releases/ast/check.go

// Copyright 2017 The OPA Authors.  All rights reserved.
// Use of this source code is governed by an Apache2
// license that can be found in the LICENSE file.

package ast

import (
	"fmt"
	"sort"
	"strings"

	"github.com/open-policy-agent/opa/types"
	"github.com/open-policy-agent/opa/util"
)

type rewriteVars func(x Ref) Ref

// exprChecker defines the interface for executing type checking on a single
// expression. The exprChecker must update the provided TypeEnv with inferred
// types of vars.
type exprChecker func(*TypeEnv, *Expr) *Error

// typeChecker implements type checking on queries and rules. Errors are
// accumulated on the typeChecker so that a single run can report multiple
// issues.
type typeChecker struct {
	errs         Errors
	exprCheckers map[string]exprChecker
	varRewriter  rewriteVars
	ss           *SchemaSet
	input        types.Type
}

// newTypeChecker returns a new typeChecker object that has no errors.
func newTypeChecker() *typeChecker {
	tc := &typeChecker{}
	tc.exprCheckers = map[string]exprChecker{
		"eq": tc.checkExprEq,
	}
	return tc
}

func (tc *typeChecker) newEnv(exist *TypeEnv) *TypeEnv {
	if exist != nil {
		return exist.wrap()
	}
	env := newTypeEnv(tc.copy)
	if tc.input != nil {
		env.tree.Put(InputRootRef, tc.input)
	}
	return env
}

func (tc *typeChecker) copy() *typeChecker {
	return newTypeChecker().
		WithVarRewriter(tc.varRewriter).
		WithSchemaSet(tc.ss).
		WithInputType(tc.input)
}

func (tc *typeChecker) WithSchemaSet(ss *SchemaSet) *typeChecker {
	tc.ss = ss
	return tc
}

func (tc *typeChecker) WithVarRewriter(f rewriteVars) *typeChecker {
	tc.varRewriter = f
	return tc
}

func (tc *typeChecker) WithInputType(tpe types.Type) *typeChecker {
	tc.input = tpe
	return tc
}

// Env returns a type environment for the specified built-ins with any other
// global types configured on the checker. In practice, this is the default
// environment that other statements will be checked against.
func (tc *typeChecker) Env(builtins map[string]*Builtin) *TypeEnv {
	env := tc.newEnv(nil)
	for _, bi := range builtins {
		env.tree.Put(bi.Ref(), bi.Decl)
	}
	return env
}

// CheckBody runs type checking on the body and returns a TypeEnv if no errors
// are found. The resulting TypeEnv wraps the provided one. The resulting
// TypeEnv will be able to resolve types of vars contained in the body.
func (tc *typeChecker) CheckBody(env *TypeEnv, body Body) (*TypeEnv, Errors) {

	errors := []*Error{}
	env = tc.newEnv(env)

	WalkExprs(body, func(expr *Expr) bool {

		closureErrs := tc.checkClosures(env, expr)
		for _, err := range closureErrs {
			errors = append(errors, err)
		}

		hasClosureErrors := len(closureErrs) > 0

		vis := newRefChecker(env, tc.varRewriter)
		NewGenericVisitor(vis.Visit).Walk(expr)
		for _, err := range vis.errs {
			errors = append(errors, err)
		}

		hasRefErrors := len(vis.errs) > 0

		if err := tc.checkExpr(env, expr); err != nil {
			// Suppress this error if a more actionable one has occurred. In
			// this case, if an error occurred in a ref or closure contained in
			// this expression, and the error is due to a nil type, then it's
			// likely to be the result of the more specific error.
			skip := (hasClosureErrors || hasRefErrors) && causedByNilType(err)
			if !skip {
				errors = append(errors, err)
			}
		}
		return true
	})

	tc.err(errors)
	return env, errors
}

// CheckTypes runs type checking on the rules returns a TypeEnv if no errors
// are found. The resulting TypeEnv wraps the provided one. The resulting
// TypeEnv will be able to resolve types of refs that refer to rules.
func (tc *typeChecker) CheckTypes(env *TypeEnv, sorted []util.T) (*TypeEnv, Errors) {
	env = tc.newEnv(env)
	var as *annotationSet
	if tc.ss != nil {
		var errs Errors
		as, errs = buildAnnotationSet(sorted)
		if len(errs) > 0 {
			return env, errs
		}
	}
	for _, s := range sorted {
		tc.checkRule(env, as, s.(*Rule))
	}
	tc.errs.Sort()
	return env, tc.errs
}

func (tc *typeChecker) checkClosures(env *TypeEnv, expr *Expr) Errors {
	var result Errors
	WalkClosures(expr, func(x interface{}) bool {
		switch x := x.(type) {
		case *ArrayComprehension:
			_, errs := tc.copy().CheckBody(env, x.Body)
			if len(errs) > 0 {
				result = errs
				return true
			}
		case *SetComprehension:
			_, errs := tc.copy().CheckBody(env, x.Body)
			if len(errs) > 0 {
				result = errs
				return true
			}
		case *ObjectComprehension:
			_, errs := tc.copy().CheckBody(env, x.Body)
			if len(errs) > 0 {
				result = errs
				return true
			}
		}
		return false
	})
	return result
}

func (tc *typeChecker) checkRule(env *TypeEnv, as *annotationSet, rule *Rule) {

	env = env.wrap()

	if schemaAnnots := getRuleAnnotation(as, rule); schemaAnnots != nil {
		for _, schemaAnnot := range schemaAnnots {
			ref, refType, err := processAnnotation(tc.ss, schemaAnnot, rule)
			if err != nil {
				tc.err([]*Error{err})
				continue
			}
			prefixRef, t := getPrefix(env, ref)
			if t == nil || len(prefixRef) == len(ref) {
				env.tree.Put(ref, refType)
			} else {
				newType, err := override(ref[len(prefixRef):], t, refType, rule)
				if err != nil {
					tc.err([]*Error{err})
					continue
				}
				env.tree.Put(prefixRef, newType)
			}
		}
	}

	cpy, err := tc.CheckBody(env, rule.Body)
	env = env.next
	path := rule.Path()

	if len(err) > 0 {
		// if the rule/function contains an error, add it to the type env so
		// that expressions that refer to this rule/function do not encounter
		// type errors.
		env.tree.Put(path, types.A)
		return
	}

	var tpe types.Type

	if len(rule.Head.Args) > 0 {

		// If args are not referred to in body, infer as any.
		WalkVars(rule.Head.Args, func(v Var) bool {
			if cpy.Get(v) == nil {
				cpy.tree.PutOne(v, types.A)
			}
			return false
		})

		// Construct function type.
		args := make([]types.Type, len(rule.Head.Args))
		for i := 0; i < len(rule.Head.Args); i++ {
			args[i] = cpy.Get(rule.Head.Args[i])
		}

		f := types.NewFunction(args, cpy.Get(rule.Head.Value))

		// Union with existing.
		exist := env.tree.Get(path)
		tpe = types.Or(exist, f)

	} else {
		switch rule.Head.DocKind() {
		case CompleteDoc:
			typeV := cpy.Get(rule.Head.Value)
			if typeV != nil {
				exist := env.tree.Get(path)
				tpe = types.Or(typeV, exist)
			}
		case PartialObjectDoc:
			typeK := cpy.Get(rule.Head.Key)
			typeV := cpy.Get(rule.Head.Value)
			if typeK != nil && typeV != nil {
				exist := env.tree.Get(path)
				typeV = types.Or(types.Values(exist), typeV)
				typeK = types.Or(types.Keys(exist), typeK)
				tpe = types.NewObject(nil, types.NewDynamicProperty(typeK, typeV))
			}
		case PartialSetDoc:
			typeK := cpy.Get(rule.Head.Key)
			if typeK != nil {
				exist := env.tree.Get(path)
				typeK = types.Or(types.Keys(exist), typeK)
				tpe = types.NewSet(typeK)
			}
		}
	}

	if tpe != nil {
		env.tree.Put(path, tpe)
	}
}

func (tc *typeChecker) checkExpr(env *TypeEnv, expr *Expr) *Error {
	if !expr.IsCall() {
		return nil
	}

	checker := tc.exprCheckers[expr.Operator().String()]
	if checker != nil {
		return checker(env, expr)
	}

	return tc.checkExprBuiltin(env, expr)
}

func (tc *typeChecker) checkExprBuiltin(env *TypeEnv, expr *Expr) *Error {

	args := expr.Operands()
	pre := getArgTypes(env, args)

	// NOTE(tsandall): undefined functions will have been caught earlier in the
	// compiler. We check for undefined functions before the safety check so
	// that references to non-existent functions result in undefined function
	// errors as opposed to unsafe var errors.
	//
	// We cannot run type checking before the safety check because part of the
	// type checker relies on reordering (in particular for references to local
	// vars).
	name := expr.Operator()
	tpe := env.Get(name)

	if tpe == nil {
		return NewError(TypeErr, expr.Location, "undefined function %v", name)
	}

	// check if the expression refers to a function that contains an error
	_, ok := tpe.(types.Any)
	if ok {
		return nil
	}

	ftpe, ok := tpe.(*types.Function)
	if !ok {
		return NewError(TypeErr, expr.Location, "undefined function %v", name)
	}

	maxArgs := len(ftpe.Args())
	expArgs := ftpe.Args()

	if ftpe.Result() != nil {
		maxArgs++
		expArgs = append(expArgs, ftpe.Result())
	}

	if len(args) > maxArgs {
		return newArgError(expr.Location, name, "too many arguments", pre, expArgs)
	} else if len(args) < len(ftpe.Args()) {
		return newArgError(expr.Location, name, "too few arguments", pre, expArgs)
	}

	for i := range args {
		if !unify1(env, args[i], expArgs[i], false) {
			post := make([]types.Type, len(args))
			for i := range args {
				post[i] = env.Get(args[i])
			}
			return newArgError(expr.Location, name, "invalid argument(s)", post, expArgs)
		}
	}

	return nil
}

func (tc *typeChecker) checkExprEq(env *TypeEnv, expr *Expr) *Error {

	pre := getArgTypes(env, expr.Operands())
	exp := Equality.Decl.Args()

	if len(pre) < len(exp) {
		return newArgError(expr.Location, expr.Operator(), "too few arguments", pre, exp)
	} else if len(exp) < len(pre) {
		return newArgError(expr.Location, expr.Operator(), "too many arguments", pre, exp)
	}

	a, b := expr.Operand(0), expr.Operand(1)
	typeA, typeB := env.Get(a), env.Get(b)

	if !unify2(env, a, typeA, b, typeB) {
		err := NewError(TypeErr, expr.Location, "match error")
		err.Details = &UnificationErrDetail{
			Left:  typeA,
			Right: typeB,
		}
		return err
	}

	return nil
}

func unify2(env *TypeEnv, a *Term, typeA types.Type, b *Term, typeB types.Type) bool {

	nilA := types.Nil(typeA)
	nilB := types.Nil(typeB)

	if nilA && !nilB {
		return unify1(env, a, typeB, false)
	} else if nilB && !nilA {
		return unify1(env, b, typeA, false)
	} else if !nilA && !nilB {
		return unifies(typeA, typeB)
	}

	switch a.Value.(type) {
	case *Array:
		return unify2Array(env, a, b)
	case *object:
		return unify2Object(env, a, b)
	case Var:
		switch b.Value.(type) {
		case Var:
			return unify1(env, a, types.A, false) && unify1(env, b, env.Get(a), false)
		case *Array:
			return unify2Array(env, b, a)
		case *object:
			return unify2Object(env, b, a)
		}
	}

	return false
}

func unify2Array(env *TypeEnv, a *Term, b *Term) bool {
	arr := a.Value.(*Array)
	switch bv := b.Value.(type) {
	case *Array:
		if arr.Len() == bv.Len() {
			for i := 0; i < arr.Len(); i++ {
				if !unify2(env, arr.Elem(i), env.Get(arr.Elem(i)), bv.Elem(i), env.Get(bv.Elem(i))) {
					return false
				}
			}
			return true
		}
	case Var:
		return unify1(env, a, types.A, false) && unify1(env, b, env.Get(a), false)
	}
	return false
}

func unify2Object(env *TypeEnv, a *Term, b *Term) bool {
	obj := a.Value.(Object)
	switch bv := b.Value.(type) {
	case *object:
		cv := obj.Intersect(bv)
		if obj.Len() == bv.Len() && bv.Len() == len(cv) {
			for i := range cv {
				if !unify2(env, cv[i][1], env.Get(cv[i][1]), cv[i][2], env.Get(cv[i][2])) {
					return false
				}
			}
			return true
		}
	case Var:
		return unify1(env, a, types.A, false) && unify1(env, b, env.Get(a), false)
	}
	return false
}

func unify1(env *TypeEnv, term *Term, tpe types.Type, union bool) bool {
	switch v := term.Value.(type) {
	case *Array:
		switch tpe := tpe.(type) {
		case *types.Array:
			return unify1Array(env, v, tpe, union)
		case types.Any:
			if types.Compare(tpe, types.A) == 0 {
				for i := 0; i < v.Len(); i++ {
					unify1(env, v.Elem(i), types.A, true)
				}
				return true
			}
			unifies := false
			for i := range tpe {
				unifies = unify1(env, term, tpe[i], true) || unifies
			}
			return unifies
		}
		return false
	case *object:
		switch tpe := tpe.(type) {
		case *types.Object:
			return unify1Object(env, v, tpe, union)
		case types.Any:
			if types.Compare(tpe, types.A) == 0 {
				v.Foreach(func(key, value *Term) {
					unify1(env, key, types.A, true)
					unify1(env, value, types.A, true)
				})
				return true
			}
			unifies := false
			for i := range tpe {
				unifies = unify1(env, term, tpe[i], true) || unifies
			}
			return unifies
		}
		return false
	case Set:
		switch tpe := tpe.(type) {
		case *types.Set:
			return unify1Set(env, v, tpe, union)
		case types.Any:
			if types.Compare(tpe, types.A) == 0 {
				v.Foreach(func(elem *Term) {
					unify1(env, elem, types.A, true)
				})
				return true
			}
			unifies := false
			for i := range tpe {
				unifies = unify1(env, term, tpe[i], true) || unifies
			}
			return unifies
		}
		return false
	case Ref, *ArrayComprehension, *ObjectComprehension, *SetComprehension:
		return unifies(env.Get(v), tpe)
	case Var:
		if !union {
			if exist := env.Get(v); exist != nil {
				return unifies(exist, tpe)
			}
			env.tree.PutOne(term.Value, tpe)
		} else {
			env.tree.PutOne(term.Value, types.Or(env.Get(v), tpe))
		}
		return true
	default:
		if !IsConstant(v) {
			panic("unreachable")
		}
		return unifies(env.Get(term), tpe)
	}
}

func unify1Array(env *TypeEnv, val *Array, tpe *types.Array, union bool) bool {
	if val.Len() != tpe.Len() && tpe.Dynamic() == nil {
		return false
	}
	for i := 0; i < val.Len(); i++ {
		if !unify1(env, val.Elem(i), tpe.Select(i), union) {
			return false
		}
	}
	return true
}

func unify1Object(env *TypeEnv, val Object, tpe *types.Object, union bool) bool {
	if val.Len() != len(tpe.Keys()) && tpe.DynamicValue() == nil {
		return false
	}
	stop := val.Until(func(k, v *Term) bool {
		if IsConstant(k.Value) {
			if child := selectConstant(tpe, k); child != nil {
				if !unify1(env, v, child, union) {
					return true
				}
			} else {
				return true
			}
		} else {
			// Inferring type of value under dynamic key would involve unioning
			// with all property values of tpe whose keys unify. For now, type
			// these values as Any. We can investigate stricter inference in
			// the future.
			unify1(env, v, types.A, union)
		}
		return false
	})
	return !stop
}

func unify1Set(env *TypeEnv, val Set, tpe *types.Set, union bool) bool {
	of := types.Values(tpe)
	return !val.Until(func(elem *Term) bool {
		return !unify1(env, elem, of, union)
	})
}

func (tc *typeChecker) err(errors []*Error) {
	tc.errs = append(tc.errs, errors...)
}

type refChecker struct {
	env         *TypeEnv
	errs        Errors
	varRewriter rewriteVars
}

func newRefChecker(env *TypeEnv, f rewriteVars) *refChecker {

	if f == nil {
		f = rewriteVarsNop
	}

	return &refChecker{
		env:         env,
		errs:        nil,
		varRewriter: f,
	}
}

func (rc *refChecker) Visit(x interface{}) bool {
	switch x := x.(type) {
	case *ArrayComprehension, *ObjectComprehension, *SetComprehension:
		return true
	case *Expr:
		switch terms := x.Terms.(type) {
		case []*Term:
			for i := 1; i < len(terms); i++ {
				NewGenericVisitor(rc.Visit).Walk(terms[i])
			}
			return true
		case *Term:
			NewGenericVisitor(rc.Visit).Walk(terms)
			return true
		}
	case Ref:
		if err := rc.checkApply(rc.env, x); err != nil {
			rc.errs = append(rc.errs, err)
			return true
		}
		if err := rc.checkRef(rc.env, rc.env.tree, x, 0); err != nil {
			rc.errs = append(rc.errs, err)
		}
	}
	return false
}

func (rc *refChecker) checkApply(curr *TypeEnv, ref Ref) *Error {
	if tpe := curr.Get(ref); tpe != nil {
		if _, ok := tpe.(*types.Function); ok {
			return newRefErrUnsupported(ref[0].Location, rc.varRewriter(ref), len(ref)-1, tpe)
		}
	}
	return nil
}

func (rc *refChecker) checkRef(curr *TypeEnv, node *typeTreeNode, ref Ref, idx int) *Error {

	if idx == len(ref) {
		return nil
	}

	head := ref[idx]

	// Handle constant ref operands, i.e., strings or the ref head.
	if _, ok := head.Value.(String); ok || idx == 0 {

		child := node.Child(head.Value)
		if child == nil {

			if curr.next != nil {
				next := curr.next
				return rc.checkRef(next, next.tree, ref, 0)
			}

			if RootDocumentNames.Contains(ref[0]) {
				return rc.checkRefLeaf(types.A, ref, 1)
			}

			return rc.checkRefLeaf(types.A, ref, 0)
		}

		if child.Leaf() {
			return rc.checkRefLeaf(child.Value(), ref, idx+1)
		}

		return rc.checkRef(curr, child, ref, idx+1)
	}

	// Handle dynamic ref operands.
	switch value := head.Value.(type) {

	case Var:

		if exist := rc.env.Get(value); exist != nil {
			if !unifies(types.S, exist) {
				return newRefErrInvalid(ref[0].Location, rc.varRewriter(ref), idx, exist, types.S, getOneOfForNode(node))
			}
		} else {
			rc.env.tree.PutOne(value, types.S)
		}

	case Ref:

		exist := rc.env.Get(value)
		if exist == nil {
			// If ref type is unknown, an error will already be reported so
			// stop here.
			return nil
		}

		if !unifies(types.S, exist) {
			return newRefErrInvalid(ref[0].Location, rc.varRewriter(ref), idx, exist, types.S, getOneOfForNode(node))
		}

	// Catch other ref operand types here. Non-leaf nodes must be referred to
	// with string values.
	default:
		return newRefErrInvalid(ref[0].Location, rc.varRewriter(ref), idx, nil, types.S, getOneOfForNode(node))
	}

	// Run checking on remaining portion of the ref. Note, since the ref
	// potentially refers to data for which no type information exists,
	// checking should never fail.
	node.Children().Iter(func(_, child util.T) bool {
		_ = rc.checkRef(curr, child.(*typeTreeNode), ref, idx+1) // ignore error
		return false
	})

	return nil
}

func (rc *refChecker) checkRefLeaf(tpe types.Type, ref Ref, idx int) *Error {

	if idx == len(ref) {
		return nil
	}

	head := ref[idx]

	keys := types.Keys(tpe)
	if keys == nil {
		return newRefErrUnsupported(ref[0].Location, rc.varRewriter(ref), idx-1, tpe)
	}

	switch value := head.Value.(type) {

	case Var:
		if exist := rc.env.Get(value); exist != nil {
			if !unifies(exist, keys) {
				return newRefErrInvalid(ref[0].Location, rc.varRewriter(ref), idx, exist, keys, getOneOfForType(tpe))
			}
		} else {
			rc.env.tree.PutOne(value, types.Keys(tpe))
		}

	case Ref:
		if exist := rc.env.Get(value); exist != nil {
			if !unifies(exist, keys) {
				return newRefErrInvalid(ref[0].Location, rc.varRewriter(ref), idx, exist, keys, getOneOfForType(tpe))
			}
		}

	case *Array, Object, Set:
		if !unify1(rc.env, head, keys, false) {
			return newRefErrInvalid(ref[0].Location, rc.varRewriter(ref), idx, rc.env.Get(head), keys, nil)
		}

	default:
		child := selectConstant(tpe, head)
		if child == nil {
			return newRefErrInvalid(ref[0].Location, rc.varRewriter(ref), idx, nil, types.Keys(tpe), getOneOfForType(tpe))
		}
		return rc.checkRefLeaf(child, ref, idx+1)
	}

	return rc.checkRefLeaf(types.Values(tpe), ref, idx+1)
}

func unifies(a, b types.Type) bool {

	if a == nil || b == nil {
		return false
	}

	anyA, ok1 := a.(types.Any)
	if ok1 {
		if unifiesAny(anyA, b) {
			return true
		}
	}

	anyB, ok2 := b.(types.Any)
	if ok2 {
		if unifiesAny(anyB, a) {
			return true
		}
	}

	if ok1 || ok2 {
		return false
	}

	switch a := a.(type) {
	case types.Null:
		_, ok := b.(types.Null)
		return ok
	case types.Boolean:
		_, ok := b.(types.Boolean)
		return ok
	case types.Number:
		_, ok := b.(types.Number)
		return ok
	case types.String:
		_, ok := b.(types.String)
		return ok
	case *types.Array:
		b, ok := b.(*types.Array)
		if !ok {
			return false
		}
		return unifiesArrays(a, b)
	case *types.Object:
		b, ok := b.(*types.Object)
		if !ok {
			return false
		}
		return unifiesObjects(a, b)
	case *types.Set:
		b, ok := b.(*types.Set)
		if !ok {
			return false
		}
		return unifies(types.Values(a), types.Values(b))
	case *types.Function:
		// TODO(tsandall): revisit once functions become first-class values.
		return false
	default:
		panic("unreachable")
	}
}

func unifiesAny(a types.Any, b types.Type) bool {
	if _, ok := b.(*types.Function); ok {
		return false
	}
	for i := range a {
		if unifies(a[i], b) {
			return true
		}
	}
	return len(a) == 0
}

func unifiesArrays(a, b *types.Array) bool {

	if !unifiesArraysStatic(a, b) {
		return false
	}

	if !unifiesArraysStatic(b, a) {
		return false
	}

	return a.Dynamic() == nil || b.Dynamic() == nil || unifies(a.Dynamic(), b.Dynamic())
}

func unifiesArraysStatic(a, b *types.Array) bool {
	if a.Len() != 0 {
		for i := 0; i < a.Len(); i++ {
			if !unifies(a.Select(i), b.Select(i)) {
				return false
			}
		}
	}
	return true
}

func unifiesObjects(a, b *types.Object) bool {
	if !unifiesObjectsStatic(a, b) {
		return false
	}

	if !unifiesObjectsStatic(b, a) {
		return false
	}

	return a.DynamicValue() == nil || b.DynamicValue() == nil || unifies(a.DynamicValue(), b.DynamicValue())
}

func unifiesObjectsStatic(a, b *types.Object) bool {
	for _, k := range a.Keys() {
		if !unifies(a.Select(k), b.Select(k)) {
			return false
		}
	}
	return true
}

// typeErrorCause defines an interface to determine the reason for a type
// error. The type error details implement this interface so that type checking
// can report more actionable errors.
type typeErrorCause interface {
	nilType() bool
}

func causedByNilType(err *Error) bool {
	cause, ok := err.Details.(typeErrorCause)
	if !ok {
		return false
	}
	return cause.nilType()
}

// ArgErrDetail represents a generic argument error.
type ArgErrDetail struct {
	Have []types.Type `json:"have"`
	Want []types.Type `json:"want"`
}

// Lines returns the string representation of the detail.
func (d *ArgErrDetail) Lines() []string {
	lines := make([]string, 2)
	lines[0] = fmt.Sprint("have: ", formatArgs(d.Have))
	lines[1] = fmt.Sprint("want: ", formatArgs(d.Want))
	return lines
}

func (d *ArgErrDetail) nilType() bool {
	for i := range d.Have {
		if types.Nil(d.Have[i]) {
			return true
		}
	}
	return false
}

// UnificationErrDetail describes a type mismatch error when two values are
// unified (e.g., x = [1,2,y]).
type UnificationErrDetail struct {
	Left  types.Type `json:"a"`
	Right types.Type `json:"b"`
}

func (a *UnificationErrDetail) nilType() bool {
	return types.Nil(a.Left) || types.Nil(a.Right)
}

// Lines returns the string representation of the detail.
func (a *UnificationErrDetail) Lines() []string {
	lines := make([]string, 2)
	lines[0] = fmt.Sprint("left  : ", types.Sprint(a.Left))
	lines[1] = fmt.Sprint("right : ", types.Sprint(a.Right))
	return lines
}

// RefErrUnsupportedDetail describes an undefined reference error where the
// referenced value does not support dereferencing (e.g., scalars).
type RefErrUnsupportedDetail struct {
	Ref  Ref        `json:"ref"`  // invalid ref
	Pos  int        `json:"pos"`  // invalid element
	Have types.Type `json:"have"` // referenced type
}

// Lines returns the string representation of the detail.
func (r *RefErrUnsupportedDetail) Lines() []string {
	lines := []string{
		r.Ref.String(),
		strings.Repeat("^", len(r.Ref[:r.Pos+1].String())),
		fmt.Sprintf("have: %v", r.Have),
	}
	return lines
}

// RefErrInvalidDetail describes an undefined reference error where the referenced
// value does not support the reference operand (e.g., missing object key,
// invalid key type, etc.)
type RefErrInvalidDetail struct {
	Ref   Ref        `json:"ref"`            // invalid ref
	Pos   int        `json:"pos"`            // invalid element
	Have  types.Type `json:"have,omitempty"` // type of invalid element (for var/ref elements)
	Want  types.Type `json:"want"`           // allowed type (for non-object values)
	OneOf []Value    `json:"oneOf"`          // allowed values (e.g., for object keys)
}

// Lines returns the string representation of the detail.
func (r *RefErrInvalidDetail) Lines() []string {
	lines := []string{r.Ref.String()}
	offset := len(r.Ref[:r.Pos].String()) + 1
	pad := strings.Repeat(" ", offset)
	lines = append(lines, fmt.Sprintf("%s^", pad))
	if r.Have != nil {
		lines = append(lines, fmt.Sprintf("%shave (type): %v", pad, r.Have))
	} else {
		lines = append(lines, fmt.Sprintf("%shave: %v", pad, r.Ref[r.Pos]))
	}
	if len(r.OneOf) > 0 {
		lines = append(lines, fmt.Sprintf("%swant (one of): %v", pad, r.OneOf))
	} else {
		lines = append(lines, fmt.Sprintf("%swant (type): %v", pad, r.Want))
	}
	return lines
}

func formatArgs(args []types.Type) string {
	buf := make([]string, len(args))
	for i := range args {
		buf[i] = types.Sprint(args[i])
	}
	return "(" + strings.Join(buf, ", ") + ")"
}

func newRefErrInvalid(loc *Location, ref Ref, idx int, have, want types.Type, oneOf []Value) *Error {
	err := newRefError(loc, ref)
	err.Details = &RefErrInvalidDetail{
		Ref:   ref,
		Pos:   idx,
		Have:  have,
		Want:  want,
		OneOf: oneOf,
	}
	return err
}

func newRefErrUnsupported(loc *Location, ref Ref, idx int, have types.Type) *Error {
	err := newRefError(loc, ref)
	err.Details = &RefErrUnsupportedDetail{
		Ref:  ref,
		Pos:  idx,
		Have: have,
	}
	return err
}

func newRefError(loc *Location, ref Ref) *Error {
	return NewError(TypeErr, loc, "undefined ref: %v", ref)
}

func newArgError(loc *Location, builtinName Ref, msg string, have []types.Type, want []types.Type) *Error {
	err := NewError(TypeErr, loc, "%v: %v", builtinName, msg)
	err.Details = &ArgErrDetail{
		Have: have,
		Want: want,
	}
	return err
}

func getOneOfForNode(node *typeTreeNode) (result []Value) {
	node.Children().Iter(func(k, _ util.T) bool {
		result = append(result, k.(Value))
		return false
	})

	sortValueSlice(result)
	return result
}

func getOneOfForType(tpe types.Type) (result []Value) {
	switch tpe := tpe.(type) {
	case *types.Object:
		for _, k := range tpe.Keys() {
			v, err := InterfaceToValue(k)
			if err != nil {
				panic(err)
			}
			result = append(result, v)
		}
	}
	sortValueSlice(result)
	return result
}

func sortValueSlice(sl []Value) {
	sort.Slice(sl, func(i, j int) bool {
		return sl[i].Compare(sl[j]) < 0
	})
}

func getArgTypes(env *TypeEnv, args []*Term) []types.Type {
	pre := make([]types.Type, len(args))
	for i := range args {
		pre[i] = env.Get(args[i])
	}
	return pre
}

// getPrefix returns the shortest prefix of ref that exists in env
func getPrefix(env *TypeEnv, ref Ref) (Ref, types.Type) {
	if len(ref) == 1 {
		t := env.Get(ref)
		if t != nil {
			return ref, t
		}
	}
	for i := 1; i < len(ref); i++ {
		t := env.Get(ref[:i])
		if t != nil {
			return ref[:i], t
		}
	}
	return nil, nil
}

// override takes a type t and returns a type obtained from t where the path represented by ref within it has type o (overriding the original type of that path)
func override(ref Ref, t types.Type, o types.Type, rule *Rule) (types.Type, *Error) {
	var newStaticProps []*types.StaticProperty
	obj, ok := t.(*types.Object)
	if !ok {
		newType, err := getObjectType(ref, o, rule, types.NewDynamicProperty(types.A, types.A))
		if err != nil {
			return nil, err
		}
		return newType, nil
	}
	found := false
	if ok {
		staticProps := obj.StaticProperties()
		for _, prop := range staticProps {
			valueCopy := prop.Value
			key, err := InterfaceToValue(prop.Key)
			if err != nil {
				return nil, NewError(TypeErr, rule.Location, "unexpected error in override: %s", err.Error())
			}
			if len(ref) > 0 && ref[0].Value.Compare(key) == 0 {
				found = true
				if len(ref) == 1 {
					valueCopy = o
				} else {
					newVal, err := override(ref[1:], valueCopy, o, rule)
					if err != nil {
						return nil, err
					}
					valueCopy = newVal
				}
			}
			newStaticProps = append(newStaticProps, types.NewStaticProperty(prop.Key, valueCopy))
		}
	}

	// ref[0] is not a top-level key in staticProps, so it must be added
	if !found {
		newType, err := getObjectType(ref, o, rule, obj.DynamicProperties())
		if err != nil {
			return nil, err
		}
		newStaticProps = append(newStaticProps, newType.StaticProperties()...)
	}
	return types.NewObject(newStaticProps, obj.DynamicProperties()), nil
}

func getKeys(ref Ref, rule *Rule) ([]interface{}, *Error) {
	keys := []interface{}{}
	for _, refElem := range ref {
		key, err := JSON(refElem.Value)
		if err != nil {
			return nil, NewError(TypeErr, rule.Location, "error getting key from value: %s", err.Error())
		}
		keys = append(keys, key)
	}
	return keys, nil
}

func getObjectTypeRec(keys []interface{}, o types.Type, d *types.DynamicProperty) *types.Object {
	if len(keys) == 1 {
		staticProps := []*types.StaticProperty{types.NewStaticProperty(keys[0], o)}
		return types.NewObject(staticProps, d)
	}

	staticProps := []*types.StaticProperty{types.NewStaticProperty(keys[0], getObjectTypeRec(keys[1:], o, d))}
	return types.NewObject(staticProps, d)
}

func getObjectType(ref Ref, o types.Type, rule *Rule, d *types.DynamicProperty) (*types.Object, *Error) {
	keys, err := getKeys(ref, rule)
	if err != nil {
		return nil, err
	}
	return getObjectTypeRec(keys, o, d), nil
}

func getRuleAnnotation(as *annotationSet, rule *Rule) (result []*SchemaAnnotation) {

	for _, x := range as.GetSubpackagesScope(rule.Module.Package.Path) {
		result = append(result, x.Schemas...)
	}

	if x := as.GetPackageScope(rule.Module.Package); x != nil {
		result = append(result, x.Schemas...)
	}

	if x := as.GetDocumentScope(rule.Path()); x != nil {
		result = append(result, x.Schemas...)
	}

	for _, x := range as.GetRuleScope(rule) {
		result = append(result, x.Schemas...)
	}

	return result
}

func processAnnotation(ss *SchemaSet, annot *SchemaAnnotation, rule *Rule) (Ref, types.Type, *Error) {

	var schema interface{}

	if annot.Schema != nil {
		schema = ss.Get(annot.Schema)
		if schema == nil {
			return nil, nil, NewError(TypeErr, rule.Location, "undefined schema: %v", annot.Schema)
		}
	} else if annot.Definition != nil {
		schema = *annot.Definition
	}

	tpe, err := loadSchema(schema)
	if err != nil {
		return nil, nil, NewError(TypeErr, rule.Location, err.Error())
	}

	return annot.Path, tpe, nil
}

func errAnnotationRedeclared(a *Annotations, other *Location) *Error {
	return NewError(TypeErr, a.Location, "%v annotation redeclared: %v", a.Scope, other)
}

type annotationSet struct {
	byRule    map[*Rule][]*Annotations
	byPackage map[*Package]*Annotations
	byPath    *annotationTreeNode
}

func buildAnnotationSet(rules []util.T) (*annotationSet, Errors) {
	as := newAnnotationSet()
	processed := map[*Module]struct{}{}
	var errs Errors
	for _, x := range rules {
		module := x.(*Rule).Module
		if _, ok := processed[module]; ok {
			continue
		}
		processed[module] = struct{}{}
		for _, a := range module.Annotations {
			if err := as.Add(a); err != nil {
				errs = append(errs, err)
			}
		}
	}
	if len(errs) > 0 {
		return nil, errs
	}
	return as, nil
}

func newAnnotationSet() *annotationSet {
	return &annotationSet{
		byRule:    map[*Rule][]*Annotations{},
		byPackage: map[*Package]*Annotations{},
		byPath:    newAnnotationTree(),
	}
}

func (as *annotationSet) Add(a *Annotations) *Error {
	switch a.Scope {
	case annotationScopeRule:
		rule := a.node.(*Rule)
		as.byRule[rule] = append(as.byRule[rule], a)
	case annotationScopePackage:
		pkg := a.node.(*Package)
		if exist, ok := as.byPackage[pkg]; ok {
			return errAnnotationRedeclared(a, exist.Location)
		}
		as.byPackage[pkg] = a
	case annotationScopeDocument:
		rule := a.node.(*Rule)
		path := rule.Path()
		x := as.byPath.Get(path)
		if x != nil {
			return errAnnotationRedeclared(a, x.Value.Location)
		}
		as.byPath.Insert(path, a)
	case annotationScopeSubpackages:
		pkg := a.node.(*Package)
		x := as.byPath.Get(pkg.Path)
		if x != nil {
			return errAnnotationRedeclared(a, x.Value.Location)
		}
		as.byPath.Insert(pkg.Path, a)
	}
	return nil
}

func (as *annotationSet) GetRuleScope(r *Rule) []*Annotations {
	if as == nil {
		return nil
	}
	return as.byRule[r]
}

func (as *annotationSet) GetSubpackagesScope(path Ref) []*Annotations {
	if as == nil {
		return nil
	}
	return as.byPath.Ancestors(path)
}

func (as *annotationSet) GetDocumentScope(path Ref) *Annotations {
	if as == nil {
		return nil
	}
	if node := as.byPath.Get(path); node != nil {
		return node.Value
	}
	return nil
}

func (as *annotationSet) GetPackageScope(pkg *Package) *Annotations {
	if as == nil {
		return nil
	}
	return as.byPackage[pkg]
}

type annotationTreeNode struct {
	Value    *Annotations
	Children map[Value]*annotationTreeNode // we assume key elements are hashable (vars and strings only!)
}

func newAnnotationTree() *annotationTreeNode {
	return &annotationTreeNode{
		Value:    nil,
		Children: map[Value]*annotationTreeNode{},
	}
}

func (t *annotationTreeNode) Insert(path Ref, value *Annotations) {
	node := t
	for _, k := range path {
		child, ok := node.Children[k.Value]
		if !ok {
			child = newAnnotationTree()
			node.Children[k.Value] = child
		}
		node = child
	}
	node.Value = value
}

func (t *annotationTreeNode) Get(path Ref) *annotationTreeNode {
	node := t
	for _, k := range path {
		if node == nil {
			return nil
		}
		child, ok := node.Children[k.Value]
		if !ok {
			return nil
		}
		node = child
	}
	return node
}

func (t *annotationTreeNode) Ancestors(path Ref) (result []*Annotations) {
	node := t
	for _, k := range path {
		if node == nil {
			return result
		}
		child, ok := node.Children[k.Value]
		if !ok {
			return result
		}
		if child.Value != nil {
			result = append(result, child.Value)
		}
		node = child
	}
	return result
}