CS计算机代考程序代写 data structure Java Haskell assembly Effects State IO QuickChecking Effects

Effects State IO QuickChecking Effects
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Software System Design and Implementation
Effects and State
Christine Rizkallah
UNSW Sydney Term 2 2021

Effects
State
IO QuickChecking Effects
Effects
Effects
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Effects are observable phenomena from the execution of a program.

Effects
State
IO QuickChecking Effects
Effects
Effects
Effects are observable phenomena from the execution of a program.
Example (Memory effects)
int *p = …
… // read and write *p = *p + 1;

Effects
State
IO QuickChecking Effects
Effects
Example (Memory effects)
int *p = …
… // read and write *p = *p + 1;
Example (IO)
// console IO
c = getchar(); printf(“%d”,32);
Example (Control flow)
// exception effect
throw new Exception();
Effects
Effects are observable phenomena from the execution of a program.

Effects
State
IO QuickChecking Effects
Effects
Effects
Effects are observable phenomena from the execution of a program.
Example (Memory effects)
int *p = …
… // read and write *p = *p + 1;
Example (Non-termination)
// infinite loop
while (1) {};
Example (IO)
// console IO
c = getchar(); printf(“%d”,32);
Example (Control flow)
// exception effect
throw new Exception();
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Effects
State IO QuickChecking Effects
Internal vs. External Effects External Observability
An external effect is an effect that is observable outside the function. Internal effects are not observable from outside.
Example (External effects)
Console, file and network I/O; termination and non-termination; non-local control flow; etc.
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Effects
State
IO QuickChecking Effects
Purity
A function with no external effects is called a pure function.
Pure functions
A pure function is the mathematical notion of a function. That is, a function of type a -> b is fully specified by a mapping from all elements of the domain type a to the codomain type b.
Consequences:
Two invocations with the same arguments result in the same value.
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Effects State IO QuickChecking Effects
Haskell Functions
Haskell functions are technically not pure.

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Effects State IO QuickChecking Effects
Haskell Functions
Haskell functions are technically not pure. They can loop infinitely.

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Effects
State IO QuickChecking Effects
Haskell Functions
Haskell functions are technically not pure.
They can loop infinitely.
They can throw exceptions (partial functions).

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Effects
State IO QuickChecking Effects
Haskell Functions
Haskell functions are technically not pure.
They can loop infinitely.
They can throw exceptions (partial functions).
They can force evaluation of unevaluated expressions.

Effects
State IO QuickChecking Effects
Haskell Functions
Haskell functions are technically not pure.
They can loop infinitely.
They can throw exceptions (partial functions).
They can force evaluation of unevaluated expressions.
Caveat
Purity only applies to a particular level of abstraction. Even ignoring the above, assembly instructions produced by GHC aren’t really pure.
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Effects State IO QuickChecking Effects
The Danger of Implicit Side Effects
They introduce (often subtle) requirements on the evaluation order.

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Effects State IO QuickChecking Effects
The Danger of Implicit Side Effects
They introduce (often subtle) requirements on the evaluation order. They are not visible from the type signature of the function.

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Effects
State IO QuickChecking Effects
The Danger of Implicit Side Effects
They introduce (often subtle) requirements on the evaluation order. They are not visible from the type signature of the function.
They introduce non-local dependencies which is bad for software design, increasing coupling.

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Effects
State IO QuickChecking Effects
The Danger of Implicit Side Effects
They introduce (often subtle) requirements on the evaluation order. They are not visible from the type signature of the function.
They introduce non-local dependencies which is bad for software design, increasing coupling.
They interfere badly with strong typing, for example mutable arrays in Java, or reference types in ML.

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Effects
State IO QuickChecking Effects
The Danger of Implicit Side Effects
They introduce (often subtle) requirements on the evaluation order. They are not visible from the type signature of the function.
They introduce non-local dependencies which is bad for software design, increasing coupling.
They interfere badly with strong typing, for example mutable arrays in Java, or reference types in ML.
We can’t, in general, reason equationally about effectful programs!

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Effects State IO QuickChecking Effects
Can we program with pure functions?
Yes! We’ve been doing it for the past 4 weeks.

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Effects
State IO QuickChecking Effects
Can we program with pure functions?
Yes! We’ve been doing it for the past 4 weeks.
Typically, a computation involving some state of type s and returning a result of type a can be expressed as a function:
s -> (s, a)

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Effects
State IO QuickChecking Effects
Can we program with pure functions?
Yes! We’ve been doing it for the past 4 weeks.
Typically, a computation involving some state of type s and returning a result of type
a can be expressed as a function:
s -> (s, a)
Rather than change the state, we return a new copy of the state.

Effects
State IO QuickChecking Effects
Can we program with pure functions?
Yes! We’ve been doing it for the past 4 weeks.
Typically, a computation involving some state of type s and returning a result of type
a can be expressed as a function:
s -> (s, a)
Rather than change the state, we return a new copy of the state. Efficiency?
All that copying might seem expensive, but by using tree data structures, we can usually reduce the cost to an O(log n) overhead.
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Effects State IO QuickChecking Effects
State Passing
Example (Labelling Nodes)
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data Tree a = Branch a (Tree a) (Tree a) | Leaf

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State IO QuickChecking Effects
State Passing
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Example (Labelling Nodes)
data Tree a = Branch a (Tree a) (Tree a) | Leaf
Given a tree, label each node with an ascending number in infix order: label :: Tree () -> Tree Int
()
()
() () () ()
()

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State IO QuickChecking Effects
State Passing
Example (Labelling Nodes)
data Tree a = Branch a (Tree a) (Tree a) | Leaf
Given a tree, label each node with an ascending number in infix order: label :: Tree () -> Tree Int
() 4
() () 2 6 () () () () 1 3 5 7
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Effects State
IO QuickChecking Effects
State
newtype State s a = A procedure that, manipulating some state of type s, returns a

Effects State
IO QuickChecking Effects
State
newtype State s a = A procedure that, manipulating some state of type s, returns a
State Operations
get :: State s s
put :: s -> State s ()
pure :: a -> State s a evalState :: State s a -> s -> a
Bind
Sequential Composition
Do one state action after another with do blocks: do put 42 desugars put 42 >> put True
=⇒
(>>) :: State s a -> State s b -> State s b
pure True
The 2nd step can depend on the first with bind: dox<-get desugars get>>=\x->pure(x+1)
pure (x+1) =⇒
(>>=) :: State s a -> (a -> State s b) -> State s b

Effects State
IO QuickChecking Effects
State
newtype State s a = A procedure that, manipulating some state of type s, returns a
State Operations
get :: State s s
put :: s -> State s ()
pure :: a -> State s a evalState :: State s a -> s -> a
Sequential Composition
Do one state action after another with do blocks: do put 42 desugars put 42 >> put True
=⇒
(>>) :: State s a -> State s b -> State s b
pure True
Example
Implement modify: (s->s)->States()
And re-do the tree labelling.
Bind
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The 2nd step can depend on the first with bind: dox<-get desugars get>>=\x->pure(x+1)
pure (x+1) =⇒
(>>=) :: State s a -> (a -> State s b) -> State s b

Effects
State IO QuickChecking Effects
State Implementation
The State type is essentially implemented as the same state-passing we did before! newtype State s a = State (s -> (s,a))
Example
Let’s implement each of the State operations for this newtype.
Caution
In the Haskell standard library mtl, the State type is actually implemented slightly differently, but the implementation essentially works the same way.
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State
IO QuickChecking Effects
Sometimes we need side effects.
Effects
We need to perform I/O, to communicate with the user or hardware.
We might need effects for maximum efficiency.
(but usually internal effects are sufficient)

Effects
State
IO QuickChecking Effects
Sometimes we need side effects.
We need to perform I/O, to communicate with the user or hardware.
We might need effects for maximum efficiency.
(but usually internal effects are sufficient)
Haskell’s approach
Pure by default. Effectful when necessary.
Effects
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Effects State IO QuickChecking Effects
The IO Type
A procedure that performs some side effects, returning a result of type a is written as IO a.

Effects
State IO QuickChecking Effects
The IO Type
A procedure that performs some side effects, returning a result of type a is written as IO a.
World interpretation
IO a is an abstract type. But we can think of it as a function: RealWorld -> (RealWorld, a)
(that’s how it’s implemented in GHC)
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Infectious IO
We can convert pure values to impure procedures with pure: pure :: a -> IO a

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Effects
State IO QuickChecking Effects
Infectious IO
We can convert pure values to impure procedures with pure: pure :: a -> IO a
But we can’t convert impure procedures to pure values: ???? :: IO a -> a

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Effects
State IO QuickChecking Effects
Infectious IO
We can convert pure values to impure procedures with pure: pure :: a -> IO a
But we can’t convert impure procedures to pure values: ???? :: IO a -> a
The only function that gets an a from an IO a is >>=: (>>=) :: IO a -> (a -> IO b) -> IO b
But it returns an IO procedure as well.

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State IO QuickChecking Effects
Infectious IO
We can convert pure values to impure procedures with pure: pure :: a -> IO a
But we can’t convert impure procedures to pure values: ???? :: IO a -> a
The only function that gets an a from an IO a is >>=: (>>=) :: IO a -> (a -> IO b) -> IO b
But it returns an IO procedure as well.
Conclusion
The moment you use an IO procedure in a function, IO shows up in the types, and you can’t get rid of it!
If a function makes use of IO effects directly or indirectly, it will have IO in its type!
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Effects State IO QuickChecking Effects
Haskell Design Strategy
We ultimately “run” IO procedures by calling them from main: main :: IO ()

Effects
State IO QuickChecking Effects
Haskell Design Strategy
We ultimately “run” IO procedures by calling them from main: main :: IO ()
Encapsulated Internal State
Pure Logic
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IO Shell

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State IO QuickChecking Effects
Examples
Example (Triangles)
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Given an input number n, print a triangle of * characters of base width n.

Effects
State IO QuickChecking Effects
Example (Triangles)
Examples
Given an input number n, print a triangle of * characters of base width n. Example (Maze Game)
Design a game that reads in a n × n maze from a file. The player starts at position
(0, 0) and must reach position (n − 1, n − 1) to win. The game accepts keyboard input to move the player around the maze.
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State IO QuickChecking Effects
Benefits of an IO Type
Absence of effects makes type system more informative:
A type signatures captures entire interface of the function.
All dependencies are explicit in the form of data dependencies. All dependencies are typed.

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Effects
State IO QuickChecking Effects
Benefits of an IO Type
Absence of effects makes type system more informative:
A type signatures captures entire interface of the function.
All dependencies are explicit in the form of data dependencies. All dependencies are typed.
It is easier to reason about pure code and it is easier to test: Testing is local, doesn’t require complex set-up and tear-down.
Reasoning is local, doesn’t require state invariants. Type checking leads to strong guarantees.

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State IO QuickChecking Effects
Mutable Variables
We can have honest-to-goodness mutability in Haskell, if we really need it, using IORef.
data IORef a
newIORef :: a -> IO (IORef a)
readIORef :: IORef a -> IO a
writeIORef :: IORef a -> a -> IO ()

Effects
State IO QuickChecking Effects
Mutable Variables
We can have honest-to-goodness mutability in Haskell, if we really need it, using IORef.
data IORef a
newIORef :: a -> IO (IORef a)
readIORef :: IORef a -> IO a
writeIORef :: IORef a -> a -> IO ()
Example (Effectful Average)
Average a list of numbers using IORefs.
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Effects State IO QuickChecking Effects
Mutable Variables, Locally
Something like averaging a list of numbers doesn’t require external effects, even if we use mutation internally.

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State IO QuickChecking Effects
Mutable Variables, Locally
Something like averaging a list of numbers doesn’t require external effects, even if we use mutation internally.
data STRef s a
newSTRef :: a -> ST (STRef s a)
readSTRef :: STRef s a -> ST s a
writeSTRef :: STRef s a -> a -> ST s ()
runST :: (forall s. ST s a) -> a

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Effects
State IO QuickChecking Effects
Mutable Variables, Locally
Something like averaging a list of numbers doesn’t require external effects, even if we use mutation internally.
data STRef s a
newSTRef :: a -> ST (STRef s a)
readSTRef :: STRef s a -> ST s a
writeSTRef :: STRef s a -> a -> ST s ()
runST :: (forall s. ST s a) -> a
The extra s parameter is called a state thread, that ensures that mutable variables don’t leak outside of the ST computation.

Effects
State IO QuickChecking Effects
Mutable Variables, Locally
Something like averaging a list of numbers doesn’t require external effects, even if we use mutation internally.
data STRef s a
newSTRef :: a -> ST (STRef s a)
readSTRef :: STRef s a -> ST s a
writeSTRef :: STRef s a -> a -> ST s ()
runST :: (forall s. ST s a) -> a
The extra s parameter is called a state thread, that ensures that mutable variables don’t leak outside of the ST computation.
Note
The ST type is not assessable in this course, but it is useful sometimes in Haskell programming.
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State IO QuickChecking Effects
QuickChecking Effects
QuickCheck lets us test IO (and ST) using this special property monad interface:
monadicIO :: PropertyM IO () -> Property
pre :: Bool -> PropertyM IO ()
assert :: Bool -> PropertyM IO ()
run :: IO a -> PropertyM IO a
Do notation and similar can be used for PropertyM IO procedures just as with State s and IO procedures.

Effects
State IO QuickChecking Effects
QuickChecking Effects
QuickCheck lets us test IO (and ST) using this special property monad interface:
monadicIO :: PropertyM IO () -> Property
pre :: Bool -> PropertyM IO ()
assert :: Bool -> PropertyM IO ()
run :: IO a -> PropertyM IO a
Do notation and similar can be used for PropertyM IO procedures just as with State s and IO procedures.
Example (Testing average)
Let’s test that our IO average function works like the non-effectful one.
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State IO QuickChecking Effects
1 New exercise out, due the week after next week.
2 Last week’s quiz is due on Friday.
3 This week’s quiz is due the Friday after the following Friday.
Homework

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