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author Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
date Mon, 27 Apr 2015 18:33:12 +0900
parents 7976efbb34c4
children
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Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
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1 title: Categorical Formalization of Program Modification
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2 author: Yasutaka Higa
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3 profile:
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Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
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4 lang: Japanese
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7 # 研究目的 (Categorical Formalization)
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Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
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8 * プログラムの信頼性を向上させるために開発手法に着目する
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9 * プログラムの信頼性が変化するのはプログラムを変更した時である
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10 * 信頼性を保ちながらプログラムを変更にプログラムの変更を形式化する
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11 * Kleisli Category の Kleisli Triple と対応のある Monad によってプログラムの変更を記述する
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13 # 研究目的 (Parallel Debugger)
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14 * 本研究では Monad を用いてプログラムの変更を定義する
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15 * Monad とは meta computation とデータ構造を対応付ける手法である
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16 * プログラムの変更は変更前の動作を保存しつつ変更後の動作を追加することで表現する
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17 * 異なるバージョンのプログラムを同時に実行し、トレースを比較することでデバッグを支援する手法を提案する
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18
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19 # 異なる型の Delta
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20 * 型を合わせるように書こうと思ったけれど無理でしたという話
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21 * それぞれのシーケンスではやっぱり型はあってます
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22 * 型情報を取ると動きました
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23
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24 # 型の変更を含む Delta
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25 * 理想
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26 * apply function
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27 * `` (x, x') >>= (f, f') ``
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28 * variable type
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29 * `` (x, x') :: (Delta a) in (x :: a)``
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30 * function type
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31 * `` (f, f') :: a -> (Delta b) in (f :: a -> b)``
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32
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33 # 型変数を減らす?
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34 * T A の中に B があっても問題無いのでは? という話
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35 * data Delta a | ModifyInt Int (Delta a) | Mono a
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36 * 問題 : 関数をどうするか
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37 * A -> T B
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38 * T B の中に (C -> D) を埋め込む?
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39 * ってことは型チェック無理
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41 # 型変数をその場で追加する ExistentialQuantification
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42 * 型変数をその場で生成できたりします
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43 `` data Delta b a = forall c. Delta a (Delta b c) | Mono a ``
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44 * こうすると headDelta の型が不定になる
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45 * a? b? c?
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46
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47 # 問題点
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48 * tuple で考えると
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49 * T A から `` (a, a') :: (A, C)`` を作る
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50 * A -> T B から `` (f, f') :: (A -> B, C -> D) `` を作る必要がある
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51 * C と (C -> D) の情報が完全に隠れているので推論できない
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54 ...
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56 <!-- vim: set filetype=markdown.slide: -->