commit b0a8d192effd90aefb5a6b6e5d1d4ddc5e172890
parent e678912c2c7d3ce8cb48670fcc597b886cfc81ae
Author: Stephen Chang <stchang@ccs.neu.edu>
Date: Thu, 9 Jul 2015 14:00:36 -0400
finish exist.rkt
Diffstat:
4 files changed, 276 insertions(+), 7 deletions(-)
diff --git a/tapl/exist.rkt b/tapl/exist.rkt
@@ -1,12 +1,95 @@
#lang racket/base
(require "typecheck.rkt")
-(require (except-in "stlc+reco+var.rkt" #%app λ)
- (prefix-in stlc: (only-in "stlc+reco+var.rkt" #%app λ)))
-(provide (rename-out [stlc:#%app #%app] [stlc:λ λ]))
-(provide (except-out (all-from-out "stlc+reco+var.rkt") stlc:#%app stlc:λ))
-
+(require (except-in "stlc+reco+var.rkt" #%app λ let type=?)
+ (prefix-in stlc: (only-in "stlc+reco+var.rkt" #%app λ let type=?))
+ (prefix-in sysf: (only-in "sysf.rkt" type=?)))
+(provide (rename-out [stlc:#%app #%app] [stlc:λ λ] [stlc:let let])
+ (for-syntax type=?))
+(provide (except-out (all-from-out "stlc+reco+var.rkt") stlc:#%app stlc:λ stlc:let
+ (for-syntax stlc:type=?)))
+(provide ∃ pack open)
+
;; existential types
+;; combine type=? from sysf (for lam, ie ∃) and stlc+reco+var (for strings)
;; Types:
;; - types from stlc+reco+var.rkt
+;; - ∃
;; Terms:
;; - terms from stlc+reco+var.rkt
+;; - pack and open
+
+(begin-for-syntax
+ (define (type=? t1 t2)
+ (or (stlc:type=? t1 t2)
+ (sysf:type=? t1 t2)))
+ (current-type=? type=?)
+ (current-typecheck-relation type=?))
+
+;; TODO: disambiguate expanded representation of ∃, ok to use lambda in this calculus
+(provide ∃)
+(define-syntax (∃ stx)
+ (syntax-parse stx
+ [(_ (tv:id) body)
+ (syntax/loc stx (#%plain-lambda (tv) body))]))
+
+(define-syntax (pack stx)
+ (syntax-parse stx
+ [(_ (τ:type e) as ∃τ:type)
+ #:with (#%plain-lambda (τ_abstract:id) τ_body) #'∃τ.norm
+ #:with [e- τ_e] (infer+erase #'e)
+ #:when (typecheck? #'τ_e (subst #'τ.norm #'τ_abstract #'τ_body))
+ (⊢ #'e- #'∃τ)]))
+
+; TODO: the colon syntax might be misleading, since tv is not the type of x
+(define-syntax (open stx)
+ (syntax-parse stx #:datum-literals (<=)
+ [(_ ([(tv:id x:id) <= e_packed]) e)
+ #:with [e_packed- τ_packed] (infer+erase #'e_packed)
+ #:with (#%plain-lambda (τ_abstract:id) τ_body) #'τ_packed ; existential
+ ;; The subst below appears to be a hack, but it's not really.
+ ;; It's the (TaPL) type rule itself that is fast and loose.
+ ;; Leveraging the macro system's management of binding reveals this.
+ ;;
+ ;; Specifically, here is the TaPL Unpack type rule, fig24-1, p366:
+ ;; Γ ⊢ t_1 : {∃X,T_12}
+ ;; Γ,X,x:T_12 ⊢ t_2 : T_2
+ ;; ------------------------------
+ ;; Γ ⊢ let {X,x}=t_1 in t_2 : T_2
+ ;;
+ ;; There's *two* separate binders, the ∃ and the let,
+ ;; which the rule conflates.
+ ;;
+ ;; Here's the rule rewritten to distinguish the two binding positions:
+ ;; Γ ⊢ t_1 : {∃X_1,T_12}
+ ;; Γ,X_???,x:T_12 ⊢ t_2 : T_2
+ ;; ------------------------------
+ ;; Γ ⊢ let {X_2,x}=t_1 in t_2 : T_2
+ ;;
+ ;; The X_1 binds references to X in T_12.
+ ;; The X_2 binds references to X in t_2.
+ ;; What should the X_??? be?
+ ;;
+ ;; A first guess might be to replace X_??? with both X_1 and X_2,
+ ;; so all the potentially referenced type vars are bound.
+ ;; Γ ⊢ t_1 : {∃X_1,T_12}
+ ;; Γ,X_1,X_2,x:T_12 ⊢ t_2 : T_2
+ ;; ------------------------------
+ ;; Γ ⊢ let {X_2,x}=t_1 in t_2 : T_2
+ ;;
+ ;; But this example demonstrates that the rule above doesnt work:
+ ;; (open ([x : X_2 (pack (Int 0) as (∃ (X_1) X_1))])
+ ;; ((λ ([y : X_2]) y) x)
+ ;; Here, x has type X_1, y has type X_2, but they should be the same thing,
+ ;; so we need to replace all X_1's with X_2
+ ;;
+ ;; Here's the fixed rule, which is implemented here
+ ;;
+ ;; Γ ⊢ t_1 : {∃X_1,T_12}
+ ;; Γ,X_2,x:[X_2/X_1]T_12 ⊢ t_2 : T_2
+ ;; ------------------------------
+ ;; Γ ⊢ let {X_2,x}=t_1 in t_2 : T_2
+ ;;
+ #:with [tvs- (x-) (e-) (τ_e)]
+ (infer #'(e) #:ctx #`([x : #,(subst #'tv #'τ_abstract #'τ_body)])
+ #:tvs #'(tv))
+ (⊢ #'(let ([x- e_packed-]) e-) #'τ_e)]))
+\ No newline at end of file
diff --git a/tapl/tests/exist-tests.rkt b/tapl/tests/exist-tests.rkt
@@ -1,6 +1,163 @@
#lang s-exp "../exist.rkt"
(require "rackunit-typechecking.rkt")
+(check-type (pack (Int 0) as (∃ (X) X)) : (∃ (X) X))
+(check-type (pack (Int 0) as (∃ (X) X)) : (∃ (Y) Y))
+(typecheck-fail (pack (Int 0) as (∃ (X) Y)))
+(check-type (pack (Bool #t) as (∃ (X) X)) : (∃ (X) X))
+(typecheck-fail (pack (Int #t) as (∃ (X) X)))
+
+; cant typecheck bc X has local scope, and no X elimination form
+;(check-type (open ([(X x) <= (pack (Int 0) as (∃ (X) X))]) x) : X)
+
+(check-type 0 : Int)
+(check-type (+ 0 1) : Int ⇒ 1)
+(check-type ((λ ([x : Int]) (+ x 1)) 0) : Int ⇒ 1)
+(typecheck-fail (open ([(X x) <= (pack (Int 0) as (∃ (X) X))]) (+ x 1))) ; can't use as Int
+
+(check-type (λ ([x : (∃ (X) X)]) x) : (→ (∃ (X) X) (∃ (Y) Y)))
+(check-type ((λ ([x : (∃ (X) X)]) x) (pack (Int 0) as (∃ (Z) Z)))
+ : (∃ (X) X) ⇒ 0)
+(check-type ((λ ([x : (∃ (X) X)]) x) (pack (Bool #t) as (∃ (Z) Z)))
+ : (∃ (X) X) ⇒ #t)
+
+;; example where the two binding X's are conflated, see exist.rkt for explanation
+(check-type (open ([(X x) <= (pack (Int 0) as (∃ (X) X))]) ((λ ([y : X]) 1) x))
+ : Int ⇒ 1)
+
+(check-type
+ (pack (Int (tup ["a" = 5] ["f" = (λ ([x : Int]) (+ x 1))]))
+ as (∃ (X) (× [: "a" X] [: "f" (→ X X)])))
+ : (∃ (X) (× [: "a" X] [: "f" (→ X X)])))
+
+(define p4
+ (pack (Int (tup ["a" = 5] ["f" = (λ ([x : Int]) (+ x 1))]))
+ as (∃ (X) (× [: "a" X] [: "f" (→ X Int)]))))
+(check-type p4 : (∃ (X) (× [: "a" X] [: "f" (→ X Int)])))
+
+(check-not-type (open ([(X x) <= p4]) (proj x "a")) : Int) ; type is X, not Int
+; type is (→ X X), not (→ Int Int)
+(check-not-type (open ([(X x) <= p4]) (proj x "f")) : (→ Int Int))
+(typecheck-fail (open ([(X x) <= p4]) (+ 1 (proj x "a"))))
+(check-type (open ([(X x) <= p4]) ((proj x "f") (proj x "a"))) : Int ⇒ 6)
+(check-type (open ([(X x) <= p4]) ((λ ([y : X]) ((proj x "f") y)) (proj x "a"))) : Int ⇒ 6)
+
+(check-type
+ (open ([(X x) <= (pack (Int 0) as (∃ (Y) Y))])
+ ((λ ([y : X]) 1) x))
+ : Int ⇒ 1)
+
+(check-type
+ (pack (Int (tup ["a" = 5] ["f" = (λ ([x : Int]) (+ x 1))]))
+ as (∃ (X) (× [: "a" Int] [: "f" (→ Int Int)])))
+ : (∃ (X) (× [: "a" Int] [: "f" (→ Int Int)])))
+
+(typecheck-fail
+ (pack (Int (tup ["a" = 5] ["f" = (λ ([x : Int]) (+ x 1))]))
+ as (∃ (X) (× [: "a" Int] [: "f" (→ Bool Int)]))))
+
+(typecheck-fail
+ (pack (Int (tup ["a" = 5] ["f" = (λ ([x : Int]) (+ x 1))]))
+ as (∃ (X) (× [: "a" X] [: "f" (→ X Bool)]))))
+
+(check-type
+ (pack (Bool (tup ["a" = #t] ["f" = (λ ([x : Bool]) (if x 1 2))]))
+ as (∃ (X) (× [: "a" X] [: "f" (→ X Int)])))
+ : (∃ (X) (× [: "a" X] [: "f" (→ X Int)])))
+
+(define counterADT
+ (pack (Int (tup ["new" = 1]
+ ["get" = (λ ([i : Int]) i)]
+ ["inc" = (λ ([i : Int]) (+ i 1))]))
+ as (∃ (Counter) (× [: "new" Counter]
+ [: "get" (→ Counter Int)]
+ [: "inc" (→ Counter Counter)]))))
+(check-type counterADT :
+ (∃ (Counter) (× [: "new" Counter]
+ [: "get" (→ Counter Int)]
+ [: "inc" (→ Counter Counter)])))
+(check-type
+ (open ([(Counter counter) <= counterADT])
+ ((proj counter "get") ((proj counter "inc") (proj counter "new"))))
+ : Int ⇒ 2)
+
+ (check-type
+ (open ([(Counter counter) <= counterADT])
+ (let ([inc (proj counter "inc")]
+ [get (proj counter "get")])
+ (let ([add3 (λ ([c : Counter]) (inc (inc (inc c))))])
+ (get (add3 (proj counter "new"))))))
+ : Int ⇒ 4)
+
+(check-type
+ (open ([(Counter counter) <= counterADT])
+ (let ([get (proj counter "get")]
+ [inc (proj counter "inc")]
+ [new (λ () (proj counter "new"))])
+ (letrec ([(is-even? : (→ Int Bool))
+ (λ ([n : Int])
+ (or (zero? n)
+ (is-odd? (sub1 n))))]
+ [(is-odd? : (→ Int Bool))
+ (λ ([n : Int])
+ (and (not (zero? n))
+ (is-even? (sub1 n))))])
+ (open ([(FlipFlop flipflop) <=
+ (pack (Counter (tup ["new" = (new)]
+ ["read" = (λ ([c : Counter]) (is-even? (get c)))]
+ ["toggle" = (λ ([c : Counter]) (inc c))]
+ ["reset" = (λ ([c : Counter]) (new))]))
+ as (∃ (FlipFlop) (× [: "new" FlipFlop]
+ [: "read" (→ FlipFlop Bool)]
+ [: "toggle" (→ FlipFlop FlipFlop)]
+ [: "reset" (→ FlipFlop FlipFlop)])))])
+ (let ([read (proj flipflop "read")]
+ [togg (proj flipflop "toggle")])
+ (read (togg (togg (togg (togg (proj flipflop "new")))))))))))
+ : Bool ⇒ #f)
+
+(define counterADT2
+ (pack ((× [: "x" Int])
+ (tup ["new" = (tup ["x" = 1])]
+ ["get" = (λ ([i : (× [: "x" Int])]) (proj i "x"))]
+ ["inc" = (λ ([i : (× [: "x" Int])]) (tup ["x" = (+ 1 (proj i "x"))]))]))
+ as (∃ (Counter) (× [: "new" Counter]
+ [: "get" (→ Counter Int)]
+ [: "inc" (→ Counter Counter)]))))
+(check-type counterADT2 :
+ (∃ (Counter) (× [: "new" Counter]
+ [: "get" (→ Counter Int)]
+ [: "inc" (→ Counter Counter)])))
+
+;; same as above, but with different internal counter representation
+(check-type
+ (open ([(Counter counter) <= counterADT2])
+ (let ([get (proj counter "get")]
+ [inc (proj counter "inc")]
+ [new (λ () (proj counter "new"))])
+ (letrec ([(is-even? : (→ Int Bool))
+ (λ ([n : Int])
+ (or (zero? n)
+ (is-odd? (sub1 n))))]
+ [(is-odd? : (→ Int Bool))
+ (λ ([n : Int])
+ (and (not (zero? n))
+ (is-even? (sub1 n))))])
+ (open ([(FlipFlop flipflop) <=
+ (pack (Counter (tup ["new" = (new)]
+ ["read" = (λ ([c : Counter]) (is-even? (get c)))]
+ ["toggle" = (λ ([c : Counter]) (inc c))]
+ ["reset" = (λ ([c : Counter]) (new))]))
+ as (∃ (FlipFlop) (× [: "new" FlipFlop]
+ [: "read" (→ FlipFlop Bool)]
+ [: "toggle" (→ FlipFlop FlipFlop)]
+ [: "reset" (→ FlipFlop FlipFlop)])))])
+ (let ([read (proj flipflop "read")]
+ [togg (proj flipflop "toggle")])
+ (read (togg (togg (togg (togg (proj flipflop "new")))))))))))
+ : Bool ⇒ #f)
+
+;; previous tets from stlc+reco+var-tests.rkt ---------------------------------
;; define-type-alias
(define-type-alias Integer Int)
(define-type-alias ArithBinOp (→ Int Int Int))
diff --git a/tapl/tests/run-all-tests.rkt b/tapl/tests/run-all-tests.rkt
@@ -1,4 +1,6 @@
#lang racket
+
+;; stlc and extensions
(require "stlc-tests.rkt")
(require "stlc+lit-tests.rkt")
(require "ext-stlc-tests.rkt")
@@ -9,10 +11,15 @@
(require "stlc+rec-iso-tests.rkt")
+(require "exist-tests.rkt")
+
+;; subtyping
(require "stlc+sub-tests.rkt")
(require "stlc+reco+sub-tests.rkt")
+;; system F
(require "sysf-tests.rkt")
-(require "exist-tests.rkt")
+
+;; F_omega
(require "fomega-tests.rkt")
(require "fomega2-tests.rkt")
\ No newline at end of file
diff --git a/tapl/typecheck.rkt b/tapl/typecheck.rkt
@@ -167,11 +167,32 @@
(define (infers+erase es)
(stx-map infer+erase es))
;; infers and erases types in an expression, in the context of given type vars
- (define (infer/tvs+erase e [tvs #'()])
+ (define (infer/tvs+erase e tvs)
(syntax-parse (expand/df #`(λ #,tvs (#%expression #,e))) #:literals (#%expression)
[(lam tvs+ (#%expression e+))
(list #'tvs+ #'e+ (syntax-local-introduce (typeof #'e+)))]))
+ (define (infer es #:ctx [ctx null] #:tvs [tvs null])
+ (syntax-parse ctx #:datum-literals (:)
+ [([x : τ] ...) ; dont expand yet bc τ may have references to tvs
+; #:with (x ...) #'(b.x ...)
+; #:with (τ ...) #'(b.τ ...)
+ #:with (e ...) es
+ #:with
+ ((~literal #%plain-lambda) tvs+
+ ((~literal #%expression)
+ ((~literal #%plain-lambda) xs+
+ ((~literal letrec-syntaxes+values) stxs1 ()
+ ((~literal letrec-syntaxes+values) stxs2 ()
+ ((~literal #%expression) e+) ...)))))
+ (expand/df
+ #`(λ #,tvs
+ (λ (x ...)
+ (let-syntax ([x (make-rename-transformer (⊢ #'x #'τ))] ...)
+ (#%expression e) ...))))
+ (list #'tvs+ #'xs+ #'(e+ ...) (stx-map syntax-local-introduce (stx-map typeof #'(e+ ...))))]
+ [([x τ] ...) (infer+erase es #:ctx #'([x : τ] ...) #:tvs tvs)]))
+
(define current-typecheck-relation (make-parameter #f))
(define (typecheck? t1 t2) ((current-typecheck-relation) t1 t2))
(define (typechecks? τs1 τs2)
