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[occurence] simple filters complete

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This commit is contained in:
Ben Greenman 2015-10-13 15:16:24 -04:00
parent d7913f7753
commit bc2e83c449
2 changed files with 177 additions and 124 deletions
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127
tapl/stlc+occurrence.rkt
View File

@ -1,17 +1,24 @@
#lang s-exp "typecheck.rkt"
(extends "stlc+sub.rkt" #:except #%datum)
;; TODO import if- form?
;; Calculus for occurrence typing.
;; - Types can be simple, or sets of simple types
;; (aka "ambiguous types".
;; The type is one of a few ambiguous possibilities at compile-time)
;; - The U constructor makes ambiguous types
;; - `(if-τ? [x : τ] e1 e2)` form will insert a run-time check to discriminate amb. types
;; - For non-top types, τ is a subtype of (∪ τ1 ... τ τ2 ...)
;; (aka "ambiguous types";
;; the run-time value will have one of a few ambiguous possible types.)
;; - The ∪ constructor makes ambiguous types
;; - `(test [τ ? x] e1 e2)` form will insert a run-time check to discriminate ∪
;; -- If the value at identifier x has type τ, then we continue to e1 with [x : τ]
;; -- Otherwise, we move to e2 with [x : (- (typeof x) τ)].
;; i.e., [x : τ] is not possible
;; - Subtyping rules:
;; -- ALL : t ... <: t' => (U t ...) <: t'
;; -- AMB : t <: (U ... t ...)
;; -- EXT : (U t' ...) <: (U t t' ...)
;; -- ONE : a<:b => (U a t' ...) <: (U b t' ...)
;; =============================================================================
(define-base-type Bot) ;; For empty unions
(define-base-type Boolean)
(define-base-type Str)
@ -28,8 +35,6 @@
;; 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)
@ -40,33 +45,34 @@
(error '∪->list (format "Given non-ambiguous type '~a'" τ))]))
(define (list->∪ τ*)
(τ-eval #`(∪ #,@τ*)))
(if (null? τ*)
#'Bot
(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
[else ; do nothing not non-union types
τ1]))
)
;; -----------------------------------------------------------------------------
;; --- Normal Form
;; Evaluate each type in the union,
;; remove duplicates
;; determinize the ordering of members
;; flatten nested unions
(begin-for-syntax
(define τ-eval (current-type-eval))
(define (τ->symbol τ)
;; TODO recurse for function types
(cadr (syntax->datum τ)))
(define (∪-eval τ-stx)
(syntax-parse (τ-eval τ-stx)
[(~∪ τ-stx* ...)
@ -82,7 +88,7 @@
(sort
(remove-duplicates (apply append τ**) (current-type=?))
symbol<?
#:key τ->symbol)) ;; TODO handle functions & other constructors
#:key τ->symbol))
;; Check for empty & singleton lists
(define τ
(cond
@ -101,13 +107,7 @@
;; -----------------------------------------------------------------------------
;; --- 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)])
@ -121,39 +121,44 @@
(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)]))
(or (Bot? τ1) (Top? τ2)
(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])]
['(#t #f)
;; - ALL : t... <: t' => (U t ...) <: t'
(andmap (lambda (τ) (sub? τ τ2)) (∪->list τ1))]
['(#f #f)
(sub? τ1 τ2)])))
(current-sub? ∪-sub?)
(current-typecheck-relation (current-sub?))
)
;; - TEST subtyping, with 'values' and with 'functions'
;; -----------------------------------------------------------------------------
;; --- Filters
;; These are stored imperatively, in a function.
;; Makes it easy to add a new filter & avoids duplicating this map
(begin-for-syntax
(define (simple-Π τ)
(syntax-parse (τ-eval τ)
@ -163,21 +168,20 @@
#'integer?]
[~Str
#'string?]
['Number
[~Num
#'number?]
['Natural
[~Nat
#'(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
;; (test (τ ? x) e1 e2)
;; TODO:
;; - check if τ0 is a union type
;; - check if τ-filter is a subtype of τ0
;; - drop absurd branches?
;; - allow x not identifier
;; - allow x not identifier (1. does nothing 2. latent filters)
(define-typed-syntax test #:datum-literals (?)
[(_ [τ-filter:type ? x-stx:id] e1 e2)
;; Get the filter type, evaluate to a runtime predicate
@ -186,17 +190,14 @@
(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")
#:with [x1 e1+ τ1] (infer/ctx+erase #'([x-stx : τ-filter]) #'e1)
#:with [x2 e2+ τ2] (infer/ctx+erase #`([x-stx : #,(∖ #'τ0 #'τ-filter)]) #'e2)
;; Expand to a conditional, using the runtime predicate
(⊢ (if (f x) e1+ e2+)
(⊢ (if (f x-stx)
((lambda x1 e1+) x-stx)
((lambda x2 e2+) x-stx))
: (∪ 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

174
tapl/tests/stlc+occurrence-tests.rkt
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@ -59,6 +59,8 @@
;; ---- basics
(check-type 1 : (∪ Int))
(check-type 1 : (∪ (∪ Int)))
(check-type (λ ([x : Int]) x)
: (→ Bot Top))
(check-not-type 1 : (∪ Boolean))
@ -93,6 +95,19 @@
(check-not-type (λ ([x : (∪ Int Str)]) x)
: (→ Top (∪ Num Str)))
;; --- ALL
(check-type (λ ([x : (∪ Boolean Int Str)]) x)
: (→ (∪ Boolean Int Str) Top))
(check-type (λ ([x : (∪ Nat Int Num)]) x)
: (→ (∪ Nat Int Num) Num))
(check-type (λ ([x : (∪ Nat Int Num)]) x)
: (→ Nat Num))
;; --- misc
;; Because Int<:(U Int ...)
(check-type (λ ([x : (∪ Int Nat)]) #t)
: (→ Int Boolean))
;; -----------------------------------------------------------------------------
;; --- Basic Filters (applying functions)
@ -117,30 +132,30 @@
: 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)
(check-type
(λ ([x : (∪ Int Boolean)])
(test (Int ? x)
(+ 1 x)
0))
: (→ (∪ Int Boolean) (∪ Num Nat)))
(check-type-and-result
((λ ([x : (∪ Int Boolean)])
(test (Int ? x)
(+ 1 x)
0)) #f)
: Num ⇒ 0)
(check-type-and-result
((λ ([x : (∪ Int Boolean)])
(test (Int ? x)
(+ 1 x)
1)) #t)
: Num ⇒ 1)
(check-type-and-result
((λ ([x : (∪ Int Boolean)])
(test (Int ? x)
(+ 1 x)
0)) 9000)
: Num ⇒ 9001)
;; ;; --- Do-nothing filter
(check-type
@ -149,40 +164,48 @@
: (→ Int Boolean))
(check-type
(λ ([x : Int])
(test (Boolean ? x) 1 0))
: (→ Int Int))
(test (Boolean ? x) 0 x))
: (→ Int (∪ Nat Int)))
;; --- Filter a subtype
;; (check-type
;; (λ ([x : (∪ Nat Boolean)])
;; (test (Int ? x)
;; x
;; x))
;; : (→ (∪ Nat Bool) (∪ Int (∪ Nat Bool))))
(check-type
(λ ([x : (∪ Nat Boolean)])
(test (Int ? x)
x
x))
: (→ (∪ Nat Boolean) (∪ Int (∪ Nat Boolean))))
;; (check-type
;; (λ ([x : (∪ Int Bool)])
;; (test (Nat ? x)
;; (+ 2 x)
;; x))
;; : (→ (∪ Bool Int) (∪ Int Bool)))
(check-type
(λ ([x : (∪ Int Boolean)])
(test (Nat ? x)
x
x))
: (→ (∪ Boolean Int) (∪ Int Nat Boolean)))
;; (check-type-and-result
;; ((λ ([x : (∪ Int Bool)])
;; (test (Num ? x)
;; #f
;; x)) #t)
;; : (→ (∪ Int Bool) Bool)
;; ⇒ #t)
;; --- Filter a supertype
(check-type
(λ ([x : (∪ Int Boolean)])
(test (Num ? x)
1
x))
: (→ (∪ Boolean Int) (∪ Nat Boolean)))
;; ;; 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)
(check-type-and-result
((λ ([x : (∪ Int Boolean)])
(test (Num ? x)
#f
x)) #t)
: Boolean
⇒ #t)
;; Should filter all the impossible types
(check-type-and-result
((λ ([x : (∪ Nat Int Num Boolean)])
(test (Num ? x)
#f
x)) #t)
: Boolean
⇒ #t)
;; -----------------------------------------------------------------------------
;; --- misc subtyping + filters (regression tests)
@ -217,16 +240,45 @@
#: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))
;; --- Subtypes should not be collapsed
(check-not-type (λ ([x : (∪ Int Nat)]) #t)
: (→ Num Boolean))
(check-type ((λ ([x : (∪ Int Nat Boolean)])
(test (Int ? x)
2
(test (Nat ? x)
1
0)))
#t)
: Nat ⇒ 0)
(check-type ((λ ([x : (∪ Int Nat)])
(test (Nat ? x)
1
(test (Int ? x)
2
0)))
1)
: Nat ⇒ 1)
(check-type ((λ ([x : (∪ Int Nat)])
(test (Int ? x)
2
(test (Nat ? x)
1
0)))
-10)
: Nat ⇒ 2)
;; ;; -----------------------------------------------------------------------------
;; ;; --- Filter values (should do nothing)
;; -----------------------------------------------------------------------------
;; --- TODO Filter values (should do nothing)
;; (check-type
;; (test (Int ? 1) #t #f)
;; : Boolean)
;; -----------------------------------------------------------------------------
;; --- TODO Filter functions
;; -----------------------------------------------------------------------------
;; --- TODO Latent filters (on data structures)