Smart constructors
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=== A first attempt === 
=== A first attempt === 

−  Code up the a typical [[Typedata type]] describing a resistor value: 
+  Code up a typical [[Typedata type]] describing a resistor value: 
<haskell> 
<haskell> 

−  data Resistor = Metal Bands 
+  data Resistor = Metal Bands 
−   Ceramic Bands 
+   Ceramic Bands 
−  deriving Show 
+  deriving Show 
−  type Bands = Int 
+  type Bands = Int 
</haskell> 
</haskell> 

−  This has a problem however, that the constructors of type ''Resistor'' are 
+  This has a problem however, that the [[constructor]]s of type ''Resistor'' are 
unable to check that only bands of size 4 to 8 are built. It is quite 
unable to check that only bands of size 4 to 8 are built. It is quite 

legal to say: 
legal to say: 

Line 46:  Line 46:  
<haskell> 
<haskell> 

−  metalResistor :: Bands > Resistor 
+  metalResistor :: Bands > Resistor 
−  metalResistor n  n < 4  n > 8 = error "Invalid number of resistor bands" 
+  metalResistor n  n < 4  n > 8 = error "Invalid number of resistor bands" 
−   otherwise = Metal n 
+   otherwise = Metal n 
</haskell> 
</haskell> 

Line 56:  Line 56:  
Running this code: 
Running this code: 

−  *Main> metalResistor 4 
+  > metalResistor 4 
−  Metal 4 
+  Metal 4 
−  *Main> metalResistor 7 
+  > metalResistor 7 
−  Metal 7 
+  Metal 7 
−  *Main> metalResistor 9 
+  > metalResistor 9 
−  *** Exception: Invalid number of resistor bands 
+  *** Exception: Invalid number of resistor bands 
−  *Main> metalResistor 0 
+  > metalResistor 0 
−  *** Exception: Invalid number of resistor bands 
+  *** Exception: Invalid number of resistor bands 
One extra step has to be made though, to make the interface safe. When 
One extra step has to be made though, to make the interface safe. When 

Line 74:  Line 74:  
<haskell> 
<haskell> 

−  module Resistor ( 
+  module Resistor ( 
−  Resistor,  abstract, hiding constructors 
+  Resistor,  abstract, hiding constructors 
−  metalResistor,  only way to build a metal resistor 
+  metalResistor,  only way to build a metal resistor 
−  ) where 
+  ) where 
... 
... 

Line 89:  Line 89:  
<haskell> 
<haskell> 

−  metalResistor :: Bands > Resistor 
+  metalResistor :: Bands > Resistor 
−  metalResistor n = assert (n >= 4 && n <= 8) $ Metal n 
+  metalResistor n = assert (n >= 4 && n <= 8) $ Metal n 
</haskell> 
</haskell> 

And now obtain more detailed error messages, automatically generated for us: 
And now obtain more detailed error messages, automatically generated for us: 

−  *Main> metalResistor 0 
+  > metalResistor 0 
−  *** Exception: A.hs:4:1823: Assertion failed 
+  *** Exception: A.hs:4:1823: Assertion failed 
We at least now are given the line and column in which the error occured. 
We at least now are given the line and column in which the error occured. 

Line 122:  Line 122:  
<haskell> 
<haskell> 

−  data Z = Z 
+  data Z = Z 
−  data S a = S a 
+  data S a = S a 
</haskell> 
</haskell> 

Line 129:  Line 129:  
<haskell> 
<haskell> 

−  class Card c where 
+  class Card c where 
−  instance Card Z where 
+  instance Card Z where 
−  instance (Card c) => Card (S c) where 
+  instance (Card c) => Card (S c) where 
</haskell> 
</haskell> 

Line 139:  Line 139:  
<haskell> 
<haskell> 

−  class Card size => InBounds size where 
+  class Card size => InBounds size where 
−  instance InBounds (S (S (S (S Z)))) where  four 
+  instance InBounds (S (S (S (S Z)))) where  four 
−  instance InBounds (S (S (S (S (S Z))))) where  five 
+  instance InBounds (S (S (S (S (S Z))))) where  five 
−  instance InBounds (S (S (S (S (S (S Z)))))) where  six 
+  instance InBounds (S (S (S (S (S (S Z)))))) where  six 
−  instance InBounds (S (S (S (S (S (S (S Z))))))) where  seven 
+  instance InBounds (S (S (S (S (S (S (S Z))))))) where  seven 
−  instance InBounds (S (S (S (S (S (S (S (S Z)))))))) where  eight 
+  instance InBounds (S (S (S (S (S (S (S (S Z)))))))) where  eight 
</haskell> 
</haskell> 

Line 152:  Line 152:  
<haskell> 
<haskell> 

−  data Resistor size = Resistor deriving Show 
+  data Resistor size = Resistor deriving Show 
</haskell> 
</haskell> 

Line 159:  Line 159:  
<haskell> 
<haskell> 

−  resistor :: InBounds size => size > Resistor size 
+  resistor :: InBounds size => size > Resistor size 
−  resistor _ = Resistor 
+  resistor _ = Resistor 
</haskell> 
</haskell> 

Line 168:  Line 168:  
<haskell> 
<haskell> 

−  d0 = undefined :: Z 
+  d0 = undefined :: Z 
−  d3 = undefined :: S (S (S Z)) 
+  d3 = undefined :: S (S (S Z)) 
−  d4 = undefined :: S (S (S (S Z))) 
+  d4 = undefined :: S (S (S (S Z))) 
−  d6 = undefined :: S (S (S (S (S (S Z))))) 
+  d6 = undefined :: S (S (S (S (S (S Z))))) 
−  d8 = undefined :: S (S (S (S (S (S (S (S Z))))))) 
+  d8 = undefined :: S (S (S (S (S (S (S (S Z))))))) 
−  d10 = undefined :: S (S (S (S (S (S (S (S (S (S Z))))))))) 
+  d10 = undefined :: S (S (S (S (S (S (S (S (S (S Z))))))))) 
</haskell> 
</haskell> 

Line 234:  Line 234:  
<haskell> 
<haskell> 

−  newtype MetalResistor = Metal Bands 
+  newtype MetalResistor = Metal Bands 
−  newtype CeramicResistor = Ceramic Bands 
+  newtype CeramicResistor = Ceramic Bands 
</haskell> 
</haskell> 

Line 242:  Line 242:  
<haskell> 
<haskell> 

−  foo :: MetalResistor > Int 
+  foo :: MetalResistor > Int 
−  foo (MetalResistor n) = n 
+  foo (MetalResistor n) = n 
</haskell> 
</haskell> 

Line 253:  Line 253:  
These ideas are also discussed in [[Dimensionalized numbers]] 
These ideas are also discussed in [[Dimensionalized numbers]] 

and on the old wiki 
and on the old wiki 

−  [http://haskell.org/hawiki/NonTrivialTypeSynonyms here] (for 
+  [http://web.archive.org/web/20050227183721/http://www.haskell.org/hawiki/NonTrivialTypeSynonyms here] (for 
compiletime unit analysis error catching at the type level). 
compiletime unit analysis error catching at the type level). 

−  More [http://haskell.org/hawiki/WrapperTypes here] too. 
+  Recently migrated are the pages on [[worker wrapper]] and [[factory function]]. 
−  
In general, the more information you place on the type level, the more 
In general, the more information you place on the type level, the more 

static checks you get  and thus less chance for bugs. 
static checks you get  and thus less chance for bugs. 

Line 264:  Line 264:  
<haskell> 
<haskell> 

−  data Expression = Variable String 
+  data Expression = Variable String 
−   Add [Expression] 
+   Add [Expression] 
−   Multiply [Expression] 
+   Multiply [Expression] 
</haskell> 
</haskell> 

Line 274:  Line 274:  
<haskell> 
<haskell> 

−  add :: [Expression] > Expression 
+  add :: [Expression] > Expression 
−  add xs = Add (concatMap fromAdd xs) 
+  add xs = Add (concatMap fromAdd xs) 
−  +  multiply :: [Expression] > Expression 

−  multiply :: [Expression] > Expression 
+  multiply xs = Multiply (concatMap fromMultiply xs) 
−  multiply xs = Multiply (concatMap fromMultiply xs) 

−  
−  fromAdd (Add xs) = xs 

−  fromAdd x = [x] 

−  fromMultiply (Multiply xs) = xs 
+  fromAdd (Add xs) = xs 
−  fromMultiply x = [x] 
+  fromAdd x = [x] 
+  fromMultiply (Multiply xs) = xs 

+  fromMultiply x = [x] 

</haskell> 
</haskell> 

[[Category:Idioms]] 
[[Category:Idioms]] 

+  [[Category:Glossary]] 
Revision as of 18:33, 25 February 2012
Smart constructors
This is an introduction to a programming idiom for placing extra constraints on the construction of values by using smart constructors.
Sometimes you need guarantees about the values in your program beyond what can be accomplished with the usual type system checks. Smart constructors can be used for this purpose.
Consider the following problem: we want to be able to specify a data type for electronic resistors. The resistors come in two forms, metal and ceramic. Resistors are labelled with a number of bands, from 4 to 8.
We'd like to be able to
 ensure only resistors with the right number of bands are constructed.
Contents 
1 Runtime checking : smart constructors
1.1 A first attempt
Code up a typical data type describing a resistor value:
data Resistor = Metal Bands  Ceramic Bands deriving Show type Bands = Int
This has a problem however, that the constructors of type Resistor are unable to check that only bands of size 4 to 8 are built. It is quite legal to say:
*Main> :t Metal 23 Metal 23 :: Resistor
for example.
1.2 Smart(er) constructors
Smart constructors are just functions that build values of the required type, but perform some extra checks when the value is constructed, like so:
metalResistor :: Bands > Resistor metalResistor n  n < 4  n > 8 = error "Invalid number of resistor bands"  otherwise = Metal n
This function behaves like the constructor Metal, but also performs a check. This check will be carried out at runtime, once, when the value is built.
Running this code:
> metalResistor 4 Metal 4
> metalResistor 7 Metal 7 > metalResistor 9 *** Exception: Invalid number of resistor bands
> metalResistor 0 *** Exception: Invalid number of resistor bands
One extra step has to be made though, to make the interface safe. When exporting the type Resistor we need to hide the (unsafe) constructors, and only export the smart constructors, otherwise a reckless user could bypass the smart constructor:
module Resistor ( Resistor,  abstract, hiding constructors metalResistor,  only way to build a metal resistor ) where ...
1.3 Using assertions
Handcoding error messages can be tedious when used often. Instead we can use the assert function, provided (from Control.Exception). We rewrite the smart constructor as:
metalResistor :: Bands > Resistor metalResistor n = assert (n >= 4 && n <= 8) $ Metal n
And now obtain more detailed error messages, automatically generated for us:
> metalResistor 0 *** Exception: A.hs:4:1823: Assertion failed
We at least now are given the line and column in which the error occured.
2 Compiletime checking : the type system
2.1 Enforcing the constraint statically
There are other ways to obtain numerical checks like this. The most interesting are probably the static checks that can be done with Type arithmetic, that enforce the number of bands at compile time, rather than runtime, by lifting the band count into the type level.
In the following example, instead of checking the band count at runtime, we instead lift the resistor band count into the type level, and have the typecheck perform the check statically, using phantom types and Peano numbers.
We thus remove the need for a runtime check, meaning faster code. A consequence of this decision is that since the band count is now represented in the type, it is no longer necessary to carry it around at runtime, meaning less data has to be allocated.
Firstly, define some Peano numbers to represent the number of bands as types:
data Z = Z data S a = S a
Now specify a class for cardinal numbers.
class Card c where instance Card Z where instance (Card c) => Card (S c) where
Ok, now we're set. So encode a typelevel version of the bounds check. Only resistors with bands >= 4 and <= 8 are valid:
class Card size => InBounds size where instance InBounds (S (S (S (S Z)))) where  four instance InBounds (S (S (S (S (S Z))))) where  five instance InBounds (S (S (S (S (S (S Z)))))) where  six instance InBounds (S (S (S (S (S (S (S Z))))))) where  seven instance InBounds (S (S (S (S (S (S (S (S Z)))))))) where  eight
Now define a new resistor type. Note that since the bounds is represented in the type, we no longer need to store the bounds in the resistor value.
data Resistor size = Resistor deriving Show
And, finally, a convenience constructor for us to use, encoding the bounds check in the type:
resistor :: InBounds size => size > Resistor size resistor _ = Resistor
2.2 Examples
First, define some convenience values:
d0 = undefined :: Z d3 = undefined :: S (S (S Z)) d4 = undefined :: S (S (S (S Z))) d6 = undefined :: S (S (S (S (S (S Z))))) d8 = undefined :: S (S (S (S (S (S (S (S Z))))))) d10 = undefined :: S (S (S (S (S (S (S (S (S (S Z)))))))))
Now try to construct some resistors:
> resistor d0 No instance for (InBounds Z)
So the value 0 isn't in bounds, as we want. And it is a compiletime error to try to create such a resistor.
> resistor d3 No instance for (InBounds (S (S (S Z))))
Ok, how about a valid resistor?
> resistor d4 Resistor
Great!
> :t resistor d4 resistor d4 :: Resistor (S (S (S (S Z))))
And it's type encodes the number of bands.
> resistor d6 Resistor > resistor d8 Resistor
> :t resistor d8 resistor d8 :: Resistor (S (S (S (S (S (S (S (S Z))))))))
Similar result for other valid resistors.
> resistor d10 No instance for (InBounds (S (S (S (S (S (S (S (S (S (S Z)))))))))))
And 10 is too big.
2.3 Summary
By using a standard encoding of numeric values on the type level we are able to encode a bounds check in the type of a value, thus removing a runtime check, and removing the need to store the numeric value at runtime. The code is safer, as it is impossible to compile the program unless all resistors have the correct number of bands.
An extension would be to use a decimal encoding for the integers (at the expense of longer code).
2.4 Extensions
Further checks can be obtained by separating the metal and ceramic values on the type level, so no function that takes a metal resistor can be accidentally passed a ceramic one.
A newtype is useful for this:
newtype MetalResistor = Metal Bands newtype CeramicResistor = Ceramic Bands
now, a function of resistors must have either a MetalResistor type, or a CeramicResistor type:
foo :: MetalResistor > Int foo (MetalResistor n) = n
You can't write a function over both resistor types (other than a purely polymorphic function).
2.5 Related work
These ideas are also discussed in Dimensionalized numbers and on the old wiki here (for compiletime unit analysis error catching at the type level). Recently migrated are the pages on worker wrapper and factory function. In general, the more information you place on the type level, the more static checks you get  and thus less chance for bugs.
3 Runtime Optimisation : smart constructors
Another use for smart constructors is to perform basic optimisations, often to obtain a normal form for constructed data. For example, consider a data structure representing addition and multiplication of variables.
data Expression = Variable String  Add [Expression]  Multiply [Expression]
In this data structure, it is possible to represent a value such as Add [Variable "a", Add [Variable "b", Variable "c"]] more compactly as Add [Variable "a", Variable "b", Variable "c"].
This can be done automatically with smart constructors such as:
add :: [Expression] > Expression add xs = Add (concatMap fromAdd xs) multiply :: [Expression] > Expression multiply xs = Multiply (concatMap fromMultiply xs) fromAdd (Add xs) = xs fromAdd x = [x] fromMultiply (Multiply xs) = xs fromMultiply x = [x]