apl: right-to-left parser + 44 tests (Phase 1, step 2)

Implement lib/apl/parser.sx — APL expression parser:
- Segment-based algorithm: scan L→R collecting {fn,val} segments
- build-tree constructs AST with leftmost-fn = root (right-to-left semantics)
- Handles: monadic/dyadic fns, strands (:vec), assignment (:assign)
- Operators: derived-fn (:derived-fn op fn), inner product (:derived-fn2)
- Outer product ∘.f (:outer), dfns {:dfn stmt...}, guards (:guard cond expr)
- split-statements is bracket-aware (depth tracking prevents splitting inside {})

44 new parser tests + 46 existing tokenizer = 90/90 green.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

lib/apl/parser.sx

@@ -0,0 +1,436 @@
+; APL Parser — right-to-left expression parser
+;
+; Takes a token list (output of apl-tokenize) and produces an AST.
+; APL evaluates right-to-left with no precedence among functions.
+; Operators bind to the function immediately to their left in the source.
+;
+; AST node types:
+;   (:num n)                     number literal
+;   (:str s)                     string literal
+;   (:vec n1 n2 ...)             strand (juxtaposed literals)
+;   (:name "x")                  name reference / alpha / omega
+;   (:assign "x" expr)           assignment  x←expr
+;   (:monad fn arg)              monadic function call
+;   (:dyad fn left right)        dyadic function call
+;   (:derived-fn op fn)          derived function: f/ f¨ f⍨
+;   (:derived-fn2 "." f g)       inner product: f.g
+;   (:outer "∘." fn)             outer product: ∘.f
+;   (:fn-glyph "⍳")             function reference
+;   (:fn-name "foo")             named-function reference (dfn variable)
+;   (:dfn stmt...)               {⍺+⍵} anonymous function
+;   (:guard cond expr)           cond:expr guard inside dfn
+;   (:program stmt...)           multi-statement sequence
+
+; ============================================================
+; Glyph classification sets
+; ============================================================
+
+(define apl-parse-op-glyphs
+  (list "/" "\\" "¨" "⍨" "∘" "." "⍣" "⍤" "⍥" "@"))
+
+(define apl-parse-fn-glyphs
+  (list "+" "-" "×" "÷" "*" "⍟" "⌈" "⌊" "|" "!" "?" "○" "~"
+        "<" "≤" "=" "≥" ">" "≠" "∊" "∧" "∨" "⍱" "⍲"
+        "," "⍪" "⍴" "⌽" "⊖" "⍉" "↑" "↓" "⊂" "⊃" "⊆"
+        "∪" "∩" "⍳" "⍸" "⌷" "⍋" "⍒" "⊥" "⊤" "⊣" "⊢" "⍎" "⍕"))
+
+(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)))
+
+; ============================================================
+; Token accessors
+; ============================================================
+
+(define tok-type
+  (fn (tok)
+    (get tok :type)))
+
+(define tok-val
+  (fn (tok)
+    (get tok :value)))
+
+(define is-op-tok?
+  (fn (tok)
+    (and (= (tok-type tok) :glyph)
+         (apl-parse-op-glyph? (tok-val tok)))))
+
+(define is-fn-tok?
+  (fn (tok)
+    (and (= (tok-type tok) :glyph)
+         (apl-parse-fn-glyph? (tok-val tok)))))
+
+; ============================================================
+; Collect trailing operators starting at index i
+; Returns {:ops (op ...) :end new-i}
+; ============================================================
+
+(define collect-ops
+  (fn (tokens i)
+    (collect-ops-loop tokens i (list))))
+
+(define collect-ops-loop
+  (fn (tokens i acc)
+    (if (>= i (len tokens))
+      {:ops acc :end i}
+      (let ((tok (nth tokens i)))
+        (if (is-op-tok? tok)
+          (collect-ops-loop tokens (+ i 1) (append acc (tok-val tok)))
+          {:ops acc :end i})))))
+
+; ============================================================
+; Build a derived-fn node by chaining operators left-to-right
+; (+/¨  →  (:derived-fn "¨" (:derived-fn "/" (:fn-glyph "+"))))
+; ============================================================
+
+(define build-derived-fn
+  (fn (fn-node ops)
+    (if (= (len ops) 0)
+      fn-node
+      (build-derived-fn
+        (list :derived-fn (first ops) fn-node)
+        (rest ops)))))
+
+; ============================================================
+; Find matching close bracket/paren/brace
+; Returns the index of the matching close token
+; ============================================================
+
+(define find-matching-close
+  (fn (tokens start open-type close-type)
+    (find-matching-close-loop tokens start open-type close-type 1)))
+
+(define find-matching-close-loop
+  (fn (tokens i open-type close-type depth)
+    (if (>= i (len tokens))
+      (len tokens)
+      (let ((tt (tok-type (nth tokens i))))
+        (cond
+          ((= tt open-type)
+           (find-matching-close-loop tokens (+ i 1) open-type close-type (+ depth 1)))
+          ((= tt close-type)
+           (if (= depth 1)
+             i
+             (find-matching-close-loop tokens (+ i 1) open-type close-type (- depth 1))))
+          (true
+           (find-matching-close-loop tokens (+ i 1) open-type close-type depth)))))))
+
+; ============================================================
+; 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 collect-segments
+  (fn (tokens)
+    (collect-segments-loop tokens 0 (list))))
+
+(define collect-segments-loop
+  (fn (tokens i acc)
+    (if (>= i (len tokens))
+      acc
+      (let ((tok (nth tokens i))
+            (n   (len tokens)))
+        (let ((tt (tok-type tok))
+              (tv (tok-val tok)))
+          (cond
+            ; Skip separators
+            ((or (= tt :diamond) (= tt :newline) (= tt :semi))
+             (collect-segments-loop tokens (+ i 1) acc))
+
+            ; Number → value segment
+            ((= tt :num)
+             (collect-segments-loop tokens (+ i 1)
+               (append acc {:kind "val" :node (list :num tv)})))
+
+            ; String → value segment
+            ((= tt :str)
+             (collect-segments-loop tokens (+ i 1)
+               (append acc {:kind "val" :node (list :str tv)})))
+
+            ; Name → always a value segment in Phase 1
+            ; (Named functions with operators like f/ are Phase 5)
+            ((= tt :name)
+             (collect-segments-loop tokens (+ i 1)
+               (append acc {:kind "val" :node (list :name tv)})))
+
+
+            ; Left paren → parse subexpression recursively
+            ((= tt :lparen)
+             (let ((end (find-matching-close tokens (+ i 1) :lparen :rparen)))
+               (let ((inner-tokens (slice tokens (+ i 1) end))
+                     (after (+ end 1)))
+                 (collect-segments-loop tokens after
+                   (append acc {:kind "val" :node (parse-apl-expr inner-tokens)})))))
+
+            ; Left brace → dfn
+            ((= tt :lbrace)
+             (let ((end (find-matching-close tokens (+ i 1) :lbrace :rbrace)))
+               (let ((inner-tokens (slice tokens (+ i 1) end))
+                     (after (+ end 1)))
+                 (collect-segments-loop tokens after
+                   (append acc {:kind "fn" :node (parse-dfn inner-tokens)})))))
+
+            ; Glyph token — need to classify
+            ((= tt :glyph)
+             (cond
+               ; Alpha (⍺) and Omega (⍵) → values inside dfn context
+               ((or (= tv "⍺") (= tv "⍵"))
+                (collect-segments-loop tokens (+ i 1)
+                  (append acc {:kind "val" :node (list :name tv)})))
+
+               ; Nabla (∇) → self-reference function in dfn context
+               ((= tv "∇")
+                (collect-segments-loop tokens (+ i 1)
+                  (append acc {:kind "fn" :node (list :fn-glyph "∇")})))
+
+               ; ∘. → outer product (special case: ∘ followed by .)
+               ((and (= tv "∘")
+                     (< (+ i 1) n)
+                     (= (tok-val (nth tokens (+ i 1))) "."))
+                (if (and (< (+ i 2) n) (is-fn-tok? (nth tokens (+ i 2))))
+                  (let ((fn-tv (tok-val (nth tokens (+ i 2)))))
+                    (let ((op-result (collect-ops tokens (+ i 3))))
+                      (let ((ops (get op-result :ops))
+                            (ni  (get op-result :end)))
+                        (let ((fn-node (build-derived-fn (list :fn-glyph fn-tv) ops)))
+                          (collect-segments-loop tokens ni
+                            (append acc {:kind "fn" :node (list :outer "∘." fn-node)}))))))
+                  ; ∘. without function — treat ∘ as plain compose operator
+                  ; skip the . and continue
+                  (collect-segments-loop tokens (+ i 1)
+                    acc)))
+
+               ; Function glyph — collect following operators
+               ((apl-parse-fn-glyph? tv)
+                (let ((op-result (collect-ops tokens (+ i 1))))
+                  (let ((ops (get op-result :ops))
+                        (ni  (get op-result :end)))
+                    ; Check for inner product: fn . fn
+                    ; (ops = ("." ) and next token is also a function glyph)
+                    (if (and (= (len ops) 1)
+                             (= (first ops) ".")
+                             (< ni n)
+                             (is-fn-tok? (nth tokens ni)))
+                      ; f.g inner product
+                      (let ((g-tv (tok-val (nth tokens ni))))
+                        (let ((op-result2 (collect-ops tokens (+ ni 1))))
+                          (let ((ops2 (get op-result2 :ops))
+                                (ni2  (get op-result2 :end)))
+                            (let ((g-node (build-derived-fn (list :fn-glyph g-tv) ops2)))
+                              (collect-segments-loop tokens ni2
+                                (append acc {:kind "fn"
+                                             :node (list :derived-fn2 "." (list :fn-glyph tv) g-node)}))))))
+                      ; Regular function with zero or more operator modifiers
+                      (let ((fn-node (build-derived-fn (list :fn-glyph tv) ops)))
+                        (collect-segments-loop tokens ni
+                          (append acc {:kind "fn" :node fn-node})))))))
+
+               ; Stray operator glyph — skip (shouldn't appear outside function context)
+               ((apl-parse-op-glyph? tv)
+                (collect-segments-loop tokens (+ i 1) acc))
+
+               ; Unknown glyph — skip
+               (true
+                (collect-segments-loop tokens (+ i 1) acc))))
+
+            ; Skip unknown token types
+            (true
+             (collect-segments-loop tokens (+ i 1) acc))))))))
+
+; ============================================================
+; 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-first-fn
+  (fn (segs)
+    (find-first-fn-loop segs 0)))
+
+(define find-first-fn-loop
+  (fn (segs i)
+    (if (>= i (len segs))
+      -1
+      (if (= (get (nth segs i) :kind) "fn")
+        i
+        (find-first-fn-loop segs (+ i 1))))))
+
+; 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 segs-to-array
+  (fn (segs)
+    (if (= (len segs) 1)
+      (get (first segs) :node)
+      (cons :vec (map (fn (s) (get s :node)) segs)))))
+
+(define build-tree
+  (fn (segs)
+    (cond
+      ; Empty → nil
+      ((= (len segs) 0) nil)
+      ; Single segment → return its node directly
+      ((= (len segs) 1) (get (first segs) :node))
+      ; All values → strand
+      ((every? (fn (s) (= (get s :kind) "val")) segs)
+       (segs-to-array segs))
+      ; Find the first function segment
+      (true
+       (let ((fn-idx (find-first-fn segs)))
+         (cond
+           ; No function found (shouldn't happen given above checks) → strand
+           ((= fn-idx -1) (segs-to-array segs))
+           ; Function is first → monadic call
+           ((= fn-idx 0)
+            (list :monad
+                  (get (first segs) :node)
+                  (build-tree (rest segs))))
+           ; Function at position fn-idx: left args are segs[0..fn-idx-1]
+           (true
+            (let ((left-segs  (slice segs 0 fn-idx))
+                  (fn-seg     (nth segs fn-idx))
+                  (right-segs (slice segs (+ fn-idx 1))))
+              (list :dyad
+                    (get fn-seg :node)
+                    (segs-to-array left-segs)
+                    (build-tree right-segs))))))))))
+
+
+; ============================================================
+; Split token list on statement separators (diamond / newline)
+; Only splits at depth 0 (ignores separators inside { } or ( ) )
+; ============================================================
+
+(define split-statements
+  (fn (tokens)
+    (split-statements-loop tokens (list) (list) 0)))
+
+(define split-statements-loop
+  (fn (tokens current-stmt acc depth)
+    (if (= (len tokens) 0)
+      (if (> (len current-stmt) 0)
+        (append acc (list current-stmt))
+        acc)
+      (let ((tok (first tokens))
+            (rest-toks (rest tokens))
+            (tt (tok-type (first tokens))))
+        (cond
+          ; Open brackets increase depth
+          ((or (= tt :lparen) (= tt :lbrace) (= tt :lbracket))
+           (split-statements-loop rest-toks (append current-stmt tok) acc (+ depth 1)))
+          ; Close brackets decrease depth
+          ((or (= tt :rparen) (= tt :rbrace) (= tt :rbracket))
+           (split-statements-loop rest-toks (append current-stmt tok) acc (- depth 1)))
+          ; Separators only split at top level (depth = 0)
+          ((and (> depth 0) (or (= tt :diamond) (= tt :newline)))
+           (split-statements-loop rest-toks (append current-stmt tok) acc depth))
+          ((and (= depth 0) (or (= tt :diamond) (= tt :newline)))
+           (if (> (len current-stmt) 0)
+             (split-statements-loop rest-toks (list) (append acc (list current-stmt)) depth)
+             (split-statements-loop rest-toks (list) acc depth)))
+          ; All other tokens go into current statement
+          (true
+           (split-statements-loop rest-toks (append current-stmt tok) acc depth)))))))
+
+; ============================================================
+; Parse a dfn body (tokens between { and })
+; Handles guard expressions: cond : expr
+; ============================================================
+
+(define parse-dfn
+  (fn (tokens)
+    (let ((stmt-groups (split-statements tokens)))
+      (let ((stmts (map parse-dfn-stmt stmt-groups)))
+        (cons :dfn stmts)))))
+
+(define parse-dfn-stmt
+  (fn (tokens)
+    ; Check for guard: expr : expr
+    ; A guard has a :colon token not inside parens/braces
+    (let ((colon-idx (find-top-level-colon tokens 0)))
+      (if (>= colon-idx 0)
+        ; Guard: cond : expr
+        (let ((cond-tokens (slice tokens 0 colon-idx))
+              (body-tokens (slice tokens (+ colon-idx 1))))
+          (list :guard
+                (parse-apl-expr cond-tokens)
+                (parse-apl-expr body-tokens)))
+        ; Regular statement
+        (parse-stmt tokens)))))
+
+(define find-top-level-colon
+  (fn (tokens i)
+    (find-top-level-colon-loop tokens i 0)))
+
+(define find-top-level-colon-loop
+  (fn (tokens i depth)
+    (if (>= i (len tokens))
+      -1
+      (let ((tok (nth tokens i))
+            (tt  (tok-type (nth tokens i))))
+        (cond
+          ((or (= tt :lparen) (= tt :lbrace) (= tt :lbracket))
+           (find-top-level-colon-loop tokens (+ i 1) (+ depth 1)))
+          ((or (= tt :rparen) (= tt :rbrace) (= tt :rbracket))
+           (find-top-level-colon-loop tokens (+ i 1) (- depth 1)))
+          ((and (= tt :colon) (= depth 0))
+           i)
+          (true
+           (find-top-level-colon-loop tokens (+ i 1) depth)))))))
+
+; ============================================================
+; Parse a single statement (assignment or expression)
+; ============================================================
+
+(define parse-stmt
+  (fn (tokens)
+    (if (and (>= (len tokens) 2)
+             (= (tok-type (nth tokens 0)) :name)
+             (= (tok-type (nth tokens 1)) :assign))
+      ; Assignment: name ← expr
+      (list :assign
+            (tok-val (nth tokens 0))
+            (parse-apl-expr (slice tokens 2)))
+      ; Expression
+      (parse-apl-expr tokens))))
+
+; ============================================================
+; Parse an expression from a flat token list
+; ============================================================
+
+(define parse-apl-expr
+  (fn (tokens)
+    (let ((segs (collect-segments tokens)))
+      (if (= (len segs) 0)
+        nil
+        (build-tree segs)))))
+
+; ============================================================
+; Main entry point
+; parse-apl: string → AST
+; ============================================================
+
+(define parse-apl
+  (fn (src)
+    (let ((tokens (apl-tokenize src)))
+      (let ((stmt-groups (split-statements tokens)))
+        (if (= (len stmt-groups) 0)
+          nil
+          (if (= (len stmt-groups) 1)
+            (parse-stmt (first stmt-groups))
+            (cons :program (map parse-stmt stmt-groups))))))))