Add -fixfn

README.md

@@ -250,6 +250,7 @@ These combinators require Emacs 24 for its lexical scope. So they are offered in
 * [-orfn](#-orfn-rest-preds) `(&rest preds)`
 * [-andfn](#-andfn-rest-preds) `(&rest preds)`
 * [-iteratefn](#-iteratefn-fn-n) `(fn n)`
+* [-fixfn](#-fixfn-fn) `(fn)`
 * [-prodfn](#-prodfn-rest-fns) `(&rest fns)`
 
 ## Anaphoric functions
@@ -1930,6 +1931,19 @@ This function satisfies the following law:
 (funcall (-iteratefn 'cdr 3) '(1 2 3 4 5)) ;; => '(4 5)
 ```
 
+#### -fixfn `(fn)`
+
+Return a function that computes the (least) fixpoint of `fn`.
+
+`fn` is a unary function, results are compared with `equal`.
+
+In types: (a -> a) -> a -> a.
+
+```cl
+(funcall (-fixfn 'cos) 0.7) ;; => 0.7390851332151607
+(funcall (-fixfn (lambda (x) (expt (+ x 10) 0.25))) 2.0) ;; => 1.8555845286409378
+```
+
 #### -prodfn `(&rest fns)`
 
 Take a list of n functions and return a function that takes a

dash-functional.el

@@ -135,6 +135,19 @@ This function satisfies the following law:
   (funcall (-iteratefn fn n) init) = (-last-item (-iterate fn init (1+ n)))."
   (lambda (x) (--dotimes n (setq x (funcall fn x))) x))
 
+(defun -fixfn (fn)
+  "Return a function that computes the (least) fixpoint of FN.
+
+FN is a unary function, results are compared with `equal'.
+
+In types: (a -> a) -> a -> a."
+  (lambda (x)
+    (let ((re (funcall fn x)))
+      (while (not (equal x re))
+        (setq x re)
+        (setq re (funcall fn re)))
+      re)))
+
 (defun -prodfn (&rest fns)
   "Take a list of n functions and return a function that takes a
 list of length n, applying i-th function to i-th element of the

dash.el

@@ -1780,6 +1780,7 @@ structure such as plist or alist."
                              "-orfn"
                              "-andfn"
                              "-iteratefn"
+                             "-fixfn"
                              "-prodfn"
                              ))
              (special-variables '(

dev/examples.el

@@ -801,6 +801,12 @@ new list."
              (equal (funcall (-iteratefn fn 5) init)
                     (-last-item (-iterate fn init (1+ 5)))))))
 
+    (defexamples -fixfn
+      ;; Find solution to cos(x) = x
+      (funcall (-fixfn 'cos) 0.7) => 0.7390851332151607
+      ;; Find solution to x^4 - x - 10 = 0
+      (funcall (-fixfn (lambda (x) (expt (+ x 10) 0.25))) 2.0) => 1.8555845286409378)
+
     (defexamples -prodfn
       (funcall (-prodfn '1+ '1- 'int-to-string) '(1 2 3)) => '(2 1 "3")
       (-map (-prodfn '1+ '1-) '((1 2) (3 4) (5 6) (7 8))) => '((2 1) (4 3) (6 5) (8 7))