apl: named function definitions f ← {…} (+7 tests, 467/467)

Parser: apl-collect-fn-bindings pre-scans stmt-groups for
`name ← { ... }` patterns and populates apl-known-fn-names.
is-fn-tok? consults this list; collect-segments-loop emits
(:fn-name nm) for known names so they parse as functions.

Resolver: apl-resolve-{monadic,dyadic} handle :fn-name by
looking up env, asserting the binding is a dfn, returning
a closure that dispatches to apl-call-dfn{-m,}.

Recursion still works: `fact ← {0=⍵:1 ⋄ ⍵×∇⍵-1} ⋄ fact 5` → 120.

lib/apl/parser.sx

@@ -84,20 +84,46 @@
 
 (define apl-quad-fn-names (list "⎕FMT" "⎕←"))
 
-(define
-  apl-parse-op-glyph?
-  (fn (v) (some (fn (g) (= g v)) apl-parse-op-glyphs)))
+(define apl-known-fn-names (list))
 
 ; ============================================================
 ; Token accessors
 ; ============================================================
 
+(define
+  apl-collect-fn-bindings
+  (fn
+    (stmt-groups)
+    (set! apl-known-fn-names (list))
+    (for-each
+      (fn
+        (toks)
+        (when
+          (and
+            (>= (len toks) 3)
+            (= (tok-type (nth toks 0)) :name)
+            (= (tok-type (nth toks 1)) :assign)
+            (= (tok-type (nth toks 2)) :lbrace))
+          (set!
+            apl-known-fn-names
+            (cons (tok-val (nth toks 0)) apl-known-fn-names))))
+      stmt-groups)))
+
+(define
+  apl-parse-op-glyph?
+  (fn (v) (some (fn (g) (= g v)) apl-parse-op-glyphs)))
+
 (define
   apl-parse-fn-glyph?
   (fn (v) (some (fn (g) (= g v)) apl-parse-fn-glyphs)))
 
 (define tok-type (fn (tok) (get tok :type)))
 
+; ============================================================
+; Collect trailing operators starting at index i
+; Returns {:ops (op ...) :end new-i}
+; ============================================================
+
 (define tok-val (fn (tok) (get tok :value)))
 
 (define
@@ -107,8 +133,8 @@
     (and (= (tok-type tok) :glyph) (apl-parse-op-glyph? (tok-val tok)))))
 
 ; ============================================================
-; Collect trailing operators starting at index i
-; Returns {:ops (op ...) :end new-i}
+; Build a derived-fn node by chaining operators left-to-right
+; (+/¨  →  (:derived-fn "¨" (:derived-fn "/" (:fn-glyph "+"))))
 ; ============================================================
 
 (define
@@ -119,15 +145,17 @@
       (and (= (tok-type tok) :glyph) (apl-parse-fn-glyph? (tok-val tok)))
       (and
         (= (tok-type tok) :name)
-        (some (fn (q) (= q (tok-val tok))) apl-quad-fn-names)))))
+        (or
+          (some (fn (q) (= q (tok-val tok))) apl-quad-fn-names)
+          (some (fn (q) (= q (tok-val tok))) apl-known-fn-names))))))
+
+; ============================================================
+; Find matching close bracket/paren/brace
+; Returns the index of the matching close token
+; ============================================================
 
 (define collect-ops (fn (tokens i) (collect-ops-loop tokens i (list))))
 
-; ============================================================
-; Build a derived-fn node by chaining operators left-to-right
-; (+/¨  →  (:derived-fn "¨" (:derived-fn "/" (:fn-glyph "+"))))
-; ============================================================
-
 (define
   collect-ops-loop
   (fn
@@ -143,8 +171,10 @@
           {:end i :ops acc})))))
 
 ; ============================================================
-; Find matching close bracket/paren/brace
-; Returns the index of the matching close token
+; Segment collection: scan tokens left-to-right, building
+; a list of {:kind "val"/"fn" :node ast} segments.
+; Operators following function glyphs are merged into
+; derived-fn nodes during this pass.
 ; ============================================================
 
 (define
@@ -163,12 +193,20 @@
     (find-matching-close-loop tokens start open-type close-type 1)))
 
 ; ============================================================
-; Segment collection: scan tokens left-to-right, building
-; a list of {:kind "val"/"fn" :node ast} segments.
-; Operators following function glyphs are merged into
-; derived-fn nodes during this pass.
+; Build tree from segment list
+;
+; The segments are in left-to-right order.
+; APL evaluates right-to-left, so the LEFTMOST function is
+; the outermost (last-evaluated) node.
+;
+; Patterns:
+;   [val]              → val node
+;   [fn val ...]       → (:monad fn (build-tree rest))
+;   [val fn val ...]   → (:dyad fn val (build-tree rest))
+;   [val val ...]      → (:vec val1 val2 ...) — strand
 ; ============================================================
 
+; Find the index of the first function segment (returns -1 if none)
 (define
   find-matching-close-loop
   (fn
@@ -208,21 +246,9 @@
   collect-segments
   (fn (tokens) (collect-segments-loop tokens 0 (list))))
 
-; ============================================================
-; Build tree from segment list
-;
-; The segments are in left-to-right order.
-; APL evaluates right-to-left, so the LEFTMOST function is
-; the outermost (last-evaluated) node.
-;
-; Patterns:
-;   [val]              → val node
-;   [fn val ...]       → (:monad fn (build-tree rest))
-;   [val fn val ...]   → (:dyad fn val (build-tree rest))
-;   [val val ...]      → (:vec val1 val2 ...) — strand
-; ============================================================
-
-; Find the index of the first function segment (returns -1 if none)
+; Build an array node from 0..n value segments
+; If n=1 → return that segment's node
+; If n>1 → return (:vec node1 node2 ...)
 (define
   collect-segments-loop
   (fn
@@ -242,24 +268,38 @@
             ((= tt :str)
               (collect-segments-loop tokens (+ i 1) (append acc {:kind "val" :node (list :str tv)})))
             ((= tt :name)
-              (if
-                (some (fn (q) (= q tv)) apl-quad-fn-names)
-                (let
-                  ((op-result (collect-ops tokens (+ i 1))))
+              (cond
+                ((some (fn (q) (= q tv)) apl-quad-fn-names)
                   (let
-                    ((ops (get op-result :ops)) (ni (get op-result :end)))
+                    ((op-result (collect-ops tokens (+ i 1))))
                     (let
-                      ((fn-node (build-derived-fn (list :fn-glyph tv) ops)))
-                      (collect-segments-loop
-                        tokens
-                        ni
-                        (append acc {:kind "fn" :node fn-node})))))
-                (let
-                  ((br (maybe-bracket (list :name tv) tokens (+ i 1))))
-                  (collect-segments-loop
-                    tokens
-                    (nth br 1)
-                    (append acc {:kind "val" :node (nth br 0)})))))
+                      ((ops (get op-result :ops))
+                        (ni (get op-result :end)))
+                      (let
+                        ((fn-node (build-derived-fn (list :fn-glyph tv) ops)))
+                        (collect-segments-loop
+                          tokens
+                          ni
+                          (append acc {:kind "fn" :node fn-node}))))))
+                ((some (fn (q) (= q tv)) apl-known-fn-names)
+                  (let
+                    ((op-result (collect-ops tokens (+ i 1))))
+                    (let
+                      ((ops (get op-result :ops))
+                        (ni (get op-result :end)))
+                      (let
+                        ((fn-node (build-derived-fn (list :fn-name tv) ops)))
+                        (collect-segments-loop
+                          tokens
+                          ni
+                          (append acc {:kind "fn" :node fn-node}))))))
+                (else
+                  (let
+                    ((br (maybe-bracket (list :name tv) tokens (+ i 1))))
+                    (collect-segments-loop
+                      tokens
+                      (nth br 1)
+                      (append acc {:kind "val" :node (nth br 0)}))))))
             ((= tt :lparen)
               (let
                 ((end (find-matching-close tokens (+ i 1) :lparen :rparen)))
@@ -346,9 +386,12 @@
 
 (define find-first-fn (fn (segs) (find-first-fn-loop segs 0)))
 
-; Build an array node from 0..n value segments
-; If n=1 → return that segment's node
-; If n>1 → return (:vec node1 node2 ...)
+
+; ============================================================
+; Split token list on statement separators (diamond / newline)
+; Only splits at depth 0 (ignores separators inside { } or ( ) )
+; ============================================================
+
 (define
   find-first-fn-loop
   (fn
@@ -370,10 +413,9 @@
       (get (first segs) :node)
       (cons :vec (map (fn (s) (get s :node)) segs)))))
 
-
 ; ============================================================
-; Split token list on statement separators (diamond / newline)
-; Only splits at depth 0 (ignores separators inside { } or ( ) )
+; Parse a dfn body (tokens between { and })
+; Handles guard expressions: cond : expr
 ; ============================================================
 
 (define
@@ -408,11 +450,6 @@
   split-statements
   (fn (tokens) (split-statements-loop tokens (list) (list) 0)))
 
-; ============================================================
-; Parse a dfn body (tokens between { and })
-; Handles guard expressions: cond : expr
-; ============================================================
-
 (define
   split-statements-loop
   (fn
@@ -467,6 +504,10 @@
       ((stmt-groups (split-statements tokens)))
       (let ((stmts (map parse-dfn-stmt stmt-groups))) (cons :dfn stmts)))))
 
+; ============================================================
+; Parse a single statement (assignment or expression)
+; ============================================================
+
 (define
   parse-dfn-stmt
   (fn
@@ -483,12 +524,17 @@
             (parse-apl-expr body-tokens)))
         (parse-stmt tokens)))))
 
+; ============================================================
+; Parse an expression from a flat token list
+; ============================================================
+
 (define
   find-top-level-colon
   (fn (tokens i) (find-top-level-colon-loop tokens i 0)))
 
 ; ============================================================
-; Parse a single statement (assignment or expression)
+; Main entry point
+; parse-apl: string → AST
 ; ============================================================
 
 (define
@@ -508,10 +554,6 @@
           ((and (= tt :colon) (= depth 0)) i)
           (true (find-top-level-colon-loop tokens (+ i 1) depth)))))))
 
-; ============================================================
-; Parse an expression from a flat token list
-; ============================================================
-
 (define
   parse-stmt
   (fn
@@ -526,11 +568,6 @@
         (parse-apl-expr (slice tokens 2)))
       (parse-apl-expr tokens))))
 
-; ============================================================
-; Main entry point
-; parse-apl: string → AST
-; ============================================================
-
 (define
   parse-apl-expr
   (fn
@@ -547,13 +584,15 @@
       ((tokens (apl-tokenize src)))
       (let
         ((stmt-groups (split-statements tokens)))
-        (if
-          (= (len stmt-groups) 0)
-          nil
+        (begin
+          (apl-collect-fn-bindings stmt-groups)
           (if
-            (= (len stmt-groups) 1)
-            (parse-stmt (first stmt-groups))
-            (cons :program (map parse-stmt stmt-groups))))))))
+            (= (len stmt-groups) 0)
+            nil
+            (if
+              (= (len stmt-groups) 1)
+              (parse-stmt (first stmt-groups))
+              (cons :program (map parse-stmt stmt-groups)))))))))
 
 (define
   maybe-bracket

lib/apl/tests/pipeline.sx

@@ -207,3 +207,38 @@
 (apl-test "string: 'a' is rank-0 scalar" (mksh (apl-run "'a'")) (list))
 
 (apl-test "string: 'hello' shape (5)" (mksh (apl-run "'hello'")) (list 5))
+
+(apl-test
+  "named-fn: f ← {⍺+⍵} ⋄ 3 f 4 → 7"
+  (mkrv (apl-run "f ← {⍺+⍵} ⋄ 3 f 4"))
+  (list 7))
+
+(apl-test
+  "named-fn monadic: sq ← {⍵×⍵} ⋄ sq 7 → 49"
+  (mkrv (apl-run "sq ← {⍵×⍵} ⋄ sq 7"))
+  (list 49))
+
+(apl-test
+  "named-fn dyadic: hyp ← {((⍺×⍺)+⍵×⍵)} ⋄ 3 hyp 4 → 25"
+  (mkrv (apl-run "hyp ← {((⍺×⍺)+⍵×⍵)} ⋄ 3 hyp 4"))
+  (list 25))
+
+(apl-test
+  "named-fn: dbl ← {⍵+⍵} ⋄ dbl ⍳5"
+  (mkrv (apl-run "dbl ← {⍵+⍵} ⋄ dbl ⍳5"))
+  (list 2 4 6 8 10))
+
+(apl-test
+  "named-fn factorial via ∇ recursion"
+  (mkrv (apl-run "fact ← {0=⍵:1 ⋄ ⍵×∇⍵-1} ⋄ fact 5"))
+  (list 120))
+
+(apl-test
+  "named-fn used twice in expr: dbl ← {⍵+⍵} ⋄ (dbl 3) + dbl 4"
+  (mkrv (apl-run "dbl ← {⍵+⍵} ⋄ (dbl 3) + dbl 4"))
+  (list 14))
+
+(apl-test
+  "named-fn with vector arg: neg ← {-⍵} ⋄ neg 1 2 3"
+  (mkrv (apl-run "neg ← {-⍵} ⋄ neg 1 2 3"))
+  (list -1 -2 -3))

lib/apl/transpile.sx

@@ -429,6 +429,18 @@
                   ((f (apl-resolve-dyadic inner env)))
                   (fn (arr) (apl-commute f arr))))
               (else (error "apl-resolve-monadic: unsupported op")))))
+        ((= tag :fn-name)
+          (let
+            ((nm (nth fn-node 1)))
+            (let
+              ((bound (get env nm)))
+              (if
+                (and
+                  (list? bound)
+                  (> (len bound) 0)
+                  (= (first bound) :dfn))
+                (fn (arg) (apl-call-dfn-m bound arg))
+                (error "apl-resolve-monadic: name not bound to dfn")))))
         (else (error "apl-resolve-monadic: unknown fn-node tag"))))))
 
 (define
@@ -452,6 +464,18 @@
                   ((f (apl-resolve-dyadic inner env)))
                   (fn (a b) (apl-commute-dyadic f a b))))
               (else (error "apl-resolve-dyadic: unsupported op")))))
+        ((= tag :fn-name)
+          (let
+            ((nm (nth fn-node 1)))
+            (let
+              ((bound (get env nm)))
+              (if
+                (and
+                  (list? bound)
+                  (> (len bound) 0)
+                  (= (first bound) :dfn))
+                (fn (a b) (apl-call-dfn bound a b))
+                (error "apl-resolve-dyadic: name not bound to dfn")))))
         ((= tag :outer)
           (let
             ((inner (nth fn-node 2)))

plans/apl-on-sx.md

@@ -148,7 +148,7 @@ programs run from source, and starts pushing on performance.
     a single `:name "⎕←"` token (don't split on the assign glyph);
   - string values in `apl-eval-ast` — handle `:str` (parser already produces
     them) by wrapping into a vector of character codes (or rank-0 string).
-- [ ] **Named function definitions** — `f ← {⍺+⍵} ⋄ 1 f 2` and `2 f 3`.
+- [x] **Named function definitions** — `f ← {⍺+⍵} ⋄ 1 f 2` and `2 f 3`.
   - parser: when `:assign`'s RHS is a `:dfn`, mark it as a function binding;
   - eval-ast: `:assign` of a dfn stores the dfn in env;
   - parser: a name in fn-position whose env value is a dfn dispatches as a fn;
@@ -186,6 +186,7 @@ data; format for string templating.
 
 _Newest first._
 
+- 2026-05-07: Phase 8 step 2 — named function defs end-to-end via parser pre-scan; apl-known-fn-names + apl-collect-fn-bindings detect `name ← {...}` patterns; collect-segments-loop emits :fn-name for known names; resolver looks up env for :fn-name; supports recursion (∇ in named dfn); +7 tests including fact via ∇; 467/467
 - 2026-05-07: Phase 8 step 1 — quick-wins bundle: decimal literals (3.7, ¯2.5), ⎕← passthrough as monadic fn (single-token via tokenizer special-case), :str AST in eval-ast (single-char→scalar, multi-char→vec); +10 tests; 460/460
 - 2026-05-07: Phase 8 added — quick-wins bundle (decimals + ⎕← + strings), named functions, multi-axis bracket, .apl-files-as-tests, trains, perf
 - 2026-05-07: Phase 7 step 6 — :Trap exception machinery via R7RS guard; apl-throw raises tagged error, apl-trap-matches? checks codes (0=catch-all), :trap clause in apl-tradfn-eval-stmt wraps try-block with guard; :throw AST for testing; **Phase 7 complete, all unchecked plan items done**; +5 tests; 450/450