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https://github.com/luohaha/lambda-calculus
lambda calculus interpreter
https://github.com/luohaha/lambda-calculus
lambda lambda-calculus scheme
Last synced: 2 months ago
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lambda calculus interpreter
- Host: GitHub
- URL: https://github.com/luohaha/lambda-calculus
- Owner: luohaha
- License: gpl-3.0
- Created: 2016-08-25T15:55:53.000Z (about 8 years ago)
- Default Branch: master
- Last Pushed: 2016-09-01T13:56:32.000Z (about 8 years ago)
- Last Synced: 2024-06-24T04:35:02.584Z (3 months ago)
- Topics: lambda, lambda-calculus, scheme
- Language: Scheme
- Size: 29.3 KB
- Stars: 9
- Watchers: 3
- Forks: 1
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
# lambda-calculus
This is a lambda calculus interpreter.
## Usage
```
cd lambda/
./run [filename]
```
> Need chezscheme
## Grammar
```
::=
::= (lambda )
::= ( )
```
## 概念介绍
更多关于lambda演算的解释在[这里](https://zh.wikipedia.org/wiki/Λ演算)可以看到。
## 辅助函数
```scheme
(Tag )
```
> id为expression的缩写。
```scheme
(display )
```
> 打印规约之后的结果。
```scheme
(display-integer )
```
> 打印规约之后结果的整数值。
```scheme
(display-boolean )
```
> 打印规约之后结果的布尔值。
## 例子
```scheme
;;Y combination
(Tag Y (lambda f ((lambda x (f (x x))) (lambda x (f (x x))))))
;;integer
(Tag 0 (lambda p (lambda x x)))
(Tag 1 (lambda p (lambda x (p x))))
(Tag 2 (lambda p (lambda x (p (p x)))))
(Tag 3 (lambda p (lambda x (p (p (p x))))))
;;boolean
(Tag true (lambda x (lambda y x)))
(Tag false (lambda x (lambda y y)))
;;condition
(Tag if (lambda x x))
(Tag zero? (lambda x ((x (lambda y false)) true)))
;;data structure
(Tag cons (lambda x (lambda y (lambda f ((f x) y)))))
(Tag car (lambda f (f (lambda x (lambda y x)))))
(Tag cdr (lambda f (f (lambda x (lambda y y)))))
;;operator
(Tag increment (lambda n (lambda p (lambda x (p ((n p) x))))))
(Tag decrement (lambda n (lambda f (lambda x (((n (lambda g (lambda h (h (g f))))) (lambda u x)) (lambda u u))))))
(Tag + (lambda m (lambda n (lambda f (lambda x ((m f) ((n f) x)))))))
(Tag - (lambda m (lambda n ((n decrement) m))))
(Tag * (lambda m (lambda n (lambda f (m (n f))))))
(Tag pow (lambda m (lambda n ((n (* m)) 1))))
(Tag >= (lambda m (lambda n (zero? ((- n) m)))))
(Tag <= (lambda m (lambda n (zero? ((- m) n)))))
(Tag and (lambda m (lambda n ((m n) false))))
(Tag or (lambda m (lambda n ((m true) n))))
(Tag not (lambda m ((m false) true)))
(Tag mod (lambda f (lambda m (lambda n (((if ((<= n) m))
((f ((- m) n)) n))
m)))))
(Tag add-list (lambda f (lambda n (((if (zero? n)) 0) ((+ (f (decrement n))) n)))))
;;求规约之后的结果
(display ((pow 3) (cdr ((cons 2) 3))))
;; => (lambda f (lambda x4 (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f x4)))))))))))))))))))))))))))))
;;求规约之后的结果，转化为integer
(display-integer ((add-list (Y add-list)) (increment 3)))
;; => 10
;;求规约后的结果
(display (((mod (Y mod)) (increment (increment 3))) 3))
;; => (lambda f1793 (lambda x1894 (f1793 (f1793 x1894))))
;;求规约之后的结果，转化为boolean
(display-boolean (((if ((and true) true)) ((or false) false)) true))
;; => #f
```