nitc/typing: document `merge_types`

[nit.git] / src / semantize / typing.nit

# This file is part of NIT ( http://www.nitlanguage.org ).
#
# Copyright 2012 Jean Privat <jean@pryen.org>
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

# Intraprocedural resolution of static types and OO-services
# By OO-services we mean message sending, attribute access, instantiation, etc.
module typing

import modelize
import local_var_init
import literal

redef class ToolContext
        var typing_phase: Phase = new TypingPhase(self, [flow_phase, modelize_property_phase, local_var_init_phase])
end

private class TypingPhase
        super Phase
        redef fun process_npropdef(npropdef) do npropdef.do_typing(toolcontext.modelbuilder)
end

private class TypeVisitor
        var modelbuilder:  ModelBuilder

        # The module of the analysis
        # Used to correctly query the model
        var mmodule: MModule

        # The static type of the receiver
        # Mainly used for type tests and type resolutions
        var anchor: nullable MClassType = null

        # The analyzed mclassdef
        var mclassdef: nullable MClassDef = null

        # The analyzed property
        var mpropdef: nullable MPropDef

        var selfvariable = new Variable("self")

        # Is `self` use restricted?
        # * no explicit `self`
        # * method called on the implicit self must be top-level
        # Currently only used for `new` factory since there is no valid receiver inside
        var is_toplevel_context = false

        init
        do
                var mpropdef = self.mpropdef

                if mpropdef != null then
                        self.mpropdef = mpropdef
                        var mclassdef = mpropdef.mclassdef
                        self.mclassdef = mclassdef
                        self.anchor = mclassdef.bound_mtype

                        var mclass = mclassdef.mclass

                        var selfvariable = new Variable("self")
                        self.selfvariable = selfvariable
                        selfvariable.declared_type = mclass.mclass_type

                        var mprop = mpropdef.mproperty
                        if mprop isa MMethod and mprop.is_new then
                                is_toplevel_context = true
                        end
                end
        end

        fun anchor_to(mtype: MType): MType
        do
                var anchor = anchor
                if anchor == null then
                        assert not mtype.need_anchor
                        return mtype
                end
                return mtype.anchor_to(mmodule, anchor)
        end

        fun is_subtype(sub, sup: MType): Bool
        do
                return sub.is_subtype(mmodule, anchor, sup)
        end

        fun resolve_for(mtype, subtype: MType, for_self: Bool): MType
        do
                #print "resolve_for {mtype} sub={subtype} forself={for_self} mmodule={mmodule} anchor={anchor}"
                var res = mtype.resolve_for(subtype, anchor, mmodule, not for_self)
                return res
        end

        # Check that `sub` is a subtype of `sup`.
        # If `sub` is not a valid suptype, then display an error on `node` and return `null`.
        # If `sub` is a safe subtype of `sup`, then return `sub`.
        # If `sub` is an unsafe subtype (i.e., an implicit cast is required), then return `sup`.
        #
        # The point of the return type is to determinate the usable type on an expression when `autocast` is true:
        # If the suptype is safe, then the return type is the one on the expression typed by `sub`.
        # Is the subtype is unsafe, then the return type is the one of an implicit cast on `sup`.
        fun check_subtype(node: ANode, sub, sup: MType, autocast: Bool): nullable MType
        do
                if self.is_subtype(sub, sup) then return sub
                if autocast and self.is_subtype(sub, self.anchor_to(sup)) then
                        # FIXME workaround to the current unsafe typing policy. To remove once fixed virtual types exists.
                        #node.debug("Unsafe typing: expected {sup}, got {sub}")
                        return sup
                end
                if sup isa MErrorType then return null # Skip error
                if sub.need_anchor then
                        var u = anchor_to(sub)
                        self.modelbuilder.error(node, "Type Error: expected `{sup}`, got `{sub}: {u}`.")
                else
                        self.modelbuilder.error(node, "Type Error: expected `{sup}`, got `{sub}`.")
                end
                return null
        end

        # Visit an expression and do not care about the return value
        fun visit_stmt(nexpr: nullable AExpr)
        do
                if nexpr == null then return
                nexpr.accept_typing(self)
        end

        # Visit an expression and expects that it is not a statement
        # Return the type of the expression
        # Display an error and return null if:
        #  * the type cannot be determined or
        #  * `nexpr` is a statement
        fun visit_expr(nexpr: AExpr): nullable MType
        do
                nexpr.accept_typing(self)
                var mtype = nexpr.mtype
                if mtype != null then return mtype
                if not nexpr.is_typed then
                        if not self.modelbuilder.toolcontext.error_count > 0 then # check that there is really an error
                                if self.modelbuilder.toolcontext.verbose_level > 1 then
                                        nexpr.debug("No return type but no error.")
                                end
                        end
                        return null # forward error
                end
                var more_message = null
                var p = nexpr.parent
                if p != null then more_message = p.bad_expr_message(nexpr)
                if more_message == null then more_message = "" else more_message = " " + more_message
                self.error(nexpr, "Error: expected an expression{more_message}.")
                return null
        end

        # Visit an expression and expect its static type is a least a `sup`
        # Return the type of the expression or null if
        #  * the type cannot be determined or
        #  * `nexpr` is a statement or
        #  * `nexpr` is not a `sup`
        fun visit_expr_subtype(nexpr: AExpr, sup: nullable MType): nullable MType
        do
                var sub = visit_expr(nexpr)
                if sub == null then return null # Forward error

                if sup == null then return null # Forward error

                var res = check_subtype(nexpr, sub, sup, true)
                if res != sub then
                        nexpr.implicit_cast_to = res
                end
                return res
        end

        # Visit an expression and expect its static type is a `Bool`
        # Return the type of the expression or null if
        #  * the type cannot be determined or
        #  * `nexpr` is a statement or
        #  * `nexpr` is not a `Bool`
        fun visit_expr_bool(nexpr: AExpr): nullable MType
        do
                return self.visit_expr_subtype(nexpr, self.type_bool(nexpr))
        end


        fun check_expr_cast(node: ANode, nexpr: AExpr, ntype: AType): nullable MType
        do
                var sub = nexpr.mtype
                if sub == null then return null # Forward error

                var sup = ntype.mtype
                if sup == null then return null # Forward error

                if sup == sub then
                        self.modelbuilder.warning(node, "useless-type-test", "Warning: expression is already a `{sup}`.")
                else if self.is_subtype(sub, sup) then
                        self.modelbuilder.warning(node, "useless-type-test", "Warning: expression is already a `{sup}` since it is a `{sub}`.")
                end
                return sup
        end

        # Can `mtype` be null (up to the current knowledge)?
        fun can_be_null(mtype: MType): Bool
        do
                if mtype isa MNullableType or mtype isa MNullType then return true
                if mtype isa MFormalType then
                        var x = anchor_to(mtype)
                        if x isa MNullableType or x isa MNullType then return true
                end
                return false
        end

        # Check that `mtype` can be null (up to the current knowledge).
        #
        # If not then display a `useless-null-test` warning on node and return false.
        # Else return true.
        fun check_can_be_null(anode: ANode, mtype: MType): Bool
        do
                if mtype isa MNullType then
                        modelbuilder.warning(anode, "useless-null-test", "Warning: expression is always `null`.")
                        return true
                end
                if can_be_null(mtype) then return true

                if mtype isa MFormalType then
                        var res = anchor_to(mtype)
                        modelbuilder.warning(anode, "useless-null-test", "Warning: expression is not null, since it is a `{mtype}: {res}`.")
                else
                        modelbuilder.warning(anode, "useless-null-test", "Warning: expression is not null, since it is a `{mtype}`.")
                end
                return false
        end

        # Special verification on != and == for null
        # Return true
        fun null_test(anode: ABinopExpr)
        do
                var mtype = anode.n_expr.mtype
                var mtype2 = anode.n_expr2.mtype

                if mtype == null or mtype2 == null then return

                if not mtype2 isa MNullType then return

                # Check of useless null
                if not can_be_null(mtype) then return

                if mtype isa MNullType then
                        # Because of type adaptation, we cannot just stop here
                        # so return use `null` as a bottom type that will be merged easily (cf) `merge_types`
                        mtype = null
                else
                        mtype = mtype.as_notnull
                end

                # Check for type adaptation
                var variable = anode.n_expr.its_variable
                if variable == null then return

                # One is null (mtype2 see above) the other is not null
                if anode isa AEqExpr then
                        anode.after_flow_context.when_true.set_var(self, variable, mtype2)
                        anode.after_flow_context.when_false.set_var(self, variable, mtype)
                else if anode isa ANeExpr then
                        anode.after_flow_context.when_false.set_var(self, variable, mtype2)
                        anode.after_flow_context.when_true.set_var(self, variable, mtype)
                else
                        abort
                end
        end

        fun try_get_mproperty_by_name2(anode: ANode, mtype: MType, name: String): nullable MProperty
        do
                return self.modelbuilder.try_get_mproperty_by_name2(anode, mmodule, mtype, name)
        end

        fun resolve_mtype(node: AType): nullable MType
        do
                return self.modelbuilder.resolve_mtype(mmodule, mclassdef, node)
        end

        fun try_get_mclass(node: ANode, name: String): nullable MClass
        do
                var mclass = modelbuilder.try_get_mclass_by_name(node, mmodule, name)
                return mclass
        end

        fun get_mclass(node: ANode, name: String): nullable MClass
        do
                var mclass = modelbuilder.get_mclass_by_name(node, mmodule, name)
                return mclass
        end

        fun type_bool(node: ANode): nullable MType
        do
                var mclass = self.get_mclass(node, "Bool")
                if mclass == null then return null
                return mclass.mclass_type
        end

        fun get_method(node: ANode, recvtype: MType, name: String, recv_is_self: Bool): nullable CallSite
        do
                var unsafe_type = self.anchor_to(recvtype)

                #debug("recv: {recvtype} (aka {unsafe_type})")
                if recvtype isa MNullType then
                        var objclass = get_mclass(node, "Object")
                        if objclass == null then return null # Forward error
                        unsafe_type = objclass.mclass_type
                end

                var mproperty = self.try_get_mproperty_by_name2(node, unsafe_type, name)
                if name == "new" and mproperty == null then
                        name = "init"
                        mproperty = self.try_get_mproperty_by_name2(node, unsafe_type, name)
                end

                if mproperty == null then
                        if recv_is_self then
                                self.modelbuilder.error(node, "Error: method or variable `{name}` unknown in `{recvtype}`.")
                        else if recvtype.need_anchor then
                                self.modelbuilder.error(node, "Error: method `{name}` does not exists in `{recvtype}: {unsafe_type}`.")
                        else
                                self.modelbuilder.error(node, "Error: method `{name}` does not exists in `{recvtype}`.")
                        end
                        return null
                end

                assert mproperty isa MMethod

                # `null` only accepts some methods of object.
                if recvtype isa MNullType and not mproperty.is_null_safe then
                        self.error(node, "Error: method `{name}` called on `null`.")
                        return null
                else if unsafe_type isa MNullableType and not mproperty.is_null_safe then
                        modelbuilder.advice(node, "call-on-nullable", "Warning: method call on a nullable receiver `{recvtype}`.")
                end

                if is_toplevel_context and recv_is_self and not mproperty.is_toplevel then
                        error(node, "Error: `{name}` is not a top-level method, thus need a receiver.")
                end
                if not recv_is_self and mproperty.is_toplevel then
                        error(node, "Error: cannot call `{name}`, a top-level method, with a receiver.")
                end

                if mproperty.visibility == protected_visibility and not recv_is_self and self.mmodule.visibility_for(mproperty.intro_mclassdef.mmodule) < intrude_visibility and not modelbuilder.toolcontext.opt_ignore_visibility.value then
                        self.modelbuilder.error(node, "Error: method `{name}` is protected and can only accessed by `self`.")
                        return null
                end

                var info = mproperty.deprecation
                if info != null and self.mpropdef.mproperty.deprecation == null then
                        var mdoc = info.mdoc
                        if mdoc != null then
                                self.modelbuilder.warning(node, "deprecated-method", "Deprecation Warning: method `{name}` is deprecated: {mdoc.content.first}")
                        else
                                self.modelbuilder.warning(node, "deprecated-method", "Deprecation Warning: method `{name}` is deprecated.")
                        end
                end

                var propdefs = mproperty.lookup_definitions(self.mmodule, unsafe_type)
                var mpropdef
                if propdefs.length == 0 then
                        self.modelbuilder.error(node, "Type Error: no definition found for property `{name}` in `{unsafe_type}`.")
                        return null
                else if propdefs.length == 1 then
                        mpropdef = propdefs.first
                else
                        self.modelbuilder.warning(node, "property-conflict", "Warning: conflicting property definitions for property `{name}` in `{unsafe_type}`: {propdefs.join(" ")}")
                        mpropdef = mproperty.intro
                end


                var msignature = mpropdef.new_msignature or else mpropdef.msignature
                if msignature == null then return null # skip error
                msignature = resolve_for(msignature, recvtype, recv_is_self).as(MSignature)

                var erasure_cast = false
                var rettype = mpropdef.msignature.return_mtype
                if not recv_is_self and rettype != null then
                        rettype = rettype.undecorate
                        if rettype isa MParameterType then
                                var erased_rettype = msignature.return_mtype
                                assert erased_rettype != null
                                #node.debug("Erasure cast: Really a {rettype} but unsafely a {erased_rettype}")
                                erasure_cast = true
                        end
                end

                var callsite = new CallSite(node.hot_location, recvtype, mmodule, anchor, recv_is_self, mproperty, mpropdef, msignature, erasure_cast)
                return callsite
        end

        fun try_get_method(node: ANode, recvtype: MType, name: String, recv_is_self: Bool): nullable CallSite
        do
                var unsafe_type = self.anchor_to(recvtype)
                var mproperty = self.try_get_mproperty_by_name2(node, unsafe_type, name)
                if mproperty == null then return null
                return get_method(node, recvtype, name, recv_is_self)
        end


        # Visit the expressions of args and check their conformity with the corresponding type in signature
        # The point of this method is to handle varargs correctly
        # Note: The signature must be correctly adapted
        fun check_signature(node: ANode, args: Array[AExpr], mproperty: MProperty, msignature: MSignature): nullable SignatureMap
        do
                var vararg_rank = msignature.vararg_rank
                if vararg_rank >= 0 then
                        if args.length < msignature.arity then
                                modelbuilder.error(node, "Error: expected at least {msignature.arity} argument(s) for `{mproperty}{msignature}`; got {args.length}. See introduction at `{mproperty.full_name}`.")
                                return null
                        end
                else if args.length != msignature.arity then
                        # Too much argument
                        if args.length > msignature.arity then
                                modelbuilder.error(node, "Error: expected {msignature.arity} argument(s) for `{mproperty}{msignature}`; got {args.length}. See introduction at `{mproperty.full_name}`.")
                                return null
                        end
                        # Other cases are managed later
                end


                #debug("CALL {unsafe_type}.{msignature}")

                # Associate each parameter to a position in the arguments
                var map = new SignatureMap

                # Special case for the isolated last argument
                # TODO: reify this method characteristics (where? the param, the signature, the method?)
                var last_is_padded = mproperty.name.chars.last == '='
                var nbargs = args.length
                if last_is_padded then
                        nbargs -= 1
                        assert not args.last isa ANamedargExpr
                        map.map[msignature.arity - 1] = args.length - 1
                        self.visit_expr_subtype(args.last, msignature.mparameters.last.mtype)
                end

                # First, handle named arguments
                for i in [0..args.length[ do
                        var e = args[i]
                        if not e isa ANamedargExpr then continue
                        var name = e.n_id.text
                        var param = msignature.mparameter_by_name(name)
                        if param == null then
                                modelbuilder.error(e.n_id, "Error: no parameter `{name}` for `{mproperty}{msignature}`.")
                                return null
                        end
                        var idx = msignature.mparameters.index_of(param)
                        var prev = map.map.get_or_null(idx)
                        if prev != null then
                                modelbuilder.error(e, "Error: parameter `{name}` already associated with argument #{prev} for `{mproperty}{msignature}`.")
                                return null
                        end
                        map.map[idx] = i
                        e.mtype = self.visit_expr_subtype(e.n_expr, param.mtype)
                end

                # Number of minimum mandatory remaining parameters
                var min_arity = 0

                # Second, associate remaining parameters
                var vararg_decl = args.length - msignature.arity
                var j = 0
                for i in [0..msignature.arity[ do
                        # Skip parameters associated by name
                        if map.map.has_key(i) then continue

                        var param = msignature.mparameters[i]

                        # Search the next free argument: skip named arguments since they are already associated
                        while j < nbargs and args[j] isa ANamedargExpr do j += 1
                        if j >= nbargs then
                                if not param.mtype isa MNullableType then
                                        min_arity = j + 1
                                end
                                j += 1
                                continue
                        end
                        var arg = args[j]
                        map.map[i] = j
                        j += 1

                        if i == vararg_rank then
                                j += vararg_decl
                                continue # skip the vararg
                        end

                        if not param.is_vararg then
                                var paramtype = param.mtype
                                self.visit_expr_subtype(arg, paramtype)
                        else
                                check_one_vararg(arg, param)
                        end
                end

                if min_arity > 0 then
                        if last_is_padded then min_arity += 1
                        if min_arity < msignature.arity then
                                modelbuilder.error(node, "Error: expected at least {min_arity} argument(s) for `{mproperty}{msignature}`; got {args.length}. See introduction at `{mproperty.full_name}`.")
                        else
                                modelbuilder.error(node, "Error: expected {min_arity} argument(s) for `{mproperty}{msignature}`; got {args.length}. See introduction at `{mproperty.full_name}`.")
                        end
                        return null
                end

                # Third, check varargs
                if vararg_rank >= 0 then
                        var paramtype = msignature.mparameters[vararg_rank].mtype
                        var first = args[vararg_rank]
                        if vararg_decl == 0 then
                                if not check_one_vararg(first, msignature.mparameters[vararg_rank]) then return null
                        else
                                first.vararg_decl = vararg_decl + 1
                                for i in [vararg_rank..vararg_rank+vararg_decl] do
                                        self.visit_expr_subtype(args[i], paramtype)
                                end
                        end
                end

                return map
        end

        # Check an expression as a single vararg.
        # The main point of the method if to handle the case of reversed vararg (see `AVarargExpr`)
        fun check_one_vararg(arg: AExpr, param: MParameter): Bool
        do
                var paramtype = param.mtype
                var mclass = get_mclass(arg, "Array")
                if mclass == null then return false # Forward error
                var array_mtype = mclass.get_mtype([paramtype])
                if arg isa AVarargExpr then
                        self.visit_expr_subtype(arg.n_expr, array_mtype)
                        arg.mtype  = arg.n_expr.mtype
                else
                        # only one vararg, maybe `...` was forgot, so be gentle!
                        var t = visit_expr(arg)
                        if t == null then return false # Forward error
                        if not is_subtype(t, paramtype) and is_subtype(t, array_mtype) then
                                # Not acceptable but could be a `...`
                                error(arg, "Type Error: expected `{paramtype}`, got `{t}`. Is an ellipsis `...` missing on the argument?")
                                return false
                        end
                        # Standard valid vararg, finish the job
                        arg.vararg_decl = 1
                        self.visit_expr_subtype(arg, paramtype)
                end
                return true
        end

        fun error(node: ANode, message: String)
        do
                self.modelbuilder.error(node, message)
        end

        fun get_variable(node: AExpr, variable: Variable): nullable MType
        do
                if not variable.is_adapted then return variable.declared_type

                var flow = node.after_flow_context
                if flow == null then return null # skip error

                if flow.vars.has_key(variable) then
                        return flow.vars[variable]
                else
                        #node.debug("*** START Collected for {variable}")
                        var mtypes = flow.collect_types(variable)
                        #node.debug("**** END Collected for {variable}")
                        if mtypes.length == 0 then
                                return variable.declared_type
                        else if mtypes.length == 1 then
                                return mtypes.first
                        else
                                var res = merge_types(node,mtypes)
                                if res == null then res = variable.declared_type
                                return res
                        end
                end
        end

        # Some variables where type-adapted during the visit
        var dirty = false

        # Some loops had been visited during the visit
        var has_loop = false

        fun set_variable(node: AExpr, variable: Variable, mtype: nullable MType)
        do
                var flow = node.after_flow_context
                assert flow != null

                flow.set_var(self, variable, mtype)
        end

        # Find the exact representable most specific common super-type in `col`.
        #
        # Try to find the most specific common type that is a super-type of each types
        # in `col`.
        # In most cases, the result is simply the most general type in `col`.
        # If nullables types are involved, then the nullable information is correctly preserved.
        # If incomparable super-types exists in `col`, them no solution is given and the `null`
        # value is returned (since union types are non representable in Nit)
        #
        # The `null` values in `col` are ignored, nulltypes (MNullType) are considered.
        #
        # Returns the `null` value if:
        #
        # * `col` is empty
        # * `col` only have null values
        # * there is a conflict
        #
        # Example (with a diamond A,B,C,D):
        #
        # * merge(A,B,C) -> A, because A is the most general type in {A,B,C}
        # * merge(C,B) -> null, there is conflict, because `B or C` cannot be represented
        # * merge(A,nullable B) -> nullable A, because A is the most general type and
        #   the nullable information is preserved
        fun merge_types(node: ANode, col: Array[nullable MType]): nullable MType
        do
                if col.length == 1 then return col.first
                for t1 in col do
                        if t1 == null then continue # return null
                        var found = true
                        for t2 in col do
                                if t2 == null then continue # return null
                                if can_be_null(t2) and not can_be_null(t1) then
                                        t1 = t1.as_nullable
                                end
                                if not is_subtype(t2, t1) then found = false
                        end
                        if found then
                                #print "merge {col.join(" ")} -> {t1}"
                                return t1
                        end
                end
                #self.modelbuilder.warning(node, "Type Error: {col.length} conflicting types: <{col.join(", ")}>")
                return null
        end
end

# Mapping between parameters and arguments in a call.
#
# Parameters and arguments are not stored in the class but referenced by their position (starting from 0)
#
# The point of this class is to help engine and other things to map arguments in the AST to parameters of the model.
class SignatureMap
        # Associate a parameter to an argument
        var map = new ArrayMap[Int, Int]
end

# A specific method call site with its associated informations.
class CallSite
        super MEntity

        redef var location: Location

        # The static type of the receiver (possibly unresolved)
        var recv: MType

        # The module where the callsite is present
        var mmodule: MModule

        # The anchor to use with `recv` or `msignature`
        var anchor: nullable MClassType

        # Is the receiver self?
        # If "for_self", virtual types of the signature are kept
        # If "not_for_self", virtual type are erased
        var recv_is_self: Bool

        # The designated method
        var mproperty: MMethod

        # The statically designated method definition
        # The most specif one, it is.
        var mpropdef: MMethodDef

        # The resolved signature for the receiver
        var msignature: MSignature

        # Is a implicit cast required on erasure typing policy?
        var erasure_cast: Bool

        # The mapping used on the call to associate arguments to parameters
        # If null then no specific association is required.
        var signaturemap: nullable SignatureMap = null

        private fun check_signature(v: TypeVisitor, node: ANode, args: Array[AExpr]): Bool
        do
                var map = v.check_signature(node, args, self.mproperty, self.msignature)
                signaturemap = map
                if map == null then is_broken = true
                return map == null
        end

        # Information about the callsite to display on a node
        fun dump_info(v: ASTDump): String do
                return "{recv}.{mpropdef}{msignature}"
        end
end

redef class Variable
        # The declared type of the variable
        var declared_type: nullable MType is writable

        # Was the variable type-adapted?
        # This is used to speedup type retrieval while it remains `false`
        private var is_adapted = false
end

redef class FlowContext
        # Store changes of types because of type evolution
        private var vars = new HashMap[Variable, nullable MType]

        # Adapt the variable to a static type
        # Warning1: do not modify vars directly.
        # Warning2: sub-flow may have cached a unadapted variable
        private fun set_var(v: TypeVisitor, variable: Variable, mtype: nullable MType)
        do
                if variable.declared_type == mtype and not variable.is_adapted then return
                if vars.has_key(variable) and vars[variable] == mtype then return
                self.vars[variable] = mtype
                v.dirty = true
                variable.is_adapted = true
                #node.debug "set {variable} to {mtype or else "X"}"
        end

        # Look in the flow and previous flow and collect all first reachable type adaptation of a local variable
        private fun collect_types(variable: Variable): Array[nullable MType]
        do
                #node.debug "flow for {variable}"
                var res = new Array[nullable MType]

                var todo = [self]
                var seen = new HashSet[FlowContext]
                while not todo.is_empty do
                        var f = todo.pop
                        if f.is_unreachable then continue
                        if seen.has(f) then continue
                        seen.add f

                        if f.vars.has_key(variable) then
                                # Found something. Collect it and do not process further on this path
                                res.add f.vars[variable]
                                #f.node.debug "process {variable}: got {f.vars[variable] or else "X"}"
                        else
                                todo.add_all f.previous
                                todo.add_all f.loops
                                if f.previous.is_empty then
                                        # Root flowcontext mean a parameter or something related
                                        res.add variable.declared_type
                                        #f.node.debug "root process {variable}: got {variable.declared_type or else "X"}"
                                end
                        end
                end
                #self.node.debug "##### end flow for {variable}: {res.join(" ")}"
                return res
        end
end

redef class APropdef
        # The entry point of the whole typing analysis
        fun do_typing(modelbuilder: ModelBuilder)
        do
        end

        # The variable associated to the receiver (if any)
        var selfvariable: nullable Variable
end

redef class AMethPropdef
        redef fun do_typing(modelbuilder: ModelBuilder)
        do
                var mpropdef = self.mpropdef
                if mpropdef == null then return # skip error

                var v = new TypeVisitor(modelbuilder, mpropdef.mclassdef.mmodule, mpropdef)
                self.selfvariable = v.selfvariable

                var mmethoddef = self.mpropdef.as(not null)
                var msignature = mmethoddef.msignature
                if msignature == null then return # skip error
                for i in [0..msignature.arity[ do
                        var mtype = msignature.mparameters[i].mtype
                        if msignature.vararg_rank == i then
                                var arrayclass = v.get_mclass(self.n_signature.n_params[i], "Array")
                                if arrayclass == null then return # Skip error
                                mtype = arrayclass.get_mtype([mtype])
                        end
                        var variable = self.n_signature.n_params[i].variable
                        assert variable != null
                        variable.declared_type = mtype
                end

                var nblock = self.n_block
                if nblock == null then return

                loop
                        v.dirty = false
                        v.visit_stmt(nblock)
                        if not v.has_loop or not v.dirty then break
                end

                var post_visitor = new PostTypingVisitor(v)
                post_visitor.enter_visit(self)

                if not nblock.after_flow_context.is_unreachable and msignature.return_mtype != null then
                        # We reach the end of the function without having a return, it is bad
                        v.error(self, "Error: reached end of function; expected `return` with a value.")
                end
        end
end

private class PostTypingVisitor
        super Visitor
        var type_visitor: TypeVisitor
        redef fun visit(n) do
                n.visit_all(self)
                n.accept_post_typing(type_visitor)
                if n isa AExpr and n.mtype == null and not n.is_typed then
                        n.is_broken = true
                end
        end
end

redef class ANode
        private fun accept_post_typing(v: TypeVisitor) do end

        # An additional information message to explain the role of a child expression.
        #
        # The point of the method is to allow some kind of double dispatch so the parent
        # choose how to describe its children.
        private fun bad_expr_message(child: AExpr): nullable String do return null
end

redef class AAttrPropdef
        redef fun do_typing(modelbuilder: ModelBuilder)
        do
                if not has_value then return

                var mpropdef = self.mreadpropdef
                if mpropdef == null or mpropdef.msignature == null then return # skip error

                var v = new TypeVisitor(modelbuilder, mpropdef.mclassdef.mmodule, mpropdef)
                self.selfvariable = v.selfvariable

                var nexpr = self.n_expr
                if nexpr != null then
                        var mtype = self.mtype
                        v.visit_expr_subtype(nexpr, mtype)
                end
                var nblock = self.n_block
                if nblock != null then
                        v.visit_stmt(nblock)
                        if not nblock.after_flow_context.is_unreachable then
                                # We reach the end of the init without having a return, it is bad
                                v.error(self, "Error: reached end of block; expected `return`.")
                        end
                end
        end
end

###

redef class AExpr
        # The static type of the expression.
        # null if self is a statement or in case of error
        var mtype: nullable MType = null

        # Is the statement correctly typed?
        # Used to distinguish errors and statements when `mtype == null`
        var is_typed: Bool = false

        # If required, the following implicit cast `.as(XXX)`
        # Such a cast may by required after evaluating the expression when
        # a unsafe operation is detected (silently accepted by the Nit language).
        # The attribute is computed by `check_subtype`
        var implicit_cast_to: nullable MType = null

        # Return the variable read (if any)
        # Used to perform adaptive typing
        fun its_variable: nullable Variable do return null

        private fun accept_typing(v: TypeVisitor)
        do
                v.error(self, "no implemented accept_typing for {self.class_name}")
        end

        # Is non-null if `self` is a leaf of a comprehension array construction.
        # In this case, the enclosing literal array node is designated.
        # The result of the evaluation of `self` must be
        # stored inside the designated array (there is an implicit `push`)
        var comprehension: nullable AArrayExpr = null

        # It indicates the number of arguments collected as a vararg.
        #
        # When 0, the argument is used as is, without transformation.
        # When 1, the argument is transformed into an singleton array.
        # Above 1, the arguments and the next ones are transformed into a common array.
        #
        # This attribute is meaning less on expressions not used as attributes.
        var vararg_decl: Int = 0

        redef fun dump_info(v) do
                var res = super
                var mtype = self.mtype
                if mtype != null then
                        res += v.yellow(":{mtype}")
                end
                var ict = self.implicit_cast_to
                if ict != null then
                        res += v.yellow("(.as({ict}))")
                end
                return res
        end
end

redef class ABlockExpr
        redef fun accept_typing(v)
        do
                for e in self.n_expr do v.visit_stmt(e)
                self.is_typed = true
        end

        # The type of a blockexpr is the one of the last expression (or null if empty)
        redef fun mtype
        do
                if self.n_expr.is_empty then return null
                return self.n_expr.last.mtype
        end
end

redef class AVardeclExpr
        redef fun accept_typing(v)
        do
                var variable = self.variable
                if variable == null then return # Skip error

                var ntype = self.n_type
                var mtype: nullable MType
                if ntype == null then
                        mtype = null
                else
                        mtype = v.resolve_mtype(ntype)
                        if mtype == null then return # Skip error
                end

                var nexpr = self.n_expr
                if nexpr != null then
                        if mtype != null then
                                var etype = v.visit_expr_subtype(nexpr, mtype)
                                if etype == mtype then
                                        assert ntype != null
                                        v.modelbuilder.advice(ntype, "useless-type", "Warning: useless type definition for variable `{variable.name}`")
                                end
                        else
                                mtype = v.visit_expr(nexpr)
                                if mtype == null then return # Skip error
                        end
                end

                var decltype = mtype
                if mtype == null or mtype isa MNullType then
                        var objclass = v.get_mclass(self, "Object")
                        if objclass == null then return # skip error
                        decltype = objclass.mclass_type.as_nullable
                        if mtype == null then mtype = decltype
                end

                variable.declared_type = decltype
                v.set_variable(self, variable, mtype)

                #debug("var {variable}: {mtype}")

                self.mtype = mtype
                self.is_typed = true
        end
end

redef class AVarExpr
        redef fun its_variable do return self.variable
        redef fun accept_typing(v)
        do
                var variable = self.variable
                if variable == null then return # Skip error

                var mtype = v.get_variable(self, variable)
                if mtype != null then
                        #debug("{variable} is {mtype}")
                else
                        #debug("{variable} is untyped")
                end

                self.mtype = mtype
        end
end

redef class AVarAssignExpr
        redef fun accept_typing(v)
        do
                var variable = self.variable
                assert variable != null

                var mtype = v.visit_expr_subtype(n_value, variable.declared_type)

                v.set_variable(self, variable, mtype)

                self.is_typed = true
        end
end

redef class AReassignFormExpr
        # The method designed by the reassign operator.
        var reassign_callsite: nullable CallSite

        var read_type: nullable MType = null

        # Determine the `reassign_property`
        # `readtype` is the type of the reading of the left value.
        # `writetype` is the type of the writing of the left value.
        # (Because of `ACallReassignExpr`, both can be different.
        # Return the static type of the value to store.
        private fun resolve_reassignment(v: TypeVisitor, readtype, writetype: MType): nullable MType
        do
                var reassign_name = self.n_assign_op.operator

                self.read_type = readtype

                var callsite = v.get_method(self.n_assign_op, readtype, reassign_name, false)
                if callsite == null then return null # Skip error
                self.reassign_callsite = callsite

                var msignature = callsite.msignature
                var rettype = msignature.return_mtype
                assert msignature.arity == 1 and rettype != null

                var value_type = v.visit_expr_subtype(self.n_value, msignature.mparameters.first.mtype)
                if value_type == null then return null # Skip error

                v.check_subtype(self, rettype, writetype, false)
                return rettype
        end
end

redef class AVarReassignExpr
        redef fun accept_typing(v)
        do
                var variable = self.variable
                assert variable != null

                var readtype = v.get_variable(self, variable)
                if readtype == null then return

                read_type = readtype

                var writetype = variable.declared_type
                if writetype == null then return

                var rettype = self.resolve_reassignment(v, readtype, writetype)

                v.set_variable(self, variable, rettype)

                self.is_typed = rettype != null
        end
end


redef class AContinueExpr
        redef fun accept_typing(v)
        do
                var nexpr = self.n_expr
                if nexpr != null then
                        v.visit_expr(nexpr)
                end
                self.is_typed = true
        end
end

redef class ABreakExpr
        redef fun accept_typing(v)
        do
                var nexpr = self.n_expr
                if nexpr != null then
                        v.visit_expr(nexpr)
                end
                self.is_typed = true
        end
end

redef class AReturnExpr
        redef fun accept_typing(v)
        do
                var nexpr = self.n_expr
                var ret_type
                var mpropdef = v.mpropdef
                if mpropdef isa MMethodDef then
                        ret_type = mpropdef.msignature.return_mtype
                else if mpropdef isa MAttributeDef then
                        ret_type = mpropdef.static_mtype
                else
                        abort
                end
                if nexpr != null then
                        if ret_type != null then
                                v.visit_expr_subtype(nexpr, ret_type)
                        else
                                v.visit_expr(nexpr)
                                v.error(nexpr, "Error: `return` with value in a procedure.")
                                return
                        end
                else if ret_type != null then
                        v.error(self, "Error: `return` without value in a function.")
                        return
                end
                self.is_typed = true
        end
end

redef class AAbortExpr
        redef fun accept_typing(v)
        do
                self.is_typed = true
        end
end

redef class AIfExpr
        redef fun accept_typing(v)
        do
                v.visit_expr_bool(n_expr)

                v.visit_stmt(n_then)
                v.visit_stmt(n_else)

                self.is_typed = true

                if n_then != null and n_else == null then
                        self.mtype = n_then.mtype
                end
        end
end

redef class AIfexprExpr
        redef fun accept_typing(v)
        do
                v.visit_expr_bool(n_expr)

                var t1 = v.visit_expr(n_then)
                var t2 = v.visit_expr(n_else)

                if t1 == null or t2 == null then
                        return # Skip error
                end

                var t = v.merge_types(self, [t1, t2])
                if t == null then
                        v.error(self, "Type Error: ambiguous type `{t1}` vs `{t2}`.")
                end
                self.mtype = t
        end
end

redef class ADoExpr
        redef fun accept_typing(v)
        do
                v.visit_stmt(n_block)
                v.visit_stmt(n_catch)
                self.is_typed = true
        end
end

redef class AWhileExpr
        redef fun accept_typing(v)
        do
                v.has_loop = true
                v.visit_expr_bool(n_expr)
                v.visit_stmt(n_block)
                self.is_typed = true
        end
end

redef class ALoopExpr
        redef fun accept_typing(v)
        do
                v.has_loop = true
                v.visit_stmt(n_block)
                self.is_typed = true
        end
end

redef class AForExpr
        redef fun accept_typing(v)
        do
                v.has_loop = true

                for g in n_groups do
                        var mtype = v.visit_expr(g.n_expr)
                        if mtype == null then return
                        g.do_type_iterator(v, mtype)
                        if g.is_broken then is_broken = true
                end

                v.visit_stmt(n_block)

                self.mtype = n_block.mtype
                self.is_typed = true
        end
end

redef class AForGroup
        var coltype: nullable MClassType

        var method_iterator: nullable CallSite
        var method_is_ok: nullable CallSite
        var method_item: nullable CallSite
        var method_next: nullable CallSite
        var method_key: nullable CallSite
        var method_finish: nullable CallSite

        var method_lt: nullable CallSite
        var method_successor: nullable CallSite

        private fun do_type_iterator(v: TypeVisitor, mtype: MType)
        do
                if mtype isa MNullType then
                        v.error(self, "Type Error: `for` cannot iterate over `null`.")
                        return
                end

                # get obj class
                var objcla = v.get_mclass(self, "Object")
                if objcla == null then return

                # check iterator method
                var itdef = v.get_method(self, mtype, "iterator", n_expr isa ASelfExpr)
                if itdef == null then
                        v.error(self, "Type Error: `for` expects a type providing an `iterator` method, got `{mtype}`.")
                        return
                end
                self.method_iterator = itdef

                # check that iterator return something
                var ittype = itdef.msignature.return_mtype
                if ittype == null then
                        v.error(self, "Type Error: `for` expects the method `iterator` to return an `Iterator` or `MapIterator` type.")
                        return
                end

                # get iterator type
                var colit_cla = v.try_get_mclass(self, "Iterator")
                var mapit_cla = v.try_get_mclass(self, "MapIterator")
                var is_col = false
                var is_map = false

                if colit_cla != null and v.is_subtype(ittype, colit_cla.get_mtype([objcla.mclass_type.as_nullable])) then
                        # Iterator
                        var coltype = ittype.supertype_to(v.mmodule, v.anchor, colit_cla)
                        var variables =  self.variables
                        if variables.length != 1 then
                                v.error(self, "Type Error: `for` expects only one variable when using `Iterator`.")
                        else
                                variables.first.declared_type = coltype.arguments.first
                        end
                        is_col = true
                end

                if mapit_cla != null and v.is_subtype(ittype, mapit_cla.get_mtype([objcla.mclass_type.as_nullable, objcla.mclass_type.as_nullable])) then
                        # Map Iterator
                        var coltype = ittype.supertype_to(v.mmodule, v.anchor, mapit_cla)
                        var variables = self.variables
                        if variables.length != 2 then
                                v.error(self, "Type Error: `for` expects two variables when using `MapIterator`.")
                        else
                                variables[0].declared_type = coltype.arguments[0]
                                variables[1].declared_type = coltype.arguments[1]
                        end
                        is_map = true
                end

                if not is_col and not is_map then
                        v.error(self, "Type Error: `for` expects the method `iterator` to return an `Iterator` or `MapIterator` type.")
                        return
                end

                # anchor formal and virtual types
                if mtype.need_anchor then mtype = v.anchor_to(mtype)

                mtype = mtype.undecorate
                self.coltype = mtype.as(MClassType)

                # get methods is_ok, next, item
                var ikdef = v.get_method(self, ittype, "is_ok", false)
                if ikdef == null then
                        v.error(self, "Type Error: `for` expects a method `is_ok` in type `{ittype}`.")
                        return
                end
                self.method_is_ok = ikdef

                var itemdef = v.get_method(self, ittype, "item", false)
                if itemdef == null then
                        v.error(self, "Type Error: `for` expects a method `item` in type `{ittype}`.")
                        return
                end
                self.method_item = itemdef

                var nextdef = v.get_method(self, ittype, "next", false)
                if nextdef == null then
                        v.error(self, "Type Error: `for` expects a method `next` in type {ittype}.")
                        return
                end
                self.method_next = nextdef

                self.method_finish = v.try_get_method(self, ittype, "finish", false)

                if is_map then
                        var keydef = v.get_method(self, ittype, "key", false)
                        if keydef == null then
                                v.error(self, "Type Error: `for` expects a method `key` in type `{ittype}`.")
                                return
                        end
                        self.method_key = keydef
                end

                if self.variables.length == 1 and n_expr isa ARangeExpr then
                        var variable = variables.first
                        var vtype = variable.declared_type.as(not null)

                        if n_expr isa AOrangeExpr then
                                self.method_lt = v.get_method(self, vtype, "<", false)
                        else
                                self.method_lt = v.get_method(self, vtype, "<=", false)
                        end

                        self.method_successor = v.get_method(self, vtype, "successor", false)
                end
        end
end

redef class AWithExpr
        var method_start: nullable CallSite
        var method_finish: nullable CallSite

        redef fun accept_typing(v: TypeVisitor)
        do
                var mtype = v.visit_expr(n_expr)
                if mtype == null then return

                method_start = v.get_method(self, mtype, "start", n_expr isa ASelfExpr)
                method_finish = v.get_method(self, mtype, "finish", n_expr isa ASelfExpr)

                v.visit_stmt(n_block)
                self.mtype = n_block.mtype
                self.is_typed = true
        end
end

redef class AAssertExpr
        redef fun accept_typing(v)
        do
                v.visit_expr_bool(n_expr)

                v.visit_stmt(n_else)
                self.is_typed = true
        end
end

redef class AOrExpr
        redef fun accept_typing(v)
        do
                v.visit_expr_bool(n_expr)
                v.visit_expr_bool(n_expr2)
                self.mtype = v.type_bool(self)
        end
end

redef class AImpliesExpr
        redef fun accept_typing(v)
        do
                v.visit_expr_bool(n_expr)
                v.visit_expr_bool(n_expr2)
                self.mtype = v.type_bool(self)
        end
end

redef class AAndExpr
        redef fun accept_typing(v)
        do
                v.visit_expr_bool(n_expr)
                v.visit_expr_bool(n_expr2)
                self.mtype = v.type_bool(self)
        end
end


redef class ANotExpr
        redef fun accept_typing(v)
        do
                v.visit_expr_bool(n_expr)
                self.mtype = v.type_bool(self)
        end
end

redef class AOrElseExpr
        redef fun accept_typing(v)
        do
                var t1 = v.visit_expr(n_expr)
                var t2 = v.visit_expr(n_expr2)

                if t1 == null or t2 == null then
                        return # Skip error
                end

                if t1 isa MNullType then
                        self.mtype = t2
                        return
                else if v.can_be_null(t1) then
                        t1 = t1.as_notnull
                end

                var t = v.merge_types(self, [t1, t2])
                if t == null then
                        var c = v.get_mclass(self, "Object")
                        if c == null then return # forward error
                        t = c.mclass_type
                        if v.can_be_null(t2) then
                                t = t.as_nullable
                        end
                        #v.error(self, "Type Error: ambiguous type {t1} vs {t2}")
                end
                self.mtype = t
        end

        redef fun accept_post_typing(v)
        do
                var t1 = n_expr.mtype
                if t1 == null then
                        return
                else
                        v.check_can_be_null(n_expr, t1)
                end
        end
end

redef class ATrueExpr
        redef fun accept_typing(v)
        do
                self.mtype = v.type_bool(self)
        end
end

redef class AFalseExpr
        redef fun accept_typing(v)
        do
                self.mtype = v.type_bool(self)
        end
end

redef class AIntegerExpr
        redef fun accept_typing(v)
        do
                var mclass: nullable MClass = null
                if value isa Byte then
                        mclass = v.get_mclass(self, "Byte")
                else if value isa Int then
                        mclass = v.get_mclass(self, "Int")
                else if value isa Int8 then
                        mclass = v.get_mclass(self, "Int8")
                else if value isa Int16 then
                        mclass = v.get_mclass(self, "Int16")
                else if value isa UInt16 then
                        mclass = v.get_mclass(self, "UInt16")
                else if value isa Int32 then
                        mclass = v.get_mclass(self, "Int32")
                else if value isa UInt32 then
                        mclass = v.get_mclass(self, "UInt32")
                end
                if mclass == null then return # Forward error
                self.mtype = mclass.mclass_type
        end
end

redef class AFloatExpr
        redef fun accept_typing(v)
        do
                var mclass = v.get_mclass(self, "Float")
                if mclass == null then return # Forward error
                self.mtype = mclass.mclass_type
        end
end

redef class ACharExpr
        redef fun accept_typing(v) do
                var mclass: nullable MClass = null
                if is_ascii then
                        mclass = v.get_mclass(self, "Byte")
                else if is_code_point then
                        mclass = v.get_mclass(self, "Int")
                else
                        mclass = v.get_mclass(self, "Char")
                end
                if mclass == null then return # Forward error
                self.mtype = mclass.mclass_type
        end
end

redef class AugmentedStringFormExpr
        super AExpr

        # Text::to_re, used for prefix `re`
        var to_re: nullable CallSite = null
        # Regex::ignore_case, used for suffix `i` on `re`
        var ignore_case: nullable CallSite = null
        # Regex::newline, used for suffix `m` on `re`
        var newline: nullable CallSite = null
        # Regex::extended, used for suffix `b` on `re`
        var extended: nullable CallSite = null
        # CString::to_bytes_with_copy, used for prefix `b`
        var to_bytes_with_copy: nullable CallSite = null

        redef fun accept_typing(v) do
                var mclass = v.get_mclass(self, "String")
                if mclass == null then return # Forward error
                if is_bytestring then
                        to_bytes_with_copy = v.get_method(self, v.mmodule.c_string_type, "to_bytes_with_copy", false)
                        mclass = v.get_mclass(self, "Bytes")
                else if is_re then
                        to_re = v.get_method(self, mclass.mclass_type, "to_re", false)
                        for i in suffix.chars do
                                mclass = v.get_mclass(self, "Regex")
                                if mclass == null then
                                        v.error(self, "Error: `Regex` class unknown")
                                        return
                                end
                                var service = ""
                                if i == 'i' then
                                        service = "ignore_case="
                                        ignore_case = v.get_method(self, mclass.mclass_type, service, false)
                                else if i == 'm' then
                                        service = "newline="
                                        newline = v.get_method(self, mclass.mclass_type, service, false)
                                else if i == 'b' then
                                        service = "extended="
                                        extended = v.get_method(self, mclass.mclass_type, service, false)
                                else
                                        v.error(self, "Type Error: Unrecognized suffix {i} in prefixed Regex")
                                        abort
                                end
                        end
                end
                if mclass == null then return # Forward error
                mtype = mclass.mclass_type
        end
end

redef class ASuperstringExpr
        redef fun accept_typing(v)
        do
                super
                var objclass = v.get_mclass(self, "Object")
                if objclass == null then return # Forward error
                var objtype = objclass.mclass_type
                for nexpr in self.n_exprs do
                        v.visit_expr_subtype(nexpr, objtype)
                end
        end
end

redef class AArrayExpr
        # The `with_capacity` method on Array
        var with_capacity_callsite: nullable CallSite

        # The `push` method on arrays
        var push_callsite: nullable CallSite

        # The element of each type
        var element_mtype: nullable MType

        # Set that `self` is a part of comprehension array `na`
        # If `self` is a `for`, or a `if`, then `set_comprehension` is recursively applied.
        private fun set_comprehension(n: nullable AExpr)
        do
                if n == null then
                        return
                else if n isa AForExpr then
                        set_comprehension(n.n_block)
                else if n isa AIfExpr then
                        set_comprehension(n.n_then)
                        set_comprehension(n.n_else)
                else
                        # is a leave
                        n.comprehension = self
                end
        end
        redef fun accept_typing(v)
        do
                var mtype: nullable MType = null
                var ntype = self.n_type
                if ntype != null then
                        mtype = v.resolve_mtype(ntype)
                        if mtype == null then return # Skip error
                end
                var mtypes = new Array[nullable MType]
                var useless = false
                for e in self.n_exprs do
                        var t = v.visit_expr(e)
                        if t == null then
                                return # Skip error
                        end
                        set_comprehension(e)
                        if mtype != null then
                                if v.check_subtype(e, t, mtype, false) == null then return # Forward error
                                if t == mtype then useless = true
                        else
                                mtypes.add(t)
                        end
                end
                if mtype == null then
                        # Ensure monotony for type adaptation on loops
                        if self.element_mtype != null then mtypes.add self.element_mtype
                        mtype = v.merge_types(self, mtypes)
                end
                if mtype == null or mtype isa MNullType then
                        v.error(self, "Type Error: ambiguous array type {mtypes.join(" ")}")
                        return
                end
                if useless then
                        assert ntype != null
                        v.modelbuilder.warning(ntype, "useless-type", "Warning: useless type declaration `{mtype}` in literal Array since it can be inferred from the elements type.")
                end

                self.element_mtype = mtype

                var mclass = v.get_mclass(self, "Array")
                if mclass == null then return # Forward error
                var array_mtype = mclass.get_mtype([mtype])

                with_capacity_callsite = v.get_method(self, array_mtype, "with_capacity", false)
                push_callsite = v.get_method(self, array_mtype, "push", false)

                self.mtype = array_mtype
        end
end

redef class ARangeExpr
        var init_callsite: nullable CallSite

        redef fun accept_typing(v)
        do
                var discrete_class = v.get_mclass(self, "Discrete")
                if discrete_class == null then return # Forward error
                var discrete_type = discrete_class.intro.bound_mtype
                var t1 = v.visit_expr_subtype(self.n_expr, discrete_type)
                var t2 = v.visit_expr_subtype(self.n_expr2, discrete_type)
                if t1 == null or t2 == null then return
                var mclass = v.get_mclass(self, "Range")
                if mclass == null then return # Forward error
                var mtype
                if v.is_subtype(t1, t2) then
                        mtype = mclass.get_mtype([t2])
                else if v.is_subtype(t2, t1) then
                        mtype = mclass.get_mtype([t1])
                else
                        v.error(self, "Type Error: cannot create range: `{t1}` vs `{t2}`.")
                        return
                end

                self.mtype = mtype

                # get the constructor
                var callsite
                if self isa ACrangeExpr then
                        callsite = v.get_method(self, mtype, "init", false)
                else if self isa AOrangeExpr then
                        callsite = v.get_method(self, mtype, "without_last", false)
                else
                        abort
                end
                init_callsite = callsite
        end
end

redef class ANullExpr
        redef fun accept_typing(v)
        do
                self.mtype = v.mmodule.model.null_type
        end
end

redef class AIsaExpr
        # The static type to cast to.
        # (different from the static type of the expression that is `Bool`).
        var cast_type: nullable MType
        redef fun accept_typing(v)
        do
                v.visit_expr(n_expr)

                var mtype = v.resolve_mtype(n_type)

                self.cast_type = mtype

                var variable = self.n_expr.its_variable
                if variable != null then
                        var orig = self.n_expr.mtype
                        #var from = if orig != null then orig.to_s else "invalid"
                        #var to = if mtype != null then mtype.to_s else "invalid"
                        #debug("adapt {variable}: {from} -> {to}")

                        # Do not adapt if there is no information gain (i.e. adapt to a supertype)
                        if mtype == null or orig == null or not v.is_subtype(orig, mtype) then
                                self.after_flow_context.when_true.set_var(v, variable, mtype)
                        end
                end

                self.mtype = v.type_bool(self)
        end

        redef fun accept_post_typing(v)
        do
                v.check_expr_cast(self, self.n_expr, self.n_type)
        end

        redef fun dump_info(v) do
                var res = super
                var mtype = self.cast_type
                if mtype != null then
                        res += v.yellow(".as({mtype})")
                end
                return res
        end

end

redef class AAsCastExpr
        redef fun accept_typing(v)
        do
                v.visit_expr(n_expr)

                self.mtype = v.resolve_mtype(n_type)
        end

        redef fun accept_post_typing(v)
        do
                v.check_expr_cast(self, self.n_expr, self.n_type)
        end
end

redef class AAsNotnullExpr
        redef fun accept_typing(v)
        do
                var mtype = v.visit_expr(self.n_expr)
                if mtype == null then return # Forward error

                if mtype isa MNullType then
                        v.error(self, "Type Error: `as(not null)` on `null`.")
                        return
                end

                if v.can_be_null(mtype) then
                        mtype = mtype.as_notnull
                end

                self.mtype = mtype
        end

        redef fun accept_post_typing(v)
        do
                var mtype = n_expr.mtype
                if mtype == null then return
                v.check_can_be_null(n_expr, mtype)
        end
end

redef class AParExpr
        redef fun accept_typing(v)
        do
                self.mtype = v.visit_expr(self.n_expr)
        end
end

redef class AOnceExpr
        redef fun accept_typing(v)
        do
                self.mtype = v.visit_expr(self.n_expr)
        end
end

redef class ASelfExpr
        redef var its_variable: nullable Variable
        redef fun accept_typing(v)
        do
                if v.is_toplevel_context and not self isa AImplicitSelfExpr then
                        v.error(self, "Error: `self` cannot be used in top-level method.")
                end
                var variable = v.selfvariable
                self.its_variable = variable
                self.mtype = v.get_variable(self, variable)
        end
end

redef class AImplicitSelfExpr
        # Is the implicit receiver `sys`?
        #
        # By default, the implicit receiver is `self`.
        # But when there is not method for `self`, `sys` is used as a fall-back.
        # Is this case this flag is set to `true`.
        var is_sys = false
end

## MESSAGE SENDING AND PROPERTY

redef class ASendExpr
        # The property invoked by the send.
        var callsite: nullable CallSite

        redef fun bad_expr_message(child)
        do
                if child == self.n_expr then
                        return "to be the receiver of `{self.property_name}`"
                end
                return null
        end

        redef fun accept_typing(v)
        do
                var nrecv = self.n_expr
                var recvtype = v.visit_expr(nrecv)
                var name = self.property_name
                var node = self.property_node

                if recvtype == null then return # Forward error

                var callsite = null
                var unsafe_type = v.anchor_to(recvtype)
                var mproperty = v.try_get_mproperty_by_name2(node, unsafe_type, name)
                if mproperty == null and nrecv isa AImplicitSelfExpr then
                        # Special fall-back search in `sys` when noting found in the implicit receiver.
                        var sysclass = v.try_get_mclass(node, "Sys")
                        if sysclass != null then
                                var systype = sysclass.mclass_type
                                mproperty = v.try_get_mproperty_by_name2(node, systype, name)
                                if mproperty != null then
                                        callsite = v.get_method(node, systype, name, false)
                                        if callsite == null then return # Forward error
                                        # Update information, we are looking at `sys` now, not `self`
                                        nrecv.is_sys = true
                                        nrecv.its_variable = null
                                        nrecv.mtype = systype
                                        recvtype = systype
                                end
                        end
                end
                if callsite == null then
                        # If still nothing, just exit
                        callsite = v.get_method(node, recvtype, name, nrecv isa ASelfExpr)
                        if callsite == null then return
                end

                self.callsite = callsite
                var msignature = callsite.msignature

                var args = compute_raw_arguments

                callsite.check_signature(v, node, args)

                if callsite.mproperty.is_init then
                        var vmpropdef = v.mpropdef
                        if not (vmpropdef isa MMethodDef and vmpropdef.mproperty.is_init) then
                                v.error(node, "Error: an `init` can only be called from another `init`.")
                        end
                        if vmpropdef isa MMethodDef and vmpropdef.mproperty.is_root_init and not callsite.mproperty.is_root_init then
                                v.error(node, "Error: `{vmpropdef}` cannot call a factory `{callsite.mproperty}`.")
                        end
                end

                var ret = msignature.return_mtype
                if ret != null then
                        self.mtype = ret
                else
                        self.is_typed = true
                end
        end

        # The name of the property
        # Each subclass simply provide the correct name.
        private fun property_name: String is abstract

        # The node identifying the name (id, operator, etc) for messages.
        #
        # Is `self` by default
        private fun property_node: ANode do return self

        # An array of all arguments (excluding self)
        fun raw_arguments: Array[AExpr] do return compute_raw_arguments

        private fun compute_raw_arguments: Array[AExpr] is abstract

        redef fun dump_info(v) do
                var res = super
                var callsite = self.callsite
                if callsite != null then
                        res += v.yellow(" call="+callsite.dump_info(v))
                end
                return res
        end
end

redef class ABinopExpr
        redef fun compute_raw_arguments do return [n_expr2]
        redef fun property_name do return operator
        redef fun property_node do return n_op
end

redef class AEqFormExpr
        redef fun accept_typing(v)
        do
                super
                v.null_test(self)
        end

        redef fun accept_post_typing(v)
        do
                var mtype = n_expr.mtype
                var mtype2 = n_expr2.mtype

                if mtype == null or mtype2 == null then return

                if not mtype2 isa MNullType then return

                v.check_can_be_null(n_expr, mtype)
        end
end

redef class AUnaryopExpr
        redef fun property_name do return "unary {operator}"
        redef fun compute_raw_arguments do return new Array[AExpr]
end


redef class ACallExpr
        redef fun property_name do return n_qid.n_id.text
        redef fun property_node do return n_qid
        redef fun compute_raw_arguments do return n_args.to_a
end

redef class ACallAssignExpr
        redef fun property_name do return n_qid.n_id.text + "="
        redef fun property_node do return n_qid
        redef fun compute_raw_arguments
        do
                var res = n_args.to_a
                res.add(n_value)
                return res
        end
end

redef class ABraExpr
        redef fun property_name do return "[]"
        redef fun compute_raw_arguments do return n_args.to_a
end

redef class ABraAssignExpr
        redef fun property_name do return "[]="
        redef fun compute_raw_arguments
        do
                var res = n_args.to_a
                res.add(n_value)
                return res
        end
end

redef class ASendReassignFormExpr
        # The property invoked for the writing
        var write_callsite: nullable CallSite

        redef fun accept_typing(v)
        do
                var recvtype = v.visit_expr(self.n_expr)
                var name = self.property_name
                var node = self.property_node

                if recvtype == null then return # Forward error

                var for_self = self.n_expr isa ASelfExpr
                var callsite = v.get_method(node, recvtype, name, for_self)

                if callsite == null then return
                self.callsite = callsite

                var args = compute_raw_arguments

                callsite.check_signature(v, node, args)

                var readtype = callsite.msignature.return_mtype
                if readtype == null then
                        v.error(node, "Error: `{name}` is not a function.")
                        return
                end

                var wcallsite = v.get_method(node, recvtype, name + "=", self.n_expr isa ASelfExpr)
                if wcallsite == null then return
                self.write_callsite = wcallsite

                var wtype = self.resolve_reassignment(v, readtype, wcallsite.msignature.mparameters.last.mtype)
                if wtype == null then return

                args = args.to_a # duplicate so raw_arguments keeps only the getter args
                args.add(self.n_value)
                wcallsite.check_signature(v, node, args)

                self.is_typed = true
        end
end

redef class ACallReassignExpr
        redef fun property_name do return n_qid.n_id.text
        redef fun property_node do return n_qid.n_id
        redef fun compute_raw_arguments do return n_args.to_a
end

redef class ABraReassignExpr
        redef fun property_name do return "[]"
        redef fun compute_raw_arguments do return n_args.to_a
end

redef class AInitExpr
        redef fun property_name do return "init"
        redef fun property_node do return n_kwinit
        redef fun compute_raw_arguments do return n_args.to_a
end

redef class AExprs
        fun to_a: Array[AExpr] do return self.n_exprs.to_a
end

###

redef class ASuperExpr
        # The method to call if the super is in fact a 'super init call'
        # Note: if the super is a normal call-next-method, then this attribute is null
        var callsite: nullable CallSite

        # The method to call is the super is a standard `call-next-method` super-call
        # Note: if the super is a special super-init-call, then this attribute is null
        var mpropdef: nullable MMethodDef

        redef fun accept_typing(v)
        do
                var anchor = v.anchor
                assert anchor != null
                var recvtype = v.get_variable(self, v.selfvariable)
                assert recvtype != null
                var mproperty = v.mpropdef.mproperty
                if not mproperty isa MMethod then
                        v.error(self, "Error: `super` only usable in a `method`.")
                        return
                end
                var superprops = mproperty.lookup_super_definitions(v.mmodule, anchor)
                if superprops.length == 0 then
                        if mproperty.is_init and v.mpropdef.is_intro then
                                process_superinit(v)
                                return
                        end
                        v.error(self, "Error: no super method to call for `{mproperty}`.")
                        return
                end
                # FIXME: covariance of return type in linear extension?
                var superprop = superprops.first

                var msignature = superprop.msignature.as(not null)
                msignature = v.resolve_for(msignature, recvtype, true).as(MSignature)
                var args = self.n_args.to_a
                if args.length > 0 then
                        signaturemap = v.check_signature(self, args, mproperty, msignature)
                end
                self.mtype = msignature.return_mtype
                self.is_typed = true
                v.mpropdef.has_supercall = true
                mpropdef = v.mpropdef.as(MMethodDef)
        end

        # The mapping used on the call to associate arguments to parameters.
        # If null then no specific association is required.
        var signaturemap: nullable SignatureMap

        private fun process_superinit(v: TypeVisitor)
        do
                var anchor = v.anchor
                assert anchor != null
                var recvtype = v.get_variable(self, v.selfvariable)
                assert recvtype != null
                var mpropdef = v.mpropdef
                assert mpropdef isa MMethodDef
                var mproperty = mpropdef.mproperty
                var superprop: nullable MMethodDef = null
                for msupertype in mpropdef.mclassdef.supertypes do
                        msupertype = msupertype.anchor_to(v.mmodule, anchor)
                        var errcount = v.modelbuilder.toolcontext.error_count
                        var candidate = v.try_get_mproperty_by_name2(self, msupertype, mproperty.name).as(nullable MMethod)
                        if candidate == null then
                                if v.modelbuilder.toolcontext.error_count > errcount then return # Forward error
                                continue # Try next super-class
                        end
                        if superprop != null and candidate.is_root_init then
                                continue
                        end
                        if superprop != null and superprop.mproperty != candidate and not superprop.mproperty.is_root_init then
                                v.error(self, "Error: conflicting super constructor to call for `{mproperty}`: `{candidate.full_name}`, `{superprop.mproperty.full_name}`")
                                return
                        end
                        var candidatedefs = candidate.lookup_definitions(v.mmodule, anchor)
                        if superprop != null and superprop.mproperty == candidate then
                                if superprop == candidatedefs.first then continue
                                candidatedefs.add(superprop)
                        end
                        if candidatedefs.length > 1 then
                                v.error(self, "Error: conflicting property definitions for property `{mproperty}` in `{recvtype}`: {candidatedefs.join(", ")}")
                                return
                        end
                        superprop = candidatedefs.first
                end
                if superprop == null then
                        v.error(self, "Error: no super method to call for `{mproperty}`.")
                        return
                end

                var msignature = superprop.new_msignature or else superprop.msignature.as(not null)
                msignature = v.resolve_for(msignature, recvtype, true).as(MSignature)

                var callsite = new CallSite(hot_location, recvtype, v.mmodule, v.anchor, true, superprop.mproperty, superprop, msignature, false)
                self.callsite = callsite

                var args = self.n_args.to_a
                if args.length > 0 then
                        callsite.check_signature(v, self, args)
                else
                        # Check there is at least enough parameters
                        if mpropdef.msignature.arity < msignature.arity then
                                v.error(self, "Error: not enough implicit arguments to pass. Got `{mpropdef.msignature.arity}`, expected at least `{msignature.arity}`. Signature is `{msignature}`.")
                                return
                        end
                        # Check that each needed parameter is conform
                        var i = 0
                        for sp in msignature.mparameters do
                                var p = mpropdef.msignature.mparameters[i]
                                if not v.is_subtype(p.mtype, sp.mtype) then
                                        v.error(self, "Type Error: expected argument #{i} of type `{sp.mtype}`, got implicit argument `{p.name}` of type `{p.mtype}`. Signature is {msignature}")
                                        return
                                end
                                i += 1
                        end
                end

                self.is_typed = true
        end

        redef fun dump_info(v) do
                var res = super
                var callsite = self.callsite
                if callsite != null then
                        res += v.yellow(" super-init="+callsite.dump_info(v))
                end
                var mpropdef = self.mpropdef
                if mpropdef != null then
                        res += v.yellow(" call-next-method="+mpropdef.to_s)
                end
                return res
        end
end

####

redef class ANewExpr
        # The constructor invoked by the new.
        var callsite: nullable CallSite

        # The designated type
        var recvtype: nullable MClassType

        redef fun accept_typing(v)
        do
                var recvtype = v.resolve_mtype(self.n_type)
                if recvtype == null then return

                if not recvtype isa MClassType then
                        if recvtype isa MNullableType then
                                v.error(self, "Type Error: cannot instantiate the nullable type `{recvtype}`.")
                                return
                        else if recvtype isa MFormalType then
                                v.error(self, "Type Error: cannot instantiate the formal type `{recvtype}`.")
                                return
                        else
                                v.error(self, "Type Error: cannot instantiate the type `{recvtype}`.")
                                return
                        end
                end

                self.recvtype = recvtype
                var kind = recvtype.mclass.kind

                var name: String
                var nqid = self.n_qid
                var node: ANode
                if nqid != null then
                        name = nqid.n_id.text
                        node = nqid
                else
                        name = "new"
                        node = self.n_kwnew
                end
                if name == "intern" then
                        if kind != concrete_kind then
                                v.error(self, "Type Error: cannot instantiate {kind} {recvtype}.")
                                return
                        end
                        if n_args.n_exprs.not_empty then
                                v.error(n_args, "Type Error: the intern constructor expects no arguments.")
                                return
                        end
                        # Our job is done
                        self.mtype = recvtype
                        return
                end

                var callsite = v.get_method(node, recvtype, name, false)
                if callsite == null then return

                if not callsite.mproperty.is_new then
                        if kind != concrete_kind then
                                v.error(self, "Type Error: cannot instantiate {kind} `{recvtype}`.")
                                return
                        end
                        self.mtype = recvtype
                else
                        self.mtype = callsite.msignature.return_mtype
                        assert self.mtype != null
                end

                self.callsite = callsite

                if not callsite.mproperty.is_init_for(recvtype.mclass) then
                        v.error(self, "Error: `{name}` is not a constructor.")
                        return
                end

                var args = n_args.to_a
                callsite.check_signature(v, node, args)
        end

        redef fun dump_info(v) do
                var res = super
                var callsite = self.callsite
                if callsite != null then
                        res += v.yellow(" call="+callsite.dump_info(v))
                end
                return res
        end
end

####

redef class AAttrFormExpr
        # The attribute accessed.
        var mproperty: nullable MAttribute

        # The static type of the attribute.
        var attr_type: nullable MType

        # Resolve the attribute accessed.
        private fun resolve_property(v: TypeVisitor)
        do
                var recvtype = v.visit_expr(self.n_expr)
                if recvtype == null then return # Skip error
                var node = self.n_id
                var name = node.text
                if recvtype isa MNullType then
                        v.error(node, "Error: attribute `{name}` access on `null`.")
                        return
                end

                var unsafe_type = v.anchor_to(recvtype)
                var mproperty = v.try_get_mproperty_by_name2(node, unsafe_type, name)
                if mproperty == null then
                        v.modelbuilder.error(node, "Error: attribute `{name}` does not exist in `{recvtype}`.")
                        return
                end
                assert mproperty isa MAttribute
                self.mproperty = mproperty

                var mpropdefs = mproperty.lookup_definitions(v.mmodule, unsafe_type)
                assert mpropdefs.length == 1
                var mpropdef = mpropdefs.first
                var attr_type = mpropdef.static_mtype
                if attr_type == null then return # skip error
                attr_type = v.resolve_for(attr_type, recvtype, self.n_expr isa ASelfExpr)
                self.attr_type = attr_type
        end

        redef fun dump_info(v) do
                var res = super
                var mproperty = self.mproperty
                var attr_type = self.attr_type
                if mproperty != null then
                        res += v.yellow(" attr={mproperty}:{attr_type or else "BROKEN"}")
                end
                return res
        end
end

redef class AAttrExpr
        redef fun accept_typing(v)
        do
                self.resolve_property(v)
                self.mtype = self.attr_type
        end
end


redef class AAttrAssignExpr
        redef fun accept_typing(v)
        do
                self.resolve_property(v)
                var mtype = self.attr_type

                v.visit_expr_subtype(self.n_value, mtype)
                self.is_typed = mtype != null
        end
end

redef class AAttrReassignExpr
        redef fun accept_typing(v)
        do
                self.resolve_property(v)
                var mtype = self.attr_type
                if mtype == null then return # Skip error

                var rettype = self.resolve_reassignment(v, mtype, mtype)

                self.is_typed = rettype != null
        end
end

redef class AIssetAttrExpr
        redef fun accept_typing(v)
        do
                self.resolve_property(v)
                var mtype = self.attr_type
                if mtype == null then return # Skip error

                var recvtype = self.n_expr.mtype.as(not null)
                var bound = v.resolve_for(mtype, recvtype, false)
                if bound isa MNullableType then
                        v.error(n_id, "Type Error: `isset` on a nullable attribute.")
                end
                self.mtype = v.type_bool(self)
        end
end

redef class AVarargExpr
        redef fun accept_typing(v)
        do
                # This kind of pseudo-expression can be only processed trough a signature
                # See `check_signature`
                # Other cases are a syntax error.
                v.error(self, "Syntax Error: unexpected `...`.")
        end
end

###

redef class ADebugTypeExpr
        redef fun accept_typing(v)
        do
                var expr = v.visit_expr(self.n_expr)
                if expr == null then return
                var unsafe = v.anchor_to(expr)
                var ntype = self.n_type
                var mtype = v.resolve_mtype(ntype)
                if mtype != null and mtype != expr then
                        var umtype = v.anchor_to(mtype)
                        v.modelbuilder.warning(self, "debug", "Found type {expr} (-> {unsafe}), expected {mtype} (-> {umtype})")
                end
                self.is_typed = true
        end
end