Module: Jade::Frontend::TypeChecking::Unification

Extended by:
Unification
Included in:
Unification
Defined in:
lib/jade/frontend/type_checking/unification.rb

Defined Under Namespace

Classes: Context, UnificationError

Instance Method Summary collapse

Instance Method Details

#unify(type1, type2, env, ctx = Context.empty) ⇒ Object 



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# File 'lib/jade/frontend/type_checking/unification.rb', line 18

def unify(type1, type2, env, ctx = Context.empty)
  return Ok[Substitution::EMPTY] if never?(type1) || never?(type2)

  case [type1, type2]
  in [Type::Application, Type::Application]
    case [type1.constructor, type2.constructor]
    in [Type::Var, _] if type1.args.length < type2.args.length
      unify_partial(type1, type2, env, ctx)
        .map_error { UnificationError.new(type1, type2) }

    in [_, Type::Var] if type2.args.length < type1.args.length
      unify_partial(type2, type1, env, ctx)
        .map_error { UnificationError.new(type1, type2) }

    else
      unify(type1.constructor, type2.constructor, env, ctx)
        .map_error { UnificationError.new(type1, type2) }
        .and_then do |cons|
          unify_many(type1.args.map { cons.apply(it) }, type2.args.map { cons.apply(it) }, env, ctx)
            .map_both { cons.compose(it) }
            .map_error do |final_sub|
              UnificationError.new(
                final_sub.apply(type1),
                final_sub.apply(type2),
              )
            end
        end
    end

  in [Type::Var, _]
    return Ok[Substitution::EMPTY] if type1 == type2

    if ctx.rigid?(type1)
      if type2.is_a?(Type::Var) && !ctx.rigid?(type2)
        return Err[UnificationError.new(type2, type1)] if occurs_in?(type2, type1)

        return Ok[Substitution::EMPTY.bind(type2.id, type1)]
      end

      return Err[UnificationError.new(type1, type2)]
    end

    return Err[UnificationError.new(type1, type2)] if occurs_in?(type1, type2)

    Ok[Substitution::EMPTY.bind(type1.id, type2)]

  in [_, Type::Var]
    unify(type2, type1, env, ctx)
      .map_error(&:flip)

  in [Type::Function, Type::Function]
    unless type1.args.size == type2.args.size
      return Err[UnificationError.new(type1, type2)]
    end

    unify_many(type1.args, type2.args, env, ctx)
      .then do |args_r|
        args_sub = substitution_of(args_r)
        unify(args_sub.apply(type1.return_type), args_sub.apply(type2.return_type), env, ctx)
          .on_err { args_r.and_then { Err[it] } }
          .and_then { |sub| args_r.map_both { it.compose(sub) } }
      end
      .map_error do |final_sub|
        UnificationError.new(
          final_sub.apply(type1),
          final_sub.apply(type2),
          final_sub,
        )
      end

  in [Type::Constructor, Type::Constructor]
    type1 == type2 ?
      Ok[Substitution::EMPTY] :
      Err[UnificationError.new(type1, type2)]

  in [Type::AnonymousRecord, Type::AnonymousRecord]
    f1 = type1.field_names
    f2 = type2.field_names

    if type1.closed? && (f2 - f1).any?
      return Err[UnificationError.new(type1, type2)]
    end

    if type2.closed? && (f1 - f2).any?
      return Err[UnificationError.new(type1, type2)]
    end

    unify_shared_fields(type1, type2, env, ctx)
      .map_error do |final_sub|
        UnificationError.new(
          final_sub.apply(type1),
          final_sub.apply(type2),
        )
      end
      .and_then do |fields_r|
        if type1.open? && type2.open?
          fresh_type = env.fresh

          Type
            .anonymous_record(type1.fields.merge(type2.fields), env.fresh)
            .then { Substitution::EMPTY.bind(fresh_type.id, it)}
            .bind(type1.row_var.id, fresh_type)
            .bind(type2.row_var.id, fresh_type)
            .compose(fields_r)
            .then { Ok[it] }

        elsif type1.open?
          unify(type1.row_var, type2, env, ctx)
            .map { fields_r.compose(it) }

        elsif type2.open?
          unify(type2.row_var, type1, env, ctx)
            .map { fields_r.compose(it) }

        else
          Ok[fields_r]
        end
      end

  in [Type::AnonymousRecord, Type::Application]
    # Only OPEN anon records (record-access queries like `{a | x: T}`)
    # can match a nominal struct. Closed records are distinct types.
    return Err[UnificationError.new(type1, type2)] if type1.closed?

    expanded = env.lookup_def(type2.constructor.name)

    return Err[UnificationError.new(type1, type2)] unless expanded.is_a?(StructDef)

    expanded
      .type_params.map(&:id).zip(type2.args).to_h
      .reduce(Substitution::EMPTY) do |acc, (k, v)|
        acc.bind(k, v)
      end
      .apply(expanded.body)
      .then { unify(type1, it, env, ctx) }
      .and_then do |body_r|
        unify(type1.row_var, type2, env, ctx).map { body_r.compose(it) }
      end
      .on_err { Err[UnificationError.new(type1, type2)] }


  in [Type::Application, Type::AnonymousRecord]
    unify(type2, type1, env, ctx)
      .map_error(&:flip)

  else
    Err[UnificationError.new(type1, type2)]
  end
end