Problem upgrading to 3.0 with UDA

Copy-pasting from nutbunnies comment on CASSANDRA-9756:

upgrading from 2.2 to 3.0 with a UDA defined will throw the exception below and fail to start when upgraded to 3.0.
Used:
2.2: ae9b7e05222b2a25eda5618cf9eb17103e4d6d8b
3.0: 5c2912d1ce95aacdacb59ccc840b12cd9aa0c8f8

org.apache.cassandra.exceptions.UnrecognizedEntityException: Undefined name function_name in where clause ('function_name = ?')
        at org.apache.cassandra.cql3.Relation.toColumnDefinition(Relation.java:259) ~[main/:na]
        at org.apache.cassandra.cql3.SingleColumnRelation.newEQRestriction(SingleColumnRelation.java:160) ~[main/:na]
        at org.apache.cassandra.cql3.Relation.toRestriction(Relation.java:137) ~[main/:na]
        at org.apache.cassandra.cql3.restrictions.StatementRestrictions.<init>(StatementRestrictions.java:151) ~[main/:na]
        at org.apache.cassandra.cql3.statements.SelectStatement$RawStatement.prepareRestrictions(SelectStatement.java:817) ~[main/:na]
        at org.apache.cassandra.cql3.statements.SelectStatement$RawStatement.prepare(SelectStatement.java:764) ~[main/:na]
        at org.apache.cassandra.cql3.statements.SelectStatement$RawStatement.prepare(SelectStatement.java:752) ~[main/:na]
        at org.apache.cassandra.cql3.QueryProcessor.getStatement(QueryProcessor.java:504) ~[main/:na]
        at org.apache.cassandra.cql3.QueryProcessor.parseStatement(QueryProcessor.java:241) ~[main/:na]
        at org.apache.cassandra.cql3.QueryProcessor.executeOnceInternal(QueryProcessor.java:336) ~[main/:na]
        at org.apache.cassandra.schema.LegacySchemaMigrator.query(LegacySchemaMigrator.java:882) ~[main/:na]
        at org.apache.cassandra.schema.LegacySchemaMigrator.readAggregateMetadata(LegacySchemaMigrator.java:849) ~[main/:na]
        at org.apache.cassandra.schema.LegacySchemaMigrator.readAggregate(LegacySchemaMigrator.java:830) ~[main/:na]
        at org.apache.cassandra.schema.LegacySchemaMigrator.lambda$readAggregates$216(LegacySchemaMigrator.java:823) ~[main/:na]
        at java.lang.Iterable.forEach(Iterable.java:75) ~[na:1.8.0_60]
        at org.apache.cassandra.schema.LegacySchemaMigrator.readAggregates(LegacySchemaMigrator.java:823) ~[main/:na]
        at org.apache.cassandra.schema.LegacySchemaMigrator.readKeyspace(LegacySchemaMigrator.java:166) ~[main/:na]
        at org.apache.cassandra.schema.LegacySchemaMigrator.lambda$readSchema$207(LegacySchemaMigrator.java:154) ~[main/:na]
        at java.util.ArrayList.forEach(ArrayList.java:1249) ~[na:1.8.0_60]
        at org.apache.cassandra.schema.LegacySchemaMigrator.readSchema(LegacySchemaMigrator.java:154) ~[main/:na]
        at org.apache.cassandra.schema.LegacySchemaMigrator.migrate(LegacySchemaMigrator.java:77) ~[main/:na]
        at org.apache.cassandra.service.CassandraDaemon.setup(CassandraDaemon.java:223) [main/:na]
        at org.apache.cassandra.service.CassandraDaemon.activate(CassandraDaemon.java:542) [main/:na]
        at org.apache.cassandra.service.CassandraDaemon.main(CassandraDaemon.java:668) [main/:na]

Can be reproduced with:

ccm stop
ccm remove uda_upgrade
ccm create -n 1 -v git:cassandra-2.2 uda_upgrade
ccm updateconf 'enable_user_defined_functions: true'
ccm start

cat << EOF | ccm node1 cqlsh
create keyspace ks WITH replication = {'class': 'SimpleStrategy', 'replication_factor': 1};
USE ks;
CREATE FUNCTION func_1(current int, candidate int)
            CALLED ON NULL INPUT
            RETURNS int LANGUAGE java AS
            'if (current == null) return candidate; else return Math.max(current, candidate);';
CREATE AGGREGATE agg_1(int)
            SFUNC func_1
            STYPE int
            INITCOND null;
EOF

sleep 10

echo "Draining all nodes"
ccm node1 nodetool drain
ccm stop

echo "Upgrading to git:cassandra-3.0"
ccm setdir -v git:cassandra-3.0
ccm start
echo "Sleeping for version migrations"
sleep 15
ccm checklogerror

ccm stop