From a2e3a80c61bdd1aa9ef4f63029bd032a8b3345aa Mon Sep 17 00:00:00 2001
From: Yuri Tatishchev <itatishch@gmail.com>
Date: Wed, 25 Feb 2026 11:19:26 -0800
Subject: [PATCH] lab07: init

---
 lab07/facetedValues.lhs | 87 +++++++++++++++++++++++++++++++++++++++++
 1 file changed, 87 insertions(+)
 create mode 100644 lab07/facetedValues.lhs

diff --git a/lab07/facetedValues.lhs b/lab07/facetedValues.lhs
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+++ b/lab07/facetedValues.lhs
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+> import Control.Applicative
+> import qualified Data.Set as Set
+
+Faceted values are an **information flow mechanism**.  Specifically, they are
+designed to store differing views of data.  For more technical details, see
+"Multiple Facets for Dynamic Information Flow", available at
+https://users.soe.ucsc.edu/~cormac/papers/popl12b.pdf.
+
+Authorized viewers should see the real value, and other viewers should see
+dummy data instead.  To do this, we need to represent the security level
+of a piece of data.  We'll define labels to encapsulate this information,
+represented as strings.
+
+> type Label = String
+
+A user may have many security privileges, so a "view" of a faceted value can
+be represented as a set of labels.
+
+> type View = Set.Set Label
+
+A faceted value can be either a raw (that is, unfaceted) value, or it can
+be node containing two nested faceted values, with a label tracking who is
+allowed to view the contents.
+
+> data FacetedValue a = Raw a
+>                     | Facet Label (FacetedValue a) (FacetedValue a)
+
+Note that we do **not** derive Show.  Instead, code must pass its
+authorizations to a view function, which will return a non-faceted value.
+If any label is not in the set, it is assumed that the view is not authorized.
+
+> view :: View -> FacetedValue a -> a
+> view _ (Raw x) = x
+> view labels (Facet k auth unauth) =
+>     if Set.member k labels then
+>       view labels auth
+>     else
+>       view labels unauth
+
+We can apply operations to a faceted value, in which case the action should
+be applied to every element of the tree.  As a review of the last lab, define
+fmap for FacetedValues.
+
+> instance Functor FacetedValue where
+>   fmap f v = error "Your code here"
+
+
+The following function gives an example of how a FacetedValue can be used.
+In this case, a customer's Visa credit card is hidden from other viewers.
+If someone with other permissions, say with the ability to view details
+about the customer's Mastercard, they will instead be presented with the
+default view of 0.  Even if someone tries to do some calculations on the
+credit card in the hope of revealing information, a consistent view will be
+presented to the observer.
+
+> testFmap = do
+>   let creditCard = Facet "visa" (Raw 4111111111111111) (Raw 0)
+>       ccPlusOne = fmap (+1) creditCard
+>   putStrLn "Credit card views:"
+>   print $ view (Set.fromList ["visa"]) ccPlusOne -- Should print 4111111111111112
+>   print $ view (Set.fromList ["mastercard"]) ccPlusOne -- Should print 1
+
+
+
+While this works, what happens if we want two faceted values to be combined?
+In order to make that work, we need need to add support for Applicative Functors.
+Define the behavior of the Functor below
+
+> instance Applicative FacetedValue where
+>   pure = error "Your code here"
+>   fv1 <*> fv2 = error "Your code here"
+
+
+The code below gives an example of how this might come up.  If code authorized
+to read your Bank of America account details runs on the same machine as code
+to read your Wells Fargo details, **neither** will be allowed to read your
+combined balance.  However, you as the customer can see the true values.
+
+> testApplicative = do
+>   let bofaBalance = Facet "Bank of America" (Raw 44) (Raw 0)
+>       wellsFargoBalance = Facet "Wells Fargo" (Raw 122) (Raw 0)
+>       combinedBalance = (+) <$> bofaBalance <*> wellsFargoBalance
+>   print $ view (Set.fromList []) combinedBalance -- Should print 0
+>   print $ view (Set.fromList ["Bank of America"]) combinedBalance -- Should print 44
+>   print $ view (Set.fromList ["Wells Fargo"]) combinedBalance -- Should print 122
+>   print $ view (Set.fromList ["Bank of America", "Wells Fargo"]) combinedBalance -- Should print 166
+