PLAI_Chapter7: Functions Anywhere

The introduction to the Scheme programming language definition establishes this design principle:

---

Programming languages should be designed not by piling feature on top of feature, but by removing the weaknesses and restrictions that make additional features appear necessary.

---

以下是到37页为止的解释器，无闭包，会导致dynamic scoping。

In other words, we’re again failing to faithfully capture what substitution would have done. A function value needs to remember the substitutions that have already been applied to it. Because we’re representing substitutions using an environment, a function value therefore needs to be bundled with an environment. This resulting data structure is called a closure.

#lang plai-typed

(define-type Value
  [numV (n : number)]
  [funV (name : symbol) (arg : symbol) (body : ExprC)])

(define-type ExprC
  [numC (n : number)]
  [idC (s : symbol)]
  [appC (fun : ExprC) (arg : ExprC)]
  [plusC (l : ExprC) (r : ExprC)]
  [multC (l : ExprC) (r : ExprC)]
  [fdC (name : symbol) (arg : symbol) (body : ExprC)])

(define (lookup [n : symbol] [env : Env]) : Value
  (cond
    [(empty? env) (error 'lookup "Symbol not found in env")]
    [(cons? env) (cond
                   [(equal? n (bind-name (first env))) (bind-val (first env))]
                   [else (lookup n (rest env))])]))

(define-type Binding
  [bind (name : symbol) (val : Value)])
(define-type-alias Env (listof Binding))
(define mt-env empty)
(define extend-env cons)

(define (num+ [l : Value] [r : Value]) : Value
  (cond
    [(and (numV? l) (numV? r))
     (numV (+ (numV-n l) (numV-n r)))]
    [else
     (error 'num+ "one argument was not a number")]))

(define (num* [l : Value] [r : Value]) : Value
  (cond
    [(and (numV? l) (numV? r))
     (numV (* (numV-n l) (numV-n r)))]
    [else
     (error 'num* "one argument was not a number")]))

(define (interp [expr : ExprC] [env : Env]) : Value
  (type-case ExprC expr
    [numC (n) (numV n)]
    [idC (n) (lookup n env)]
    [plusC (l r) (num+ (interp l env) (interp r env))]
    [multC (l r) (num* (interp l env) (interp r env))]
    [fdC (n a b) (funV n a b)]
    [appC (f a) (local ([define fd (interp f env)])
                  (interp (funV-body fd)
                          (extend-env (bind (funV-arg fd)
                                            (interp a env))
                                      mt-env)))]))

---

改为带closure的

#lang plai-typed

(define-type Value
  [numV (n : number)]
  [closV (arg : symbol) (body : ExprC) (env : Env)])

(define-type ExprC
  [numC (n : number)]
  [idC (s : symbol)]
  [appC (fun : ExprC) (arg : ExprC)]
  [plusC (l : ExprC) (r : ExprC)]
  [multC (l : ExprC) (r : ExprC)]
  [lamC (arg : symbol) (body : ExprC)])

(define (lookup [n : symbol] [env : Env]) : Value
  (cond
    [(empty? env) (error 'lookup "Symbol not found in env")]
    [(cons? env) (cond
                   [(equal? n (bind-name (first env))) (bind-val (first env))]
                   [else (lookup n (rest env))])]))

(define-type Binding
  [bind (name : symbol) (val : Value)])
(define-type-alias Env (listof Binding))
(define mt-env empty)
(define extend-env cons)

(define (num+ [l : Value] [r : Value]) : Value
  (cond
    [(and (numV? l) (numV? r))
     (numV (+ (numV-n l) (numV-n r)))]
    [else
     (error 'num+ "one argument was not a number")]))

(define (num* [l : Value] [r : Value]) : Value
  (cond
    [(and (numV? l) (numV? r))
     (numV (* (numV-n l) (numV-n r)))]
    [else
     (error 'num+ "one argument was not a number")]))

(define (interp [expr : ExprC] [env : Env]) : Value
  (type-case ExprC expr
    [numC (n) (numV n)]
    [idC (n) (lookup n env)]
    [plusC (l r) (num+ (interp l env) (interp r env))]
    [multC (l r) (num* (interp l env) (interp r env))]
    [lamC (a b) (closV a b env)]
    [appC (f a) (local ([define f-value (interp f env)])
                  (interp (closV-body f-value)
                          (extend-env (bind (closV-arg f-value)
                                            (interp a env))
                                      (closV-env f-value))))]))

Sugaring Over Anonymity

left-left-lambda

((lambda (double)
    (double 10))
 (lambda (x) (+ x x)))
;=>
(let ([double (lambda (x) (+ x x))])
    (double 10))

7.4 Substitution, Again

(lambda (f)
  (lambda (x)
 (f 10)))
;其中f是
  (lambda (y) (+ x y))

直接替换会导致dynamic scoping.
利用α-convention。

  (lambda (f1)
      (lambda (x1)
    (f1 10)))
(lambda (y1) (+ x y1))

(lambda (x1)
    ((lambda (y1) (+ x y1)) 10))
;x是未定义的自由变量，正是期待的行为