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

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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