manual: Add the documentation for make-compose.

main.rkt

@@ -16,11 +16,17 @@
 ;;; along with this program.  If not, see
 ;;; <https://www.gnu.org/licenses/>.
 
-#lang typed/racket
+#lang typed/racket/base
 
-(require (for-syntax syntax/parse))
+(require syntax/parse/define
+         (for-syntax racket/base
+                     racket/match
+                     racket/list
+                     racket/syntax
+                     syntax/parse))
 
-(provide compose-n
+(provide make-compose
+         compose-n
          compose-3 compose-4 compose-5 compose-6 compose-7 compose-8 compose-9
          multi-compose multi-chain)
 
@@ -37,82 +43,30 @@
   (test-case "compose-n"
     (check-equal? ((compose-n add1 add1 add1) 3) 6)))
 
-(: compose-3 (All (a b c d)
-                  (-> (-> c d)
-                      (-> b c)
-                      (-> a b)
-                      (-> a d))))
-(define (compose-3 f1 f2 f3)
-  (λ (x) (f1 (f2 (f3 x)))))
+(define-for-syntax (make-compose-type n)
+  (with-syntax* ([(t ...) (generate-temporaries (make-list n 't))]
+                 [(_ ... t₀) #'(a t ...)]
+                 [(F ...)
+                  (let step ([u #'a] [ts (syntax->list #'(t ...))])
+                    (match ts
+                      ['() '()]
+                      [(cons t ts*) (cons #`(#,t → #,u) (step t ts*))]))])
+    #'(∀ (a t ...) (F ... → t₀ → a))))
 
-(: compose-4 (All (a b c d e)
-                  (-> (-> d e)
-                      (-> c d)
-                      (-> b c)
-                      (-> a b)
-                      (-> a e))))
-(define (compose-4 f1 f2 f3 f4)
-  (λ (x) (f1 (f2 (f3 (f4 x))))))
+(define-syntax-parser make-compose
+  [(_ n:nat)
+     (with-syntax* ([(f ...) (generate-temporaries (make-list (syntax-e #'n) 'f))]
+                    [T (make-compose-type (syntax-e #'n))]
+                    [body (foldr (λ (fᵢ res) #`(#,fᵢ #,res)) #'x (syntax->list #'(f ...)))])
+       #'(ann (λ (f ...) (λ (x) body)) T))])
 
-(: compose-5 (All (a b c d e f)
-                  (-> (-> e f)
-                      (-> d e)
-                      (-> c d)
-                      (-> b c)
-                      (-> a b)
-                      (-> a f))))
-(define (compose-5 f1 f2 f3 f4 f5)
-  (λ (x) (f1 (f2 (f3 (f4 (f5 x)))))))
-
-(: compose-6 (All (a b c d e f g)
-                  (-> (-> f g)
-                      (-> e f)
-                      (-> d e)
-                      (-> c d)
-                      (-> b c)
-                      (-> a b)
-                      (-> a g))))
-(define (compose-6 f1 f2 f3 f4 f5 f6)
-  (λ (x) (f1 (f2 (f3 (f4 (f5 (f6 x))))))))
-
-(: compose-7 (All (a b c d e f g h)
-                  (-> (-> g h)
-                      (-> f g)
-                      (-> e f)
-                      (-> d e)
-                      (-> c d)
-                      (-> b c)
-                      (-> a b)
-                      (-> a h))))
-(define (compose-7 f1 f2 f3 f4 f5 f6 f7)
-  (λ (x) (f1 (f2 (f3 (f4 (f5 (f6 (f7 x)))))))))
-
-(: compose-8 (All (a b c d e f g h i)
-                  (-> (-> h i)
-                      (-> g h)
-                      (-> f g)
-                      (-> e f)
-                      (-> d e)
-                      (-> c d)
-                      (-> b c)
-                      (-> a b)
-                      (-> a i))))
-(define (compose-8 f1 f2 f3 f4 f5 f6 f7 f8)
-  (λ (x) (f1 (f2 (f3 (f4 (f5 (f6 (f7 (f8 x))))))))))
-
-(: compose-9 (All (a b c d e f g h i j)
-                  (-> (-> i j)
-                      (-> h i)
-                      (-> g h)
-                      (-> f g)
-                      (-> e f)
-                      (-> d e)
-                      (-> c d)
-                      (-> b c)
-                      (-> a b)
-                      (-> a j))))
-(define (compose-9 f1 f2 f3 f4 f5 f6 f7 f8 f9)
-  (λ (x) (f1 (f2 (f3 (f4 (f5 (f6 (f7 (f8 (f9 x)))))))))))
+(define compose-3 (make-compose 3))
+(define compose-4 (make-compose 4))
+(define compose-5 (make-compose 5))
+(define compose-6 (make-compose 6))
+(define compose-7 (make-compose 7))
+(define compose-8 (make-compose 8))
+(define compose-9 (make-compose 9))
 
 (module+ test
   (test-case "compose-3 to compose-9"
@@ -152,6 +106,7 @@
      #`(multi-compose #,@rev-funcs)]))
 
 (module+ test
+  (require racket/port)
   (test-case "multi-chain and multi-compose"
     (define f1 (λ ([x : Number]) (displayln "f1") (+ x 1)))
     (define f2 (λ ([x : Number]) (displayln "f2") (+ x 1)))

manual.scrbl

@@ -65,6 +65,18 @@ fancy-add1
 (fancy-add1 "1")
 ]}
 
+@section{Macros for composing functions}
+
+@defform[(make-compose n)
+         #:contracts ([n exact-nonnegative-integer])]{
+
+Expants to a typed @racket[lambda] form composing exactly @racket[n]
+one-argument functions.  For example, @racket[compose-3] is defined as:
+@racket[(define compose-3 (make-compose 3))].  The rest of the functions of the
+@racket[compose-i] family are defined using this macro as well.
+
+}
+
 @defform[(multi-compose func ...)
 	 #:contracts ([func expression])]{