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|
defmodule Module.Types.Unify do
@moduledoc false
import Module.Types.Helpers
# Those are the simple types known to the system:
#
# :dynamic
# {:var, var}
# {:atom, atom} < :atom
# :integer
# :float
# :pid
# :port
# :reference
#
# Those are the composite types:
#
# {:list, type}
# {:tuple, size, [type]} < :tuple
# {:union, [type]}
# {:map, [{:required | :optional, key_type, value_type}]}
#
# Once new types are added, they should be considered in:
#
# * unify (all)
# * format_type (all)
# * subtype? (subtypes only)
# * has_unbound_var? (composite only)
# * recursive_type? (composite only)
# * collect_vars (composite only)
#
@doc """
Unifies two types and returns the unified type and an updated typing context
or an error in case of a typing conflict.
"""
def unify(source, target, stack, context) do
case do_unify(source, target, stack, context) do
{:ok, type, context} ->
{:ok, type, context}
{:error, reason} ->
if stack.context == :pattern do
case do_unify(target, source, stack, context) do
{:ok, type, context} ->
{:ok, type, context}
{:error, _} ->
{:error, reason}
end
else
{:error, reason}
end
end
end
defp do_unify(same, same, _stack, context) do
{:ok, same, context}
end
defp do_unify(type, {:var, var}, stack, context) do
unify_var(var, type, stack, context, _var_source = false)
end
defp do_unify({:var, var}, type, stack, context) do
unify_var(var, type, stack, context, _var_source = true)
end
defp do_unify({:tuple, n, sources}, {:tuple, n, targets}, stack, context) do
result =
map_reduce_ok(Enum.zip(sources, targets), context, fn {source, target}, context ->
unify(source, target, stack, context)
end)
case result do
{:ok, types, context} -> {:ok, {:tuple, n, types}, context}
{:error, reason} -> {:error, reason}
end
end
defp do_unify({:list, source}, {:list, target}, stack, context) do
case unify(source, target, stack, context) do
{:ok, type, context} -> {:ok, {:list, type}, context}
{:error, reason} -> {:error, reason}
end
end
defp do_unify({:map, source_pairs}, {:map, target_pairs}, stack, context) do
unify_maps(source_pairs, target_pairs, stack, context)
end
defp do_unify(source, :dynamic, _stack, context) do
{:ok, source, context}
end
defp do_unify(:dynamic, target, _stack, context) do
{:ok, target, context}
end
defp do_unify({:union, types}, target, stack, context) do
unify_result =
map_reduce_ok(types, context, fn type, context ->
unify(type, target, stack, context)
end)
case unify_result do
{:ok, types, context} -> {:ok, to_union(types, context), context}
{:error, context} -> {:error, context}
end
end
defp do_unify(source, target, stack, context) do
cond do
# TODO: This condition exists to handle unions with unbound vars.
match?({:union, _}, target) and has_unbound_var?(target, context) ->
{:ok, source, context}
subtype?(source, target, context) ->
{:ok, source, context}
true ->
error(:unable_unify, {source, target, stack}, context)
end
end
defp unify_var(var, :dynamic, _stack, context, _var_source?) do
{:ok, {:var, var}, context}
end
defp unify_var(var, type, stack, context, var_source?) do
case context.types do
%{^var => :unbound} ->
context = refine_var!(var, type, stack, context)
stack = push_unify_stack(var, stack)
if recursive_type?(type, [], context) do
if var_source? do
error(:unable_unify, {{:var, var}, type, stack}, context)
else
error(:unable_unify, {type, {:var, var}, stack}, context)
end
else
{:ok, {:var, var}, context}
end
%{^var => {:var, new_var} = var_type} ->
unify_result =
if var_source? do
unify(var_type, type, stack, context)
else
unify(type, var_type, stack, context)
end
case unify_result do
{:ok, type, context} ->
{:ok, type, context}
{:error, {type, reason, %{traces: error_traces} = error_context}} ->
old_var_traces = Map.get(context.traces, new_var, [])
new_var_traces = Map.get(error_traces, new_var, [])
add_var_traces = Enum.drop(new_var_traces, -length(old_var_traces))
error_traces =
error_traces
|> Map.update(var, add_var_traces, &(add_var_traces ++ &1))
|> Map.put(new_var, old_var_traces)
{:error, {type, reason, %{error_context | traces: error_traces}}}
end
%{^var => var_type} ->
# Only add trace if the variable wasn't already "expanded"
context =
if variable_expanded?(var, stack, context) do
context
else
trace_var(var, type, stack, context)
end
stack = push_unify_stack(var, stack)
unify_result =
if var_source? do
unify(var_type, type, stack, context)
else
unify(type, var_type, stack, context)
end
case unify_result do
{:ok, var_type, context} ->
context = refine_var!(var, var_type, stack, context)
{:ok, {:var, var}, context}
{:error, reason} ->
{:error, reason}
end
end
end
# * All required keys on each side need to match to the other side.
# * All optional keys on each side that do not match must be discarded.
defp unify_maps(source_pairs, target_pairs, stack, context) do
{source_required, source_optional} = split_pairs(source_pairs)
{target_required, target_optional} = split_pairs(target_pairs)
with {:ok, source_required_pairs, context} <-
unify_source_required(source_required, target_pairs, stack, context),
{:ok, target_required_pairs, context} <-
unify_target_required(target_required, source_pairs, stack, context),
{:ok, source_optional_pairs, context} <-
unify_source_optional(source_optional, target_optional, stack, context),
{:ok, target_optional_pairs, context} <-
unify_target_optional(target_optional, source_optional, stack, context) do
# Remove duplicate pairs from matching in both left and right directions
pairs =
Enum.uniq(
source_required_pairs ++
target_required_pairs ++
source_optional_pairs ++
target_optional_pairs
)
{:ok, {:map, pairs}, context}
else
{:error, :unify} ->
error(:unable_unify, {{:map, source_pairs}, {:map, target_pairs}, stack}, context)
{:error, context} ->
{:error, context}
end
end
defp unify_source_required(source_required, target_pairs, stack, context) do
map_reduce_ok(source_required, context, fn {source_key, source_value}, context ->
Enum.find_value(target_pairs, fn {target_kind, target_key, target_value} ->
with {:ok, key, context} <- unify(source_key, target_key, stack, context) do
case unify(source_value, target_value, stack, context) do
{:ok, value, context} ->
{:ok, {:required, key, value}, context}
{:error, _reason} ->
source_map = {:map, [{:required, source_key, source_value}]}
target_map = {:map, [{target_kind, target_key, target_value}]}
error(:unable_unify, {source_map, target_map, stack}, context)
end
else
{:error, _reason} -> nil
end
end) || {:error, :unify}
end)
end
defp unify_target_required(target_required, source_pairs, stack, context) do
map_reduce_ok(target_required, context, fn {target_key, target_value}, context ->
Enum.find_value(source_pairs, fn {source_kind, source_key, source_value} ->
with {:ok, key, context} <- unify(source_key, target_key, stack, context) do
case unify(source_value, target_value, stack, context) do
{:ok, value, context} ->
{:ok, {:required, key, value}, context}
{:error, _reason} ->
source_map = {:map, [{source_kind, source_key, source_value}]}
target_map = {:map, [{:required, target_key, target_value}]}
error(:unable_unify, {source_map, target_map, stack}, context)
end
else
{:error, _reason} -> nil
end
end) || {:error, :unify}
end)
end
defp unify_source_optional(source_optional, target_optional, stack, context) do
flat_map_reduce_ok(source_optional, context, fn {source_key, source_value}, context ->
Enum.find_value(target_optional, fn {target_key, target_value} ->
with {:ok, key, context} <- unify(source_key, target_key, stack, context) do
case unify(source_value, target_value, stack, context) do
{:ok, value, context} ->
{:ok, [{:optional, key, value}], context}
{:error, _reason} ->
source_map = {:map, [{:optional, source_key, source_value}]}
target_map = {:map, [{:optional, target_key, target_value}]}
error(:unable_unify, {source_map, target_map, stack}, context)
end
else
_ -> nil
end
end) || {:ok, [], context}
end)
end
defp unify_target_optional(target_optional, source_optional, stack, context) do
flat_map_reduce_ok(target_optional, context, fn {target_key, target_value}, context ->
Enum.find_value(source_optional, fn {source_key, source_value} ->
with {:ok, key, context} <- unify(source_key, target_key, stack, context) do
case unify(source_value, target_value, stack, context) do
{:ok, value, context} ->
{:ok, [{:optional, key, value}], context}
{:error, _reason} ->
source_map = {:map, [{:optional, source_key, source_value}]}
target_map = {:map, [{:optional, target_key, target_value}]}
error(:unable_unify, {source_map, target_map, stack}, context)
end
else
_ -> nil
end
end) || {:ok, [], context}
end)
end
defp split_pairs(pairs) do
{required, optional} =
Enum.split_with(pairs, fn {kind, _key, _value} -> kind == :required end)
required = Enum.map(required, fn {_kind, key, value} -> {key, value} end)
optional = Enum.map(optional, fn {_kind, key, value} -> {key, value} end)
{required, optional}
end
defp error(type, reason, context), do: {:error, {type, reason, context}}
@doc """
Push expression to stack.
The expression stack is used to give the context where a type variable
was refined when show a type conflict error.
"""
def push_expr_stack(expr, stack) do
%{stack | last_expr: expr}
end
@doc """
Gets a variable.
"""
def get_var!(var, context) do
Map.fetch!(context.vars, var_name(var))
end
@doc """
Adds a variable to the typing context and returns its type variable.
If the variable has already been added, return the existing type variable.
"""
def new_var(var, context) do
var_name = var_name(var)
case context.vars do
%{^var_name => type} ->
{type, context}
%{} ->
type = {:var, context.counter}
vars = Map.put(context.vars, var_name, type)
types_to_vars = Map.put(context.types_to_vars, context.counter, var)
types = Map.put(context.types, context.counter, :unbound)
traces = Map.put(context.traces, context.counter, [])
context = %{
context
| vars: vars,
types_to_vars: types_to_vars,
types: types,
traces: traces,
counter: context.counter + 1
}
{type, context}
end
end
@doc """
Adds an internal variable to the typing context and returns its type variable.
An internal variable is used to help unify complex expressions,
it does not belong to a specific AST expression.
"""
def add_var(context) do
type = {:var, context.counter}
types = Map.put(context.types, context.counter, :unbound)
traces = Map.put(context.traces, context.counter, [])
context = %{
context
| types: types,
traces: traces,
counter: context.counter + 1
}
{type, context}
end
@doc """
Resolves a variable raising if it is unbound.
"""
def resolve_var({:var, var}, context) do
case context.types do
%{^var => :unbound} -> raise "cannot resolve unbound var"
%{^var => type} -> resolve_var(type, context)
end
end
def resolve_var(other, _context), do: other
# Check unify stack to see if variable was already expanded
defp variable_expanded?(var, stack, context) do
Enum.any?(stack.unify_stack, &variable_same?(var, &1, context))
end
defp variable_same?(left, right, context) do
case context.types do
%{^left => {:var, new_left}} ->
variable_same?(new_left, right, context)
%{^right => {:var, new_right}} ->
variable_same?(left, new_right, context)
%{} ->
false
end
end
defp push_unify_stack(var, stack) do
%{stack | unify_stack: [var | stack.unify_stack]}
end
@doc """
Restores the variable information from the old context into new context.
"""
def restore_var!(var, new_context, old_context) do
%{^var => type} = old_context.types
%{^var => trace} = old_context.traces
types = Map.put(new_context.types, var, type)
traces = Map.put(new_context.traces, var, trace)
%{new_context | types: types, traces: traces}
end
@doc """
Set the type for a variable and add trace.
"""
def refine_var!(var, type, stack, context) do
types = Map.put(context.types, var, type)
context = %{context | types: types}
trace_var(var, type, stack, context)
end
@doc """
Remove type variable and all its traces.
"""
def remove_var(var, context) do
types = Map.delete(context.types, var)
traces = Map.delete(context.traces, var)
%{context | types: types, traces: traces}
end
defp trace_var(var, type, %{trace: true, last_expr: last_expr} = _stack, context) do
line = get_meta(last_expr)[:line]
trace = {type, last_expr, {context.file, line}}
traces = Map.update!(context.traces, var, &[trace | &1])
%{context | traces: traces}
end
defp trace_var(_var, _type, %{trace: false} = _stack, context) do
context
end
# Check if a variable is recursive and incompatible with itself
# Bad: `{var} = var`
# Good: `x = y; y = z; z = x`
defp recursive_type?({:var, var} = parent, parents, context) do
case context.types do
%{^var => :unbound} ->
false
%{^var => type} ->
if type in parents do
not Enum.all?(parents, &match?({:var, _}, &1))
else
recursive_type?(type, [parent | parents], context)
end
end
end
defp recursive_type?({:list, type} = parent, parents, context) do
recursive_type?(type, [parent | parents], context)
end
defp recursive_type?({:union, types} = parent, parents, context) do
Enum.any?(types, &recursive_type?(&1, [parent | parents], context))
end
defp recursive_type?({:tuple, _, types} = parent, parents, context) do
Enum.any?(types, &recursive_type?(&1, [parent | parents], context))
end
defp recursive_type?({:map, pairs} = parent, parents, context) do
Enum.any?(pairs, fn {_kind, key, value} ->
recursive_type?(key, [parent | parents], context) or
recursive_type?(value, [parent | parents], context)
end)
end
defp recursive_type?(_other, _parents, _context) do
false
end
@doc """
Collects all type vars recursively.
"""
def collect_var_indexes(type, context, acc \\ %{})
def collect_var_indexes({:var, var}, context, acc) do
case acc do
%{^var => _} ->
acc
%{} ->
case context.types do
%{^var => :unbound} -> Map.put(acc, var, true)
%{^var => type} -> collect_var_indexes(type, context, Map.put(acc, var, true))
end
end
end
def collect_var_indexes({:tuple, _, args}, context, acc),
do: Enum.reduce(args, acc, &collect_var_indexes(&1, context, &2))
def collect_var_indexes({:union, args}, context, acc),
do: Enum.reduce(args, acc, &collect_var_indexes(&1, context, &2))
def collect_var_indexes({:list, arg}, context, acc),
do: collect_var_indexes(arg, context, acc)
def collect_var_indexes({:map, pairs}, context, acc) do
Enum.reduce(pairs, acc, fn {_, key, value}, acc ->
collect_var_indexes(value, context, collect_var_indexes(key, context, acc))
end)
end
def collect_var_indexes(_type, _context, acc), do: acc
@doc """
Checks if the type has a type var.
"""
def has_unbound_var?({:var, var}, context) do
case context.types do
%{^var => :unbound} -> true
%{^var => type} -> has_unbound_var?(type, context)
end
end
def has_unbound_var?({:tuple, _, args}, context),
do: Enum.any?(args, &has_unbound_var?(&1, context))
def has_unbound_var?({:union, args}, context),
do: Enum.any?(args, &has_unbound_var?(&1, context))
def has_unbound_var?({:list, arg}, context),
do: has_unbound_var?(arg, context)
def has_unbound_var?({:map, pairs}, context) do
Enum.any?(pairs, fn {_, key, value} ->
has_unbound_var?(key, context) or has_unbound_var?(value, context)
end)
end
def has_unbound_var?(_type, _context), do: false
@doc """
Returns true if it is a singleton type.
Only atoms are singleton types. Unbound vars are not
considered singleton types.
"""
def singleton?({:var, var}, context) do
case context.types do
%{^var => :unbound} -> false
%{^var => type} -> singleton?(type, context)
end
end
def singleton?({:atom, _}, _context), do: true
def singleton?(_type, _context), do: false
@doc """
Checks if the first argument is a subtype of the second argument.
This function assumes that:
* unbound variables are not subtype of anything
* dynamic is not considered a subtype of all other types but the top type.
This allows this function can be used for ordering, in other cases, you
may need to check for both sides
"""
def subtype?(type, type, _context), do: true
def subtype?({:var, var}, other, context) do
case context.types do
%{^var => :unbound} -> false
%{^var => type} -> subtype?(type, other, context)
end
end
def subtype?(other, {:var, var}, context) do
case context.types do
%{^var => :unbound} -> false
%{^var => type} -> subtype?(other, type, context)
end
end
def subtype?(_, :dynamic, _context), do: true
def subtype?({:atom, atom}, :atom, _context) when is_atom(atom), do: true
# Composite
def subtype?({:tuple, _, _}, :tuple, _context), do: true
def subtype?({:tuple, n, left_types}, {:tuple, n, right_types}, context) do
left_types
|> Enum.zip(right_types)
|> Enum.any?(fn {left, right} -> subtype?(left, right, context) end)
end
def subtype?({:map, left_pairs}, {:map, right_pairs}, context) do
Enum.all?(left_pairs, fn
{:required, left_key, left_value} ->
Enum.any?(right_pairs, fn {_, right_key, right_value} ->
subtype?(left_key, right_key, context) and subtype?(left_value, right_value, context)
end)
{:optional, _, _} ->
true
end)
end
def subtype?({:list, left}, {:list, right}, context) do
subtype?(left, right, context)
end
def subtype?({:union, left_types}, {:union, _} = right_union, context) do
Enum.all?(left_types, &subtype?(&1, right_union, context))
end
def subtype?(left, {:union, right_types}, context) do
Enum.any?(right_types, &subtype?(left, &1, context))
end
def subtype?({:union, left_types}, right, context) do
Enum.all?(left_types, &subtype?(&1, right, context))
end
def subtype?(_left, _right, _context), do: false
@doc """
Returns a "simplified" union using `subtype?/3` to remove redundant types.
Due to limitations in `subtype?/3` some overlapping types may still be
included. For example unions with overlapping non-concrete types such as
`{boolean()} | {atom()}` will not be merged or types with variables that
are distinct but equivalent such as `a | b when a ~ b`.
"""
def to_union([type], _context), do: type
def to_union(types, context) when types != [] do
flat_types = flatten_union(types)
case unique_super_types(flat_types, context) do
[type] -> type
types -> {:union, types}
end
end
defp flatten_union(types) do
Enum.flat_map(types, fn
{:union, types} -> flatten_union(types)
type -> [type]
end)
end
# Filter subtypes
#
# `boolean() | atom()` => `atom()`
# `:foo | atom()` => `atom()`
#
# Does not merge `true | false` => `boolean()`
defp unique_super_types([type | types], context) do
types = Enum.reject(types, &subtype?(&1, type, context))
if Enum.any?(types, &subtype?(type, &1, context)) do
unique_super_types(types, context)
else
[type | unique_super_types(types, context)]
end
end
defp unique_super_types([], _context) do
[]
end
@doc """
Formats types.
The second argument says when complex types such as maps and
structs should be simplified and not shown.
"""
def format_type({:map, pairs}, true) do
case List.keyfind(pairs, {:atom, :__struct__}, 1) do
{:required, {:atom, :__struct__}, {:atom, struct}} ->
"%#{inspect(struct)}{}"
_ ->
"map()"
end
end
def format_type({:union, types}, simplify?) do
"#{Enum.map_join(types, " | ", &format_type(&1, simplify?))}"
end
def format_type({:tuple, _, types}, simplify?) do
"{#{Enum.map_join(types, ", ", &format_type(&1, simplify?))}}"
end
def format_type({:list, type}, simplify?) do
"[#{format_type(type, simplify?)}]"
end
def format_type({:map, pairs}, false) do
case List.keytake(pairs, {:atom, :__struct__}, 1) do
{{:required, {:atom, :__struct__}, {:atom, struct}}, pairs} ->
"%#{inspect(struct)}{#{format_map_pairs(pairs)}}"
_ ->
"%{#{format_map_pairs(pairs)}}"
end
end
def format_type({:atom, literal}, _simplify?) do
inspect(literal)
end
def format_type({:var, index}, _simplify?) do
"var#{index}"
end
def format_type(atom, _simplify?) when is_atom(atom) do
"#{atom}()"
end
defp format_map_pairs(pairs) do
{atoms, others} = Enum.split_with(pairs, &match?({:required, {:atom, _}, _}, &1))
{required, optional} = Enum.split_with(others, &match?({:required, _, _}, &1))
Enum.map_join(atoms ++ required ++ optional, ", ", fn
{:required, {:atom, atom}, right} ->
"#{atom}: #{format_type(right, false)}"
{:required, left, right} ->
"#{format_type(left, false)} => #{format_type(right, false)}"
{:optional, left, right} ->
"optional(#{format_type(left, false)}) => #{format_type(right, false)}"
end)
end
end
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