November 2017
Beginner to intermediate
344 pages
7h 2m
Chinese
Content preview from 深入理解運算原理｜從簡單的機器到無所不能的程式
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第 7 章
也就是說，
RUN
是個可以模擬任何圖靈機的 lambda 演算程式
3
。結果證明相反的情況也可
以運作：將 lambda 演算運算式儲存到磁帶，並且根據一組化簡規則重複更新它（如同
第 208 頁『語意』的操作語意），圖靈機可以作為 lambda 演算的直譯器。
由於每個圖靈機都可以藉由 lambda 演算程式進行模擬，而且每個 lambda
演算程式都可以由圖靈機進行模擬，所以兩個系統的能力完全相同。這是
一個令人驚訝的結果，因為圖靈機器和 lambda 演算程式是以完全不同的
方式運作，沒有任何理由期待它們擁有完全相同的功能。
這意謂著它本身至少有一種模擬 lambda 演算的方式：首先在 lambda 演算裡實作圖靈
機，然後使用那個模擬機器執行 lambda 演算直譯器。這個模擬物內部的模擬物是一種
效率非常低落的方式，而我們可以更簡潔的藉由設計資料結構來表示 lambda 演算運算
式，然後直接實作操作語意，來得到相同的結果，但它的確證明了 lambda 演算必須通
用且不需建置任何新事物。自我直譯器是通用圖靈機的 lambda 演算版本：即使底層的
直譯器程式是固定的，我們還是可以提供適合的 lambda 演算運算式當作輸入來完成任
何工作。
正如我們所見，通用系統真正的好處在於可以將它程式化而執行不同的工作，而非總是
以寫死的程式碼執行單一工作。尤其可以程式化的將通用系統模擬任何其他的通用系
統；通用圖靈機可以估算 lambda 演算運算式，而 lambda 演算直譯器則可以模擬圖靈 ...
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