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

Of course, now we all know who to thank, the *real* brain behind this
outfit, thank you, Most Functional Man In The World.


On Fri, Dec 28, 2012 at 10:04 PM, Ray Racine <ray.racine at gmail.com> wrote:

> Heh, defined the type predicate and never leveraged it.  This is looking
> very promising.
>
> #lang typed/racket
>
> (provide
>  Even Even? +e)
>
> (declare-refinement even?)
> (define-type Even (Refinement even?))
> (define-predicate Even? Even)
>
> ;; Optimizer says this is in-lined away. Now I'm getting down right giddy.
> (: An-Even (Number -> Even))
> (define (An-Even num)
>   (assert num Even?))
>
> (: +e (Even Even -> Even))
> (define (+e e1 e2)
>   (An-Even (+ e1 e2)))
>
> (+e (An-Even 4) (An-Even 6))
> (+e (An-Even 2) (An-Even 3))
>
>
> On Fri, Dec 28, 2012 at 9:37 PM, Ray Racine <ray.racine at gmail.com> wrote:
>
>> Can I just say, "DAMN YOU GUYS ARE GOOD."  Thank you.
>>
>> #lang typed/racket
>>
>> (declare-refinement even?)
>>
>> (define-type Even (Refinement even?))
>>
>> (define-predicate Even? Even)
>>
>> (: An-Even (Number -> Even))
>> (define (An-Even num)
>>   (if (Even? num)
>>       num
>>       (error 'I-DONT-DO-ODD)))
>>
>> (: +e (Even Even -> Even))
>> (define (+e e1 e2)
>>   (let ((y (+ e1 e2)))
>>     (if (Even? y)
>>         y
>>         (error 'RING-OF-EVEN-VIOLATION))))
>>
>> (+e (An-Even 4) (An-Even 6))
>> (+e (An-Even 2) (An-Even 3))
>>
>>
>> On Fri, Dec 28, 2012 at 9:01 PM, Ray Racine <ray.racine at gmail.com> wrote:
>>
>>> 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.
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> ____________________
>>>>>>>   Racket Users list:
>>>>>>>   http://lists.racket-lang.org/users
>>>>>>>
>>>>>>>
>>>>>>
>>>>>
>>>>> ____________________
>>>>>   Racket Users list:
>>>>>   http://lists.racket-lang.org/users
>>>>>
>>>>>
>>>>
>>>
>>
>
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