (b *builder) addInFlowEdge(s, d node) {
 	if hasInFlow(d) {
 		b.graph.addEdge(b.representative(s), b.representative(d))
 	}
 }
 
 // Creates const, pointer, global, func, and local nodes based on register instructions.
 func (b *builder) nodeFromVal(val ssa.Value) node {
 	if p, ok := types.Unalias(val.Type()).(*types.Pointer); ok && !types.IsInterface(p.Elem()) && !isFunction(p.Elem()) {
 		// Nested pointer to interfaces are modeled as a special
 		// nestedPtrInterface node.
 		if i := interfaceUnderPtr(p.Elem()); i != nil {
 			return nestedPtrInterface{typ: i}
 		}
 		// The same goes for nested function types.
 		if f := functionUnderPtr(p.Elem()); f != nil {
 			return nestedPtrFunction{typ: f}
 		}
 		return pointer{typ: p}
 	}
 
 	switch v := val.(type) {
 	case *ssa.Const:
 		return constant{typ: val.Type()}
 	case *ssa.Global:
 		return global{val: v}
 	case *ssa.Function:
 		return function{f: v}
 	case *ssa.Parameter, *ssa.FreeVar, ssa.Instruction:
 		// ssa.Param, ssa.FreeVar, and a specific set of "register" instructions,
 		// satisfying the ssa.Value interface, can serve as local variables.
 		return local{val: v}
 	default:
 		panic(fmt.Errorf("unsupported value %v in node creation", val))
 	}
 }
 
 // representative returns a unique representative for node `n`. Since
 // semantically equivalent types can have different implementations,
 // this method guarantees the same implementation is always used.
 func (b *builder) representative(n node) node {
 	if n.Type() == nil {
 		// panicArg and recoverReturn do not have
 		// types and are unique by definition.
 		return n
 	}
 	t := canonicalize(n.Type(), &b.canon)
 
 	switch i := n.(type) {
 	case constant:
 		return constant{typ: t}
 	case pointer:
 		return pointer{typ: t.(*types.Pointer)}
 	case sliceElem:
 		return sliceElem{typ: t}
 	case mapKey:
 		return mapKey{typ: t}
 	case mapValue:
 		return mapValue{typ: t}
 	case channelElem:
 		return channelElem{typ: t}
 	case nestedPtrInterface:
 		return nestedPtrInterface{typ: t}
 	case nestedPtrFunction:
 		return nestedPtrFunction{typ: t}
 	case field:
 		return field{StructType: canonicalize(i.StructType, &b.canon), index: i.index}
 	case indexedLocal:
 		return indexedLocal{typ: t, val: i.val, index: i.index}
 	case local, global, panicArg, recoverReturn, function, resultVar:
 		return n
 	default:
 		panic(fmt.Errorf("canonicalizing unrecognized node %v", n))
 	}
 }
 
 // canonicalize returns a type representative of `t` unique subject
 // to type map `canon`.
 func canonicalize(t types.Type, canon *typeutil.Map) types.Type {
 	rep := canon.At(t)
 	if rep != nil {
 		return rep.(types.Type)
 	}
 	canon.Set(t, t)
 	return t
 }