Tiffany Canada String

Defaulting
 Ambiguous Sorts, and Defaults for Overloaded Numeric Operations within the Haskell 98 Report.
Problems together with the current defaulting rule:
Defaults are minimal to Prelude numeric classes. A tool like Hat, which transforms Haskell supply, can not change the defaults, because there's no way make defaults use to the transformed courses rather than the initial ones.
Defaults can't be utilized to user-defined classes. It could be good for some applications in order to let a default clause to name the class being defaulted over, together with the type to choose. Examples consist of QuickCheck, exactly where you would possibly desire to default the Arbitrary class to something modest (e.g. Bool) any time a value is in any other case unconstrained.
Report specification of defaulting is impossible to put into action inside the presence of recursive modules. (Need to it be specified that a group of mutually recursive modules need to have exactly the same defaulting?)
A default clause applies only in the module that contains the declaration. Defaults could be neither
exported nor imported. Does anyone desire to propose import/export of defaults?
For import/export: less difficult to propagate user-defined class defaults throughout a project
In opposition to import/export: a modify inside the imports of the module may well silently alter habits
A compromise may possibly be to permit defaults that will be inherited for being specified only from the module that defines a class, but teams of mutually recursive modules may possibly override defaulting locally. this can steer clear of the import modifying habits problem and permit some type of inheritence of defaults.
Proposal one - name the class
Allow defaulting clauses from the next type
default <classname> (type1,type2,Pandora Earrings,type3,...)
The defaulting rule will simply select the first unambiguous form that satisfies all the constrained courses
listed within the default decls.
Lessons without defaults will have the equivalent of an empty list of kinds, so defaulting will not occur.
One issue of course is what does "unambiguous" mean? Within the case of
default A (Int,Pandora Ohrringe, String, ())
default B (String, Int, ())
(A t, B t) => t
any from the three kinds would satisfy the rule that it is an instance of all the courses. So what is the intepretation of "first" in the list?
The only unambiguous interpretation of "first" valid sort in both lessons A and B could be (), to stay away from making an arbitrary choice between Int and String.
However, this is still far from clearcut. Consider the subsequent examples:
default A (Int,String,Tiffany Bracelets,())
default B (String,(),Int)
(A t, B t) => t default C (Int, Double, String, ())
default D (Double,String,Int,())
(C t, D t) => t
Pro
very useful in interactive interpreter
less ad hoc than existing method
overcomes the Hat transformation issue
Con
can not exactly replicate habits of existing defaulting mechanism, but can come close.
may possibly hide errors,Pandora Bijoux, an optional warning on defaulting really should be possible.
not clear how to choose a single unambiguous member of more than one list of types
Proposal 2 - title the class + no lists
Modify default decls to (a) title the class becoming defaulted, and (b) permit only one default form per class, instead of a list.
Possible syntax, by analogy with instance decls:
topdecl -> default tycls type
Semantically, which form is chosen is determined by the class context at the choice point (after context simplification). That is,Pandora Jewellery Nz, in
default C T
(C a) => a
the kind 'a', constrained by class 'C' but or else unresolved, is instantiated for the sole sort 'T'.
If there is no unique choice, for instance because more than one class-with-a-default is mentioned inside the context (and their default kinds are different), then it is a static error.
Note that it is OK to have several lessons inside the context from the defaultable value,
provided only one of them is declared to yield a default sort,
or if more than one yields a form, those types are the identical.
Choosing a default after context simplification means that no conflicts between super- and sub-classes can arise.
Examples
Here are some examples, to clarify the idea:
default Eq Integer
default Fractional Float
(Eq a, Fractional a) => a
After simplification, this becomes (Fractional a)=>a, since Eq is a superclass of Fractional. Thus, there exists a single class to become defaulted, and Float is chosen.
default Ord Integer
default Fractional Float
(Ord a, Fractional a) => a
A static error, due to the fact Ord is not a superclass of Fractional, so the context does not simplify, and the default types disagree.
default Bounded Int default Ord Int (Ord a, Bounded a) => a
Default is Int, because even though the context does not simplify, the lessons involved do agree on which default to pick.
default Bounded Int default Ord Int (Ord a, Bounded a, Show a) => a
Default is Int, exact same as above, except for the extra constraint Show a. There's no default declared for Show, so the remaining context is used to make the choice.
(Show a, Read a) => a
A static error, because there are no defaults declared for any from the classes involved.
Backwards compatibility
The present Haskell'98 default-default behaviour can (nearly) be specified as:
default Num Integer
default Real Integer
default Enum Integer
default Integral Integer
default Fractional Double
default RealFrac Double
default Floating Double
default RealFloat Double
However, there are some incompatible cases where the new rule would cause a valid H'98 program for being rejected. For instance the expression toRational pi has the constraints Floating on pi and Real on toRational: in H'98, the type Double is the first sort that satisfies both constraints, but with the proposed new rule no kind would satisfy the constraints, so the expression would be rejected. To fix, you would need to annotate pi with a type.
Turning off defaults
In Haskell'98, the default decl not only declares a new default form for some courses, but can also implicitly remove defaults for other classes (at exactly the same time,Tiffany Jewelry On Sale In Drupal five!).
Whilst default () switches off all defaulting,Pandora Bead, default (Int) changes the default form for the Num, Real, Enum, Integral courses, and also declares there's no
default for the Fractional, RealFrac, Floating, and RealFloat classes (by virtue of Int's failure for being a instance of those).
Under the current proposal, there is certainly no explicit means to turn off defaults. A minor modification rectifies this shortcoming - simply permit the omission from the sort part with the default decl. An omitted type indicates there's no default form for this class.
Multi-parameter kind courses
Defaulting for MPTC follows the scheme for single-parameter lessons.
topdecl -> default tycls type_1 type_2 ... type_n
That is, there is a single unique relation between sorts that might be chosen if all of its variables are or else unconstrained.
Open questions: if some in the variables are already resolved to actual types, is it OK to default the remaining variables? Assuming the resolved types are inside the default relation anyway? What if the already-resolved kinds are not within the default relation? Would anyone ever want to use defaulting to choose different varieties depending on what other varieties have already been resolved?
What happens if the choice of default types is not confluent? For example:
instance Foo Float Integer
instance Foo Double Int
default Fractional Double
default Num Integer
(Fractional a, Foo a b, Num b) => e
Here, if you pick 'a' first, using the default Fractional Double, then simply because you have an instance of Foo Double Int, then 'b' ought to be Int. But if you pick 'b' first, using the default Num Integer, then simply because you have an instance Foo Float Integer, then 'a' need to be Float. One suggestion might be that defaulting will only occur if the results are confluent,Tiffany Canada, i.e. the compiler really should try all possible orderings in
which to default variables, and if they do not come up together with the identical
answer, then reject the program.
Pros
simpler, more general,Tiffany And Co Uk, and less ad hoc than existing method
overcomes the Hat transformation issue
does not rely on textual ordering of decl
permits defaulting of user-defined lessons, not just Prelude ones
Cons
not sure if this just captures the existing Haskell'98 module (but because defaults are currently constrained to Prelude lessons, it probably does)
the story for MPTC is not altogether clear yet
Proposal 3 - global scope
Orthogonal towards the issue of how to specify defaults, is the question of whether they ought to be module-local, or if instead we need to treat them like instance declarations - global in scope. One can also imagine permitting explicit lexical scoping, i.e. a local override from the defaults, purely within a single function definition.
Concrete proposal: a default decl can occur anywhere that a type signature can be valid, and has exactly the same scope. However, since default decls cannot be named, all default topdecls must be unique throughout a program. By contrast, a local default decl can override one at an outer scope, but only in its own inner scope.
Pros
Arguably, when user-defined lessons and varieties are involved, it is a lot clearer to make any necessary default decls once only, in a library, and just have them apply everywhere, rather than to require end-users to understand the issues and make their own default decls.
Having consistent defaults all through a program is semantically nicer (but you still get the opportunity to override them locally if you _really_ need to - just like with operator fixities).
Cons
Changes the Haskell'98 behaviour (where defaults are module-local). Question: Do any real programs actually rely on the Haskell'98 spec here?
Proposal 4 - remove defaulting
It is generally agreed that defaulting, in its current sort at least, is a wart on the language. The main motivation behind it is to make simple calculator-like uses of interactive Haskell environments possible.
This proposal, then, is to remove defaulting from the language; we would expect that interactive environments will continue to default as they think best. Note that implementations already go beyond what is stated from the report when defaulting.
Most(?) instances of defaulting in Real Programs are due to (^). If this proposal is adopted then we would recommend modifying the sort of (^) and introducing genericPower (or some better identify) thus:
(^) :: (Num a) => a -> Int -> a
genericPower :: (Num a, Integral b) => a -> b -> a
This is similar for the scheme used by, for example, genericIndex.
Pros
Easy to carry out and explain.
Makes the language smaller.
Trivially fixes any difficulties tools like hat have with defaulting.
Cons
No pretense at trying to remain compatible with Haskell '98, but how many uses of defaulting are there from the wild? And how many not covered by (^)?