[racket] TR define-new-type, Value Types

Thanks, I'll poke around with TR's refinement types.  If anyone has a
reference detailing on the nature of TR's refinement types, please forward.
 In progress paper etc.


On Fri, Dec 28, 2012 at 8:53 PM, Carl Eastlund <cce at ccs.neu.edu> wrote:

> What you describe sounds exactly like Typed Racket's refinement types.
> Statically typed languages like SML often incorporate refinements that can
> be determined entirely statically.  TR allows arbitrary dynamic checks for
> its refinements, so it gets the "weak sort of Dependent Type" results you
> mention.  So I wouldn't judge the capabilities of TR's refinement types
> based on papers about SML.
>
> Carl Eastlund
>
> On Fri, Dec 28, 2012 at 8:35 PM, Ray Racine <ray.racine at gmail.com> wrote:
>
>> Based on a google of a paper on refinement types in SML, no.  Useful in
>> their own right, and thanks for pointing out their
>> (experimental) existence.  I'm thinking more along the line of a quick win
>> of a weak sort of Dependent Type for value types such as Number and String
>> by leveraging existent Racket machinery.
>>
>> See
>> https://docs.google.com/document/d/10TQKgMiJTbVtkdRG53wsLYwWM2MkhtmdV25-NZvLLMA/edit for
>> a Scala endeavor along similar lines.
>>
>> The goal is to support efficient generative, constrained, sub-types of
>> primitive value types, specifically String and Number with minimal surgery
>> to Racket.
>>
>> Consider:
>>
>> (define-value-type Age : Integer [1 .. 120])
>> (define-value-type SSN : String [1 .. 9 | 11] ssn-validation-predicate)
>>
>> Goals:
>>
>> 1) Avoid boxing/unboxing (struct cell / cell-refs).
>> 2) Create generative sub-types of certain base types, String, Number to
>> satisfy TR.  Note they are not opaque types but, i.e.  T <: String
>>
>> Item 2) means
>>
>> ;; works as Ages are Integers
>> (: add-ages (Age Age -> Age))
>> (define (sum-ages a1 a2)
>>   (Age (+ a1 a2)) ;; + defined on Integers
>>
>> ;; not the same as (define-type Age Integer) because ...
>> (sum-ages 12 16) ;; fails as Integers are not Ages
>>
>> ;; lifting Integer to Age involves a runtime contract check, but no
>> allocation.
>> (sum-ages (Age 12) (Age 16)) ;; fine, no allocation
>>
>> A hand waved way of getting there, which got ugly quick and as I typed.
>> I was sort of brainstorming if I could get Value Types without any Racket
>> internal surgery and with no more than a bit of macrology.
>>
>> So waving both hands wildly...
>>
>> 0) Modify the TR `cast' operator to recognize Value Type structures.
>>
>>  a) The generated contract from the `cast' operator of a value type to an
>> appropriate Value Type structure succeeds at runtime for an instance of the
>> value type.
>>  b) The generated contract from the `cast' operator applies the
>> gen:validator on the Value Type structure as part of the contract.
>>
>> 1) Extend the struct: macro to allow a struct: parent to be not only
>> another struct: but a  [struct: | String | Number]
>>
>>   a) IF the parent is a struct: nothing new to do here.
>>
>>   b) If parent is a value type, String or a Number (value type)
>>     - This is a Value Type structure.
>>     - A value type structure has only one mandatory value which is of the
>> same type as the parent.
>>     - A Value Type structure is -sealed- and may not be used as the
>> parent in another struct: definition.
>>     - A Value Type structure's constructor is a (A -> A) pass-thru of the
>> value.  i.e., the struct: is never allocated to wrap the value.
>>     - A Value Type structure _may_ have a gen:validate generic method
>> associated with it.
>>
>> 4) To avoid creating a true Value Type structure instance via low level
>> apis, they would need to be modified to prohibit creating any instance of a
>> Value Type structure.
>>
>> What we are trying to achieve is all of the type checking from TR using
>> struct: to generate a new type at compile time, yet at runtime the instance
>> values of the Value Type are the primitive values and are NOT manifested as
>> the struct: instances.
>>
>> Example:
>> Create an SSN Value Type.
>>
>> ;; An SSN is String value, of length 9 or 11, which is validated by a
>> regular expression.
>>
>> (: ssn-validation-predicate (String -> Boolean : SSN))
>> (define (ssn-validation-predicate str-ssn)
>>   (regexp-match? ssn #rx(....)))
>>
>> (define-value-type SSN String [9 | 11] ssn-validation-predicate) ;;
>>
>> The above roughly expands to:
>>
>> (struct: SSN String ([value : String])
>>    #:methods gen:validate ssn-validation-predicate)
>>
>> (define SSN-validator-contract (and/contract ....))  ;;; combines
>> string-length 9|11 check with ssn-validation-predicate into a contract
>>
>> The struct: macro notes that this is a Value Type structure definition
>> because its parent is a value type, String, and not another struct:.  So
>> the generated SSN constructor function avoids creating an actual structure
>> at runtime and allows a string value as successfully cast to a SSN after
>> applying any associated validation contract.
>>
>> (: SSN (String -> SSN))
>> (define (SSN ssn)
>>   (cast ssn SSN))
>>
>> In the above ...
>>  - `cast' knows we are casting to a Value Type, SSN, so generated runtime
>> contract allows a String value (and _not_ a SSN struct type instance) to be
>> "passed-thru" but lifted to type SSN for TR purposes.
>>  - Therefore, the cast fails an actual instance of an SSN structure, if
>> one somehow managed to construct an instance.
>>  - As part of the `cast' generated contract the SSN-validator-contract
>> and length checks are combined and applied interstitial in the pass-thru of
>> (String -> String).
>>
>> And finally since SSN at runtime is a string value, at compile time it's
>> a subtype of String so...
>>
>> (substring (SSN "123-45-6789") 0 3) ;; works at TR compile time checking
>> and at runtime running
>> (substring (SSN "123x456-5689") 0 3) ;; fails validation at runtime,
>> though a sufficiently smart compiler would apply the contract validation
>> check at compile time for values known at compile time.
>>
>> Given:
>>
>> (: parse-ssn (SSN -> (Listof String)))
>> (define (parse-ssn ssn)
>>    (regexp-split ssn #rx"-"))
>>
>> (parse-ssn "123-456-6789") ;; nope as strings are not SSNs
>> (parse-ssn (SSN "123-456-6789")) ;; works but runtime representation
>> remained as a string value, no struct: box/unbox.
>>
>>
>>
>>
>>
>>
>> On Fri, Dec 28, 2012 at 5:58 PM, Eric Dobson <eric.n.dobson at gmail.com>wrote:
>>
>>> Do refinement types work for what you want?
>>>
>>>
>>> http://docs.racket-lang.org/ts-reference/Experimental_Features.html?q=refinement#(form._((lib._typed-racket/base-env/prims..rkt)._declare-refinement))
>>>
>>> #lang typed/racket
>>> (declare-refinement even?)
>>> (: two (Refinement even?))
>>> (define two
>>>   (let ((x 2))
>>>     (if (even? x) x (error 'bad))))
>>>
>>> There are a couple of issues with them, mostly that they are not sound
>>> when dealing with mutable objects or non pure functions, which allows you
>>> to break the soundness of TR.
>>> http://bugs.racket-lang.org/query/?cmd=view+audit-trail&pr=13059
>>>
>>>
>>>  On Fri, Dec 28, 2012 at 2:17 PM, Ray Racine <ray.racine at gmail.com>wrote:
>>>
>>>>  Any plans something along the lines of Scala's proposed Value Types.
>>>>
>>>> A path:
>>>>
>>>> Allow for "special" struct: decls (vstruct: ?) where the parent is a
>>>> limited subset of non structure parent types (base value types such as
>>>> String, Number).
>>>>
>>>> These special structures MUST contain one and only one value of the
>>>> parent "special" type or it is a compile error.
>>>> The structure constructor does not construct the wrapping structure but
>>>> instead passes through the wrapped value, but *always* invokes the
>>>> validator during pass-thru.
>>>> TR treats the type as a subtype of the base value type.
>>>>
>>>> e.g.
>>>>
>>>> (struct: Identifier String ([value : String])
>>>>   #:methods gen:validator (lambda (thing) ...) ;; is of type (Any ->
>>>> Boolean : Identifier))
>>>>
>>>> (define id (Identifier "myidentifier")) ;; validator invoked, no
>>>> structure was allocated, `id' is just a String value, is a subtype of
>>>> String.
>>>>
>>>> (define uc-id (Identifer (string-upcase id))) ;; validator invoked, as
>>>> id is a just a string no unboxing in (string-upcase id), in fact no
>>>> allocations here at all.
>>>>
>>>> Under the covers the Identifier constructor never creates the
>>>> structure, it acts as a pass through id : (String -> String) function.
>>>>  i.e. the runtime representation of `id' is always as a String so any
>>>> struct <-> value boxing / unboxing is avoided.   I think there is enough
>>>> machinery in place to get pretty close to this.
>>>>
>>>> What is gained?
>>>>
>>>> What is done internally in TR defining Natural, Index,
>>>> Exact-Positive-Integer can now be done without special internal defining,
>>>> just another constrained base type.  One can start to define things like
>>>> Age [1 .. 120].
>>>> Another is IMHO a HUGE source of program error is just not enough time
>>>> to do proper validation at IO boundries where entering data is of the form
>>>> Strings and Bytes and it needs to be lifted.
>>>>
>>>> Consider the following typical use case from Amazon's AWS API, a
>>>> Tasklist parameter.
>>>>
>>>> Parameter - Tasklist : String[1-256]
>>>>
>>>> Specifies the task list to poll for activity tasks.
>>>>
>>>> The specified string must not start or end with whitespace. It must not
>>>> contain a : (colon), / (slash), | (vertical bar), or any control characters
>>>> (\u0000-\u001f | \u007f - \u009f). Also, it must not contain the literal
>>>> string "arn".
>>>>
>>>> Most likely, I'll punt.
>>>>
>>>> (: call-it (String ... -> ...))
>>>> (define (call-it task-list ...)
>>>>
>>>> If I'm ambitious today.
>>>>
>>>> ;; would prefer (define-new-type Tasklist String)
>>>> (define-type Tasklist String) ;; tighten things later down the road,
>>>> <sigh> none type generative
>>>>
>>>> (: call-it (Tasklist ... -> ...))
>>>> (define (call-it task-list ...)
>>>>
>>>> What I'd like to do.
>>>>
>>>> (define-value-type Tasklist String [1 .. 256] (lambda (this) ....)) ;;
>>>> mad use of regexp in validator fn (Any -> Boolean : Tasklist)
>>>>
>>>> (call-it (Tasklist "mytasklist") ...)
>>>>
>>>> (call-it (Tasklist "arn:bad/tasklist") ...)
>>>>
>>>> (define-value-type Age Integer [1 .. 120]) ;; no special validation
>>>> beyond bounds check.
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
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>>>>
>>>>
>>>
>>
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>>
>
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