[Lua]50行代码的解释器，用来演示lambda calculus
嗯，来写写经过：
在知乎上看见用Belleve牛用javascript写了一个精简的lisp解释器
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我也想写一个，用lua写，能多简单呢？
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写了一个阉割的scheme解释器，包含lambda/if两个special form，以及+-=print几个过程，60行代码
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能再精简吗？比如把if给去掉？
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搜索，嗯，lambda calculus能帮我
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阅读wiki上lambda calculus的"Encoding datatypes"部分
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改写scheme脚本，用Y-combinator帮助实现递归，用church numeral表示数字，以及实现church numeral之上的基本逻辑、算数、关系运算，最后用这些基本运算编写for-each和fib过程
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从解释器里移除关键字if，移除过程+-=，改写print过程使之能够打印church numeral
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进一步把lambda实现为单参数过程，多参数lambda的声明和调用变成了语法糖，于是所有过程都是fully curried的了，和haskell一样
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虽然scheme脚本为了打印fibonacci数列需要做更多的事情，但解释器仅仅为这门阉割scheme提供了一个lambda关键字；就结果而言，它演示了如何在只支持“匿名过程”这个基本元素的语言中实现强大的计算能力；当然，完成这一切靠的是lambda calculus理论。过程和结果都非常有趣~
scheme代码，只支持lambda这个special form和基本过程print：
1 ((lambda (zero one add mul pow sub1 true false and or) 2 ((lambda (sub not zero? two Y) 3 ((lambda (less-equal? equal? three four) 4 ;------------------------------ 5 ((lambda (for-each fib) 6 (for-each (lambda (i) (print (fib zero one zero i))) zero (mul four four)) 7 ) 8 (Y 9 (lambda (self) 10 (lambda (f i n) 11 (f i) 12 (((equal? i n) 13 (lambda () i) 14 (lambda () (self f (add i one) n)))) 15 ) 16 )) 17 (Y 18 (lambda (self) 19 (lambda (a b i n) 20 (((equal? i n) 21 (lambda () a) 22 (lambda () (self b (add a b) (add i one) n)))) 23 ) 24 )) 25 ) 26 ;------------------------------ 27 ) 28 (lambda (m n) (zero? (sub m n))) 29 (lambda (m n) (and (zero? (sub m n)) (zero? (sub n m)))) 30 (add two one) 31 (add two two) 32 )) 33 (lambda (m n) (n sub1 m)) 34 (lambda (a) (a false true)) 35 (lambda (n) (n (lambda (x) false) true)) 36 (add one one) 37 (lambda (f) 38 ((lambda (g) (g g)) 39 (lambda (g) (f (lambda (a) ((g g) a)))))) 40 )) 41 (lambda (f x) x) 42 (lambda (f x) (f x)) 43 (lambda (m n f x) (m f (n f x))) 44 (lambda (m n f) (m (n f))) 45 (lambda (e b) (e b)) 46 (lambda (n f x) 47 (((n 48 (lambda (g h) (h (g f)))) 49 (lambda (u) x)) 50 (lambda (u) u))) 51 (lambda (a b) a) 52 (lambda (a b) b) 53 (lambda (a b) (a b a)) 54 (lambda (a b) (a a b)) 55 )
lua解释器代码：
1 function S_parse(s) 2 s = string.gsub(s, ';[^\n]+\n', '') 3 s = string.gsub(s, '%s+', ',') 4 s = string.gsub(s, '[%(%)]', {['(']='{',[')']='}'}) 5 s = string.gsub(s, '[^{},%d][^{},]*', '"%1"') 6 return assert(loadstring(string.format("return {%s}", s)))()[1] 7 end 8 function S_lookupVar(vm, env, name) 9 while env do 10 if env[name] then return env[name] end 11 env = env[vm] 12 end 13 end 14 function S_createLambda(vm, env, argIdx, expArgs, expBody) 15 return function(arg) 16 local newEnv = {[vm]=env, [expArgs[argIdx]]=arg} 17 if argIdx == #expArgs then 18 for i = 3, #expBody - 1 do S_interpret(vm, newEnv, expBody[i]) end 19 return S_interpret(vm, newEnv, expBody[#expBody]) 20 else 21 return S_createLambda(vm, newEnv, argIdx + 1, expArgs, expBody) 22 end 23 end 24 end 25 function S_interpret(vm, env, exp) 26 if type(exp) == 'string' then 27 return S_lookupVar(vm, env, exp) 28 elseif exp[1] == 'lambda' then 29 return S_createLambda(vm, env, 1, #exp[2] > 0 and exp[2] or {'_'}, exp) 30 else 31 local p = S_interpret(vm, env, exp[1]) 32 for i = 2, math.max(#exp, 2) do 33 p = p(exp[i] and S_interpret(vm, env, exp[i]) or nil) 34 end 35 return p 36 end 37 end 38 function S_createVM() 39 return { 40 G = { 41 ['print'] = function(n) print(n(function(i) return i + 1 end)(0)) end, 42 }, 43 } 44 end 45 function S_eval(vm, s) 46 return S_interpret(vm, vm.G, S_parse(s)) 47 end 48 49 S_eval(S_createVM(), io.read('*a'))
驱动：
1 #! /bin/bash 2 cat script.rkt | lua main.lua
结果：
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987
源码放这儿：https://github.com/PublicScan/LambdaCalculus/tree/c4a64b162b7049a6d278c86aaaa4a7c0750d7fa7
