基于 PALI第七章:任意位置的函数
增加 if分支表达式，let表达式, begin表达式; desuger,prase,deprase组。
重写 number-calculate，
Code:
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#lang plai-typed
;;;------------------Inner Expression---------------------------
(define-type Expr
[Nmb (n : number)]
[Add (l : Expr) (r : Expr)]
[Sub (l : Expr) (r : Expr)]
[Mul (l : Expr) (r : Expr)]
[Div (l : Expr) (r : Expr)]
[Idf (e : symbol)]
[Lambda (para : symbol) (body : Expr)]
[Apply (fun : Expr) (argu : Expr)]
[If (test : Expr) (t-expr : Expr) (f-expr : Expr)]
[Test (mktest : symbol) (f-test : Expr) (t-test : Expr)])
(define-type S-Expr
[S-Nmb (n : number)]
[S-Add (l : S-Expr) (r : S-Expr)]
[S-Sub (l : S-Expr) (r : S-Expr)]
[S-Mul (l : S-Expr) (r : S-Expr)]
[S-Div (l : S-Expr) (r : S-Expr)]
[S-Idf (e : symbol)]
[S-Lambda (para : symbol) (body : S-Expr)]
[S-Apply (fun : S-Expr) (argu : S-Expr)]
[S-If (test : S-Expr) (t-expr : S-Expr) (f-expr : S-Expr)]
[S-Test (mktest : symbol) (f-test : S-Expr) (t-test : S-Expr)]
[Let (idf : symbol) (expr : S-Expr) (in : S-Expr)]
[Begin (first : S-Expr) (then : S-Expr)])
(define-type Value
[NmbV (n : number)]
[Bool (test-result : Boolen)]
[Closure (para : symbol) (body : Expr) (env : Env)])
(define-type Boolen [True] [False])
;;;------------------Envrionment Expression---------------------
(define-type Binding
[Bind (idf : symbol) (value : Value)])
(define-type-alias Env [listof Binding])
;;--envrionment handler-------
(define globle-env empty)
(define (extend-env [bind : Binding] [env : Env]) (cons bind env))
;;----find-idf-value symbol & Env -> Value -----
(define (find-idf-value [idf : symbol] [env : Env]) : Value
(cond
[(empty? env) (error 'find-idf-value "No such idf!")]
[(equal? idf (Bind-idf (first env))) (Bind-value (first env))]
[else (find-idf-value idf (rest env))]))
;;-------------------Core prase :: s-expression -> Expr -------------------
(define (prase [expr : s-expression]) : S-Expr
(cond
[(s-exp-number? expr) (S-Nmb (s-exp->number expr))]
[(s-exp-symbol? expr) (S-Idf (s-exp->symbol expr))]
[(s-exp-list? expr)
(let ([expr-list (s-exp->list expr)])
(cond
[(s-exp-list? (first expr-list))
(S-Apply (prase (first expr-list))
(prase (second expr-list)))]
[else (case (s-exp->symbol (first expr-list))
[(lambda) (S-Lambda (s-exp->symbol (second expr-list))
(prase (third expr-list)))]
[(+) (S-Add (prase (second expr-list))
(prase (third expr-list)))]
[(-) (S-Sub (prase (second expr-list))
(prase (third expr-list)))]
[(*) (S-Mul (prase (second expr-list))
(prase (third expr-list)))]
[(/) (S-Div (prase (second expr-list))
(prase (third expr-list)))]
[(=) (S-Test '= (prase (second expr-list)) (prase (third expr-list)))]
[(>) (S-Test '> (prase (second expr-list)) (prase (third expr-list)))]
[(<) (S-Test '< (prase (second expr-list)) (prase (third expr-list)))]
[(if) (S-If (let ([test (s-exp->list (second expr-list))])
(S-Test (s-exp->symbol (first test))
(prase (second test))
(prase (third test))))
(prase (third expr-list))
(prase (fourth expr-list)))]
;;<suger>
[(let) (let ([bind (s-exp->list (second expr-list))]
[in (prase (third expr-list))])
(let ([idf (s-exp->symbol (first bind))]
[expr (prase (second bind))])
(Let idf expr in)))]
[(begin) (Begin (prase (second expr-list))
(prase (third expr-list)))]
[else (S-Apply (prase (first expr-list))
(prase (second expr-list)))])]))]))
;; desuger :: Expr -> S-Expr
(define (desuger [s-expr : S-Expr]) : Expr
(type-case S-Expr s-expr
[S-Nmb (n) (Nmb n)]
[S-Add (l r) (Add (desuger l)
(desuger r))]
[S-Sub (l r) (Sub (desuger l)
(desuger r))]
[S-Mul (l r) (Mul (desuger l)
(desuger r))]
[S-Div (l r) (Div (desuger l)
(desuger r))]
[S-Idf (idf) (Idf idf)]
[S-Lambda (para body) (Lambda para (desuger body))]
[S-Apply (fun argu) (Apply (desuger fun)
(desuger argu))]
[S-If (test t-expr f-expr) (If (desuger test)
(desuger t-expr)
(desuger f-expr))]
[S-Test (mktest f-test t-test) (Test mktest
(desuger f-test)
(desuger t-test))]
;;<desuger-core>
[Let (idf expr in) (Apply (Lambda idf (desuger in))
(desuger expr))]
[Begin (first then) (Apply (Lambda 'Nil (desuger then))
(desuger first))]))
;;------------Core interp ::Expr & Env -> Value---------------
(define (interp [expr : Expr] [env : Env]) : Value
(type-case Expr expr
[Nmb (n) (NmbV n)]
[Idf (idf) (find-idf-value idf env)]
[Lambda (para body) (Closure para body env)]
[Apply (fun argu) (let ([fundef (interp fun env)])
(interp (Closure-body fundef)
(extend-env (Bind (Closure-para fundef)
(interp argu env))
(Closure-env fundef))))]
[If (test t-expr f-expr) (let ([test-result (Bool-test-result (interp test env))])
(type-case Boolen test-result
[True () (interp t-expr env)]
[False () (interp f-expr env)]))]
[Test (mktest f-test t-test) (test-handle mktest (interp f-test env)
(interp t-test env))]
[else (calcu-handle expr env)]))
;;----interp hepler----
(define (calcu-handle [expr : Expr] [env : Env]) : Value
(type-case Expr expr
[Add (l r) (calculate + (interp l env) (interp r env))]
[Sub (l r) (calculate - (interp l env) (interp r env))]
[Mul (l r) (calculate * (interp l env) (interp r env))]
[Div (l r) (calculate / (interp l env) (interp r env))]
[else (error 'calcu-handle "operater error!")]))
(define (calculate fun [l : Value] [r : Value]) : Value
(cond
[(and (NmbV? l) (NmbV? r))
(NmbV (fun (NmbV-n l)
(NmbV-n r)))]
[else (error 'caculate "One of input isn`t number!")]))
(define (test-handle [mktest : symbol] [l-value : Value] [r-value : Value]) : Value
(case mktest
((=) (if (= (NmbV-n l-value) (NmbV-n r-value))
(Bool (True)) (Bool (False))))
((>) (if (> (NmbV-n l-value) (NmbV-n r-value))
(Bool (True)) (Bool (False))))
((<) (if (< (NmbV-n l-value) (NmbV-n r-value))
(Bool (True)) (Bool (False))))))
;;---------------------Out Expression------------------------
(define (devalue [value : Value]) : s-expression
(type-case Value value
[NmbV (n) (number->s-exp n)]
[Bool (boolen) (type-case Boolen boolen
[True () (symbol->s-exp 'True)]
[False () (symbol->s-exp 'False)])]
[Closure (para body env) `(lambda ,(symbol->s-exp para) ,(deprase body)
Env: < ,(deenv env) >)]))
(define (deenv [env : Env]) : s-expression
(cond
[(empty? env) '()]
[else `((let ([bind (first env)])
`(,(symbol->s-exp (Bind-idf bind)) ,(devalue (Bind-value bind))))
(deenv (rest env)))]))
(define (deprase [expr : Expr]) : s-expression
(cond
[(Idf? expr) (symbol->s-exp (Idf-e expr))]
[(Lambda? expr) `(lambda ,(symbol->s-exp (Lambda-para expr))
,(deprase (Lambda-body expr)))]
[else `(,(deprase (Apply-fun expr))
,(deprase (Apply-argu expr)))]))
;;;Ohhh! finally it works!!!
(define (eval [s-expr : s-expression]) : s-expression
(devalue (interp (desuger (prase s-expr)) globle-env)))
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