From d7913f775356cd442b686f9548405033fc920e26 Mon Sep 17 00:00:00 2001
From: Ben Greenman <types@ccs.neu.edu>
Date: Tue, 13 Oct 2015 12:51:24 -0400
Subject: [PATCH] [occurrence] subtyping, normal form, and VERY BASIC filters.
 Having trouble propogating variables.

---
 tapl/stlc+occurrence.rkt             | 166 +++++++++++++++++++++--
 tapl/tests/stlc+occurrence-tests.rkt | 192 +++++++++++++++++++++++++--
 2 files changed, 336 insertions(+), 22 deletions(-)

diff --git a/tapl/stlc+occurrence.rkt b/tapl/stlc+occurrence.rkt
index ab19beb..32cb7f8 100644
--- a/tapl/stlc+occurrence.rkt
+++ b/tapl/stlc+occurrence.rkt
@@ -21,21 +21,69 @@
   [(_ . x) #'(stlc+sub:#%datum . x)])
 
 (define-type-constructor ∪ #:arity >= 1)
-;; TODO disallow recursive ∪
+
+;; -----------------------------------------------------------------------------
+;; --- Union operations
+
+;; Occurrence type operations
+;; These assume that τ is a type in 'normal form'
+(begin-for-syntax
+  ;; True if τ is a union type, otherwise #f
+
+  (define (∪->list τ)
+    ;; Ignore type constructor & the kind
+    ;;  (because there are no bound identifiers)
+    (syntax-parse τ
+     [(~∪ τ* ...)
+      (syntax->list #'(τ* ...))]
+     [_
+      (error '∪->list (format "Given non-ambiguous type '~a'" τ))]))
+
+  (define (list->∪ τ*)
+    (τ-eval #`(∪ #,@τ*)))
+    
+  (define (type->filter τ)
+    ;; Going to have the same problem here, matching on types
+    ;; (Γ is stored insisde τ)
+    ;; (define Π (get-context τ 'filter))
+    ;; (Π τ))
+    ;; TODO filter properly
+    #'boolean?)
+
+  (define (∖ τ1 τ2)
+    (cond
+     [(∪? τ1)
+      (printf "SETMINUS got an ∪ ~a\n" τ1)
+      (define (not-τ2? τ)
+        (not (typecheck? τ τ2)))
+      (list->∪ (filter not-τ2? (∪->list τ1)))]
+     [else ; do nothing
+      τ1]))
+)
+
+;; -----------------------------------------------------------------------------
+;; --- Normal Form
 (begin-for-syntax
   (define τ-eval (current-type-eval))
+  (define (τ->symbol τ)
+    (cadr (syntax->datum τ)))
   (define (∪-eval τ-stx)
-    (syntax-parse τ-stx #:datum-literals (∪)
-     [(∪ τ-stx* ...)
-      ;; TODO Assumes that each τ is non-∪
-      ;; TODO just make a set?
-      ;;      will that work if we have ∪ inside the ∪ ?
-      ;(printf "Syntax prop type is ~a\n" (syntax-property (τ-eval τ) 'type))
+    (syntax-parse (τ-eval τ-stx)
+     [(~∪ τ-stx* ...)
+      ;; Recursively evaluate members
+      (define τ**
+        (for/list ([τ (in-list (syntax->list #'(τ-stx* ...)))])
+          (let ([τ+ (∪-eval τ)])
+            (if (∪? τ+)
+                (∪->list τ+)
+                (list τ+)))))
+      ;; Remove duplicates from the union, sort members
       (define τ*
         (sort
-         (remove-duplicates (syntax->list #'(τ-stx* ...)) (current-type=?))
+         (remove-duplicates (apply append τ**) (current-type=?))
          symbol<?
-         #:key syntax->datum))
+         #:key τ->symbol)) ;; TODO handle functions & other constructors
+      ;; Check for empty & singleton lists
       (define τ
         (cond
          [(null? τ*)
@@ -51,15 +99,107 @@
       (τ-eval τ-stx)]))
   (current-type-eval ∪-eval))
 
+;; -----------------------------------------------------------------------------
+;; --- Subtyping
+;; Problem: matching on normal forms is tricky
+;; (use stlc+reco+sub as an example)
+
 ;; - subtype U with simple, U with contained
+;; - AMB : t <: (U ... t ...)
+;; - SUB : a<:b => (U a t' ...) <: (U b t' ...)
+;; - EXT : (U t' ...) <: (U t t' ...)
+(begin-for-syntax
+ ;; True if one ordered list (of types) is a subset of another
+ (define (subset? x* y* #:leq [cmp (current-typecheck-relation)])
+   (let loop ([x* x*] [y* y*])
+     (cond
+      [(null? x*) #t]
+      [(null? y*) #f]
+      [(cmp (car x*) (car y*))
+       (loop (cdr x*) (cdr y*))]
+      [else
+       (loop x* (cdr y*))])))
+
+ (define sub? (current-sub?))
+ (define (∪-sub? τ1-stx τ2-stx)
+   (define τ1 ((current-type-eval) τ1-stx))
+   (define τ2 ((current-type-eval) τ2-stx))
+   (match `(,(∪? τ1) ,(∪? τ2))
+     ['(#f #t)
+      ;; AMB : a<:b => a <: (U ... b ...)
+      (for/or ([τ (in-list (∪->list τ2))])
+        (sub? τ1 τ))]
+     ['(#t #t)
+      (define τ1* (∪->list τ1))
+      (define τ2* (∪->list τ2))
+      (match `(,(length τ1*) ,(length τ2*))
+        [`(,L1 ,L2) #:when (< L1 L2)
+         ;; - EXT : (U t' ...) <: (U t t' ...)
+         (subset? τ1* τ2* #:leq sub?)]
+        [`(,L1 ,L2) #:when (= L1 L2)
+         ;; - SUB : a<:b => (U a t' ...) <: (U b t' ...)
+         ;; `∪->list` guarantees same order on type members
+         ;; `sub?` is reflexive
+         (andmap sub? τ1* τ2*)]
+        [_ #f])]
+     [_
+      ;; Could be (U ...) <: T
+      (sub? τ1 τ2)]))
+     
+ (current-sub? ∪-sub?)
+ (current-typecheck-relation (current-sub?))
+)
+
 ;; - TEST subtyping, with 'values' and with 'functions'
-;; - add filters
+
+;; -----------------------------------------------------------------------------
+;; --- Filters
+(begin-for-syntax
+ (define (simple-Π τ)
+   (syntax-parse (τ-eval τ)
+    [~Boolean
+     #'boolean?]
+    [~Int
+     #'integer?]
+    [~Str
+     #'string?]
+    ['Number
+     #'number?]
+    ['Natural
+     #'(lambda (n) (and (integer? n) (not (negative? n))))]
+    [_
+     (error 'Π "Cannot make filter for type ~a\n" (syntax->datum τ))]))
+ (define current-Π (make-parameter simple-Π)))
+
+;; - "simple", (Int ? e)
+;; - "correct", where the function is effectful and independent of cond
+
+;; - check if τ0 is a union type
+;; - check if τ-filter is a subtype of τ0
+;; - drop absurd branches?
+;; - allow x not identifier
+(define-typed-syntax test #:datum-literals (?)
+  [(_ [τ-filter:type ? x-stx:id] e1 e2)
+   ;; Get the filter type, evaluate to a runtime predicate
+   #:with f ((current-Π) #'τ-filter)
+   #:fail-unless (syntax-e #'f)
+     (format "Could not express type '~a' as a filter." #'τ-filter-stx)
+   ;; TypeCheck e0:normally, e1:positive, e2:negative
+   #:with (x τ0) (infer+erase #'x-stx)
+   ;; #:when (printf "Check'd e0, type is ~a\n" (syntax->datum #'τ0))
+   #:with [_ e1+ τ1] (infer/tyctx+erase #'([x-stx : τ-filter]) #'e1)
+   ;; #:when (printf "Check'd e1\n")
+   #:with [_ e2+ τ2] (infer/tyctx+erase #`([x-stx : #,(∖ #'τ0 #'τ-filter)]) #'e2)
+   ;; #:when (printf "Checked e2\n")
+   ;; Expand to a conditional, using the runtime predicate
+   (⊢ (if (f x) e1+ e2+)
+      : (∪ τ1 τ2))])
+
+;; - add filters (install filters, at start of file)
 ;; - TEST basic filters
 ;; - TEST function filters (delayed filters?)
 ;; - disallow (U (-> ...) (-> ...))
 ;; - TEST latent filters -- listof BLAH
+
 ;; - integrate with sysf
 
-;; (begin-for-syntax
-;;   (define stlc:sub? (current-sub?))
-;; )
diff --git a/tapl/tests/stlc+occurrence-tests.rkt b/tapl/tests/stlc+occurrence-tests.rkt
index 61d5dba..a4f7d77 100644
--- a/tapl/tests/stlc+occurrence-tests.rkt
+++ b/tapl/tests/stlc+occurrence-tests.rkt
@@ -16,7 +16,7 @@
  #:with-msg "Improper usage of type constructor ∪: ∪, expected >= 1 arguments")
 (typecheck-fail
  (λ ([x : (∪)]) x)
- #:with-msg "empty union type")
+ #:with-msg "Improper usage of type constructor ∪")
 (typecheck-fail
  (λ ([x : (∪ ∪)]) x)
  #:with-msg "Improper usage of type constructor ∪")
@@ -45,14 +45,188 @@
             : (→ (∪ Boolean Int) Int))
 (check-type (λ ([x : (∪ Int Boolean Boolean Int)]) x)
             : (→ (∪ Boolean Int) (∪ Boolean Int)))
+(check-type (λ ([x : (∪ (∪ Int Boolean))]) 42)
+            : (→ (∪ Int Boolean) Int))
+(check-type (λ ([x : (∪ Int Boolean)]) 42)
+            : (→ (∪ (∪ Int Boolean)) Int))
+(check-type (λ ([x : (∪ Int Boolean)]) 42)
+            : (→ (∪ (∪ Int Boolean) (∪ Int Boolean)) Int))
+
 
 ;; -----------------------------------------------------------------------------
-;; --- basic subtyping
-;; (check-type 1 : (∪ Int))
-;; (check-type 1 : (∪ Int Boolean))
-;; (check-type 1 : (∪ Boolean Int))
-;; (check-type 1 : (∪ Boolean Int (→ Boolean Boolean)))
-;; (check-type 1 : (∪ (∪ Int)))
+;; --- subtyping
 
-;; (check-not-type 1 : (∪ Boolean))
-;; (check-not-type 1 : (∪ Boolean (→ Int Int)))
+;; ---- basics
+(check-type 1 : (∪ Int))
+(check-type 1 : (∪ (∪ Int)))
+
+(check-not-type 1 : (∪ Boolean))
+
+;; - AMB : t <: t' => t <: (U ... t' ...)
+(check-type 1 : (∪ Boolean Int))
+(check-type -1 : (∪ Int Boolean))
+(check-type 1 : (∪ Boolean Int (→ Boolean Boolean)))
+(check-type 1 : (∪ (∪ Int Boolean) (∪ Int Boolean)))
+
+(check-not-type 1 : (∪ Boolean (→ Int Int)))
+
+;; --- EXT : (U t' ...) <: (U t t' ...)
+(check-type (λ ([x : (∪ Int Boolean)]) x)
+            : (→ (∪ Int Boolean) (∪ Int Boolean Str)))
+(check-type (λ ([x : (∪ Int Boolean)]) x)
+            : (→ (∪ Boolean) (∪ Int Boolean Str)))
+
+(check-not-type (λ ([x : (∪ Int Boolean)]) x)
+            : (→ (∪ Int Boolean) (∪ Int)))
+(check-not-type (λ ([x : (∪ Int Boolean)]) x)
+            : (→ (∪ Boolean Int Str) (∪ Int Boolean)))
+
+;; --- SUB : a<:b => (U a t' ...) <: (U b t' ...)
+(check-type (λ ([x : (∪ Int Str)]) x)
+            : (→ (∪ Int Str) (∪ Num Str)))
+(check-type (λ ([x : (∪ Int Str)]) x)
+            : (→ (∪ Nat Str) (∪ Num Str)))
+
+(check-type (λ ([x : (∪ Int Str)]) x)
+            : (→ (∪ Int Str) Top))
+
+(check-not-type (λ ([x : (∪ Int Str)]) x)
+            : (→ Top (∪ Num Str)))
+
+;; -----------------------------------------------------------------------------
+;; --- Basic Filters (applying functions)
+
+;; --- is-boolean?
+(check-type
+ (λ ([x : (∪ Boolean Int)])
+    (test [Boolean ? x]
+          #t
+          #f))
+ : (→ (∪ Boolean Int) Boolean))
+(check-type-and-result
+ ((λ ([x : (∪ Boolean Int)])
+     (test (Boolean ? x)
+           #t
+           #f)) #t)
+  : Boolean ⇒ #t)
+(check-type-and-result
+ ((λ ([x : (∪ Boolean Int)])
+     (test (Boolean ? x)
+           #t
+           #f)) 902)
+  : Boolean ⇒ #f)
+
+;; --- successor
+;; (check-type
+;;  (λ ([x : (∪ Int Boolean)])
+;;     (test (Int ? x)
+;;           (+ 1 x)
+;;           (if x 1 0)))
+;;  : Int)
+;; (check-type-and-result
+;;  ((λ ([x : (∪ Int Boolean)])
+;;     (test (Int ? x)
+;;           (+ 1 x)
+;;           (if x 1 0))) #f)
+;;  : Int ⇒ 0)
+;; (check-type-and-result
+;;  ((λ ([x : (∪ Int Boolean)])
+;;     (test (Int ? x)
+;;           (+ 1 x)
+;;           (if x 1 0))) #t)
+;;  : Int ⇒ 1)
+;; (check-type-and-result
+;;  ((λ ([x : (∪ Int Boolean)])
+;;     (test (Int ? x)
+;;           (+ 1 x)
+;;           (if x 1 0))) 9000)
+;;  : Int ⇒ 9001)
+
+;; ;; --- Do-nothing filter
+(check-type
+ (λ ([x : Int])
+    (test (Int ? x) #t #f))
+ : (→ Int Boolean))
+(check-type
+ (λ ([x : Int])
+    (test (Boolean ? x) 1 0))
+ : (→ Int Int))
+
+;; --- Filter a subtype
+;; (check-type
+;;  (λ ([x : (∪ Nat Boolean)])
+;;     (test (Int ? x)
+;;           x
+;;           x))
+;;  : (→ (∪ Nat Bool) (∪ Int (∪ Nat Bool))))
+
+;; (check-type
+;;  (λ ([x : (∪ Int Bool)])
+;;     (test (Nat ? x)
+;;           (+ 2 x)
+;;           x))
+;;  : (→ (∪ Bool Int) (∪ Int Bool)))
+
+;; (check-type-and-result
+;;  ((λ ([x : (∪ Int Bool)])
+;;      (test (Num ? x)
+;;            #f
+;;            x)) #t)
+;;  : (→ (∪ Int Bool) Bool)
+;;  ⇒ #t)
+
+;; ;; Should filter all the impossible types 
+;; (check-type-and-result
+;;  ((λ ([x : (∪ Nat Int Num Bool)])
+;;      (test (Num ? x)
+;;            #f
+;;            x)) #t)
+;;  : (→ (∪ Nat Int Num Bool) Bool)
+;;  ⇒ #t)
+
+;; ----------------------------------------------------------------------------- 
+;; --- misc subtyping + filters (regression tests)
+(check-type
+ (λ ([x : (∪ Int Boolean)])
+    (test (Int ? x)
+          0
+          1))
+ : (→ (∪ Int Boolean) Nat))
+(check-type
+ (λ ([x : (∪ Int Boolean)])
+    (test (Int ? x)
+          0
+          1))
+ : (→ (∪ Int Boolean) Int))
+
+;; -----------------------------------------------------------------------------
+;; --- Invalid filters
+
+(typecheck-fail
+ (λ ([x : (∪ Int Boolean)])
+    (test (1 ? x) #t #f))
+ #:with-msg "not a valid type")
+(typecheck-fail
+ (test (1 ? 1) #t #f)
+ #:with-msg "not a valid type")
+(typecheck-fail
+ (test (1 ? 1) #t #f)
+ #:with-msg "not a valid type")
+(typecheck-fail
+ (test (#f ? #t) #t #f)
+ #:with-msg "not a valid type")
+
+;; -----------------------------------------------------------------------------
+;; --- TODO Subtypes should not be collapsed
+;; (Not sure how to test this, because type=? is subtyping and these ARE subtypes)
+;; (check-not-type (λ ([x : (∪ Int Nat)]) #t)
+;;                   : (→ Nat Boolean))
+;; (check-not-type (λ ([x : (∪ Int Nat)]) #t)
+;;                 : (→ Int Boolean))
+               
+;; ;; -----------------------------------------------------------------------------
+;; ;; --- Filter values (should do nothing)
+
+;; (check-type
+;;  (test (Int ? 1) #t #f)
+;;  : Boolean)