From 5c0119253f246e5e9b7aa6da0979875201d78f48 Mon Sep 17 00:00:00 2001
From: NoahStoryM <noahstorym@gmail.com>
Date: Mon, 29 Aug 2022 18:30:24 +0800
Subject: [PATCH 01/16] Define identity elements for `tee` and `relay`.

---
 qi-lib/flow/compiler.rkt | 16 +++++-----------
 qi-lib/flow/impl.rkt     | 21 +++++++++++++++++++--
 2 files changed, 24 insertions(+), 13 deletions(-)

diff --git a/qi-lib/flow/compiler.rkt b/qi-lib/flow/compiler.rkt
index 823452eb4..dcf82683b 100644
--- a/qi-lib/flow/compiler.rkt
+++ b/qi-lib/flow/compiler.rkt
@@ -91,7 +91,7 @@
     ;;; Core routing elements
 
     [(~or* (~datum ⏚) (~datum ground))
-     #'(qi0->racket (select))]
+     #'*->1]
     [((~or* (~datum ~>) (~datum thread)) onex:clause ...)
      #`(compose . #,(reverse
                      (syntax->list
@@ -105,11 +105,7 @@
      (with-syntax ([len #`#,(length (syntax->list #'(onex ...)))])
        #'(qi0->racket (group len (== onex ...) rest-onex) ))]
     [((~or* (~datum -<) (~datum tee)) onex:clause ...)
-     #'(λ args
-         (apply values
-                (append (values->list
-                         (apply (qi0->racket onex) args))
-                        ...)))]
+     #'(tee (qi0->racket onex) ...)]
     [e:select-form (select-parser #'e)]
     [e:block-form (block-parser #'e)]
     [((~datum bundle) (n:number ...)
@@ -308,6 +304,7 @@ the DSL.
 
   (define (select-parser stx)
     (syntax-parse stx
+      [(_) #'*->1]
       [(_ n:number ...) #'(qi0->racket (-< (esc (arg n)) ...))]
       [(_ arg ...) ; error handling catch-all
        (report-syntax-error 'select
@@ -488,17 +485,14 @@ the DSL.
   (define (fanout-parser stx)
     (syntax-parse stx
       [_:id #'repeat-values]
+      [(_ 0) #'*->1]
       [(_ n:number)
        ;; a slightly more efficient compile-time implementation
        ;; for literally indicated N
        #`(λ args
            (apply values
                   (append #,@(make-list (syntax->datum #'n) 'args))) )]
-      [(_ n:expr)
-       #'(lambda args
-           (apply values
-                  (apply append
-                         (make-list n args))))]))
+      [(_ e:expr) #`(let ([n e]) (#,fanout-parser n))]))
 
   (define (feedback-parser stx)
     (syntax-parse stx
diff --git a/qi-lib/flow/impl.rkt b/qi-lib/flow/impl.rkt
index 16df7327c..a82b71789 100644
--- a/qi-lib/flow/impl.rkt
+++ b/qi-lib/flow/impl.rkt
@@ -10,7 +10,10 @@
          map-values
          filter-values
          partition-values
+         1->1
+         *->1
          relay
+         tee
          loom-compose
          parity-xor
          arg
@@ -198,6 +201,9 @@
         (append (values->list (apply op vs))
                 (apply zip-with op (map rest seqs))))))
 
+(define 1->1 (λ () (values)))
+(define *->1 (λ _ (values)))
+
 ;; from mischief/function - requiring it runs aground
 ;; of some "name is protected" error while building docs, not sure why;
 ;; so including the implementation directly here for now
@@ -207,8 +213,19 @@
      (keyword-apply f ks vs xs))))
 
 (define (relay . fs)
-  (λ args
-    (apply values (zip-with call fs args))))
+  (if (null? fs)
+      1->1
+      (λ args (apply values (zip-with call fs args)))))
+
+(define (tee . fs)
+  (let ([fs (remq* (list *->1) fs)])
+    (if (null? fs)
+        *->1
+        (λ args
+          (apply values
+            (append*
+             (for/list ([f (in-list fs)])
+               (values->list (apply f args)))))))))
 
 (define (~all? . args)
   (match args

From ad78814f340471897d006e642dfa4f1ed6a0e778 Mon Sep 17 00:00:00 2001
From: NoahStoryM <noahstorym@gmail.com>
Date: Mon, 29 Aug 2022 20:00:22 +0800
Subject: [PATCH 02/16] Update.

---
 qi-lib/flow/impl.rkt | 18 +++++++++++-------
 1 file changed, 11 insertions(+), 7 deletions(-)

diff --git a/qi-lib/flow/impl.rkt b/qi-lib/flow/impl.rkt
index a82b71789..74e82198a 100644
--- a/qi-lib/flow/impl.rkt
+++ b/qi-lib/flow/impl.rkt
@@ -219,13 +219,17 @@
 
 (define (tee . fs)
   (let ([fs (remq* (list *->1) fs)])
-    (if (null? fs)
-        *->1
-        (λ args
-          (apply values
-            (append*
-             (for/list ([f (in-list fs)])
-               (values->list (apply f args)))))))))
+    (match fs
+      ['() *->1]
+      [`(,f) f]
+      [_
+       (define teed
+         (λ args
+           (apply values
+             (append*
+              (for/list ([f (in-list fs)])
+                (values->list (apply f args)))))))
+       teed])))
 
 (define (~all? . args)
   (match args

From 9618e10d8ef981f77a96bf4f739f0fc3dba6ccd3 Mon Sep 17 00:00:00 2001
From: NoahStoryM <noahstorym@gmail.com>
Date: Mon, 29 Aug 2022 20:15:25 +0800
Subject: [PATCH 03/16] Fix `fanout-parser`.

---
 qi-lib/flow/compiler.rkt | 9 ++++++++-
 1 file changed, 8 insertions(+), 1 deletion(-)

diff --git a/qi-lib/flow/compiler.rkt b/qi-lib/flow/compiler.rkt
index dcf82683b..287bc175d 100644
--- a/qi-lib/flow/compiler.rkt
+++ b/qi-lib/flow/compiler.rkt
@@ -492,7 +492,14 @@ the DSL.
        #`(λ args
            (apply values
                   (append #,@(make-list (syntax->datum #'n) 'args))) )]
-      [(_ e:expr) #`(let ([n e]) (#,fanout-parser n))]))
+      [(_ e:expr)
+       #'(let ([n e])
+           (if (zero? n)
+               *->1
+               (λ args
+                 (apply values
+                   (apply append
+                     (make-list n args))))))]))
 
   (define (feedback-parser stx)
     (syntax-parse stx

From 37b7e14afda67b8900aa1313354dc160ce01481d Mon Sep 17 00:00:00 2001
From: NoahStoryM <noahstorym@gmail.com>
Date: Mon, 29 Aug 2022 20:30:51 +0800
Subject: [PATCH 04/16] Use thunk.

---
 qi-lib/flow/impl.rkt | 6 ++++--
 1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/qi-lib/flow/impl.rkt b/qi-lib/flow/impl.rkt
index 74e82198a..a3ee51c77 100644
--- a/qi-lib/flow/impl.rkt
+++ b/qi-lib/flow/impl.rkt
@@ -29,6 +29,8 @@
 
 (require racket/match
          (only-in racket/function
+                  thunk
+                  thunk*
                   const
                   negate)
          racket/bool
@@ -201,8 +203,8 @@
         (append (values->list (apply op vs))
                 (apply zip-with op (map rest seqs))))))
 
-(define 1->1 (λ () (values)))
-(define *->1 (λ _ (values)))
+(define 1->1 (thunk  (values)))
+(define *->1 (thunk* (values)))
 
 ;; from mischief/function - requiring it runs aground
 ;; of some "name is protected" error while building docs, not sure why;

From c0506bc2d4c8a7058adcad3dfc8a46b63be48970 Mon Sep 17 00:00:00 2001
From: NoahStoryM <noahstorym@gmail.com>
Date: Tue, 30 Aug 2022 12:25:32 +0800
Subject: [PATCH 05/16] Add identity element for `gen`.

---
 qi-lib/flow/compiler.rkt | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/qi-lib/flow/compiler.rkt b/qi-lib/flow/compiler.rkt
index 287bc175d..1d53b2db2 100644
--- a/qi-lib/flow/compiler.rkt
+++ b/qi-lib/flow/compiler.rkt
@@ -63,8 +63,10 @@
      #'(disjoin (qi0->racket onex) ...)]
     [((~datum not) onex:clause)
      #'(negate (qi0->racket onex))]
+    [((~datum gen))
+     #'*->1]
     [((~datum gen) ex:expr ...)
-     #'(λ _ (values ex ...))]
+     #'(thunk* (values ex ...))]
     [(~or* (~datum NOT) (~datum !))
      #'not]
     [(~or* (~datum AND) (~datum &))

From 063cd215fa2ac1fa289f8f036bd39927ff37845a Mon Sep 17 00:00:00 2001
From: NoahStoryM <noahstorym@gmail.com>
Date: Tue, 30 Aug 2022 12:51:56 +0800
Subject: [PATCH 06/16] Optimize `(fanout 1)`.

---
 qi-lib/flow/compiler.rkt | 15 ++++++---------
 1 file changed, 6 insertions(+), 9 deletions(-)

diff --git a/qi-lib/flow/compiler.rkt b/qi-lib/flow/compiler.rkt
index 1d53b2db2..153a91520 100644
--- a/qi-lib/flow/compiler.rkt
+++ b/qi-lib/flow/compiler.rkt
@@ -488,20 +488,17 @@ the DSL.
     (syntax-parse stx
       [_:id #'repeat-values]
       [(_ 0) #'*->1]
+      [(_ 1) #'values]
       [(_ n:number)
        ;; a slightly more efficient compile-time implementation
        ;; for literally indicated N
-       #`(λ args
-           (apply values
-                  (append #,@(make-list (syntax->datum #'n) 'args))) )]
+       #'(curry repeat-values n)]
       [(_ e:expr)
        #'(let ([n e])
-           (if (zero? n)
-               *->1
-               (λ args
-                 (apply values
-                   (apply append
-                     (make-list n args))))))]))
+           (case n
+             [(0) *->1]
+             [(1) values]
+             [else (curry repeat-values n)]))]))
 
   (define (feedback-parser stx)
     (syntax-parse stx

From 8f6eca01819ba9b4c229d99d6981bda5e9331544 Mon Sep 17 00:00:00 2001
From: NoahStoryM <noahstorym@gmail.com>
Date: Tue, 30 Aug 2022 12:55:43 +0800
Subject: [PATCH 07/16] Use `append*` instead of `apply append`.

---
 qi-lib/flow/impl.rkt | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/qi-lib/flow/impl.rkt b/qi-lib/flow/impl.rkt
index a3ee51c77..d5e8ab4ed 100644
--- a/qi-lib/flow/impl.rkt
+++ b/qi-lib/flow/impl.rkt
@@ -174,7 +174,7 @@
                 [b (in-value (cdr c+b))]
                 [args (in-value (hash-ref by-cs c))])
       (call-with-values (λ () (apply b args)) list)))
-  (apply values (apply append results)))
+  (apply values (append* results)))
 
 (define (->boolean v)
   (not (not v)))
@@ -255,7 +255,7 @@
 (define none? (compose not not ~none?))
 
 (define (repeat-values n . vs)
-  (apply values (apply append (make-list n vs))))
+  (apply values (append* (make-list n vs))))
 
 (define (power n f)
   (apply compose (make-list n f)))

From f74b270dd9906e7f0a80efafbbfb27c22c22543b Mon Sep 17 00:00:00 2001
From: NoahStoryM <noahstorym@gmail.com>
Date: Tue, 30 Aug 2022 18:21:01 +0800
Subject: [PATCH 08/16] Update `tee`.

---
 qi-lib/flow/impl.rkt | 22 ++++++++++------------
 1 file changed, 10 insertions(+), 12 deletions(-)

diff --git a/qi-lib/flow/impl.rkt b/qi-lib/flow/impl.rkt
index d5e8ab4ed..7664eef8f 100644
--- a/qi-lib/flow/impl.rkt
+++ b/qi-lib/flow/impl.rkt
@@ -220,18 +220,16 @@
       (λ args (apply values (zip-with call fs args)))))
 
 (define (tee . fs)
-  (let ([fs (remq* (list *->1) fs)])
-    (match fs
-      ['() *->1]
-      [`(,f) f]
-      [_
-       (define teed
-         (λ args
-           (apply values
-             (append*
-              (for/list ([f (in-list fs)])
-                (values->list (apply f args)))))))
-       teed])))
+  (match (remq* (list *->1) fs)
+    ['() *->1]
+    [`(,f) f]
+    [fs
+     (define (teed . args)
+       (apply values
+         (append*
+          (for/list ([f (in-list fs)])
+            (values->list (apply f args))))))
+     teed]))
 
 (define (~all? . args)
   (match args

From 845aa79728c4c40bf4669c3b1f997f15c36613d4 Mon Sep 17 00:00:00 2001
From: NoahStoryM <noahstorym@gmail.com>
Date: Tue, 30 Aug 2022 18:25:35 +0800
Subject: [PATCH 09/16] Name `relayed`.

---
 qi-lib/flow/impl.rkt | 9 ++++++---
 1 file changed, 6 insertions(+), 3 deletions(-)

diff --git a/qi-lib/flow/impl.rkt b/qi-lib/flow/impl.rkt
index 7664eef8f..b1535f12e 100644
--- a/qi-lib/flow/impl.rkt
+++ b/qi-lib/flow/impl.rkt
@@ -215,9 +215,12 @@
      (keyword-apply f ks vs xs))))
 
 (define (relay . fs)
-  (if (null? fs)
-      1->1
-      (λ args (apply values (zip-with call fs args)))))
+  (cond
+    [(null? fs) 1->1]
+    [else
+     (define (relayed . args)
+       (apply values (zip-with call fs args)))
+     relayed]))
 
 (define (tee . fs)
   (match (remq* (list *->1) fs)

From f429750fa72bc09484b618d4f83f17d81e6aa3c6 Mon Sep 17 00:00:00 2001
From: NoahStoryM <noahstorym@gmail.com>
Date: Wed, 31 Aug 2022 11:44:17 +0800
Subject: [PATCH 10/16] Remove `const`.

---
 qi-lib/flow/impl.rkt | 1 -
 1 file changed, 1 deletion(-)

diff --git a/qi-lib/flow/impl.rkt b/qi-lib/flow/impl.rkt
index b1535f12e..6c9dab059 100644
--- a/qi-lib/flow/impl.rkt
+++ b/qi-lib/flow/impl.rkt
@@ -31,7 +31,6 @@
          (only-in racket/function
                   thunk
                   thunk*
-                  const
                   negate)
          racket/bool
          racket/list

From 9ad9257f8c69eafc698cc283954186c63b19bb6f Mon Sep 17 00:00:00 2001
From: NoahStoryM <noahstorym@gmail.com>
Date: Thu, 1 Sep 2022 11:19:55 +0800
Subject: [PATCH 11/16] Name some flows.

---
 qi-lib/flow/compiler.rkt | 132 ++++++++++++++++++++++++---------------
 qi-lib/flow/impl.rkt     |  38 +++++------
 2 files changed, 102 insertions(+), 68 deletions(-)

diff --git a/qi-lib/flow/compiler.rkt b/qi-lib/flow/compiler.rkt
index 153a91520..032d01992 100644
--- a/qi-lib/flow/compiler.rkt
+++ b/qi-lib/flow/compiler.rkt
@@ -301,8 +301,11 @@ the DSL.
                                                 "list?"
                                                 _)))]
       [(_ onex:clause)
-       #'(λ (v . vs)
-           ((qi0->racket (~> △ (>< (apply (qi0->racket onex) _ vs)))) v))]))
+       #'(let ([compiled-sep-flow
+                (λ (v . vs)
+                  ((qi0->racket (~> △ (>< (apply (qi0->racket onex) _ vs))))
+                   v))])
+           compiled-sep-flow)]))
 
   (define (select-parser stx)
     (syntax-parse stx
@@ -332,8 +335,10 @@ the DSL.
                        (qi0->racket remainder-onex)
                        n)]
       [_:id
-       #'(λ (n selection-flo remainder-flo . vs)
-           (apply (qi0->racket (group n selection-flo remainder-flo)) vs))]
+       #'(let ([compiled-group-flow
+                (λ (n selection-flo remainder-flo . vs)
+                  (apply (qi0->racket (group n selection-flo remainder-flo)) vs))])
+           compiled-group-flow)]
       [(_ arg ...) ; error handling catch-all
        (report-syntax-error 'group
                             (syntax->datum #'(arg ...))
@@ -341,7 +346,7 @@ the DSL.
 
   (define (switch-parser stx)
     (syntax-parse stx
-      [(_) #'(qi0->racket _)]
+      [(_) #'values]
       [(_ ((~or* (~datum divert) (~datum %))
            condition-gate:clause
            consequent-gate:clause))
@@ -410,10 +415,12 @@ the DSL.
        #'(qi0->racket (-< (~> (pass condition) sonex)
                           (~> (pass (not condition)) ronex)))]
       [_:id
-       #'(λ (condition sonex ronex . args)
-           (apply (qi0->racket (-< (~> (pass condition) sonex)
-                                   (~> (pass (not condition)) ronex)))
-                  args))]
+       #'(let ([compiled-sieve-flow
+                (λ (condition sonex ronex . args)
+                  (apply (qi0->racket (-< (~> (pass condition) sonex)
+                                          (~> (pass (not condition)) ronex)))
+                    args))])
+           compiled-sieve-flow)]
       [(_ arg ...) ; error handling catch-all
        (report-syntax-error 'sieve
                             (syntax->datum #'(arg ...))
@@ -434,14 +441,16 @@ the DSL.
       [(_ flo
           [error-condition-flo error-handler-flo]
           ...+)
-       #'(λ args
-           (with-handlers ([(qi0->racket error-condition-flo)
-                            (λ (e)
-                              ;; TODO: may be good to support reference to the
-                              ;; error via a binding / syntax parameter
-                              (apply (qi0->racket error-handler-flo) args))]
-                           ...)
-             (apply (qi0->racket flo) args)))]
+       #'(let ([compiled-try-flow
+                (λ args
+                  (with-handlers ([(qi0->racket error-condition-flo)
+                                   (λ (e)
+                                     ;; TODO: may be good to support reference to the
+                                     ;; error via a binding / syntax parameter
+                                     (apply (qi0->racket error-handler-flo) args))]
+                                  ...)
+                    (apply (qi0->racket flo) args)))])
+           compiled-try-flow)]
       [(_ arg ...)
        (report-syntax-error 'try
                             (syntax->datum #'(arg ...))
@@ -472,17 +481,21 @@ the DSL.
     (syntax-parse stx
       [(_ consequent:clause
           alternative:clause)
-       #'(λ (f . args)
-           (if (apply f args)
-               (apply (qi0->racket consequent) args)
-               (apply (qi0->racket alternative) args)))]
+       #'(let ([compiled-if-flow
+                (λ (f . args)
+                  (if (apply f args)
+                      (apply (qi0->racket consequent) args)
+                      (apply (qi0->racket alternative) args)))])
+           compiled-if-flow)]
       [(_ condition:clause
           consequent:clause
           alternative:clause)
-       #'(λ args
-           (if (apply (qi0->racket condition) args)
-               (apply (qi0->racket consequent) args)
-               (apply (qi0->racket alternative) args)))]))
+       #'(let ([compiled-if-flow
+                (λ args
+                  (if (apply (qi0->racket condition) args)
+                      (apply (qi0->racket consequent) args)
+                      (apply (qi0->racket alternative) args)))])
+           compiled-if-flow)]))
 
   (define (fanout-parser stx)
     (syntax-parse stx
@@ -492,13 +505,18 @@ the DSL.
       [(_ n:number)
        ;; a slightly more efficient compile-time implementation
        ;; for literally indicated N
-       #'(curry repeat-values n)]
+       #'(procedure-rename
+          (curry repeat-values n)
+          'compiled-fanout-flow)]
       [(_ e:expr)
        #'(let ([n e])
            (case n
              [(0) *->1]
              [(1) values]
-             [else (curry repeat-values n)]))]))
+             [else
+              (procedure-rename
+               (curry repeat-values n)
+               'compiled-fanout-flow)]))]))
 
   (define (feedback-parser stx)
     (syntax-parse stx
@@ -510,9 +528,10 @@ the DSL.
                          (qi0->racket thenex))]
       [(_ ((~datum while) tilex:clause)
           ((~datum then) thenex:clause))
-       #'(λ (f . args)
-           (apply (qi0->racket (feedback (while tilex) (then thenex) f))
-                  args))]
+       #'(let ([compiled-feedback-flow
+                (λ (f . args)
+                  (apply (qi0->racket (feedback (while tilex) (then thenex) f)) args))])
+           compiled-feedback-flow)]
       [(_ ((~datum while) tilex:clause) onex:clause)
        #'(qi0->racket (feedback (while tilex) (then _) onex))]
       [(_ ((~datum while) tilex:clause))
@@ -523,17 +542,23 @@ the DSL.
        #'(feedback-times (qi0->racket onex) n (qi0->racket thenex))]
       [(_ n:expr
           ((~datum then) thenex:clause))
-       #'(λ (f . args)
-           (apply (qi0->racket (feedback n (then thenex) f)) args))]
+       #'(let ([compiled-feedback-flow
+                (λ (f . args)
+                  (apply (qi0->racket (feedback n (then thenex) f)) args))])
+           compiled-feedback-flow)]
       [(_ n:expr onex:clause)
        #'(qi0->racket (feedback n (then _) onex))]
       [(_ onex:clause)
-       #'(λ (n . args)
-           (apply (qi0->racket (feedback n onex)) args))]
+       #'(let ([compiled-feedback-flow
+                (λ (n . args)
+                  (apply (qi0->racket (feedback n onex)) args))])
+           compiled-feedback-flow)]
       [_:id
-       #'(λ (n flo . args)
-           (apply (qi0->racket (feedback n flo))
-                  args))]))
+       #'(let ([compiled-feedback-flow
+                (λ (n flo . args)
+                  (apply (qi0->racket (feedback n flo))
+                    args))])
+           compiled-feedback-flow)]))
 
   (define (side-effect-parser stx)
     (syntax-parse stx
@@ -549,7 +574,9 @@ the DSL.
       [_:id
        #'map-values]
       [(_ onex:clause)
-       #'(curry map-values (qi0->racket onex))]
+       #'(procedure-rename
+          (curry map-values (qi0->racket onex))
+          'compiled-amp-flow)]
       [(_ onex0:clause onex:clause ...)
        (report-syntax-error
         'amp
@@ -562,7 +589,9 @@ the DSL.
       [_:id
        #'filter-values]
       [(_ onex:clause)
-       #'(curry filter-values (qi0->racket onex))]))
+       #'(procedure-rename
+          (curry filter-values (qi0->racket onex))
+          'compiled-pass-flow)]))
 
   (define (fold-left-parser stx)
     (syntax-parse stx
@@ -607,18 +636,23 @@ the DSL.
     (syntax-parse stx
       [_:id
        #:do [(define chirality (syntax-property stx 'chirality))]
-       (if (and chirality (eq? chirality 'right))
-           #'(λ (f . args) (apply curryr f args))
-           #'(λ (f . args) (apply curry f args)))]
+       #`(let ([compiled-clos-flow
+                (λ (f . args)
+                  (apply #,(if (and chirality (eq? chirality 'right))
+                               #'curryr #'curry)
+                    f args))])
+           compiled-clos-flow)]
       [(_ onex:clause)
        #:do [(define chirality (syntax-property stx 'chirality))]
-       (if (and chirality (eq? chirality 'right))
-           #'(λ args
-               (qi0->racket (~> (-< _ (~> (gen args) △))
-                                onex)))
-           #'(λ args
-               (qi0->racket (~> (-< (~> (gen args) △) _)
-                                onex))))]))
+       #`(let ([compiled-clos-flow
+                (λ args
+                  (qi0->racket
+                   (~>
+                     #,(if (and chirality (eq? chirality 'right))
+                           #'(-< _ (~> (gen args) △))
+                           #'(-< (~> (gen args) △) _))
+                     onex)))])
+         compiled-clos-flow)]))
 
   (define (literal-parser stx)
     (syntax-parse stx
diff --git a/qi-lib/flow/impl.rkt b/qi-lib/flow/impl.rkt
index f1f54849f..ec02bded1 100644
--- a/qi-lib/flow/impl.rkt
+++ b/qi-lib/flow/impl.rkt
@@ -43,22 +43,22 @@
 
 ;; we use a lambda to capture the arguments at runtime
 ;; since they aren't available at compile time
-(define (loom-compose f g [n #f])
-  (let ([n (or n (procedure-arity f))])
+(define (loom-compose f g [n (procedure-arity f)])
+  (define compiled-group-flow
     (λ args
-      (let ([num-args (length args)])
-        (if (< num-args n)
-            (if (= 0 num-args)
-                (values)
-                (error 'group (~a "Can't select "
-                                  n
-                                  " arguments from "
-                                  args)))
-            (let ([sargs (take args n)]
-                  [rargs (drop args n)])
-              (apply values
-                     (append (values->list (apply f sargs))
-                             (values->list (apply g rargs))))))))))
+      (define num-args (length args))
+      (if (< num-args n)
+          (if (= 0 num-args)
+              (values)
+              (error 'group (~a "Can't select "
+                                n
+                                " arguments from "
+                                args)))
+          (let-values ([(sargs rargs) (split-at args n)])
+            (apply values
+              (append (values->list (apply f sargs))
+                      (values->list (apply g rargs))))))))
+  compiled-group-flow)
 
 (define (parity-xor . args) (and (foldl xor #f args) #t))
 
@@ -204,21 +204,21 @@
   (cond
     [(null? fs) 1->1]
     [else
-     (define (relayed . args)
+     (define (compiled-relay-flow . args)
        (apply values (zip-with call fs args)))
-     relayed]))
+     compiled-relay-flow]))
 
 (define (tee . fs)
   (match (remq* (list *->1) fs)
     ['() *->1]
     [`(,f) f]
     [fs
-     (define (teed . args)
+     (define (compiled-tee-flow . args)
        (apply values
          (append*
           (for/list ([f (in-list fs)])
             (values->list (apply f args))))))
-     teed]))
+     compiled-tee-flow]))
 
 (define (all? . args)
   (and (for/and ([v (in-list args)]) v) #t))

From ee6b1f89453bf6bc05dd2dea8c8c87a72c8de861 Mon Sep 17 00:00:00 2001
From: NoahStoryM <noahstorym@gmail.com>
Date: Thu, 1 Sep 2022 13:29:35 +0800
Subject: [PATCH 12/16] Update.

---
 qi-lib/flow/compiler.rkt | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/qi-lib/flow/compiler.rkt b/qi-lib/flow/compiler.rkt
index 032d01992..c35f68f36 100644
--- a/qi-lib/flow/compiler.rkt
+++ b/qi-lib/flow/compiler.rkt
@@ -103,6 +103,8 @@
      #'(qi0->racket (~> ▽ reverse △))]
     [((~or* (~datum ==) (~datum relay)) onex:clause ...)
      #'(relay (qi0->racket onex) ...)]
+    [((~or* (~datum ==*) (~datum relay*)))
+     #'1->1]
     [((~or* (~datum ==*) (~datum relay*)) onex:clause ... rest-onex:clause)
      (with-syntax ([len #`#,(length (syntax->list #'(onex ...)))])
        #'(qi0->racket (group len (== onex ...) rest-onex) ))]

From 575b27f8c775beab87ff77aa71da2f183c0c4319 Mon Sep 17 00:00:00 2001
From: NoahStoryM <noahstorym@gmail.com>
Date: Tue, 11 Oct 2022 11:17:30 +0800
Subject: [PATCH 13/16] Undo `(fanout n:number)` case.

---
 qi-lib/flow/compiler.rkt | 8 +++++---
 1 file changed, 5 insertions(+), 3 deletions(-)

diff --git a/qi-lib/flow/compiler.rkt b/qi-lib/flow/compiler.rkt
index c35f68f36..1a9793513 100644
--- a/qi-lib/flow/compiler.rkt
+++ b/qi-lib/flow/compiler.rkt
@@ -507,9 +507,11 @@ the DSL.
       [(_ n:number)
        ;; a slightly more efficient compile-time implementation
        ;; for literally indicated N
-       #'(procedure-rename
-          (curry repeat-values n)
-          'compiled-fanout-flow)]
+       #`(let ([compiled-fanout-flow
+                (λ args
+                  (apply values
+                    (append #,@(make-list (syntax->datum #'n) 'args))))])
+           compiled-fanout-flow)]
       [(_ e:expr)
        #'(let ([n e])
            (case n

From b5ea1c047462ac5423f9e4c00c454dc30f29df34 Mon Sep 17 00:00:00 2001
From: NoahStoryM <noahstorym@gmail.com>
Date: Tue, 11 Oct 2022 17:22:03 +0800
Subject: [PATCH 14/16] More tests for edge cases.

---
 qi-test/tests/flow.rkt | 20 +++++++++++++++++++-
 1 file changed, 19 insertions(+), 1 deletion(-)

diff --git a/qi-test/tests/flow.rkt b/qi-test/tests/flow.rkt
index 7f41fe490..2c8508a78 100644
--- a/qi-test/tests/flow.rkt
+++ b/qi-test/tests/flow.rkt
@@ -242,6 +242,9 @@
                    "separate into a non-primitive flow with presupplied values"))
     (test-suite
      "gen"
+     (check-eq? (☯ (gen)) (☯ ⏚))
+     (check-eq? ((☯ (~> (gen) ▽)))
+                '())
      (check-equal? ((☯ (gen 5)))
                    5)
      (check-equal? ((☯ (gen 5)) 3)
@@ -420,6 +423,11 @@
                    "a"))
     (test-suite
      "-<"
+     (check-eq? (☯ (-<)) (☯ ⏚))
+     (check-eq? (☯ (-< add1 (-<)))
+                add1)
+     (check-eq? (☯ (-< (-<) add1))
+                add1)
      (check-equal? ((☯ (~> (-< sqr add1) ▽))
                     5)
                    (list 25 6))
@@ -452,6 +460,8 @@
                    "named tee junction form"))
     (test-suite
      "=="
+     (check-eq? ((☯ (~> (==) ▽)))
+                '())
      (check-equal? ((☯ (~> (== sqr add1) ▽))
                     5 7)
                    (list 25 8))
@@ -486,6 +496,8 @@
                    "named relay form"))
     (test-suite
      "==*"
+     (check-eq? ((☯ (~> (==*) ▽)))
+                '())
      (check-equal? ((☯ (~> (==* add1 sub1 +) ▽))
                     1 1 1 1 1)
                    (list 2 0 3))
@@ -503,7 +515,9 @@
                    6)
      (check-equal? ((☯ (-< ground add1))
                     5)
-                   6)))
+                   6)
+     (check-eq? (☯ (-< ⏚ add1)) add1)
+     (check-eq? (☯ ⏚) (☯ (-<)))))
 
    (test-suite
     "Exceptions"
@@ -939,6 +953,9 @@
      (check-equal? (~> (2 3) (fanout 0) ▽)
                    null
                    "N=0 produces no values.")
+     (check-equal? (~> (2 3) (fanout 1) ▽)
+                   (list 2 3)
+                   "N=1 produces original values.")
      (check-equal? (~> () (fanout 3) ▽)
                    null
                    "No inputs produces no outputs.")
@@ -1051,6 +1068,7 @@
                 "grouping more inputs than are available shows a helpful error"))
     (test-suite
      "select"
+     (check-equal? (☯ (~> (select))) (☯ ⏚))
      (check-equal? ((☯ (~> (select) ▽))
                     1)
                    null)

From 46aed9f7d7631cc849656e2b8fa20a14bc58c73c Mon Sep 17 00:00:00 2001
From: NoahStoryM <noahstorym@gmail.com>
Date: Fri, 14 Oct 2022 20:34:57 +0800
Subject: [PATCH 15/16] Optimize `relay` and `relay*`.

---
 qi-lib/flow/compiler.rkt | 2 ++
 qi-lib/flow/impl.rkt     | 9 +++++----
 qi-test/tests/flow.rkt   | 9 ++++++++-
 3 files changed, 15 insertions(+), 5 deletions(-)

diff --git a/qi-lib/flow/compiler.rkt b/qi-lib/flow/compiler.rkt
index 1a9793513..049d9f943 100644
--- a/qi-lib/flow/compiler.rkt
+++ b/qi-lib/flow/compiler.rkt
@@ -105,6 +105,8 @@
      #'(relay (qi0->racket onex) ...)]
     [((~or* (~datum ==*) (~datum relay*)))
      #'1->1]
+    [((~or* (~datum ==*) (~datum relay*)) onex:clause)
+     #'onex]
     [((~or* (~datum ==*) (~datum relay*)) onex:clause ... rest-onex:clause)
      (with-syntax ([len #`#,(length (syntax->list #'(onex ...)))])
        #'(qi0->racket (group len (== onex ...) rest-onex) ))]
diff --git a/qi-lib/flow/impl.rkt b/qi-lib/flow/impl.rkt
index ec02bded1..331008cf9 100644
--- a/qi-lib/flow/impl.rkt
+++ b/qi-lib/flow/impl.rkt
@@ -200,10 +200,11 @@
    (lambda (ks vs f . xs)
      (keyword-apply f ks vs xs))))
 
-(define (relay . fs)
-  (cond
-    [(null? fs) 1->1]
-    [else
+(define relay
+  (case-lambda
+    [() 1->1]
+    [(f) (procedure-reduce-arity-mask f 2)]
+    [fs
      (define (compiled-relay-flow . args)
        (apply values (zip-with call fs args)))
      compiled-relay-flow]))
diff --git a/qi-test/tests/flow.rkt b/qi-test/tests/flow.rkt
index 2c8508a78..e2bf1df5f 100644
--- a/qi-test/tests/flow.rkt
+++ b/qi-test/tests/flow.rkt
@@ -486,7 +486,11 @@
                     5 7)
                    (list 5 5 8)
                    "relay with arity-increasing clause")
-     (check-exn exn:fail?
+     (check-eq? ((☯ (~> (== add1))) 1) 2)
+     (check-exn exn:fail:contract:arity?
+                (thunk ((☯ (~> (== +)))
+                        1 2 3)))
+     (check-exn exn:fail:contract:arity?
                 (thunk ((☯ (~> (== ⏚ add1) ▽))
                         5 7 8))
                 "relay elements must be in one-to-one correspondence with input")
@@ -498,6 +502,9 @@
      "==*"
      (check-eq? ((☯ (~> (==*) ▽)))
                 '())
+     (check-eq? ((☯ (~> (==* +)))
+                 1 2 3 4 5)
+                15)
      (check-equal? ((☯ (~> (==* add1 sub1 +) ▽))
                     1 1 1 1 1)
                    (list 2 0 3))

From 88a740650680fa2e996f483386cb0387542ef977 Mon Sep 17 00:00:00 2001
From: NoahStoryM <noahstorym@gmail.com>
Date: Sat, 15 Oct 2022 16:23:59 +0800
Subject: [PATCH 16/16] Fix `==*`.

---
 qi-lib/flow/compiler.rkt | 2 +-
 qi-test/tests/flow.rkt   | 3 +++
 2 files changed, 4 insertions(+), 1 deletion(-)

diff --git a/qi-lib/flow/compiler.rkt b/qi-lib/flow/compiler.rkt
index 049d9f943..df8c4e772 100644
--- a/qi-lib/flow/compiler.rkt
+++ b/qi-lib/flow/compiler.rkt
@@ -106,7 +106,7 @@
     [((~or* (~datum ==*) (~datum relay*)))
      #'1->1]
     [((~or* (~datum ==*) (~datum relay*)) onex:clause)
-     #'onex]
+     #'(qi0->racket onex)]
     [((~or* (~datum ==*) (~datum relay*)) onex:clause ... rest-onex:clause)
      (with-syntax ([len #`#,(length (syntax->list #'(onex ...)))])
        #'(qi0->racket (group len (== onex ...) rest-onex) ))]
diff --git a/qi-test/tests/flow.rkt b/qi-test/tests/flow.rkt
index e2bf1df5f..2d596cebb 100644
--- a/qi-test/tests/flow.rkt
+++ b/qi-test/tests/flow.rkt
@@ -505,6 +505,9 @@
      (check-eq? ((☯ (~> (==* +)))
                  1 2 3 4 5)
                 15)
+     (check-eq? ((☯ (~> (==* (~> +))))
+                 1 2 3 4 5)
+                15)
      (check-equal? ((☯ (~> (==* add1 sub1 +) ▽))
                     1 1 1 1 1)
                    (list 2 0 3))