inference: inter-procedural conditional constraint back-propagation

This PR propagates `Conditional`s inter-procedurally when a
`Conditional` at return site imposes a constraint on the call arguments.
When inference exits local frame and the return type is annotated as
`Conditional`, it will be converted into `InterConditional` object,
which is implemented in `Core` and can be directly put into the global
cache. Finally after going back to caller frame, `InterConditional` will
be re-converted into `Conditional` in the context of the caller frame.

So now some simple "is-wrapper" functions will propagate its constraint
as expected, e.g.:
```julia
isaint(a) = isa(a, Int)
@test Base.return_types((Any,)) do a
    isaint(a) && return a # a::Int
    return 0
end == [Int]

isaint2(::Any) = false
isaint2(::Int) = true
@test Base.return_types((Any,)) do a
    isaint2(a) && return a # a::Int
    return 0
end == [Int]
```

This PR also tweaks `isnothing` and `ismissing` so that there is no
longer any inferrability penalties to use them instead of
`x === nothing` or `x === missing` e.g.:
```julia
@test Base.return_types((Union{Nothing,Int},)) do a
    isnothing(a) && return 0
    return a # a::Int
end == [Int]
```
(and now we don't need something like JuliaLang#38636)

---

A compile time comparison:
> on the current master (82d79ce)
```
Sysimage built. Summary:
Total ───────  55.295376 seconds
Base: ───────  23.359226 seconds 42.2444%
Stdlibs: ────  31.934773 seconds 57.7531%
    JULIA usr/lib/julia/sys-o.a
Generating REPL precompile statements... 29/29
Executing precompile statements... 1283/1283
Precompilation complete. Summary:
Total ───────  91.129162 seconds
Generation ──  68.800937 seconds 75.4983%
Execution ───  22.328225 seconds 24.5017%
    LINK usr/lib/julia/sys.dylib
```

> on this PR (37e279b)
```
Sysimage built. Summary:
Total ───────  51.694730 seconds
Base: ───────  21.943914 seconds 42.449%
Stdlibs: ────  29.748987 seconds 57.5474%
    JULIA usr/lib/julia/sys-o.a
Generating REPL precompile statements... 29/29
Executing precompile statements... 1357/1357
Precompilation complete. Summary:
Total ───────  88.956226 seconds
Generation ──  67.077710 seconds 75.4053%
Execution ───  21.878515 seconds 24.5947%
    LINK usr/lib/julia/sys.dylib
```

Here is a sample code that benefits from this PR:
```julia
function summer(ary)
    r = 0
    for a in ary
        if ispositive(a)
            r += a
        end
    end
    r
end

ispositive(a) = isa(a, Int) && a > 0

ary = Any[]
for _ in 1:100_000
    if rand(Bool)
        push!(ary, rand(-100:100))
    elseif rand(Bool)
        push!(ary, rand('a':'z'))
    else
        push!(ary, nothing)
    end
end

using BenchmarkTools
@Btime summer($(ary))
```

> on the current master (82d79ce)
```
❯ julia summer.jl
  1.214 ms (24923 allocations: 389.42 KiB)
```

> on this PR (37e279b)
```
❯ julia summer.jl
  421.223 μs (0 allocations: 0 bytes)
```

---

Within the `Conditional`/`InterConditional` framework, only a single
constraint can be back-propagated inter-procedurally. This PR implements
a naive heuristic to "pick up" a constraint to be propagated when a
return type is a boolean. The heuristic may fail to select an
"interesting" constraint in some cases. For example, we may expect
`::Expr` constraint to be imposed on the first argument of
`Meta.isexpr`, but with the original definition of `Meta.isexpr`, the
heuristic ends up picking up a constraint on the second argument
(i.e. `ex.head === head`).
```julia
isexpr(@nospecialize(ex), head::Symbol) = isa(ex, Expr) && ex.head ===
head

x::Any
if isexpr(x, :call)
    x.args # ideally `x::Expr`
end
```

I think We can get rid of this limitation by extending `Conditional` and
`InterConditional`
so that they can convey multiple constraints, but I'd like to leave this
as a future work.

---

- closes JuliaLang#38636
- closes JuliaLang#37342

base/boot.jl

@@ -424,6 +424,7 @@ eval(Core, :(CodeInstance(mi::MethodInstance, @nospecialize(rettype), @nospecial
                     mi, rettype, inferred_const, inferred, const_flags, min_world, max_world)))
 eval(Core, :(Const(@nospecialize(v)) = $(Expr(:new, :Const, :v))))
 eval(Core, :(PartialStruct(@nospecialize(typ), fields::Array{Any, 1}) = $(Expr(:new, :PartialStruct, :typ, :fields))))
+eval(Core, :(InterConditional(slot::Int, @nospecialize(vtype), @nospecialize(elsetype)) = $(Expr(:new, :InterConditional, :slot, :vtype, :elsetype))))
 eval(Core, :(MethodMatch(@nospecialize(spec_types), sparams::SimpleVector, method::Method, fully_covers::Bool) =
     $(Expr(:new, :MethodMatch, :spec_types, :sparams, :method, :fully_covers))))
 

base/compiler/abstractinterpretation.jl

@@ -24,8 +24,8 @@ function is_improvable(@nospecialize(rtype))
         # already at Bottom
         return rtype !== Union{}
     end
-    # Could be improved to `Const` or a more precise PartialStruct
-    return isa(rtype, PartialStruct)
+    # Could be improved to `Const` or a more precise wrapper
+    return isa(rtype, PartialStruct) || isa(rtype, InterConditional)
 end
 
 function abstract_call_gf_by_type(interp::AbstractInterpreter, @nospecialize(f), argtypes::Vector{Any}, @nospecialize(atype), sv::InferenceState,
@@ -191,6 +191,8 @@ function abstract_call_gf_by_type(interp::AbstractInterpreter, @nospecialize(f),
             end
         end
     end
+
+    @assert !(rettype isa Conditional) "invalid lattice element returned from inter-procedural context"
     #print("=> ", rettype, "\n")
     return CallMeta(rettype, info)
 end
@@ -1035,9 +1037,29 @@ function abstract_call(interp::AbstractInterpreter, fargs::Union{Nothing,Vector{
             add_remark!(interp, sv, "Could not identify method table for call")
             return CallMeta(Any, false)
         end
-        return abstract_call_gf_by_type(interp, nothing, argtypes, argtypes_to_type(argtypes), sv, max_methods)
+        callinfo = abstract_call_gf_by_type(interp, nothing, argtypes, argtypes_to_type(argtypes), sv, max_methods)
+        return callinfo_from_interprocedural(callinfo, fargs)
+    end
+    callinfo = abstract_call_known(interp, f, fargs, argtypes, sv, max_methods)
+    return callinfo_from_interprocedural(callinfo, fargs)
+end
+
+function callinfo_from_interprocedural(callinfo::CallMeta, ea::Union{Nothing,Vector{Any}})
+    rt = callinfo.rt
+    if isa(rt, InterConditional)
+        if ea !== nothing
+            # convert inter-procedural conditional constraint from callee into the constraint
+            # on slots of the current frame; `InterConditional` only comes from a "valid"
+            # `abstract_call` as such its slot should always be within the bound of this
+            # call arguments `ea`
+            e = ea[rt.slot]
+            if isa(e, Slot)
+                return CallMeta(Conditional(e, rt.vtype, rt.elsetype), callinfo.info)
+            end
+        end
+        return CallMeta(widenconditional(rt), callinfo.info)
     end
-    return abstract_call_known(interp, f, fargs, argtypes, sv, max_methods)
+    return callinfo
 end
 
 function sp_type_rewrap(@nospecialize(T), linfo::MethodInstance, isreturn::Bool)
@@ -1279,6 +1301,9 @@ function typeinf_local(interp::AbstractInterpreter, frame::InferenceState)
     W = frame.ip
     s = frame.stmt_types
     n = frame.nstmts
+    nargs = frame.nargs
+    def = frame.linfo.def
+    isva = isa(def, Method) && def.isva
     while frame.pc´´ <= n
         # make progress on the active ip set
         local pc::Int = frame.pc´´ # current program-counter
@@ -1321,12 +1346,8 @@ function typeinf_local(interp::AbstractInterpreter, frame::InferenceState)
                     frame.handler_at[l] = frame.cur_hand
                     changes_else = changes
                     if isa(condt, Conditional)
-                        if condt.elsetype !== Any && condt.elsetype !== changes[slot_id(condt.var)]
-                            changes_else = StateUpdate(condt.var, VarState(condt.elsetype, false), changes_else)
-                        end
-                        if condt.vtype !== Any && condt.vtype !== changes[slot_id(condt.var)]
-                            changes = StateUpdate(condt.var, VarState(condt.vtype, false), changes)
-                        end
+                        changes_else = conditional_changes(changes_else, condt.elsetype, condt.var)
+                        changes      = conditional_changes(changes,      condt.vtype,    condt.var)
                     end
                     newstate_else = stupdate!(s[l], changes_else)
                     if newstate_else !== false
@@ -1340,15 +1361,42 @@ function typeinf_local(interp::AbstractInterpreter, frame::InferenceState)
                 end
             elseif isa(stmt, ReturnNode)
                 pc´ = n + 1
-                rt = widenconditional(abstract_eval_value(interp, stmt.val, s[pc], frame))
-                if !isa(rt, Const) && !isa(rt, Type) && !isa(rt, PartialStruct)
-                    # only propagate information we know we can store
-                    # and is valid inter-procedurally
+                bestguess = frame.bestguess
+                rt = abstract_eval_value(interp, stmt.val, s[pc], frame)
+                if isva
+                    # give up inter-procedural constraint back-propagation from vararg methods
+                    # because types of same slot may differ between callee and caller
+                    rt = widenconditional(rt)
+                else
+                    if isa(rt, Conditional) && !(1 ≤ slot_id(rt.var) ≤ nargs)
+                        # discard this `Conditional` imposed on non-call arguments,
+                        # since it's not interesting in inter-procedural context;
+                        # we may give constraints on other call argument
+                        rt = widenconditional(rt)
+                    end
+                    if !isa(rt, Conditional) && rt ⊑ Bool
+                        if isa(bestguess, InterConditional)
+                            # if the bestguess so far is already `Conditional`, try to convert
+                            # this `rt` into `Conditional` on the slot to avoid overapproximation
+                            # due to conflict of different slots
+                            rt = boolean_rt_to_conditional(rt, changes, bestguess.slot)
+                        elseif nargs ≥ 1
+                            # pick up the first "interesting" slot, convert `rt` to its `Conditional`
+                            # TODO: this is very naive heuristic, ideally we want `Conditional`
+                            # and `InterConditional` to convey constraints on multiple slots
+                            rt = boolean_rt_to_conditional(rt, changes, nargs > 1 ? 2 : 1)
+                        end
+                    end
+                end
+                # only propagate information we know we can store and is valid inter-procedurally
+                if isa(rt, Conditional)
+                    rt = InterConditional(slot_id(rt.var), rt.vtype, rt.elsetype)
+                elseif !isa(rt, Const) && !isa(rt, Type) && !isa(rt, PartialStruct)
                     rt = widenconst(rt)
                 end
-                if tchanged(rt, frame.bestguess)
+                if tchanged(rt, bestguess)
                     # new (wider) return type for frame
-                    frame.bestguess = tmerge(frame.bestguess, rt)
+                    frame.bestguess = tmerge(bestguess, rt)
                     for (caller, caller_pc) in frame.cycle_backedges
                         # notify backedges of updated type information
                         typeassert(caller.stmt_types[caller_pc], VarTable) # we must have visited this statement before
@@ -1452,6 +1500,27 @@ function typeinf_local(interp::AbstractInterpreter, frame::InferenceState)
     nothing
 end
 
+function conditional_changes(changes::VarTable, @nospecialize(typ), var::Slot)
+    if typ ⊑ (changes[slot_id(var)]::VarState).typ
+        return StateUpdate(var, VarState(typ, false), changes)
+    end
+    return changes
+end
+
+function boolean_rt_to_conditional(@nospecialize(rt), state::VarTable, slot_id::Int)
+    typ = widenconditional((state[slot_id]::VarState).typ) # avoid nested conditional
+    if isa(rt, Const)
+        if rt.val === true
+            return Conditional(SlotNumber(slot_id), typ, Bottom)
+        elseif rt.val === false
+            return Conditional(SlotNumber(slot_id), Bottom, typ)
+        end
+    elseif rt === Bool
+        return Conditional(SlotNumber(slot_id), typ, typ)
+    end
+    return rt
+end
+
 # make as much progress on `frame` as possible (by handling cycles)
 function typeinf_nocycle(interp::AbstractInterpreter, frame::InferenceState)
     typeinf_local(interp, frame)

base/compiler/typeinfer.jl

@@ -286,28 +286,32 @@ end
 function CodeInstance(result::InferenceResult, @nospecialize(inferred_result::Any),
                       valid_worlds::WorldRange)
     local const_flags::Int32
+    res = result.result
     if inferred_result isa Const
         # use constant calling convention
         rettype_const = (result.src::Const).val
         const_flags = 0x3
         inferred_result = nothing
     else
-        if isa(result.result, Const)
-            rettype_const = (result.result::Const).val
+        if isa(res, Const)
+            rettype_const = res.val
             const_flags = 0x2
-        elseif isconstType(result.result)
-            rettype_const = result.result.parameters[1]
+        elseif isconstType(res)
+            rettype_const = res.parameters[1]
             const_flags = 0x2
-        elseif isa(result.result, PartialStruct)
-            rettype_const = (result.result::PartialStruct).fields
+        elseif isa(res, PartialStruct)
+            rettype_const = res.fields
+            const_flags = 0x2
+        elseif isa(res, InterConditional)
+            rettype_const = res
             const_flags = 0x2
         else
             rettype_const = nothing
             const_flags = 0x00
         end
     end
     return CodeInstance(result.linfo,
-        widenconst(result.result), rettype_const, inferred_result,
+        widenconst(res), rettype_const, inferred_result,
         const_flags, first(valid_worlds), last(valid_worlds))
 end
 
@@ -724,14 +728,18 @@ function typeinf_edge(interp::AbstractInterpreter, method::Method, @nospecialize
     code = get(code_cache(interp), mi, nothing)
     if code isa CodeInstance # return existing rettype if the code is already inferred
         update_valid_age!(caller, WorldRange(min_world(code), max_world(code)))
+        rettype = code.rettype
         if isdefined(code, :rettype_const)
-            if isa(code.rettype_const, Vector{Any}) && !(Vector{Any} <: code.rettype)
-                return PartialStruct(code.rettype, code.rettype_const), mi
+            rettype_const = code.rettype_const
+            if isa(rettype_const, InterConditional)
+                return rettype_const, mi
+            elseif isa(rettype_const, Vector{Any}) && !(Vector{Any} <: rettype)
+                return PartialStruct(rettype, rettype_const), mi
             else
-                return Const(code.rettype_const), mi
+                return Const(rettype_const), mi
             end
         else
-            return code.rettype, mi
+            return rettype, mi
         end
     end
     if ccall(:jl_get_module_infer, Cint, (Any,), method.module) == 0

base/compiler/typelattice.jl

@@ -4,7 +4,7 @@
 # structs/constants #
 #####################
 
-# N.B.: Const/PartialStruct are defined in Core, to allow them to be used
+# N.B.: Const/PartialStruct/InterConditional are defined in Core, to allow them to be used
 # inside the global code cache.
 #
 # # The type of a value might be constant
@@ -18,7 +18,6 @@
 # end
 import Core: Const, PartialStruct
 
-
 # The type of this value might be Bool.
 # However, to enable a limited amount of back-propagagation,
 # we also keep some information about how this Bool value was created.
@@ -45,6 +44,18 @@ struct Conditional
     end
 end
 
+# # Similar to `Conditional`, but conveys inter-procedural constraints imposed on call arguments.
+# # This is separate from `Conditional` to catch logic errors: the lattice element name is InterConditional
+# # while processing a call, then Conditional everywhere else. Thus InterConditional does not appear in
+# # CompilerTypes—these type's usages are disjoint—though we define the lattice for InterConditional.
+# struct InterConditional
+#     slot::Int
+#     vtype
+#     elsetype
+# end
+import Core: InterConditional
+const AnyConditional = Union{Conditional,InterConditional}
+
 struct PartialTypeVar
     tv::TypeVar
     # N.B.: Currently unused, but would allow turning something back
@@ -90,11 +101,10 @@ const CompilerTypes = Union{MaybeUndef, Const, Conditional, NotFound, PartialStr
 # lattice logic #
 #################
 
-function issubconditional(a::Conditional, b::Conditional)
-    avar = a.var
-    bvar = b.var
-    if (isa(avar, Slot) && isa(bvar, Slot) && slot_id(avar) === slot_id(bvar)) ||
-       (isa(avar, SSAValue) && isa(bvar, SSAValue) && avar === bvar)
+# `Conditional` and `InterConditional` are valid in opposite contexts
+# (i.e. local inference and inter-procedural call), as such they will never be compared
+function issubconditional(a::C, b::C) where {C<:AnyConditional}
+    if is_same_conditionals(a, b)
         if a.vtype ⊑ b.vtype
             if a.elsetype ⊑ b.elsetype
                 return true
@@ -103,9 +113,11 @@ function issubconditional(a::Conditional, b::Conditional)
     end
     return false
 end
+is_same_conditionals(a::Conditional,      b::Conditional)      = slot_id(a.var) === slot_id(b.var)
+is_same_conditionals(a::InterConditional, b::InterConditional) = a.slot === b.slot
 
-maybe_extract_const_bool(c::Const) = isa(c.val, Bool) ? c.val : nothing
-function maybe_extract_const_bool(c::Conditional)
+maybe_extract_const_bool(c::Const) = (val = c.val; isa(val, Bool)) ? val : nothing
+function maybe_extract_const_bool(c::AnyConditional)
     (c.vtype === Bottom && !(c.elsetype === Bottom)) && return false
     (c.elsetype === Bottom && !(c.vtype === Bottom)) && return true
     nothing
@@ -124,14 +136,14 @@ function ⊑(@nospecialize(a), @nospecialize(b))
     b === Union{} && return false
     @assert !isa(a, TypeVar) "invalid lattice item"
     @assert !isa(b, TypeVar) "invalid lattice item"
-    if isa(a, Conditional)
-        if isa(b, Conditional)
+    if isa(a, AnyConditional)
+        if isa(b, AnyConditional)
             return issubconditional(a, b)
         elseif isa(b, Const) && isa(b.val, Bool)
             return maybe_extract_const_bool(a) === b.val
         end
         a = Bool
-    elseif isa(b, Conditional)
+    elseif isa(b, AnyConditional)
         return false
     end
     if isa(a, PartialStruct)
@@ -205,7 +217,7 @@ function is_lattice_equal(@nospecialize(a), @nospecialize(b))
     return a ⊑ b && b ⊑ a
 end
 
-widenconst(c::Conditional) = Bool
+widenconst(c::AnyConditional) = Bool
 function widenconst(c::Const)
     if isa(c.val, Type)
         if isvarargtype(c.val)
@@ -238,7 +250,7 @@ end
 @inline schanged(@nospecialize(n), @nospecialize(o)) = (n !== o) && (o === NOT_FOUND || (n !== NOT_FOUND && !issubstate(n, o)))
 
 widenconditional(@nospecialize typ) = typ
-function widenconditional(typ::Conditional)
+function widenconditional(typ::AnyConditional)
     if typ.vtype === Union{}
         return Const(false)
     elseif typ.elsetype === Union{}

base/compiler/typelimits.jl

@@ -314,7 +314,7 @@ function tmerge(@nospecialize(typea), @nospecialize(typeb))
         end
     end
     if isa(typea, Conditional) && isa(typeb, Conditional)
-        if typea.var === typeb.var
+        if is_same_conditionals(typea, typeb)
             vtype = tmerge(typea.vtype, typeb.vtype)
             elsetype = tmerge(typea.elsetype, typeb.elsetype)
             if vtype != elsetype
@@ -327,6 +327,36 @@ function tmerge(@nospecialize(typea), @nospecialize(typeb))
         end
         return Bool
     end
+    # type-lattice for InterConditional wrapper, InterConditional will never be merged with Conditional
+    if isa(typea, InterConditional) && isa(typeb, Const)
+        if typeb.val === true
+            typeb = InterConditional(typea.slot, Any, Union{})
+        elseif typeb.val === false
+            typeb = InterConditional(typea.slot, Union{}, Any)
+        end
+    end
+    if isa(typeb, InterConditional) && isa(typea, Const)
+        if typea.val === true
+            typea = InterConditional(typeb.slot, Any, Union{})
+        elseif typea.val === false
+            typea = InterConditional(typeb.slot, Union{}, Any)
+        end
+    end
+    if isa(typea, InterConditional) && isa(typeb, InterConditional)
+        if is_same_conditionals(typea, typeb)
+            vtype = tmerge(typea.vtype, typeb.vtype)
+            elsetype = tmerge(typea.elsetype, typeb.elsetype)
+            if vtype != elsetype
+                return InterConditional(typea.slot, vtype, elsetype)
+            end
+        end
+        val = maybe_extract_const_bool(typea)
+        if val isa Bool && val === maybe_extract_const_bool(typeb)
+            return Const(val)
+        end
+        return Bool
+    end
+    # type-lattice for Const and PartialStruct wrappers
     if (isa(typea, PartialStruct) || isa(typea, Const)) &&
        (isa(typeb, PartialStruct) || isa(typeb, Const)) &&
         widenconst(typea) === widenconst(typeb)

src/builtins.c

@@ -1608,6 +1608,7 @@ void jl_init_primitives(void) JL_GC_DISABLED
     add_builtin("Argument", (jl_value_t*)jl_argument_type);
     add_builtin("Const", (jl_value_t*)jl_const_type);
     add_builtin("PartialStruct", (jl_value_t*)jl_partial_struct_type);
+    add_builtin("InterConditional", (jl_value_t*)jl_interconditional_type);
     add_builtin("MethodMatch", (jl_value_t*)jl_method_match_type);
     add_builtin("IntrinsicFunction", (jl_value_t*)jl_intrinsic_type);
     add_builtin("Function", (jl_value_t*)jl_function_type);

src/jl_exported_data.inc

@@ -71,6 +71,7 @@
     XX(jl_nothing_type) \
     XX(jl_number_type) \
     XX(jl_partial_struct_type) \
+    XX(jl_interconditional_type) \
     XX(jl_phicnode_type) \
     XX(jl_phinode_type) \
     XX(jl_pinode_type) \

src/jltypes.c

@@ -2302,6 +2302,10 @@ void jl_init_types(void) JL_GC_DISABLED
                                        jl_perm_symsvec(2, "typ", "fields"),
                                        jl_svec2(jl_any_type, jl_array_any_type), 0, 0, 2);
 
+    jl_interconditional_type = jl_new_datatype(jl_symbol("InterConditional"), core, jl_any_type, jl_emptysvec,
+                                          jl_perm_symsvec(3, "slot", "vtype", "elsetype"),
+                                          jl_svec(3, jl_long_type, jl_any_type, jl_any_type), 0, 0, 3);
+
     jl_method_match_type = jl_new_datatype(jl_symbol("MethodMatch"), core, jl_any_type, jl_emptysvec,
                                        jl_perm_symsvec(4, "spec_types", "sparams", "method", "fully_covers"),
                                        jl_svec(4, jl_type_type, jl_simplevector_type, jl_method_type, jl_bool_type), 0, 0, 4);