From 4c9dc3138b634feb8de1a629f7808c99448fd3b9 Mon Sep 17 00:00:00 2001
From: Felix Martin <mail@felixm.de>
Date: Sat, 23 Jan 2021 14:02:35 -0500
Subject: [PATCH] Answer till 4.18

---
 ex-4_11-xx.scm | 104 ++++++++++++++++++++++++++++++++++++++++++-------
 1 file changed, 91 insertions(+), 13 deletions(-)

diff --git a/ex-4_11-xx.scm b/ex-4_11-xx.scm
index 591b7f6..2e4ccc5 100644
--- a/ex-4_11-xx.scm
+++ b/ex-4_11-xx.scm
@@ -190,7 +190,7 @@
 
 (display "[answered]\n")
 
-(display "\nex-4.16\n")
+(display "\nex-4.16 - scan-out-defines\n")
 
 (define (lookup-variable-value var env)
   (let ((pair (find-pair-env var env)))
@@ -201,20 +201,98 @@
           (error "Unassigned variable" var)
           value)))))
 
-(define env-0 the-empty-environment)
-(define env-1 (extend-environment '(a b) '(1 2) env-0))
-(define env-2 (extend-environment '(c d) '(3 *unassigned*) env-1))
-
 (define (scan-out-defines body)
-  (cond
-    ((null? body) '())
-    ((definition? (car body)) (cons (car body) (scan-out-defines (cdr body))))
-    (else (scan-out-defines (cdr body)))))
+  (define (get-defines body)
+    (cond
+      ((null? body) '())
+      ((definition? (car body)) (cons (car body) (get-defines (cdr body))))
+      (else (get-defines (cdr body)))))
+  (define (expression->new-expression exp)
+    (if (definition? exp)
+      (define->set exp)
+      exp))
+  (define (define->let-assignment def)
+    (list (definition-variable def) '*unassigned*))
+  (define (define->set def)
+    (list 'set! (definition-variable def) (definition-value def)))
+  (let* ((defines (get-defines body))
+         (let-assignments (map define->let-assignment defines))
+         (let-expression (list 'let let-assignments))
+         (expressions (map expression->new-expression body)))
+    (append let-expression expressions)))
 
-(define body '((define x 3)
-               (if #t 1 2)
-               (define b 2)))
+(define body
+  '((define x 3)
+    (if #t 1 2)
+    (define b 2)
+    (display "hello")))
 
-(display (scan-out-defines body)) (newline)
+(define body-transformed
+  '(let ((x *unassigned*)
+         (b *unassigned*))
+     (set! x 3)
+     (if #t 1 2)
+     (set! b 2)
+     (display "hello")))
+
+(assert (scan-out-defines body) body-transformed)
+
+; I would install scan-out-defines into make-procedure. We might run into a
+; situation where we update the body of a procedure and call procedure-body
+; twice.
+
+(define (make-procedure parameters body env)
+  (list 'procedure parameters (scan-out-defines body) env))
 
 (display "\nex-4.17\n")
+
+; Why is there an extra frame in the transformed program? We have implemented
+; let via an additional transformation. Therefore, there is another
+; lambda-expression that results in an extra frame.
+
+; Explain why this difference in environment structure can never make a
+; difference in the behavior of a correct program? The transformation keeps the
+; order of the assignments. Hence, the behavior will not change.
+
+; Design a way to make the interpreter implement the ``simultaneous'' scope
+; rule for internal definitions without constructing the extra frame? We could
+; simply add a list of (define symbol *unassigned*) at the beginning of the
+; body and get the same behavior without an extra frame.
+
+(display "[answered]\n")
+
+(display "\nex-4.18 - alternative-scan-out\n")
+
+(define (solve f y0 dt)
+  (define y (integral (delay dy) y0 dt))
+  (define dy (stream-map f y))
+  y)
+
+; Transformation from text:
+(lambda (f y0 dt)
+  (let ((y '*unassigned*)
+        (dy '*unassigned*))
+    (set! y (integral (delay dy) y0 dt))
+    (set! dy (stream-map f y))
+    y))
+
+; Transformation from this exercise:
+(lambda (f y0 dt)
+  (let ((y '*unassigned*)
+        (dy '*unassigned*))
+    (let ((a (integral (delay dy) y0 dt))
+          (b (stream-map f y)))
+      (set! y a)
+      (set! dy b)
+      y)))
+
+; The second transformation will not work because when b is evaluated y is not
+; yet assigned. The first transformation works because y was already set when
+; dy is set.
+
+(display "[answered]\n")
+
+(display "\nex-4.19\n")
+
+; (display "\nex-4.20\n")
+