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dtr-tests-tc.rkt
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dtr-tests-tc.rkt
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#lang racket
(require redex "dtr-lang.rkt" "dtr-logic.rkt" "dtr-tc.rkt" rackunit)
(define-judgment-form λDTR
#:mode (typeof* I I I I)
#:contract (typeof* Γ e τ (ψ ψ oo))
[(where o (id ,(gensym)))
(typeof Γ e_1 τ_2 (ψ_2+ ψ_2- oo_2))
(subtype Γ o τ_2 τ_1)
(proves (env/implied-by-ψ* Γ ψ_2+) ψ_1+)
(proves (env/implied-by-ψ* Γ ψ_2-) ψ_1-)
(subobj oo_2 oo_1)
-------------- "T-Subsume"
(typeof* Γ e_1 τ_1 (ψ_1+ ψ_1- oo_1))])
(define-metafunction λDTR
and : e e -> e
[(and e_1 e_2) (if e_1 e_2 #f)])
(define-metafunction λDTR
or : e e -> e
[(or e_1 e_2) (let (tmp e_1)
(if (ann tmp (U #t #f))
(ann tmp (U #t #f))
e_2))])
(define-metafunction λDTR
Option : τ -> τ
[(Option τ) (U τ #f)])
;; T-Int
(check-true
(judgment-holds
(typeof* (empty-env)
42
Int
(TT FF Ø))))
;; T-Str
(check-true
(judgment-holds
(typeof* (empty-env)
"Hello World"
Str
(TT FF Ø))))
;; T-True
(check-true
(judgment-holds
(typeof* (empty-env)
#t
#t
(TT FF Ø))))
;; T-False
(check-true
(judgment-holds
(typeof* (empty-env)
#f
#f
(FF TT Ø))))
;; T-Var
(check-true
(judgment-holds
(typeof* (env: (is x Int))
(ann x Int)
Int
(TT FF Ø))))
;; T-Abs
(check-true
(judgment-holds
(typeof* (empty-env)
(λ (x : Int) (ann x Int))
(x : Int → Int (TT FF (id x)))
(TT FF Ø))))
;; T-App
(check-true
(judgment-holds
(typeof* (empty-env)
(add1 41)
Int
(TT FF Ø))))
(check-true
(judgment-holds
(typeof* (empty-env)
(add1 41)
(Int= 42)
(TT FF 42))))
;; T-App w/ τ-update
(check-true
(judgment-holds
(typeof* (empty-env)
(neg 41)
Int
(TT FF Ø))))
(check-true
(judgment-holds
(typeof* (env: (is x Int))
(neg (ann x Int))
Int
(TT FF Ø))))
(check-true
(judgment-holds
(typeof* (env: (is x Int))
(neg (zero? (ann x Int)))
(U #t #f)
(TT FF Ø))))
;; T-If
(check-true
(judgment-holds
(typeof* (env: (is x (U #t #f)))
(if (ann x (U #t #f))
(add1 41)
42)
(Int= 42)
(TT TT 42))))
(check-true
(judgment-holds
(typeof* (env: (is x (U #t #f)))
(if (ann x (U #t #f))
42
"Hello World")
(U Int Str)
(TT FF Ø))))
;; T-Let
(check-true
(judgment-holds
(typeof* (env: (is x (U #t #f)))
(let (y (ann x (U #t #f)))
(if (ann y (U #t #f))
42
"Hello World"))
(U Int Str)
(TT FF Ø))))
(check-true
(judgment-holds
(typeof* (env: (is x Top))
(let (y (ann x Top))
(ann y Top))
Top
((! x #f) (is x #f) (id x)))))
(check-true
(judgment-holds
(typeof* (env: (is x Top))
(let (y (int? (ann x Top)))
(ann y (U #t #f)))
(U #t #f)
((is x Int) (! x Int) Ø))))
;; T-Cons
(check-true
(judgment-holds
(typeof* (empty-env)
(cons 42 "Hello World")
(Int × Str)
(TT FF Ø))))
(check-true
(judgment-holds
(typeof* (empty-env)
(cons (cons 40 2) (cons "Hello" "World"))
((Int × Int) × (Str × Str))
(TT FF Ø))))
;; T-Car
(check-true
(judgment-holds
(typeof* (empty-env)
(car (cons 42 "Hello World"))
Int
(TT FF Ø))))
(check-true
(judgment-holds
(typeof* (env: (is p (Int × Str)))
(car (ann p (Int × Str)))
Int
(TT FF ((CAR) @ p)))))
;; T-Cdr
(check-true
(judgment-holds
(typeof* (empty-env)
(cdr (cons 42 "Hello World"))
Str
(TT FF Ø))))
(check-true
(judgment-holds
(typeof* (env: (is p (Int × Str)))
(cdr (ann p (Int × Str)))
Str
(TT FF ((CDR) @ p)))))
;; T-Vec
(check-true
(judgment-holds
(typeof* (empty-env)
(vec 42)
(♯ Int)
(TT FF Ø))))
(check-true
(judgment-holds
(typeof* (empty-env)
(vec 42 "Hello World")
(♯ (U Int Str))
(TT FF Ø))))
(check-true
(judgment-holds
(typeof* (empty-env)
(vec 42 "All" "Your" "Base" "Are" "Belong" "To" "Us!")
(♯ (U Int Str))
(TT FF Ø))))
;; T-VecRef
;; i.e. tests that require reasoning about linear combinations
;; *and* vector bounds
(check-true
(judgment-holds
(typeof* (empty-env)
(vec-ref (vec 42 "All" "Your" "Base" "Are" "Belong" "To" "Us!") 0)
(U Int Str)
(TT TT Ø))))
(check-true
(judgment-holds
(typeof* (empty-env)
(vec-ref (vec 42 "All" "Your" "Base" "Are" "Belong" "To" "Us!") ((* 2) 2))
(U Int Str)
(TT TT Ø))))
(check-false
(judgment-holds
(typeof* (empty-env)
(vec-ref (vec 42 "All" "Your" "Base" "Are" "Belong" "To" "Us!") ((+ 0) -1))
(U Int Str)
(TT TT Ø))))
(check-true
(judgment-holds
(typeof* (empty-env)
(vec-ref (vec 42 "All" "Your" "Base" "Are" "Belong" "To" "Us!") 7)
(U Int Str)
(TT TT Ø))))
(check-false
(judgment-holds
(typeof* (empty-env)
(vec-ref (vec 42 "All" "Your" "Base" "Are" "Belong" "To" "Us!") ((* 2) 4))
(U Int Str)
(TT TT Ø))))
(check-true
(judgment-holds
(typeof* (env: (is x Int) (is v (♯ Str)))
(if (and ((<= 0) (ann x Int))
((<= (ann x Int)) ((+ -1) (vec-len (ann v (♯ Str))))))
(vec-ref (ann v (♯ Str)) (ann x (IntRange 0 (+ -1 (o-len (id v))))))
(error "bad index!"))
Str
(TT FF Ø))))
;;; Original tests+
;;; Example 1
(check-true
(judgment-holds
(typeof* (env: (is x Top))
(if (int? (ann x Top))
(add1 (ann x Int))
0)
Int
(TT FF Ø))))
(check-true
(judgment-holds
(typeof* (empty-env)
(λ (x : Int)
(add1 (ann x Int)))
(x : Int → Int (TT FF Ø))
(TT FF Ø))))
(check-true
(judgment-holds
(typeof* (env: (is x (U Str Int)))
(if (int? (ann x Top))
(add1 (ann x Int))
(str-len (ann x Str)))
Int
(TT FF Ø))))
(check-true
(judgment-holds
(typeof* (env: (is x Top))
(int? (ann x Top))
(U #t #f)
((is x Int) (! x Int) Ø))))
(check-true
(judgment-holds
(typeof* (empty-env)
(λ (x : Top)
(int? (ann x Top)))
(x : Top → (U #t #f) ((is x Int) (! x Int) Ø))
(TT FF Ø))))
;;; Example 2
(check-true
(judgment-holds
(typeof* (empty-env)
(λ (x : (U Str Int))
(if (int? (ann x Top))
(add1 (ann x Int))
(str-len (ann x Str))))
(x : (U Str Int) → Int (TT FF Ø))
(TT FF Ø))))
(check-true
(judgment-holds
(typeof* (env: (is x Top))
(if (int? (ann x Top))
#t
(str? (ann x Top)))
(U #t #f)
((is x (U Int Str)) (! x (U Int Str)) Ø))))
;;; Example 3
(check-true
(judgment-holds
(typeof* (env: (is x (Option Str)))
(if (ann x Top)
(str-len (ann x Str))
(error "string not found!"))
Int
(TT FF Ø))))
(check-true
(judgment-holds
(typeof* (env: (is x Top))
(let (tmp (int? (ann x Top)))
(ann tmp (U #t #f)))
(U #t #f)
((is x Int) (! x Int) Ø))))
(check-true
(judgment-holds
(typeof* (env: (is x Top))
(let (tmp (int? (ann x Top)))
(if (ann tmp (U #t #f))
(ann tmp (U #t #f))
(str? (ann x Top))))
(U #t #f)
((is x (U Int Str)) (! x (U Int Str)) Ø))))
(check-true
(judgment-holds
(typeof* (env: (is x Top))
(or (int? (ann x Top))
(str? (ann x Top)))
(U #t #f)
((is x (U Int Str)) (! x (U Int Str)) Ø))))
;;; Example 4
(check-true (judgment-holds
(typeof* (env: (is f (x : (U Int Str) → Int (TT FF Ø)))
(is x Top))
(if (or (int? (ann x Top))
(str? (ann x Top)))
((ann f (x : (U Int Str) → Int (TT FF Ø)))
(ann x (U Int Str)))
0)
Int
(TT FF Ø))))
;;; Example 5
(check-true
(judgment-holds
(typeof* (env: (is x Top) (is y Top))
(if (and (int? (ann x Top)) (str? (ann y Top)))
((+ (ann x Int)) (str-len (ann y Str)))
0)
Int
(TT FF Ø))))
;;; Example 6
(check-false
(judgment-holds
(typeof* (env: (is x Top) (is y Top))
(if (and (int? (ann x Top)) (str? (ann y Top)))
((+ (ann x Int)) (str-len (ann y Str)))
(str-len (ann y Str)))
Int
(TT FF Ø))))
;;; Example 7
(check-true
(judgment-holds
(typeof* (env: (is x Top) (is y Top))
(if (if (int? (ann x Top)) (str? (ann y Top)) #f)
((+ (ann x Int)) (str-len (ann y Str)))
0)
Int
(TT FF Ø))))
;;; Example 8
(check-true
(judgment-holds
(typeof* (env: (is x Top))
(let (tmp (str? (ann x Top)))
(if (ann tmp Top)
(ann tmp Top)
(int? (ann x Top))))
Top
((is x (U Str Int)) (! x (U Str Int)) Ø))))
;;; Example 9
(check-true
(judgment-holds
(typeof* (env: (is x Top))
(if (let (tmp (int? (ann x Top)))
(if (ann tmp Top)
(ann tmp Top)
(str? (ann x Top))))
((λ (x : (U Str Int))
(if (int? (ann x Top))
(add1 (ann x Int))
(str-len (ann x Str))))
(ann x (U Int Str)))
0)
Int
(TT FF Ø))))
;;; Example 10
(check-true
(judgment-holds
(typeof* (env: (is p (Top × Top)))
(if (int? (car (ann p (Top × Top))))
(add1 (car (ann p (Int × Top))))
7)
Int
(TT FF Ø))))
;;; Example 11
(check-true
(judgment-holds
(typeof* (env: (is p (Top × Top))
(is g (x : (Int × Int) → Int (TT FF Ø))))
(if (and (int? (car (ann p (Top × Top))))
(int? (cdr (ann p (Top × Top)))))
((ann g (x : (Int × Int) → Int (TT FF Ø)))
(ann p (Int × Int)))
42)
Int
(TT FF Ø))))
;;; Example 12
(check-true
(judgment-holds
(typeof* (empty-env)
(λ (p : (Top × Top))
(int? (car (ann p (Top × Top)))))
(x : (Top × Top) →
(U #t #f)
((((CAR) @ x) -: Int)
(((CAR) @ x) -! Int)
Ø))
(TT FF Ø))))
(check-true
(judgment-holds
(typeof* (empty-env)
(λ (p : (Top × Top))
(int? (cdr (ann p (Top × Top)))))
(x : (Top × Top) →
(U #t #f)
((((CDR) @ x) -: Int)
(((CDR) @ x) -! Int)
Ø))
(TT FF Ø))))
;;; Example 13
(check-true
(judgment-holds
(typeof* (env: (is x Top) (is y (U Int Str)))
(if (and (int? (ann x Top)) (str? (ann y Top)))
((+ (ann x Int)) (str-len (ann y Str)))
(if (int? (ann x Top))
((+ (ann x Int)) (ann y Int))
0))
Int
(TT FF Ø))))
;;; Example 14
(check-true
(judgment-holds
(typeof* (env: (is x Top))
(λ (y : (U Int Str))
(if (and (int? (ann x Top)) (str? (ann y Top)))
((+ (ann x Int)) (str-len (ann y Str)))
(if (int? (ann x Top))
((+ (ann x Int)) (ann y Int))
0)))
(x : (U Str Int) → Int (TT FF Ø))
(TT FF Ø))))