#
# Define and share Functions
#

# Add attribute Address to messages based on PartitionFunction()
let AddRoutingAddress = fun (messages: stream(tuple([Id: int, Value: real]))) (messages extend[Address: PartitionFunction(.Id)]);

# Remove attribute Address from incoming messages
let RemoveRoutingAddress = fun (messages: stream(tuple([Id: int, Value: real, Address: int]))) (messages project[Id, Value]);

# Calculate the value of messages sent from a Node (Page) = ItsValue / outdeg
let CalculateBroadcastValue = fun (pages: stream(tuple([Id: int, Value: real])), linksjoining: stream(tuple([Source: int, Target: int]))) (pages linksjoining sortmergejoin[Id, Source] groupby[Id; NewValue: (group feed extract[Value]) / (group feed count) ]);

# Generate a message for each outgoing edge
let GenerateMessages = fun (pages: stream(tuple([Id: int, Value: real])), linksjoining: stream(tuple([Source: int, Target: int]))) (CalculateBroadcastValue(pages, linksjoining) linksjoining feed sortmergejoin[Id, Source] projectextend[; Id: .Target, Value: .NewValue]);

# Calculate the new Value of a Page from the incoming Messages (rel, because it's used in groupby[])
let PageRank = fun (incoming: rel (tuple([Id: int, Value: real]))) (Minimum + D * (incoming feed sum[Value]));

# Merge all messages to the same Page together
let Reduce = fun (messages: stream(tuple([Id: int, Value: real]))) (messages sortby[Id] groupby[Id; Value: PageRank(group)]);

# In a sense this merges the new values with the current relation
let UpdateRelById = fun (pages: mpointer(mem(rel(tuple([Id: int, Value: real])))), messages: stream(tuple([Id: int, Value: real]))) (pages mfeed addid project[Id, TID] messages pages mfeed projectextend[Id; Value: Minimum] concat sortby[Id] groupby[Id; Value: group feed max[Value]] rename[m] mergejoin[Id, Id_m] pages mupdatedirect2[TID; Value: .Value_m]);

# Compute function
let ComputeRouted = fun (messages: stream(tuple([Id: int, Value: real, Address: int]))) (AddRoutingAddress(GenerateMessages(UpdateRelById(Pages, Reduce(RemoveRoutingAddress(messages))), Links feed)));