Multicast using Isabelle - isabelle

I'm trying to send messages to an agent list. To do so, I wrote this function:
fun multicast :: "[msg, agent, agent list]=> event set"
where
multicast_Nil: " multicast M A [] ={}"
| multicast_Cons: " multicast M A (x#xs) = {Says x A M} Un multicast M A xs"
fun knows :: "[agent, event list] => msg set" where
knows_Nil: "knows A [] = initState A"
| knows_Cons: "knows A (ev # evs) =
(case ev of Says A' B X =>
if A'=A then insert X (knows A evs) else knows A evs)
The problem is that I wasn't able to define the corresponding code in the knows function in order to add the sent message to the knowledge of all the agents in the agent list.

Related

Escaped Skolem with hoistCofree in Purescript

I'm playing in Purescript with a representation of Graphs that uses Cofree and the Algebraic Graph approach from https://hackage.haskell.org/package/algebraic-graphs (coming from https://hackage.haskell.org/package/apart-0.1.3/docs/Data-Apart-Structures-Graph.html)
type Graph = Cofree Edges
data Edges a = Empty | Connect a | Overlay a
connect :: forall a. Graph a -> Graph a
connect g = hoistCofree step g
where
step (Empty) = Empty
step (Connect ys) = Connect ys
step (Overlay ys) = Connect ys
Unfortunately, using hoistCofree for instance above to fully connect an existing graph, leads to an EscapedSkolem error.
However, using a simpler typed hoistCofree (borrowed from https://github.com/coot/purescript-redox/blob/v7.0.1/src/Redox/Utils.purs#L27-L32):
hoistCofree'
:: forall f state
. (Functor f)
=> (f (Cofree f state) -> f (Cofree f state))
-> Cofree f state
-> Cofree f state
hoistCofree' nat cf = head cf :< nat (hoistCofree' nat <$> tail cf)
Just works.
Is there a way I can make the code work with hoistCofree instead?

How to use logShow inside the handleAction function in Halogen 5

As the title says, I am trying to use logShow inside of my handleAction function.
I imported the Effect.Console (logShow)
and tried to use it like this, everytime a button is clicked:
handleAction ∷ forall o m. Action → H.HalogenM State Action () o m Unit
handleAction = case _ of
Update -> do
logShow "Hello"
H.modify_ \st -> st { field3 = st.field3 + 1 }
But I only get the following Error, and I don't understand very much, as I am very new to purescript and functional programming at all.
Could not match type
Effect
with type
HalogenM
{ field1 :: Int
, field2 :: Int
, field3 :: Int
}
Action
()
o0
m1
while trying to match type Effect t2
with type HalogenM
{ field1 :: Int
, field2 :: Int
, field3 :: Int
}
Action
()
o0
m1
Unit
while checking that expression (discard (logShow "Hello")) (\$__unused -> modify_ (\st -> ... ))
has type HalogenM
{ field1 :: Int
, field2 :: Int
, field3 :: Int
}
Action
()
o0
m1
Unit
in value declaration handleAction
where m1 is a rigid type variable
bound at (line 77, column 16 - line 80, column 51)
o0 is a rigid type variable
bound at (line 77, column 16 - line 80, column 51)
t2 is an unknown type
PureScript(TypesDoNotUnify)
I am glad about any clue.
I'm not an expert in PS but I'll try my best to answer it. So please correct me if I'm wrong:
logShow type signature is MonadEffect m => Show a => a -> m Unit, means that the caller of this function should have an instance of or be constrained by MonadEffect.
In your case, handleAction has a type signature of forall o m. Action → H.HalogenM State Action () o m Unit and you call logShow inside it. Your m here doesn't describe any particular monad while as we knew already, the caller of logShow should be constrained by MonadEffect.
There are a couple of ways to solve this:
You can add MonadEffect constraint to your handleAction type signature like so
forall o m. (MonadEffect m) => Action → H.HalogenM State Action () o m Unit
This should work since HalogenM has instance of MonadEffect as long as your m also has MonadEffect instance. See here
Change your m to Aff as Aff has instance of MonadEffect. IIRC, Halogen requires your m to be or has an instance of Aff
Or you could use your own monad stack that has an instance of Aff as you can see in Thomas' great repository here
EDIT: The explanation above assumes you import logShow from Effect.Class.Console
But if you're using logShow from Effect.Console which has type signature Show a => a -> Effect Unit, then we need some function that converts the Effect monad to your m (this function should have type sig Effect a -> m a). And liftEffect is exactly what you're looking for.
handleAction :: forall o m. (MonadEffect m) => Action → H.HalogenM State Action () o m Unit
handleAction _ = do
liftEffect $ logShow "something"
...
Hope this helps :)

Function cannot use type inference, but I don't understand why

So here is my goofy sandbox to play with Applicatives in PureScript
module Main where
import Debug.Trace
data Foo a
= Foo a
instance showFoo :: (Show a) => Show (Foo a) where
show (Foo a) = "I pity da (Foo " ++ (show a) ++ ")"
instance functorFoo :: Functor Foo where
(<$>) f (Foo a) = Foo (f a)
instance applyFoo :: Apply Foo where
(<*>) (Foo a) (Foo b) = Foo (a b)
m :: Number -> Number -> Number -> Number
m x y z = x * y - z
main = trace <<< show $ m <$> Foo 14
<*> Foo 2
<*> Foo 5
The above works fine, but if I remove:
m :: Number -> Number -> Number -> Number
it does not compile
Error at pure.purs line 18, column 1:
Error in declaration m
No instance found for Prelude.Num u1150
However (+) and (-) are both of type
forall a. (Prelude.Num a) => a -> a -> a
Why can't Number be inferred?
The reality is that when learning PureScript and coming from a dynamic language (JavaScript), I run into type errors frequently. Developing skills in diagnosing and understanding these errors is challenging without a grasp of when inference can occur and when it can't. Otherwise I will have to write types every single time in order to feel confident in my code (lameness).
This is because at the moment the compiler can't infer typeclass constraints, and as you noted the arithmetic operators are all defined in the Num typeclass.
The type that would be inferred for m (if the compiler could) would be something like:
m :: forall a. (Num a) => a -> a -> a -> a
On your second point typing top level declarations is considered good style anyway, as it helps to document your code: see here for a fuller explanation.

Graph with sets as vertices

I have a tiny grammar represented as a variant type term with strings that are tokens/part of tokens (type term).
Given expressions from the grammar, I am collecting all strings from expressions and pack them into sets (function vars). Finally, I want to create some graph with these sets as vertices (lines 48-49).
For some reason, the graph created in the such sophisticated way does not recognise sets containing same variables and creates multiple vertices with the same content. I don't really understand why this is happening.
Here is minimal working example with this behaviour:
(* demo.ml *)
type term =
| Var of string
| List of term list * string option
| Tuple of term list
module SSet = Set.Make(
struct
let compare = String.compare
type t = string
end)
let rec vars = function
| Var v -> SSet.singleton v
| List (x, tail) ->
let tl = match tail with
| None -> SSet.empty
| Some var -> SSet.singleton var in
SSet.union tl (List.fold_left SSet.union SSet.empty (List.map vars x))
| Tuple x -> List.fold_left SSet.union SSet.empty (List.map vars x)
module Node = struct
type t = SSet.t
let compare = SSet.compare
let equal = SSet.equal
let hash = Hashtbl.hash
end
module G = Graph.Imperative.Digraph.ConcreteBidirectional(Node)
(* dot output for the graph for illustration purposes *)
module Dot = Graph.Graphviz.Dot(struct
include G
let edge_attributes _ = []
let default_edge_attributes _ = []
let get_subgraph _ = None
let vertex_attributes _ = []
let vertex_name v = Printf.sprintf "{%s}" (String.concat ", " (SSet.elements v))
let default_vertex_attributes _ = []
let graph_attributes _ = []
end)
let _ =
(* creation of two terms *)
let a, b = List ([Var "a"], Some "b"), Tuple [Var "a"; Var "b"] in
(* get strings from terms packed into sets *)
let avars, bvars = vars a, vars b in
let g = G.create () in
G.add_edge g avars bvars;
Printf.printf "The content is the same: [%s] [%s]\n"
(String.concat ", " (SSet.elements avars))
(String.concat ", " (SSet.elements bvars));
Printf.printf "compare/equal output: %d %b\n"
(SSet.compare avars bvars)
(SSet.equal avars bvars);
Printf.printf "Hash values are different: %d %d\n"
(Hashtbl.hash avars) (Hashtbl.hash bvars);
Dot.fprint_graph Format.str_formatter g;
Printf.printf "Graph representation:\n%s" (Format.flush_str_formatter ())
In order to compile, type ocamlc -c -I +ocamlgraph demo.ml; ocamlc -I +ocamlgraph graph.cma demo.cmo. When the program is executed you get this output:
The content is the same: [a, b] [a, b]
compare/equal output: 0 true
Hash values are different: 814436103 1017954833
Graph representation:
digraph G {
{a, b};
{a, b};
{a, b} -> {a, b};
{a, b} -> {a, b};
}
To sum up, I am curious why there are non-equal hash values for sets and two identical vertices are created in the graph, despite the fact these sets are equal by all other means.
I suspect the general answer is that OCaml's built-in hashing is based on rather physical properties of a value, while set equality is a more abstract notion. If you represent sets as ordered binary trees, there are many trees that represent the same set (as is well known). These will be equal as sets but might very well hash to different values.
If you want hashing to work for sets, you might have to supply your own function.
As Jeffrey pointed out, it seems that the problem is in the definition of the hash function that is part of Node module.
Changing it to let hash x = Hashtbl.hash (SSet.elements x) fixed the issue.

Conduits - multiple "attempts" into one Source

I am trying to do the following:
sourceIRC
:: (MonadBaseControl IO m, MonadLogger m)
=> NetworkSettings
-> Producer (ConnectionT m) Message
sourceIRC networkSettings = do
withConnectionForever networkSettings $ \socket -> do
bracket (liftBase $ Network.socketToHandle socket IO.ReadWriteMode)
(\handle -> liftBase $ IO.hClose handle)
(\handle -> do
mvar <- newMVar False
bracket (fork $ do
threadDelay 5000000
_ <- swapMVar mvar True
return ())
(killThread)
(\_ -> runConnectionT handle (sourceHandle handle))
takeMVar mvar)
As you can see, I am trying to create a Producer in terms of a primitive withConnectionForever. That primitive is of type:
withConnectionForever
:: (MonadBaseControl IO m, MonadLogger m)
=> NetworkSettings
-> (Network.Socket -> m Bool)
-> m ()
As you can imagine, I am getting an error message on compilation! It is:
Haskell/IRC.hs:128:54:
Couldn't match expected type `ConnectionT m0 a0'
with actual type `ConduitM i0 ByteString.ByteString m1 ()'
In the return type of a call of `sourceHandle'
In the second argument of `runConnectionT', namely
`(sourceHandle handle)'
In the expression: runConnectionT handle (sourceHandle handle)
Now, I know that the type of the call to withConnectionForever is not obviously a conduit, but I had hoped that it could manage to be one, by virtue of the fact that a conduit is also a monad and withConnectionForever uses a free monad instead of a hardcoded one. My understanding of what the message is trying to communicate is that that's not happening, and I'd like to know why and what I can do about it.
Here, for completeness, is the source of the primitive:
withConnectionForever
:: (MonadBaseControl IO m, MonadLogger m)
=> NetworkSettings
-> (Network.Socket -> m Bool)
-> m ()
withConnectionForever networkSettings action = do
let loop nFailures = do
maybeSocket <- newConnection networkSettings
case maybeSocket of
Nothing -> return ()
Just socket -> do
terminatedNormally <- action socket
if terminatedNormally
then loop 0
else do
exponentTwiddle <- liftBase $ Random.randomRIO (0, 100)
let exponent =
1.25 + fromIntegral (exponentTwiddle - 50) / 100.0
delay = floor $ 1000000.0 *
((0.5 ** (fromIntegral nFailures * negate exponent))
- 1.0 :: Double)
$(logInfo) (Text.concat
["Abnormal disconnection from the network ",
networkSettingsName networkSettings,
"; pausing attempts for ",
Text.pack $ show $ fromIntegral delay / 1000000.0,
" seconds..."])
liftBase $ threadDelay delay
loop (nFailures + 1)
loop 0
I'd really prefer not to rewrite the primitive, unless it can be done in minimally invasive fashion, but I suppose that's on the table.
Thanks in advance!
The relevant thing to do was
(\_ -> transPipe (runConnectionT handle) (sourceHandle handle))
instead of
(\_ -> runConnectionT handle (sourceHandle handle))
Thanks for your time! :D

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