Started writing phantom invariants representation, optimized flex records.
This commit is contained in:
Georges Dupéron
parent
de1f11dbf7
commit
e9255ca439
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@ -1,14 +1,14 @@
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<!-- Do Not Remove: Saved date Wed Dec 28 16:01:31 CET 2016 by georges on platform Linux 4.4.38 in JVM 1.8.0_122-04 -->
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<!-- Do Not Remove: Saved date Thu Dec 29 22:27:01 CET 2016 by georges on platform Linux 4.4.38 in JVM 1.8.0_122-04 -->
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@ -42,46 +42,74 @@ with a new one.
|
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|
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@CHUNK[<make-replace-in-tree-body>
|
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(if (= i 1)
|
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replacement-thunk
|
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#'(delay/pure/stateless replacement)
|
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(let* ([bits (to-bits i)]
|
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[next (from-bits (cons #t (cddr bits)))]
|
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[mod (cadr bits)])
|
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(define/with-syntax next-id (vector-ref names (sub1 next)))
|
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(define/with-syntax next-id (vector-ref low-names (sub1 next)))
|
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(if mod
|
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#`(delay/pure/stateless
|
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(let ([tree (force tree-thunk)])
|
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(let ([left-subtree (car tree)]
|
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[right-subtree (cdr tree)])
|
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(cons left-subtree
|
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(force (next-id (delay/pure/stateless right-subtree)
|
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. replacement?))))))
|
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(let ([tree (force tree-thunk)])
|
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(let ([left-subtree (car tree)]
|
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[right-subtree (cdr tree)])
|
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(cons left-subtree
|
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(force (next-id (delay/pure/stateless right-subtree)
|
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. replacement?))))))
|
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#`(delay/pure/stateless
|
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(let ([tree (force tree-thunk)])
|
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(let ([left-subtree (car tree)]
|
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[right-subtree (cdr tree)])
|
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(cons (force (next-id (delay/pure/stateless left-subtree)
|
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. replacement?))
|
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right-subtree)))))))]
|
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(let ([tree (force tree-thunk)])
|
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(let ([left-subtree (car tree)]
|
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[right-subtree (cdr tree)])
|
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(cons (force (next-id (delay/pure/stateless left-subtree)
|
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. replacement?))
|
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right-subtree)))))))]
|
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|
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@CHUNK[<define-replace-in-tree>
|
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(define-for-syntax (define-replace-in-tree names τ* i depth)
|
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(define-for-syntax (define-replace-in-tree low-names names rm-names τ* i depth)
|
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(define/with-syntax name (vector-ref names (sub1 i)))
|
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(define/with-syntax rm-name (vector-ref rm-names (sub1 i)))
|
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(define/with-syntax low-name (vector-ref low-names (sub1 i)))
|
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(define/with-syntax tree-type-with-replacement-name (gensym 'tree-type-with-replacement))
|
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(define/with-syntax replacement? #'(replacement))
|
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(define τ*-limited (take τ* depth))
|
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#`(begin
|
||||
(provide name)
|
||||
(: name
|
||||
(provide name rm-name)
|
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(define-type (tree-type-with-replacement-name #,@τ*-limited T)
|
||||
(Promise #,(tree-type-with-replacement i #'T τ*-limited)))
|
||||
(: low-name
|
||||
(∀ (#,@τ*-limited T)
|
||||
(→ (Promise #,(tree-type-with-replacement i #'Any τ*-limited))
|
||||
(→ (tree-type-with-replacement-name #,@τ*-limited Any)
|
||||
T
|
||||
(Promise #,(tree-type-with-replacement i #'(Some T) τ*-limited)))))
|
||||
(tree-type-with-replacement-name #,@τ*-limited T))))
|
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(define-pure/stateless
|
||||
#:∀ (#,@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)))))
|
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(define (name tree-thunk replacement)
|
||||
(low-name tree-thunk (Some replacement)))
|
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#;(define-pure/stateless
|
||||
#:∀ (#,@τ*-limited T)
|
||||
(name [tree-thunk : (tree-type-with-replacement-name #,@τ*-limited Any)]
|
||||
[replacement : T])
|
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: (Promise #,(tree-type-with-replacement i #'(Some T) τ*-limited))
|
||||
#,(let ([replacement-thunk #'(delay/pure/stateless (Some replacement))])
|
||||
<make-replace-in-tree-body>))))]
|
||||
(low-name tree-thunk (Some replacement)))
|
||||
|
||||
(: rm-name
|
||||
(∀ (#,@τ*-limited)
|
||||
(→ (tree-type-with-replacement-name #,@τ*-limited (Some Any))
|
||||
(tree-type-with-replacement-name #,@τ*-limited 'NONE))))
|
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(define (rm-name tree-thunk)
|
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(low-name tree-thunk 'NONE))
|
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#;(define-pure/stateless
|
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#:∀ (#,@τ*-limited)
|
||||
(rm-name [tree-thunk : (tree-type-with-replacement-name #,@τ*-limited (Some Any))])
|
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(low-name tree-thunk 'NONE))))]
|
||||
|
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@subsection{Removing fields}
|
||||
|
||||
|
|
@ -126,7 +154,12 @@ fields:
|
|||
(append (map (λ (i) (format-id #'here "-without-~a" i))
|
||||
i*-above)
|
||||
(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}
|
||||
|
||||
|
|
@ -190,7 +223,7 @@ fields:
|
|||
all-fields)))))
|
||||
(define (fields→tree-name field …)
|
||||
(delay/pure/stateless
|
||||
#,(convert-fields (* offset 2) fields+indices)))
|
||||
#,(convert-fields (* offset 2) fields+indices)))
|
||||
|
||||
(: tree→fields-name (∀ (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}
|
||||
|
||||
@chunk[<define-trees>
|
||||
@CHUNK[<define-trees>
|
||||
(define-for-syntax (define-trees stx)
|
||||
(syntax-case stx ()
|
||||
[(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-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>
|
||||
#`(begin
|
||||
(define-type-expander (bt-fields-id stx)
|
||||
(syntax-case stx ()
|
||||
[(_ . fs)
|
||||
#`(∀ 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 %))
|
||||
(define-type-expander bt-fields-id
|
||||
(bt-fields-type #'#,(syntax-local-introduce #'(field …))))
|
||||
#,@(map #λ(define-replace-in-tree low-names names rm-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)))
|
||||
#,@(map #λ(define-struct↔tree
|
||||
offset all-fields ∀-types %1 %2)
|
||||
(syntax->list #'(struct …))
|
||||
|
|
@ -320,11 +358,12 @@ interesting subparts of the trees (those where there are fields).
|
|||
<maybe>
|
||||
<tree-type-with-replacement>
|
||||
<define-replace-in-tree>
|
||||
<define-remove-in-tree>
|
||||
;<define-remove-in-tree>
|
||||
<convert-fields>
|
||||
<convert-back-fields>
|
||||
<τ-tree-with-fields>
|
||||
<define-struct↔tree>
|
||||
<define-trees>]
|
||||
<define-trees>
|
||||
<bt-fields-type>]
|
||||
|
||||
@include-section[(submod "flexible-with-utils.hl.rkt" doc)]
|
||||
98
invariants-phantom.hl.rkt
Normal file
98
invariants-phantom.hl.rkt
Normal file
|
|
@ -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)]
|
||||
|
|
@ -12,4 +12,5 @@ the @other-doc['(lib "phc-graph/scribblings/phc-graph.scrbl")] document.
|
|||
@(table-of-contents)
|
||||
|
||||
@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)]
|
||||
|
|
@ -5,7 +5,8 @@
|
|||
racket/list
|
||||
(rename-in racket/base [... …]))
|
||||
phc-toolkit
|
||||
typed-map)
|
||||
typed-map
|
||||
type-expander)
|
||||
|
||||
(define-syntax (gs stx)
|
||||
(syntax-case stx ()
|
||||
|
|
@ -21,12 +22,16 @@
|
|||
[struct struct-field …] …)))]))
|
||||
|
||||
(gs bt-fields
|
||||
16
|
||||
512
|
||||
(a b c)
|
||||
[sab a b]
|
||||
[sbc b c]
|
||||
[sabc a b c])
|
||||
|
||||
;(define-type btac (bt-fields a c))
|
||||
|
||||
#|
|
||||
|
||||
(check-equal?:
|
||||
(~> (ann (with-c (sab→tree 1 2) 'nine)
|
||||
((bt-fields a b c) One Positive-Byte 'nine))
|
||||
|
|
@ -73,4 +78,5 @@
|
|||
(call-with-values
|
||||
#λ(tree→sbc (without-a (with-c (sab→tree 1 2) 3)))
|
||||
list)
|
||||
'(2 3))
|
||||
'(2 3))
|
||||
|#
|
||||
58
times.rkt
Normal file
58
times.rkt
Normal file
|
|
@ -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
|
||||
))))
|
||||
Loading…
Reference in New Issue
Block a user