Macros are now properly getting baked in Modules bug still persists
This commit is contained in:
Felix Brendel
+33
-33
@@ -14,7 +14,7 @@
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(define the-empty-stream ())
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(define (stream-null? s) (if s t ()))
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(define (stream-null? s) (when s t))
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(define-syntax (delay expr)
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`(,lambda () ,expr))
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@@ -26,7 +26,7 @@
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(define-syntax (add . args) (pair '+ args))
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(define-syntax (when condition . body)
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:doc "Special form for when multiple actions should be done if a
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"Special form for when multiple actions should be done if a
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condition is true.
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{{{example_start}}}
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@@ -46,14 +46,14 @@ condition is true.
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(define-syntax (unless condition . body)
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:doc "Special form for when multiple actions should be done if a
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"Special form for when multiple actions should be done if a
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condition is false."
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(if (= (rest body) ())
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`(if ,condition nil ,@body)
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`(if ,condition nil (begin ,@body))))
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(define-syntax (n-times times action)
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:doc "Executes action times times."
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"Executes action times times."
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(define (repeat times elem)
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(unless (> 1 times)
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(pair elem (repeat (- times 1) elem))))
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@@ -102,7 +102,7 @@ condition is false."
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(rec clauses))
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(define-syntax (construct-list . body)
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:doc "
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"
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{{{example_start}}}
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(construct-list
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i <- '(1 2 3 4 5)
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@@ -143,7 +143,7 @@ condition is false."
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(rec body))
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;; (define-syntax (apply fun seq)
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;; :doc "Applies the function to the sequence, as in calls the function with
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;; "Applies the function to the sequence, as in calls the function with
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;; ithe sequence as arguemens."
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;; `(eval (pair ,fun ,seq)))
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@@ -160,9 +160,9 @@ condition is false."
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,@body)))
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(define-syntax (define-module module-name (:imports ()) :exports . body)
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(define-syntax (define-module module-name (:imports ()) (:exports ()) . body)
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(let ((module-prefix (concat-strings (symbol->string module-name) "::")))
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(eval `(begin ,@(map (lambda (x) `(,import ,x)) imports) ,@body))
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(eval `(,begin ,@(map (lambda (x) `(,import ,x)) imports) ,@body))
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(pair 'begin
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(map (lambda (orig-export-name)
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((lambda (export-name)
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@@ -235,11 +235,11 @@ condition is false."
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)
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(define (null? x)
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:doc "Checks if the argument is =nil=."
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"Checks if the argument is =nil=."
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(= x ()))
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(define (type=? obj typ)
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:doc "Checks if the argument =obj= is of type =typ="
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"Checks if the argument =obj= is of type =typ="
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(= (type obj) typ))
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(define (types=? . objs)
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@@ -264,43 +264,43 @@ condition is false."
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(inner objs))
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(define (number? x)
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:doc "Checks if the argument is a number."
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"Checks if the argument is a number."
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(type=? x :number))
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(define (symbol? x)
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:doc "Checks if the argument is a symbol."
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"Checks if the argument is a symbol."
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(type=? x :symbol))
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(define (keyword? x)
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:doc "Checks if the argument is a keyword."
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"Checks if the argument is a keyword."
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(type=? x :keyword))
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(define (pair? x)
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:doc "Checks if the argument is a pair."
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"Checks if the argument is a pair."
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(type=? x :pair))
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(define (string? x)
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:doc "Checks if the argument is a string."
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"Checks if the argument is a string."
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(type=? x :string))
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(define (lambda? x)
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:doc "Checks if the argument is a function."
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"Checks if the argument is a function."
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(type=? x :lambda))
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(define (macro? x)
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:doc "Checks if the argument is a macro."
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"Checks if the argument is a macro."
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(type=? x :macro))
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(define (special-lambda? x)
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:doc "Checks if the argument is a special-lambda."
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"Checks if the argument is a special-lambda."
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(type=? x :dynamic-macro))
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(define (built-in-function? x)
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:doc "Checks if the argument is a built-in function."
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"Checks if the argument is a built-in function."
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(type=? x :cfunction))
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(define (continuation? x)
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:doc "Checks if the argument is a continuation."
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"Checks if the argument is a continuation."
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(type=? x :continuation))
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(define (procedure? x)
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@@ -311,7 +311,7 @@ condition is false."
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(continuation? x)))
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(define (end seq)
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:doc "Returns the last pair in the sqeuence.
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"Returns the last pair in the sqeuence.
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{{{example_start}}}
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(define a (list 1 2 3 4))
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@@ -323,7 +323,7 @@ condition is false."
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(end (rest seq))))
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(define (last seq)
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:doc "Returns the (first) of the last (pair) of the given sequence.
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"Returns the (first) of the last (pair) of the given sequence.
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{{{example_start}}}
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(define a (list 1 2 3 4))
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@@ -333,7 +333,7 @@ condition is false."
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(first (end seq)))
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(define (extend seq elem)
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:doc "Extends a list with the given element, by putting it in
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"Extends a list with the given element, by putting it in
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the (rest) of the last element of the sequence."
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(if (pair? seq)
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(begin
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@@ -343,7 +343,7 @@ the (rest) of the last element of the sequence."
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elem))
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(define (extend2 seq elem)
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:doc "Extends a list with the given element, by putting it in
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"Extends a list with the given element, by putting it in
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the (rest) of the last element of the sequence."
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(print "addr of (end seq)" (addr-of (end seq)))
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(if (pair? seq)
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@@ -354,12 +354,12 @@ the (rest) of the last element of the sequence."
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elem)
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(define (append seq elem)
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:doc "Appends an element to a sequence, by extendeing the list
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"Appends an element to a sequence, by extendeing the list
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with (pair elem nil)."
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(extend seq (pair elem ())))
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(define (length seq)
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:doc "Returns the length of the given sequence."
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"Returns the length of the given sequence."
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(if (null? seq)
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0
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(+ 1 (length (rest seq)))))
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@@ -384,21 +384,21 @@ with (pair elem nil)."
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(else (pair (first seq) (list-without-index (rest seq) (- index 1))))))
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(define (increment val)
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:doc "Adds one to the argument."
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"Adds one to the argument."
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(+ val 1))
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(define (decrement val)
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:doc "Subtracts one from the argument."
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"Subtracts one from the argument."
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(- val 1))
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(define (range (:from 0) :to)
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:doc "Returns a sequence of numbers starting with the number defined
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"Returns a sequence of numbers starting with the number defined
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by the key =from= and ends with the number defined in =to=."
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(when (< from to)
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(pair from (range :from (+ 1 from) :to to))))
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(define (range-while (:from 0) :to)
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:doc "Returns a sequence of numbers starting with the number defined
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"Returns a sequence of numbers starting with the number defined
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by the key 'from' and ends with the number defined in 'to'."
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(define result (list (copy from)))
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(define head result)
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@@ -420,7 +420,7 @@ elemens as argument to that function."
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(map fun (rest seq)))))
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(define (reduce fun seq)
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:doc "Takes a function and a sequence as arguments and applies the
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"Takes a function and a sequence as arguments and applies the
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function to the argument sequence. This only works correctly if the
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given function accepts a variable amount of parameters. If your
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funciton is limited to two arguments, use [[=reduce-binary=]]
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@@ -428,7 +428,7 @@ instead."
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(apply fun seq))
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(define (reduce-binary fun seq)
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:doc "Takes a function and a sequence as arguments and applies the
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"Takes a function and a sequence as arguments and applies the
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function to the argument sequence. reduce-binary applies the arguments
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*pair-wise* which means it works with binary functions as compared to
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[[=reduce=]]."
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@@ -438,7 +438,7 @@ function to the argument sequence. reduce-binary applies the arguments
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(reduce-binary fun (rest seq)))))
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(define (filter fun seq)
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:doc "Takes a function and a sequence as arguments and applies the
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"Takes a function and a sequence as arguments and applies the
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function to every value in the sequence. If the result of that
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funciton application returns a truthy value, the original value is
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added to a list, which in the end is returned."
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+18
-19
@@ -1,22 +1,21 @@
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;; (define-module math
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;; :exports
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;; (pi tau pow sqrt)
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;; (define pi 3.1415)
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;; (define tau (* 2 pi))
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;; (define (pow a b) (** a b))
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;; (define (sqrt a) (** a 0.5)))
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;; (assert (= math::pi 3.1415))
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;; (assert (= math::tau (* 2 math::tau)))
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(tdefine-module 'math
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(define-module math
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:exports
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'(pi tau pow sqrt)
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(pi tau pow sqrt)
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'(define pi 3.1415)
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'(define tau (* 2 pi))
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'(define (pow a b) (** a b))
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'(define (sqrt a) (** a 0.5)))
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(define pi 3.1415)
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(define tau (* 2 pi))
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(define (pow a b) (** a b))
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(define (sqrt a) (** a 0.5)))
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(assert (= math::pi 3.1415))
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(assert (= math::tau (* 2 math::tau)))
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;; (tdefine-module 'math
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;; :exports
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;; '(pi tau pow sqrt)
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;; '(define pi 3.1415)
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;; '(define tau (* 2 pi))
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;; '(define (pow a b) (** a b))
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;; '(define (sqrt a) (** a 0.5)))
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+226
-233
@@ -1,149 +1,149 @@
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;; (define (abs x)
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;; (cond ((< x 0) (- x))
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;; (else x)))
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(define (abs x)
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(cond ((< x 0) (- x))
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(else x)))
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;; (assert (= (abs 1) 1))
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;; (assert (= (abs (- 2)) 2))
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(assert (= (abs 1) 1))
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(assert (= (abs (- 2)) 2))
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;; (define (abs x)
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;; (if (< x 0)
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;; (- x)
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;; x))
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(define (abs x)
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(if (< x 0)
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(- x)
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x))
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;; (assert (= (abs 12) 12))
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;; (assert (= (abs (- 32)) 32))
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(assert (= (abs 12) 12))
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(assert (= (abs (- 32)) 32))
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;; (define (>= x y)
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;; (or (> x y)
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;; (= x y)))
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(define (>= x y)
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(or (> x y)
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(= x y)))
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;; (assert (>= 2 2))
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;; (assert (>= 3 2))
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;; (assert (not (>= 1 2)))
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;; (assert (not (>= 12 44)))
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(assert (>= 2 2))
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(assert (>= 3 2))
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(assert (not (>= 1 2)))
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(assert (not (>= 12 44)))
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;; (define (>= x y)
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;; (not (< x y)))
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(define (>= x y)
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(not (< x y)))
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;; (assert (>= 2 2))
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;; (assert (>= 3 2))
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;; (assert (not (>= 1 2)))
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;; (assert (not (>= 12 44)))
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(assert (>= 2 2))
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(assert (>= 3 2))
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(assert (not (>= 1 2)))
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(assert (not (>= 12 44)))
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;; (define (a-plus-abs-b a b)
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;; ((if (> b 0) + -) a b))
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(define (a-plus-abs-b a b)
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((if (> b 0) + -) a b))
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;; (assert (= (a-plus-abs-b 1 2) 3))
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;; (assert (= (a-plus-abs-b 1 -2) 3))
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(assert (= (a-plus-abs-b 1 2) 3))
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(assert (= (a-plus-abs-b 1 -2) 3))
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;; (define (square x) (* x x))
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;; (define (cube x) (* x x x))
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(define (square x) (* x x))
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(define (cube x) (* x x x))
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;; (assert (= ((lambda (x y z)
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;; (+ x y (square z)))
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;; 1 2 3)
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;; 12))
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(assert (= ((lambda (x y z)
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(+ x y (square z)))
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1 2 3)
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12))
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;; ;;; --------------------
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;; ;;; newtons method
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;; ;;; --------------------
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;; (define tolerance 0.001)
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(define tolerance 0.001)
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;; (define (square x)
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;; (* x x))
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(define (square x)
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(* x x))
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;; (define (average x y)
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;; (/ (+ x y) 2))
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(define (average x y)
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(/ (+ x y) 2))
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;; (define (improve guess x)
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;; (average guess (/ x guess)))
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(define (improve guess x)
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(average guess (/ x guess)))
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;; (define (good-enough? guess x)
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;; (< (abs (- (square guess) x)) tolerance))
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(define (good-enough? guess x)
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(< (abs (- (square guess) x)) tolerance))
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;; (define (sqrt-iter guess x)
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;; (if (good-enough? guess x)
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;; guess
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;; (sqrt-iter (improve guess x) x)))
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(define (sqrt-iter guess x)
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(if (good-enough? guess x)
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guess
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(sqrt-iter (improve guess x) x)))
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;; (define (sqrt x)
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;; (sqrt-iter 1.0 x))
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(define (sqrt x)
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(sqrt-iter 1.0 x))
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|
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;; (define (sqrt2 x)
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;; (define (good-enough? guess x)
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;; (< (abs (- (square guess) x)) 0.001))
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(define (sqrt2 x)
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(define (good-enough? guess x)
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(< (abs (- (square guess) x)) 0.001))
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;; (define (improve guess x)
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;; (average guess (/ x guess)))
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(define (improve guess x)
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(average guess (/ x guess)))
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;; (define (sqrt-iter guess x)
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;; (if (good-enough? guess x)
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;; guess
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;; (sqrt-iter (improve guess x) x)))
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(define (sqrt-iter guess x)
|
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(if (good-enough? guess x)
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guess
|
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(sqrt-iter (improve guess x) x)))
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|
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;; (sqrt-iter 1.0 x))
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(sqrt-iter 1.0 x))
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|
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;; (define (sqrt3 x)
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;; (define (good-enough? guess)
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;; (< (abs (- (square guess) x)) 0.001))
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(define (sqrt3 x)
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(define (good-enough? guess)
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(< (abs (- (square guess) x)) 0.001))
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|
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;; (define (improve guess)
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;; (average guess (/ x guess)))
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(define (improve guess)
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(average guess (/ x guess)))
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|
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;; (define (sqrt-iter guess)
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;; (if (good-enough? guess)
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;; guess
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;; (sqrt-iter (improve guess))))
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(define (sqrt-iter guess)
|
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(if (good-enough? guess)
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guess
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(sqrt-iter (improve guess))))
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|
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;; (sqrt-iter 1.0))
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(sqrt-iter 1.0))
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;; (assert (< (abs (- 3 (sqrt 9))) tolerance))
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;; (assert (< (abs (- 4 (sqrt 16))) tolerance))
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;; (assert (not (< (abs (- 4 (sqrt 15))) tolerance)))
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(assert (< (abs (- 3 (sqrt 9))) tolerance))
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(assert (< (abs (- 4 (sqrt 16))) tolerance))
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(assert (not (< (abs (- 4 (sqrt 15))) tolerance)))
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;; (assert (< (abs (- 3 (sqrt2 9))) tolerance))
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;; (assert (< (abs (- 4 (sqrt2 16))) tolerance))
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;; (assert (not (< (abs (- 4 (sqrt2 15))) tolerance)))
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(assert (< (abs (- 3 (sqrt2 9))) tolerance))
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(assert (< (abs (- 4 (sqrt2 16))) tolerance))
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(assert (not (< (abs (- 4 (sqrt2 15))) tolerance)))
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;; (assert (< (abs (- 3 (sqrt3 9))) tolerance))
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;; (assert (< (abs (- 4 (sqrt3 16))) tolerance))
|
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;; (assert (not (< (abs (- 4 (sqrt3 15))) tolerance)))
|
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(assert (< (abs (- 3 (sqrt3 9))) tolerance))
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(assert (< (abs (- 4 (sqrt3 16))) tolerance))
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||||
(assert (not (< (abs (- 4 (sqrt3 15))) tolerance)))
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;; ;;; -----------------
|
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;; ;;; factorial
|
||||
;; ;;; -----------------
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;;; -----------------
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||||
;;; factorial
|
||||
;;; -----------------
|
||||
|
||||
;; (define (factorial n)
|
||||
;; (if (= n 1)
|
||||
;; 1
|
||||
;; (* n (factorial (- n 1)))))
|
||||
(define (factorial n)
|
||||
(if (= n 1)
|
||||
1
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||||
(* n (factorial (- n 1)))))
|
||||
|
||||
;; (define (factorial2 n)
|
||||
;; (fact-iter 1 1 n))
|
||||
(define (factorial2 n)
|
||||
(fact-iter 1 1 n))
|
||||
|
||||
;; (define (fact-iter product counter max-count)
|
||||
;; (if (> counter max-count)
|
||||
;; product
|
||||
;; (fact-iter (* counter product) (+ counter 1) max-count)))
|
||||
(define (fact-iter product counter max-count)
|
||||
(if (> counter max-count)
|
||||
product
|
||||
(fact-iter (* counter product) (+ counter 1) max-count)))
|
||||
|
||||
;; (define (factorial3 n)
|
||||
;; (define (iter product counter)
|
||||
;; (if (> counter n)
|
||||
;; product
|
||||
;; (iter (* counter product) (+ counter 1))))
|
||||
(define (factorial3 n)
|
||||
(define (iter product counter)
|
||||
(if (> counter n)
|
||||
product
|
||||
(iter (* counter product) (+ counter 1))))
|
||||
|
||||
;; (iter 1 1))
|
||||
(iter 1 1))
|
||||
|
||||
;; (assert (= (factorial 6) 720))
|
||||
;; (assert (= (factorial2 6) 720))
|
||||
;; (assert (= (factorial3 6) 720))
|
||||
(assert (= (factorial 6) 720))
|
||||
(assert (= (factorial2 6) 720))
|
||||
(assert (= (factorial3 6) 720))
|
||||
|
||||
;;; ----------------
|
||||
;;; ackermann
|
||||
@@ -154,13 +154,6 @@
|
||||
((= n 0) (A (- m 1) 1))
|
||||
(else (A (- m 1) (A m (- n 1))))))
|
||||
|
||||
;; (define (A m n)
|
||||
;; (if (= m 0)
|
||||
;; (+ n 1)
|
||||
;; (if (= n 0)
|
||||
;; (A (- m 1) 1)
|
||||
;; (A (- m 1) (A m (- n 1))))))
|
||||
|
||||
(assert (= (A 0 0) 1))
|
||||
(assert (= (A 1 2) 4))
|
||||
(assert (= (A 3 1) 13))
|
||||
@@ -170,50 +163,50 @@
|
||||
;; ;;; Fibonacci
|
||||
;; ;;; ---------------
|
||||
|
||||
;; (define (fib n)
|
||||
;; (cond ((= n 0) 0)
|
||||
;; ((= n 1) 1)
|
||||
;; (else (+ (fib (- n 1)) (fib (- n 2))))))
|
||||
(define (fib n)
|
||||
(cond ((= n 0) 0)
|
||||
((= n 1) 1)
|
||||
(else (+ (fib (- n 1)) (fib (- n 2))))))
|
||||
|
||||
;; (define (fib2 n)
|
||||
;; (fib-iter 1 0 n))
|
||||
(define (fib2 n)
|
||||
(fib-iter 1 0 n))
|
||||
|
||||
;; (define (fib-iter a b count)
|
||||
;; (if (= count 0)
|
||||
;; b
|
||||
;; (fib-iter (+ a b) a (- count 1))))
|
||||
(define (fib-iter a b count)
|
||||
(if (= count 0)
|
||||
b
|
||||
(fib-iter (+ a b) a (- count 1))))
|
||||
|
||||
;; (assert (= (fib 2) 1))
|
||||
;; (assert (= (fib 3) 2))
|
||||
;; (assert (= (fib 4) 3))
|
||||
;; (assert (= (fib 5) 5))
|
||||
;; (assert (= (fib 6) 8))
|
||||
(assert (= (fib 2) 1))
|
||||
(assert (= (fib 3) 2))
|
||||
(assert (= (fib 4) 3))
|
||||
(assert (= (fib 5) 5))
|
||||
(assert (= (fib 6) 8))
|
||||
|
||||
;; (assert (= (fib2 2) 1))
|
||||
;; (assert (= (fib2 3) 2))
|
||||
;; (assert (= (fib2 4) 3))
|
||||
;; (assert (= (fib2 5) 5))
|
||||
;; (assert (= (fib2 6) 8))
|
||||
(assert (= (fib2 2) 1))
|
||||
(assert (= (fib2 3) 2))
|
||||
(assert (= (fib2 4) 3))
|
||||
(assert (= (fib2 5) 5))
|
||||
(assert (= (fib2 6) 8))
|
||||
|
||||
;; ;;; ------------------
|
||||
;; ;;; count change
|
||||
;; ;;; ------------------
|
||||
;;; ------------------
|
||||
;;; count change
|
||||
;;; ------------------
|
||||
|
||||
;; (define (count-change amount)
|
||||
;; (define (cc amount kinds-of-coins)
|
||||
;; (cond ((= amount 0) 1)
|
||||
;; ((or (< amount 0) (= kinds-of-coins 0)) 0)
|
||||
;; (else (+ (cc amount (- kinds-of-coins 1))
|
||||
;; (cc (- amount (first-denomination kinds-of-coins)) kinds-of-coins)))))
|
||||
(define (count-change amount)
|
||||
(define (cc amount kinds-of-coins)
|
||||
(cond ((= amount 0) 1)
|
||||
((or (< amount 0) (= kinds-of-coins 0)) 0)
|
||||
(else (+ (cc amount (- kinds-of-coins 1))
|
||||
(cc (- amount (first-denomination kinds-of-coins)) kinds-of-coins)))))
|
||||
|
||||
;; (define (first-denomination kinds-of-coins)
|
||||
;; (cond ((= kinds-of-coins 1) 1)
|
||||
;; ((= kinds-of-coins 2) 5)
|
||||
;; ((= kinds-of-coins 3) 10)
|
||||
;; ((= kinds-of-coins 4) 25)
|
||||
;; ((= kinds-of-coins 5) 50)))
|
||||
(define (first-denomination kinds-of-coins)
|
||||
(cond ((= kinds-of-coins 1) 1)
|
||||
((= kinds-of-coins 2) 5)
|
||||
((= kinds-of-coins 3) 10)
|
||||
((= kinds-of-coins 4) 25)
|
||||
((= kinds-of-coins 5) 50)))
|
||||
|
||||
;; (cc amount 5))
|
||||
(cc amount 5))
|
||||
|
||||
;; (assert (= (count-change 100) 292))
|
||||
|
||||
@@ -221,128 +214,128 @@
|
||||
;; ;;; exponentiation
|
||||
;; ;;; --------------------
|
||||
|
||||
;; (define (expt b n)
|
||||
;; (if (= n 0)
|
||||
;; 1
|
||||
;; (* b (expt b (- n 1)))))
|
||||
(define (expt b n)
|
||||
(if (= n 0)
|
||||
1
|
||||
(* b (expt b (- n 1)))))
|
||||
|
||||
;; (define (expt2 b n)
|
||||
;; (define (expt-iter b counter product)
|
||||
;; (if (= counter 0)
|
||||
;; product
|
||||
;; (expt-iter b (- counter 1) (* b product))))
|
||||
(define (expt2 b n)
|
||||
(define (expt-iter b counter product)
|
||||
(if (= counter 0)
|
||||
product
|
||||
(expt-iter b (- counter 1) (* b product))))
|
||||
|
||||
;; (expt-iter b n 1))
|
||||
(expt-iter b n 1))
|
||||
|
||||
;; (define (fast-expt b n)
|
||||
;; (define (even? n)
|
||||
;; (= (% n 2) 0))
|
||||
(define (fast-expt b n)
|
||||
(define (even? n)
|
||||
(= (% n 2) 0))
|
||||
|
||||
;; (cond ((= n 0) 1)
|
||||
;; ((even? n) (square (fast-expt b (/ n 2))))
|
||||
;; (else (* b (fast-expt b (- n 1))))))
|
||||
(cond ((= n 0) 1)
|
||||
((even? n) (square (fast-expt b (/ n 2))))
|
||||
(else (* b (fast-expt b (- n 1))))))
|
||||
|
||||
;; (assert (= (expt 1 2) 1))
|
||||
;; (assert (= (expt 2 2) 4))
|
||||
;; (assert (= (expt 2 3) 8))
|
||||
(assert (= (expt 1 2) 1))
|
||||
(assert (= (expt 2 2) 4))
|
||||
(assert (= (expt 2 3) 8))
|
||||
|
||||
;; (assert (= (expt2 1 2) 1))
|
||||
;; (assert (= (expt2 2 2) 4))
|
||||
;; (assert (= (expt2 2 3) 8))
|
||||
(assert (= (expt2 1 2) 1))
|
||||
(assert (= (expt2 2 2) 4))
|
||||
(assert (= (expt2 2 3) 8))
|
||||
|
||||
;; (assert (= (fast-expt 1 2) 1))
|
||||
;; (assert (= (fast-expt 2 2) 4))
|
||||
;; (assert (= (fast-expt 2 3) 8))
|
||||
(assert (= (fast-expt 1 2) 1))
|
||||
(assert (= (fast-expt 2 2) 4))
|
||||
(assert (= (fast-expt 2 3) 8))
|
||||
|
||||
;; ;;; ----------
|
||||
;; ;;; gcd
|
||||
;; ;;; ----------
|
||||
;;; ----------
|
||||
;;; gcd
|
||||
;;; ----------
|
||||
|
||||
;; (define (gcd a b)
|
||||
;; (if (= b 0)
|
||||
;; a
|
||||
;; (gcd b (% a b))))
|
||||
(define (gcd a b)
|
||||
(if (= b 0)
|
||||
a
|
||||
(gcd b (% a b))))
|
||||
|
||||
;; (assert (= (gcd 40 6) 2))
|
||||
;; (assert (= (gcd 13 4) 1))
|
||||
(assert (= (gcd 40 6) 2))
|
||||
(assert (= (gcd 13 4) 1))
|
||||
|
||||
|
||||
;; ;;; ----------
|
||||
;; ;;; primes
|
||||
;; ;;; ----------
|
||||
;;; ----------
|
||||
;;; primes
|
||||
;;; ----------
|
||||
|
||||
;; (define (smallest-divisor n)
|
||||
;; (find-divisor n 2))
|
||||
(define (smallest-divisor n)
|
||||
(find-divisor n 2))
|
||||
|
||||
;; (define (find-divisor n test-divisor)
|
||||
;; (cond ((> (square test-divisor) n) n)
|
||||
;; ((divides? test-divisor n) test-divisor)
|
||||
;; (else (find-divisor n (+ test-divisor 1)))))
|
||||
(define (find-divisor n test-divisor)
|
||||
(cond ((> (square test-divisor) n) n)
|
||||
((divides? test-divisor n) test-divisor)
|
||||
(else (find-divisor n (+ test-divisor 1)))))
|
||||
|
||||
;; (define (divides? a b)
|
||||
;; (= (% b a) 0))
|
||||
(define (divides? a b)
|
||||
(= (% b a) 0))
|
||||
|
||||
;; (define (prime? n)
|
||||
;; (= n (smallest-divisor n)))
|
||||
(define (prime? n)
|
||||
(= n (smallest-divisor n)))
|
||||
|
||||
;; (assert (prime? 13))
|
||||
;; (assert (prime? 11))
|
||||
;; (assert (not (prime? 12)))
|
||||
(assert (prime? 13))
|
||||
(assert (prime? 11))
|
||||
(assert (not (prime? 12)))
|
||||
|
||||
|
||||
;;; ----------------------
|
||||
;;; simple integral
|
||||
;;; ----------------------
|
||||
;; ----------------------
|
||||
;; simple integral
|
||||
;; ----------------------
|
||||
|
||||
;; (define (sum term a next b)
|
||||
;; (if (> a b)
|
||||
;; 0
|
||||
;; (+ (term a) (sum term (next a) next b))))
|
||||
(define (sum term a next b)
|
||||
(if (> a b)
|
||||
0
|
||||
(+ (term a) (sum term (next a) next b))))
|
||||
|
||||
;; (define (integral f a b dx)
|
||||
;; (define (add-dx x) (+ x dx))
|
||||
;; (* (sum f (+ a (/ dx 2.0)) add-dx b) dx))
|
||||
(define (integral f a b dx)
|
||||
(define (add-dx x) (+ x dx))
|
||||
(* (sum f (+ a (/ dx 2.0)) add-dx b) dx))
|
||||
|
||||
;; (define (pi-sum a b)
|
||||
;; (define (pi-term x) (/ 1.0 (* x (+ x 2))))
|
||||
;; (define (pi-next x) (+ x 4))
|
||||
;; (sum pi-term a pi-next b))
|
||||
(define (pi-sum a b)
|
||||
(define (pi-term x) (/ 1.0 (* x (+ x 2))))
|
||||
(define (pi-next x) (+ x 4))
|
||||
(sum pi-term a pi-next b))
|
||||
|
||||
;; (assert (< (abs (- (* 8 (pi-sum 1 100)) 3.121595)) 0.0001))
|
||||
;; (assert (< (abs (- (integral cube 0 1 0.02) 0.249950)) 0.0001))
|
||||
(assert (< (abs (- (* 8 (pi-sum 1 100)) 3.121595)) 0.0001))
|
||||
(assert (< (abs (- (integral cube 0 1 0.02) 0.249950)) 0.0001))
|
||||
|
||||
|
||||
;; ------------------------------------------------------------
|
||||
;; F(x,y) = x(1 + xy)^2 + y(1 − y) + (1 + xy)(1 − y)
|
||||
;; F(x,y) = x(1 + xy)^2 + y(1 − y) + (1 + xy)(1 − y)
|
||||
;; ------------------------------------------------------------
|
||||
|
||||
;; (define (f x y)
|
||||
;; (let ((a (+ 1 (* x y)))
|
||||
;; (b (- 1 y)))
|
||||
;; (+ (* x (square a))
|
||||
;; (* y b)
|
||||
;; (* a b))))
|
||||
(define (f x y)
|
||||
(let ((a (+ 1 (* x y)))
|
||||
(b (- 1 y)))
|
||||
(+ (* x (square a))
|
||||
(* y b)
|
||||
(* a b))))
|
||||
|
||||
;; (assert (= (f 0 0) 1))
|
||||
;; (assert (= (f 1 1) 4))
|
||||
(assert (= (f 0 0) 1))
|
||||
(assert (= (f 1 1) 4))
|
||||
|
||||
|
||||
;; ;;; ---------------
|
||||
;; ;;; find zero
|
||||
;; ;;; ---------------
|
||||
;;; ---------------
|
||||
;;; find zero
|
||||
;;; ---------------
|
||||
|
||||
;; (define (positive? x) (< 0 x))
|
||||
;; (define (negative? x) (< x 0))
|
||||
(define (positive? x) (< 0 x))
|
||||
(define (negative? x) (< x 0))
|
||||
|
||||
;; (define (search f neg-point pos-point)
|
||||
;; (let ((midpoint (average neg-point pos-point)))
|
||||
;; (if (close-enough? neg-point pos-point)
|
||||
;; midpoint
|
||||
;; (let ((test-value (f midpoint)))
|
||||
;; (cond ((positive? test-value) (search f neg-point midpoint))
|
||||
;; ((negative? test-value) (search f midpoint pos-point))
|
||||
;; (else midpoint))))))
|
||||
(define (search f neg-point pos-point)
|
||||
(let ((midpoint (average neg-point pos-point)))
|
||||
(if (close-enough? neg-point pos-point)
|
||||
midpoint
|
||||
(let ((test-value (f midpoint)))
|
||||
(cond ((positive? test-value) (search f neg-point midpoint))
|
||||
((negative? test-value) (search f midpoint pos-point))
|
||||
(else midpoint))))))
|
||||
|
||||
;; (define (close-enough? x y) (< (abs (- x y)) 0.001))
|
||||
(define (close-enough? x y) (< (abs (- x y)) 0.001))
|
||||
|
||||
;; (assert (close-enough? (search (lambda (x) (- 1 (square x))) -3 3) -1))
|
||||
(assert (close-enough? (search (lambda (x) (- 1 (square x))) -3 3) -1))
|
||||
|
||||
Reference in New Issue
Block a user