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Started writing phantom invariants representation, optimized flex records.

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Georges Dupéron 2016-12-30 02:25:20 +01:00
parent de1f11dbf7
commit e9255ca439
6 changed files with 476 additions and 105 deletions
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Graph-notes-copy2.vue
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111
flexible-with.hl.rkt
View File

@ -42,46 +42,74 @@ with a new one.
@CHUNK[<make-replace-in-tree-body> @CHUNK[<make-replace-in-tree-body>
(if (= i 1) (if (= i 1)
replacement-thunk #'(delay/pure/stateless replacement)
(let* ([bits (to-bits i)] (let* ([bits (to-bits i)]
[next (from-bits (cons #t (cddr bits)))] [next (from-bits (cons #t (cddr bits)))]
[mod (cadr bits)]) [mod (cadr bits)])
(define/with-syntax next-id (vector-ref names (sub1 next))) (define/with-syntax next-id (vector-ref low-names (sub1 next)))
(if mod (if mod
#`(delay/pure/stateless #`(delay/pure/stateless
(let ([tree (force tree-thunk)]) (let ([tree (force tree-thunk)])
(let ([left-subtree (car tree)] (let ([left-subtree (car tree)]
[right-subtree (cdr tree)]) [right-subtree (cdr tree)])
(cons left-subtree (cons left-subtree
(force (next-id (delay/pure/stateless right-subtree) (force (next-id (delay/pure/stateless right-subtree)
. replacement?)))))) . replacement?))))))
#`(delay/pure/stateless #`(delay/pure/stateless
(let ([tree (force tree-thunk)]) (let ([tree (force tree-thunk)])
(let ([left-subtree (car tree)] (let ([left-subtree (car tree)]
[right-subtree (cdr tree)]) [right-subtree (cdr tree)])
(cons (force (next-id (delay/pure/stateless left-subtree) (cons (force (next-id (delay/pure/stateless left-subtree)
. replacement?)) . replacement?))
right-subtree)))))))] right-subtree)))))))]
@CHUNK[<define-replace-in-tree> @CHUNK[<define-replace-in-tree>
(define-for-syntax (define-replace-in-tree names τ* i depth) (define-for-syntax (define-replace-in-tree low-names names rm-names τ* i depth)
(define/with-syntax name (vector-ref names (sub1 i))) (define/with-syntax name (vector-ref names (sub1 i)))
(define/with-syntax rm-name (vector-ref rm-names (sub1 i)))
(define/with-syntax low-name (vector-ref low-names (sub1 i)))
(define/with-syntax tree-type-with-replacement-name (gensym 'tree-type-with-replacement))
(define/with-syntax replacement? #'(replacement)) (define/with-syntax replacement? #'(replacement))
(define τ*-limited (take τ* depth)) (define τ*-limited (take τ* depth))
#`(begin #`(begin
(provide name) (provide name rm-name)
(: name (define-type (tree-type-with-replacement-name #,@τ*-limited T)
(Promise #,(tree-type-with-replacement i #'T τ*-limited)))
(: low-name
(∀ (#,@τ*-limited T) (∀ (#,@τ*-limited T)
(→ (Promise #,(tree-type-with-replacement i #'Any τ*-limited)) (→ (tree-type-with-replacement-name #,@τ*-limited Any)
T T
(Promise #,(tree-type-with-replacement i #'(Some T) τ*-limited))))) (tree-type-with-replacement-name #,@τ*-limited T))))
(define-pure/stateless (define-pure/stateless
#:∀ (#,@τ*-limited T) #:∀ (#,@τ*-limited T)
(name [tree-thunk : (Promise #,(tree-type-with-replacement i #'Any τ*-limited))] (low-name [tree-thunk : (tree-type-with-replacement-name #,@τ*-limited Any)]
[replacement : T])
: (Promise #,(tree-type-with-replacement i #'T τ*-limited))
#,<make-replace-in-tree-body>)
(: name
(∀ (#,@τ*-limited T)
(→ (tree-type-with-replacement-name #,@τ*-limited Any)
T
(tree-type-with-replacement-name #,@τ*-limited (Some T)))))
(define (name tree-thunk replacement)
(low-name tree-thunk (Some replacement)))
#;(define-pure/stateless
#:∀ (#,@τ*-limited T)
(name [tree-thunk : (tree-type-with-replacement-name #,@τ*-limited Any)]
[replacement : T]) [replacement : T])
: (Promise #,(tree-type-with-replacement i #'(Some T) τ*-limited)) (low-name tree-thunk (Some replacement)))
#,(let ([replacement-thunk #'(delay/pure/stateless (Some replacement))])
<make-replace-in-tree-body>))))] (: rm-name
(∀ (#,@τ*-limited)
(→ (tree-type-with-replacement-name #,@τ*-limited (Some Any))
(tree-type-with-replacement-name #,@τ*-limited 'NONE))))
(define (rm-name tree-thunk)
(low-name tree-thunk 'NONE))
#;(define-pure/stateless
#:∀ (#,@τ*-limited)
(rm-name [tree-thunk : (tree-type-with-replacement-name #,@τ*-limited (Some Any))])
(low-name tree-thunk 'NONE))))]
@subsection{Removing fields} @subsection{Removing fields}
@ -126,7 +154,12 @@ fields:
(append (map (λ (i) (format-id #'here "-without-~a" i)) (append (map (λ (i) (format-id #'here "-without-~a" i))
i*-above) i*-above)
(stx-map (λ (f) (format-id f "without-~a" f)) (stx-map (λ (f) (format-id f "without-~a" f))
#'(field …)))))] #'(field …)))))
(define low-names (list->vector
(append (map (λ (i) (format-id #'here "-u-with-~a" i))
i*-above)
(stx-map (λ (f) (format-id f "u-with-~a" f))
#'(field …)))))]
@section{Type of a tree-record} @section{Type of a tree-record}
@ -190,7 +223,7 @@ fields:
all-fields))))) all-fields)))))
(define (fields→tree-name field …) (define (fields→tree-name field …)
(delay/pure/stateless (delay/pure/stateless
#,(convert-fields (* offset 2) fields+indices))) #,(convert-fields (* offset 2) fields+indices)))
(: tree→fields-name (∀ (field …) (: tree→fields-name (∀ (field …)
(→ (Promise #,(τ-tree-with-fields #'(field …) (→ (Promise #,(τ-tree-with-fields #'(field …)
@ -265,7 +298,7 @@ interesting subparts of the trees (those where there are fields).
@section{Defining the converters and accessors for each known record type} @section{Defining the converters and accessors for each known record type}
@chunk[<define-trees> @CHUNK[<define-trees>
(define-for-syntax (define-trees stx) (define-for-syntax (define-trees stx)
(syntax-case stx () (syntax-case stx ()
[(bt-fields-id (field …) [struct struct-field …] …) [(bt-fields-id (field …) [struct struct-field …] …)
@ -276,17 +309,22 @@ interesting subparts of the trees (those where there are fields).
(define total-nb-functions (vector-length names)) (define total-nb-functions (vector-length names))
<define-trees-result>)]))] <define-trees-result>)]))]
@CHUNK[<bt-fields-type>
(define-for-syntax (bt-fields-type fields)
(λ (stx)
(syntax-case stx ()
[(_ . fs)
#`(∀ fs (Promise #,(τ-tree-with-fields #'fs
fields)))])))]
@CHUNK[<define-trees-result> @CHUNK[<define-trees-result>
#`(begin #`(begin
(define-type-expander (bt-fields-id stx) (define-type-expander bt-fields-id
(syntax-case stx () (bt-fields-type #'#,(syntax-local-introduce #'(field …))))
[(_ . fs) #,@(map #λ(define-replace-in-tree low-names names rm-names ∀-types % (floor-log2 %))
#`(∀ fs (Promise #,(τ-tree-with-fields #'fs
#'(field …))))]))
#,@(map #λ(define-replace-in-tree names ∀-types % (floor-log2 %))
(range 1 (add1 total-nb-functions)))
#,@(map #λ(define-remove-in-tree rm-names ∀-types % (floor-log2 %))
(range 1 (add1 total-nb-functions))) (range 1 (add1 total-nb-functions)))
#;#,@(map #λ(define-remove-in-tree rm-names ∀-types % (floor-log2 %))
(range 1 (add1 total-nb-functions)))
#,@(map #λ(define-struct↔tree #,@(map #λ(define-struct↔tree
offset all-fields ∀-types %1 %2) offset all-fields ∀-types %1 %2)
(syntax->list #'(struct …)) (syntax->list #'(struct …))
@ -320,11 +358,12 @@ interesting subparts of the trees (those where there are fields).
<maybe> <maybe>
<tree-type-with-replacement> <tree-type-with-replacement>
<define-replace-in-tree> <define-replace-in-tree>
<define-remove-in-tree> ;<define-remove-in-tree>
<convert-fields> <convert-fields>
<convert-back-fields> <convert-back-fields>
<τ-tree-with-fields> <τ-tree-with-fields>
<define-struct↔tree> <define-struct↔tree>
<define-trees>] <define-trees>
<bt-fields-type>]
@include-section[(submod "flexible-with-utils.hl.rkt" doc)] @include-section[(submod "flexible-with-utils.hl.rkt" doc)]

98
invariants-phantom.hl.rkt Normal file
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@ -0,0 +1,98 @@
#lang aful/unhygienic hyper-literate type-expander/lang
@title[#;#:style #;(with-html5 manual-doc-style)
#:tag "invariants-phantom"
#:tag-prefix "phc-graph/invariants-phantom"]{Tracking checked contracts
via phantom types}
@(chunks-toc-prefix
'("(lib phc-graph/scribblings/phc-graph-implementation.scrbl)"
"phc-graph/invariants-phantom"))
@section{Overview}
The cautious compiler writer will no doubt want to check that the graph used
to represent the program verifies some structural properties. For example, the
compiled language might not allow cycles between types. Another desirable
property is that the @racket[in-method] field of an instruction points back to
the method containing it. We will use this second property as a running
example in this section.
It is possible to express with Typed/Racket that a @racket[Method] should
contain a list of @racket[Instruction]s, and that @racket[Instruction]s should
point to a @racket[Method]@note{We are not concerned here about the ability to
create such values, which necessarily contain some form of cycle. The goal of
the graph library is indeed to handle the creation and traversal of such
cyclic data structures in a safe way}:
@chunk[<invariant-1>
(struct Instruction ([opcode : Byte]
[in-method : Method]))
(struct Method ([body : (Listof Instruction)]))]
This type does not, however, encode the fact that an instruction should point
to the method containing it. Typed/Racket does not really have a notion of
singleton types, aside from symbols and other primitive data. It also lacks a
way to type "the value itself" (e.g. to describe a single-field structure
pointing to itself, possibly via a @racket[Promise]). This means that the
property could only be expressed in a rather contrived way, if it is at all
possible.
@; (define-type Self-Loop (∀ (A) (→ (Pairof Integer (Self-Loop A)))))
We decide to rely instead on a run-time check, i.e. a sort of contract which
checks the structural invariant on the whole graph. In order to let the
type-checker know whether a value was checked against that contract or not, we
include within the node a phantom type which is used as a flag, indicating
that the graph was checked against that contract.
@chunk[<invariant-2>
(struct (Flag) Instruction ([opcode : Byte]
[in-method : (Method Flag)]))
(struct (Flag) Method ([body : (Listof (Instruction Flag))]))]
We would then write a function accepting a @racket[Method] for which the
contract @racket[method→instruction→same-method] was checked like this:
@chunk[<invariant-2-use>
(λ ([m : (Method 'method→instruction→same-method)])
…)]
Unfortunately, this attempt fails to catch errors as one would expect, because
Typed/Racket discards unused polymorphic arguments, as can be seen in the
following example, which type-checks without any complaint:
@chunk[<phantom-types-ignored>
(struct (Phantom) S ([x : Integer]))
(define inst-sa : (S 'a) (S 1))
(ann inst-sa (S 'b))]
We must therefore make a field with the @racket[Flag] type actually appear
within the instance:
@chunk[<invariant-3>
(struct (Flag) Instruction ([opcode : Byte]
[in-method : (Method Flag)]
[flag : Flag]))
(struct (Flag) Method ([body : (Listof (Instruction Flag))]
[flag : Flag]))]
Another issue is that the flag can easily be forged. We would therefore like
to wrap it in a struct type which is only accessible by the graph library:
@chunk[<invariant-4>
(struct (Flag) Flag-Wrapper-Struct ([flag : Flag]))
(define-type Flag-Wrapper Flag-Wrapper-Struct)
(code:comment "provide only the type, not the constructor or accessor")
(provide Flag-Wrapper)]
@; size → use a dummy function which errors when called
@; (accepts an opaque token to prevent calling)
@; Subtyping: multiple contracts with case→
@; Subtyping: when C1 ⇒ C2,
@; make the marker for C1 a subtype of the marker for C2
@chunk[<*>
(void)]

3
scribblings/phc-graph-implementation.scrbl
View File

@ -12,4 +12,5 @@ the @other-doc['(lib "phc-graph/scribblings/phc-graph.scrbl")] document.
@(table-of-contents) @(table-of-contents)
@include-section[(submod "../traversal.hl.rkt" doc)] @include-section[(submod "../traversal.hl.rkt" doc)]
@include-section[(submod "../flexible-with.hl.rkt" doc)] @include-section[(submod "../flexible-with.hl.rkt" doc)]
@include-section[(submod "../invariants-phantom.hl.rkt" doc)]

12
test/test-flexible-with.rkt
View File

@ -5,7 +5,8 @@
racket/list racket/list
(rename-in racket/base [... …])) (rename-in racket/base [... …]))
phc-toolkit phc-toolkit
typed-map) typed-map
type-expander)
(define-syntax (gs stx) (define-syntax (gs stx)
(syntax-case stx () (syntax-case stx ()
@ -21,12 +22,16 @@
[struct struct-field …] …)))])) [struct struct-field …] …)))]))
(gs bt-fields (gs bt-fields
16 512
(a b c) (a b c)
[sab a b] [sab a b]
[sbc b c] [sbc b c]
[sabc a b c]) [sabc a b c])
;(define-type btac (bt-fields a c))
#|
(check-equal?: (check-equal?:
(~> (ann (with-c (sab→tree 1 2) 'nine) (~> (ann (with-c (sab→tree 1 2) 'nine)
((bt-fields a b c) One Positive-Byte 'nine)) ((bt-fields a b c) One Positive-Byte 'nine))
@ -73,4 +78,5 @@
(call-with-values (call-with-values
#λ(tree→sbc (without-a (with-c (sab→tree 1 2) 3))) #λ(tree→sbc (without-a (with-c (sab→tree 1 2) 3)))
list) list)
'(2 3)) '(2 3))
|#

58
times.rkt Normal file
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@ -0,0 +1,58 @@
#lang racket
(require plot)
(parameterize ([plot-x-transform log-transform]
[plot-x-ticks (log-ticks #:base 2)]
[plot-y-transform log-transform]
[plot-y-ticks (log-ticks #:base 2)])
(plot
#:x-min 1 #:x-max 3000
#:y-min 1 #:y-max 3000
(points '(#(16 16)
#(17 25)
#(20 26)
#(24 29)
#(28 31)
#(32 35) ;; 20 with shared implementation & type, 22 shrd impl only
#(33 60)
#(40 67)
#(48 77)
#(56 80)
#(64 92) ;; 46
#(65 168)
#(80 189)
#(96 216)
#(128 276)
#(129 562)
#(256 911)
#(257 2078)
#(512 3000) ;; rough estimation
))))
;; with shared implementation & type:
(parameterize ([plot-x-transform log-transform]
[plot-x-ticks (log-ticks #:base 2)]
[plot-y-transform log-transform]
[plot-y-ticks (log-ticks #:base 2)])
(plot
#:x-min 1 #:x-max 600
#:y-min 1 #:y-max 600
(points '(#(16 11)
;#(17 25)
;#(20 26)
;#(24 29)
;#(28 31)
#(32 20)
;#(33 60)
;#(40 67)
;#(48 77)
;#(56 80)
#(64 46)
;#(65 168)
;#(80 189)
;#(96 216)
#(128 120)
;#(129 562)
#(256 363)
;#(257 2078)
;#(512 3000) ;; rough estimation
))))