From 62717b52649129131ae69381e22b2bc09ff93dc7 Mon Sep 17 00:00:00 2001
From: JJ
Date: Sat, 31 Aug 2024 14:00:35 -0700
Subject: stlc-full: implement multisets

---
 stlc-full.rkt | 70 +++++++++++++++++++++++++++++++++++++++++++++++++++--------
 1 file changed, 61 insertions(+), 9 deletions(-)

diff --git a/stlc-full.rkt b/stlc-full.rkt
index 3df2fa8..b355292 100644
--- a/stlc-full.rkt
+++ b/stlc-full.rkt
@@ -149,6 +149,56 @@
     [`(ptr ,l ,a) (and (level? l) (symbol? a))]
     [_ #f]))
 
+;; Creates a new multiset from a list.
+(define/contract (list->multiset l) (-> list? dict?)
+  (foldl
+    (λ (x acc)
+      (if (dict-has-key? acc x)
+        (dict-set acc x (+ (dict-ref acc x) 1))
+        (dict-set acc x 1)))
+    #hash() l))
+
+;; Creates a new list from a multiset.
+(define/contract (multiset->list m) (-> dict? list?)
+  (foldl
+    (λ (x acc)
+      (append acc (build-list (dict-ref m x) (λ (_) x))))
+    '() (dict-keys m)))
+
+;; Adds a symbol to a multiset.
+(define/contract (multiset-add m1 s) (-> dict? symbol? dict?)
+  (if (dict-has-key? m1 s)
+    (dict-set m1 s (+ (dict-ref m1 s) 1))
+    (dict-set m1 s 1)))
+
+;; Queries two multisets for equality.
+(define/contract (multiset-eq m1 m2) (-> dict? dict? boolean?)
+  (if (equal? (length m1) (length m2)) #f
+    (foldl
+      (λ (x acc)
+        (if (and acc (dict-has-key? m1 x))
+          (equal? (dict-ref m1 x) (dict-ref m2 x))
+          acc))
+      #t (dict-keys m2))))
+
+;; Unions two multisets. Shared members take the maximum count of each other.
+(define/contract (multiset-union m1 m2) (-> dict? dict? dict?)
+  (foldl
+    (λ (x acc)
+      (if (dict-has-key? acc x)
+        (dict-set acc x (max (dict-ref acc x) (dict-ref m2 x)))
+        (dict-set acc x (dict-ref m2 x))))
+    m1 (dict-keys m2)))
+
+;; Intersects two multisets. Shared members take the minimum count of each other.
+(define/contract (multiset-intersect m1 m2) (-> dict? dict? dict?)
+  (foldl
+    (λ (x acc)
+      (if (dict-has-key? m1 x)
+        (dict-set acc x (min (dict-ref m1 x) (dict-ref m2 x)))
+        acc))
+    #hash() (dict-keys m2)))
+
 ;; Checks if a level is at its "base" form.
 (define/contract (level-base? l) (-> level? boolean?)
   (match l
@@ -166,7 +216,7 @@
     [(`(+ ,s1 ... ,n1) `(+ ,s2 ... ,n2)) #:when (and (natural? n1) (natural? n2))
       (and (equal? n1 n2) (level-eq? `(+ ,@s1) `(+ ,@s2)))]
     [(`(+ ,s1 ...) `(+ ,s2 ...))
-      todo] ; need to check for equality as multisets
+      (multiset-eq (list->multiset s1) (list->multiset s2))]
     [(_ _) #f]))
 
 ;; Levels can carry natural numbers, and so we define a stratification between them.
@@ -182,7 +232,8 @@
     [(`(+ ,s1 ... ,n) `(+ ,s2 ...)) #:when (natural? n)
       (level-eq? `(+ ,@s1) `(+ ,@s2))]
     [(`(+ ,s1 ...) `(+ ,s2 ...))
-      todo] ; this needs to inspect the levels... ugh
+      (multiset-eq (list->multiset s1)
+        (multiset-intersect (list->multiset s1) (list->multiset s2)))]
     [(_ _) #f]))
 
 ;; We define a maximum of two levels.
@@ -196,15 +247,15 @@
     [(`(+ ,s1 ... ,n1) `(+ ,s2 ... ,n2)) #:when (and (natural? n1) (natural? n2))
       (if (equal? s1 s2)
         `(+ ,@s1 ,(max n1 n2))
-        (level-intersect `(+ ,@s1) `(+ ,@s2)))]
+        (level-union `(+ ,@s1) `(+ ,@s2)))]
     [(`(+ ,s1 ... ,n) `(+ ,s2 ...)) #:when (natural? n)
       (if (level-geq? s1 s2)
         `(+ ,@s1 ,n)
-        (level-intersect `(+ ,@s1) `(+ ,@s2)))]
+        (level-union `(+ ,@s1) `(+ ,@s2)))]
     [(`(+ ,s1 ...) `(+ ,s2 ... ,n)) #:when (natural? n)
       (if (level-geq? s2 s1)
         `(+ ,@s2 ,n)
-        (level-intersect `(+ ,@s1) `(+ ,@s2)))]
+        (level-union `(+ ,@s1) `(+ ,@s2)))]
     [(`(+ ,s ... ,n1) n2) #:when (and (natural? n1) (natural? n2))
       `(+ ,s ... ,n1)]
     [(n1 `(+ ,s ... ,n2)) #:when (and (natural? n1) (natural? n2))
@@ -214,14 +265,15 @@
     [(n `(+ ,s ...)) #:when (natural? n)
       `(+ ,@s ,n)]
     [(`(+ ,s1 ...) `(+ ,s2 ...))
-      (level-intersect `(+ ,@s1) `(+ ,@s2))]))
+      (level-union `(+ ,@s1) `(+ ,@s2))]))
 
-;; A helper function to perform intersection of levels.
-(define/contract (level-intersect l1 l2) (-> level-base? level-base? level-base?)
+;; A helper function to perform the union of levels.
+(define/contract (level-union l1 l2) (-> level-base? level-base? level-base?)
   (match* (l1 l2)
     [(0 l) l]
     [(l 0) l]
-    [(`(+ ,s1 ...) `(+ ,s2 ...)) todo])) ; we need multisets. this is gross.
+    [(`(+ ,s1 ...) `(+ ,s2 ...))
+      `(+ ,@(multiset->list (multiset-union (list->multiset s1) (list->multiset s2))))]))
 
 ;; We define addition in terms of our syntactic constructs.
 (define/contract (level-add l1 l2) (-> level? level? level?)
-- 
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