sysf: basic forall type working

This commit is contained in:
Stephen Chang 2014-08-15 15:33:07 -04:00
parent 1a327fc8f9
commit 0a82e9298c

443
sysf.rkt
View File

@ -1,272 +1,114 @@
#lang racket/base
(require
racket/match
(for-syntax racket/base syntax/parse syntax/parse/experimental/template
racket/set syntax/id-table syntax/stx racket/list racket/syntax
"stx-utils.rkt")
(for-meta 2 racket/base syntax/parse))
(for-syntax
racket/base syntax/parse syntax/parse/experimental/template
syntax/stx racket/syntax racket/set
"stx-utils.rkt")
(for-meta 2 racket/base syntax/parse)
"typecheck.rkt")
(require
(except-in
"stlc.rkt"
define-type begin letrec #%module-begin #%app λ
check-type-error check-type check-type-and-result check-not-type check-equal?))
(require (prefix-in stlc: (only-in "stlc.rkt" #%app define-type λ begin)))
(provide (all-from-out "stlc.rkt"))
(provide
(except-out
(all-from-out racket/base)
λ #%app + #%datum let letrec cons null null? begin void
#%module-begin if
))
(provide
define-type cases
(rename-out
[λ/tc λ] [app/tc #%app] [let/tc let] [letrec/tc letrec]
[begin/tc begin] [void/tc void]
[if/tc if] [+/tc +]
[datum/tc #%datum] [module-begin/tc #%module-begin]
[cons/tc cons] [null/tc null] [null?/tc null?] [first/tc first] [rest/tc rest]))
;; System F (copied from stlc.rkt 2014-08-13)
;;
;; Features:
;; - letrec
;; - lists
;; - user (recursive) function definitions
;; - user (recursive) (variant) type-definitions
;; for types, just need the identifier bound
(define-syntax-rule (define-builtin-type τ) (begin (define τ #f) (provide τ)))
(define-syntax-rule (define-builtin-types τ ...) (begin (define-builtin-type τ) ...))
(define-builtin-types Int String Bool Listof Unit)
;; type environment
(begin-for-syntax
(define base-type-env (hash))
;; Γ : [Hashof var-symbol => type-stx]
;; - can't use free-identifier=? for the hash table (or free-id-table)
;; because env must be set before expanding λ body (ie before going under λ)
;; so x's in the body won't be free-id=? to the one in the table
;; use symbols instead of identifiers for now --- should be fine because
;; I'm manually managing the environment
(define Γ (make-parameter base-type-env))
;; generated type vars
(define fvs (make-parameter (set)))
(define fvs-subst (make-parameter (hash)))
(define (fvs-subst-set x τ)
(hash-set (fvs-subst) (syntax->datum x) τ))
(define (do-subst/τ τ)
(syntax-parse τ
[x:id
#:when (set-member? (fvs) (syntax->datum #'x))
(hash-ref (fvs-subst) (syntax->datum #'x) #'???)]
[τ:id #'τ]
[(tycon τ ...)
#:with (τ-subst ...) (stx-map do-subst/τ #'(τ ...))
#'(tycon τ-subst ...)]))
(define (do-subst h)
(for/hash ([(x τ) (in-hash h)])
(values x (do-subst/τ τ)))))
;; testing fns ----------------------------------------------------------------
(require (for-syntax rackunit))
(provide check-type-error check-type check-type-and-result check-not-type)
(define-syntax (check-type-error stx)
(syntax-parse stx
[(_ e)
#:when (check-exn exn:fail? (λ () (expand/df #'e)))
#'(void)]))
(define-syntax (check-type stx)
(syntax-parse stx #:datum-literals (:)
[(_ e : τ)
#:with e+ (expand/df #'e)
#:when (check-true (assert-type #'e+ #'τ)
(format "Expected type ~a but got type ~a" #'τ (typeof #'e)))
#'(void)]))
(define-syntax (check-not-type stx)
(syntax-parse stx #:datum-literals (:)
[(_ e : τ)
#:with e+ (expand/df #'e)
#:when (check-false (type=? (typeof #'e+) #'τ)
(format "Expected type to not be ~a but got type ~a" #'τ (typeof #'e)))
#'(void)]))
(define-syntax (check-type-and-result stx)
(syntax-parse stx #:datum-literals (: =>)
[(_ e : τ => v)
#'(begin (check-type e : τ)
(check-equal? e v))]))
(require rackunit)
(provide (rename-out [my-check-equal? check-equal?]))
(define-syntax-rule (my-check-equal? x y) (check-equal? x y))
(define-for-syntax (type=? τ1 τ2)
; (printf "type= ~a ~a\n" (syntax->datum τ1) (syntax->datum τ2))
(syntax-parse #`(#,τ1 #,τ2) #:literals ()
[(x:id τ)
#:when (and (set-member? (fvs) (syntax->datum #'x))
(hash-has-key? (fvs-subst) (syntax->datum #'x)))
(type=? (hash-ref (fvs-subst) (syntax->datum #'x)) #'τ)]
[(x:id τ)
#:when (set-member? (fvs) (syntax->datum #'x))
#:when (fvs-subst (fvs-subst-set #'x #'τ))
#t]
[(τ x:id)
#:when (and (set-member? (fvs) (syntax->datum #'x))
(hash-has-key? (fvs-subst) (syntax->datum #'x)))
(type=? (hash-ref (fvs-subst) (syntax->datum #'x)) #'τ)]
[(τ x:id)
#:when (set-member? (fvs) (syntax->datum #'x))
#:when (fvs-subst (fvs-subst-set #'x #'τ))
#t]
[(x:id y:id) (free-identifier=? τ1 τ2)]
[((tycon1 τ1 ...) (tycon2 τ2 ...))
(and (free-identifier=? #'tycon1 #'tycon2)
(stx-andmap type=? #'(τ1 ...) #'(τ2 ...)))]
[_ #f]))
;; return #t if (typeof e)=τ, else type error
(begin-for-syntax
(define (assert-type e τ)
(or (type=? (typeof e) τ)
(error 'TYPE-ERROR "~a (~a:~a) has type ~a, but should have type ~a"
(syntax->datum e)
(syntax-line e) (syntax-column e)
(syntax->datum (typeof e))
(syntax->datum τ))))
(define (assert-Unit-type e) (assert-type e #'Unit))
(define (assert-Int-type e) (assert-type e #'Int)))
;; type env and other helper fns ----------------------------------------------
;; attaches type τ to e (as syntax property)
(define-for-syntax ( e τ) (syntax-property e 'type τ))
;; retrieves type of τ (from syntax property)
(define-for-syntax (typeof stx) (syntax-property stx 'type))
(define-for-syntax (type-env-lookup x) (hash-ref (Γ) (syntax->datum x)))
;; returns a new hash table extended with type associations x:τs
(define-for-syntax (type-env-extend x:τs)
(define xs (stx-map stx-car x:τs))
(define τs (stx-map stx-cadr x:τs))
(apply hash-set* (Γ) (append-map (λ (x τ) (list (syntax->datum x) τ)) xs τs)))
;; must be macro because type env must be extended first, before expandinb body
(begin-for-syntax
(define-syntax (with-extended-type-env stx)
(syntax-parse stx
[(_ x-τs e)
#'(parameterize ([Γ (type-env-extend x-τs)]) e)])))
;; expand/df ------------------------------------------------------------------
;; depth-first expand
(define-for-syntax (expand/df e [ctx #f])
; (printf "expanding: ~a\n" e)
; (printf "typeenv: ~a\n" (Γ))
(cond
;; 1st case handles struct constructors that are not the same name as struct
;; (should always be an identifier)
[(syntax-property e 'constructor-for) => (λ (Cons)
( e (type-env-lookup Cons)))]
;; 2nd case handles identifiers that are not struct constructors
[(identifier? e) ( e (type-env-lookup e))] ; handle this here bc there's no #%var form
;; local-expand must expand all the way down, ie have no stop-list, ie stop list can't be #f
;; ow forms like lambda and app won't get properly assigned types
[else (local-expand e 'expression null ctx)]))
(define-for-syntax (expand/df/module-ctx def)
(local-expand def 'module #f))
(define-for-syntax (expand/df/mb-ctx def)
(local-expand def 'module-begin #f))
define-type
(rename-out
[stlc:begin begin]
[letrec/tc letrec]
[module-begin/tc #%module-begin]
[app/tc #%app]
[λ/tc λ]))
;; define-type ----------------------------------------------------------------
(define-syntax (define-type stx)
(syntax-parse stx #:datum-literals (variant)
#;[(_ (Tycon:id X ...) (variant (Cons:id τ_fld ...) ...))
[(_ (Tycon:id X ...) (variant (Cons:id τ_fld ...) ...))
#:with ((x ...) ...) (stx-map generate-temporaries #'((τ_fld ...) ...))
#:when (Γ (type-env-extend #'([Cons ( (X ...) ( τ_fld ... Tycon))] ...)))
;; weird, generate-temporaries doesnt automatically produces ids with the right scope
; #:with (Cons-tmp ...) (stx-map (λ (x) (format-id #'Tycon "~a" x)) (generate-temporaries #'(Cons ...)))
; #:when (expand/df/module-ctx
; #'(begin
; (define-syntax (Cons-tmp stx)
; (syntax-parse stx
; [(_ τ (... ...))
; #:with (X ...) #'(τ (... ...))
; #'(→ τ_fld ... (Tycon X ...))])) ...))
#:when (Γ (type-env-extend #'([Cons ( (X ...) ( τ_fld ... (Tycon X ...)))] ...)))
; #:when (Γ (type-env-extend #'([Cons (Cons-tmp (∀ (X ...) (→ τ_fld ... (Tycon X ...))))] ...)))
; #:when (Γ (type-env-extend #'([Cons (→ τ_fld ... Tycon)] ...)))
#'(begin
(define-syntax (Tycon stx)
; (define-syntax (Cons-tmp stx)
; (syntax-parse stx
; [(_ τ (... ...))
; #:with (X ...) #'(τ (... ...))
; #'(→ τ_fld ... (Tycon X ...))])) ...
#;(define-syntax (Tycon stx)
(syntax-parse stx
[(_ τ (... ...))
#:with (X ...) (τ (... ...))
#:with (X ...) #'(τ (... ...))
#'(variant (Cons τ_fld ...) ...)]))
(struct Cons (x ...) #:transparent) ...)]
[(_ τ:id (variant (Cons:id τ_fld ...) ...))
#:with ((x ...) ...) (stx-map generate-temporaries #'((τ_fld ...) ...))
#:when (Γ (type-env-extend #'([Cons ( τ_fld ... τ)] ...)))
#'(begin
(struct Cons (x ...) #:transparent) ...)]))
(define-syntax (cases stx)
(syntax-parse stx
[(_ e [Cons (x ...) body ... body_result] ...)
#:with e+ (expand/df #'e)
#:with (Cons+ ...) (stx-map expand/df #'(Cons ...))
#:with (( τ ... τ_Cons) ...) (stx-map typeof #'(Cons+ ...))
#:when (stx-andmap (λ (τ) (assert-type #'e+ τ)) #'(τ_Cons ...))
#:with ((lam (x+ ...) body+ ... body_result+) ...)
(stx-map (λ (bods xs τs)
(with-extended-type-env
(stx-map list xs τs)
(expand/df #`(λ #,xs #,@bods))))
#'((body ... body_result) ...)
#'((x ...) ...)
#'((τ ...) ...))
#:when (stx-andmap (λ (bods) (stx-andmap assert-Unit-type bods)) #'((body+ ...) ...))
#:with (τ_result ...) (stx-map typeof #'(body_result+ ...))
#:when (or (null? (syntax->list #'(τ_result ...))) ; shouldnt happen
(andmap (λ (τ) (type=? τ (car (syntax->list #'(τ_result ...)))))
(cdr (syntax->list #'(τ_result ...)))))
( (syntax/loc stx (match e+ [(Cons+ x+ ...) body+ ... body_result+] ...))
(car (syntax->list #'(τ_result ...))))]))
;; typed forms ----------------------------------------------------------------
(define-syntax (datum/tc stx)
(syntax-parse stx
[(_ . n:integer) ( (syntax/loc stx (#%datum . n)) #'Int)]
[(_ . s:str) ( (syntax/loc stx (#%datum . s)) #'String)]
[(_ . b:boolean) ( (syntax/loc stx (#%datum . b)) #'Bool)]
[(_ . x)
#:when (error 'TYPE-ERROR "~a (~a:~a) has unknown type"
#'x (syntax-line #'x) (syntax-column #'x))
(syntax/loc stx (#%datum . x))]))
(define-syntax (begin/tc stx)
(syntax-parse stx
[(_ e ... e_result)
#:with (e+ ... e_result+) (stx-map expand/df #'(e ... e_result))
#:when (stx-andmap assert-Unit-type #'(e+ ...))
( (syntax/loc stx (begin e+ ... e_result+)) (typeof #'e_result+))]))
(define-syntax (void/tc stx)
(syntax-parse stx
[(_) ( (syntax/loc stx (void)) #'Unit)]))
(define-syntax (+/tc stx)
(syntax-parse stx
[(_ e ...)
#:with (e+ ...) (stx-map expand/df #'(e ...))
#:when (stx-andmap assert-Int-type #'(e+ ...))
( (syntax/loc stx (+ e+ ...)) #'Int)]))
[(_ any ...) #'(stlc:define-type any ...)]))
;; lambda ---------------------------------------------------------------------
(define-syntax (λ/tc stx)
(syntax-parse stx #:datum-literals (:)
[(_ ([x:id : τ] ...) e ... e_result)
[(_ τs ([x:id : τ] ...) e ... e_result)
#:when (curly-parens? #'τs)
;; the with-extended-type-env must be outside the expand/df (instead of
;; around just the body) bc ow the parameter will get restored to the old
;; value before the local-expand happens
#:with (lam xs e+ ... e_result+) (with-extended-type-env #'([x τ] ...)
(expand/df #'(λ (x ...) e ... e_result)))
;; manually handle identifiers here
;; - since Racket has no #%var hook, ids didn't get "expanded" in the previous line
;; and thus didn't get a type
;; TODO: can I put this somewhere else where it's more elegant?
#:with (e++ ... e_result++) (with-extended-type-env #'([x τ] ...)
(stx-map
(λ (e) (if (identifier? e) (expand/df e) e))
#'(e+ ... e_result+)))
;; manually handle the implicit begin
#:when (stx-map assert-Unit-type #'(e+ ...))
#:with τ_body (typeof #'e_result+)
( (syntax/loc stx (lam xs e+ ... e_result+)) #'( τ ... τ_body))]))
#:when (stx-map assert-Unit-type #'(e++ ...))
#:with τ_body (typeof #'e_result++)
( (syntax/loc stx (lam xs e++ ... e_result++))
#'( τs ( τ ... τ_body)))]
[(_ any ...) #'(stlc:λ any ...)]))
(define-syntax (let/tc stx)
(syntax-parse stx #:datum-literals (:)
[(_ ([x:id e_x] ...) e ... e_result)
#:with (e_x+ ...) (stx-map expand/df #'(e_x ...))
#:with (τ ...) (stx-map typeof #'(e_x+ ...))
#:with (lam (x+ ...) e+ ... e_result+)
(with-extended-type-env #'([x τ] ...)
(expand/df #'(λ (x ...) e ... e_result)))
#:when (stx-andmap assert-Unit-type #'(e+ ...))
( (syntax/loc stx (let ([x+ e_x+] ...) e+ ... e_result+)) (typeof #'e_result+))]))
(define-for-syntax (apply-forall ∀τ τs)
(define ctx (syntax-local-make-definition-context))
(define id (generate-temporary))
(syntax-local-bind-syntaxes
(list id)
(syntax-parse ∀τ #:datum-literals ()
[( (X ...) τbody)
#'(λ (stx)
(syntax-parse stx
[(_ (τ (... ...)))
#:with (X ...) #'(τ (... ...))
#'τbody]))])
ctx)
(local-expand #`(#,id #,τs) 'expression (list #'#%app) ctx))
; #%app -----------------------------------------------------------------------
(define-syntax (app/tc stx)
(syntax-parse stx #:literals ( void)
; #:datum-literals (:t)
; [(_ :t x) #'(printf "~a : ~a\n" 'x (hash-ref runtime-env 'x))]
[(_ e_fn τs e_arg ...)
#:when (curly-parens? #'τs)
; #:with (τ ...) #'τs
#:with (e_fn+ e_arg+ ...) (stx-map expand/df #'(e_fn e_arg ...))
; #:when (printf "e_fn: ~a\n" (typeof #'e_fn+))
; #:when (printf "τs: ~a\n" #'τs)
#:with ( (X ...) ( τX ...)) (typeof #'e_fn+)
; #:when (printf "applied: ~a\n" (apply-forall (typeof #'e_fn+) #'τs))
#:with ( τ_arg ... τ_res) (apply-forall (typeof #'e_fn+) #'τs)
#:when (stx-andmap assert-type #'(e_arg+ ...) #'(τ_arg ...))
( (syntax/loc stx (#%app e_fn+ e_arg+ ...)) #'τ_res)]
[(_ any ...) #:when (printf "shouldnt get here\n") #'(stlc:#%app any ...)]))
(define-syntax (letrec/tc stx)
(syntax-parse stx #:datum-literals (:)
@ -275,73 +117,8 @@
(expand/df #'(letrec ([f e_f] ...) body ... body_result))
(syntax/loc stx (letrec ([f+ e_f+] ...) body+ ... body_result+))]))
; #%app
(define-syntax (app/tc stx)
(syntax-parse stx #:literals ( void)
#:datum-literals (:t)
[(_ :t x) #'(printf "~a : ~a\n" 'x (hash-ref runtime-env 'x))]
[(_ e_fn e_arg ...)
#:with (e_fn+ e_arg+ ...) (stx-map expand/df #'(e_fn e_arg ...))
#:with ( τ ... τ_res) (typeof #'e_fn+)
#:when (stx-andmap assert-type #'(e_arg+ ...) #'(τ ...))
( (syntax/loc stx (#%app e_fn+ e_arg+ ...)) #'τ_res)]))
(define-syntax (if/tc stx)
(syntax-parse stx
[(_ e_test e1 e2)
#:with e_test+ (expand/df #'e_test)
#:when (assert-type #'e_test+ #'Bool)
#:with e1+ (expand/df #'e1)
#:with e2+ (expand/df #'e2)
#:when (type=? (typeof #'e1+) (typeof #'e2+))
( (syntax/loc stx (if e_test+ e1+ e2+)) (typeof #'e1+))]))
;; lists ----------------------------------------------------------------------
(define-syntax (cons/tc stx)
(syntax-parse stx
[(_ {T} e1 e2)
#:with e1+ (expand/df #'e1)
#:with e2+ (expand/df #'e2)
#:when (assert-type #'e1+ #'T)
#:when (assert-type #'e2+ #'(Listof T))
( (syntax/loc stx (cons e1+ e2+)) #'(Listof T))]))
(define-syntax (null/tc stx)
(syntax-parse stx
[(_ {T}) ( (syntax/loc stx null) #'(Listof T))]))
(define-syntax (null?/tc stx)
(syntax-parse stx
[(_ {T} e)
#:with e+ (expand/df #'e)
#:when (assert-type #'e+ #'(Listof T))
( (syntax/loc stx (null? e+)) #'Bool)]))
(define-syntax (first/tc stx)
(syntax-parse stx
[(_ {T} e)
#:with e+ (expand/df #'e)
#:when (assert-type #'e+ #'(Listof T))
( (syntax/loc stx (car e+)) #'T)]))
(define-syntax (rest/tc stx)
(syntax-parse stx
[(_ {T} e)
#:with e+ (expand/df #'e)
#:when (assert-type #'e+ #'(Listof T))
( (syntax/loc stx (cdr e+)) #'(Listof T))]))
;; define, module-begin -------------------------------------------------------
#;(define-syntax (define/tc stx)
(syntax-parse stx #:datum-literals (:)
[(_ (f:id [x:id : τ] ...) e ... e_result)
#:with (g ...) (map (λ (fn) (datum->syntax (car (syntax->list #'(x ...))) fn)) (hash-keys (Γ)))
#:with (lam1 (g+ ...) (#%exp (lam2 (x+ ...) e+ ... e_result+)))
(with-extended-type-env #'([x τ] ...)
(expand/df #'(λ (g ...) (λ (x ...) e ... e_result))))
#:when (stx-andmap assert-Unit-type #'(e+ ...))
#:with τ_result (typeof #'e_result+)
#:when (Γ (type-env-extend #'([f ( τ ... τ_result)])))
( (syntax/loc stx (define (f x+ ...) e+ ... e_result+)) #'Unit)]
))
;; module-begin and associated stx-classes
;; - copied from stlc.rkt: 2014-08-14
(begin-for-syntax
(define-syntax-class maybe-def #:datum-literals (: define variant) #:literals (define-type)
(pattern (define (f:id [x:id : τx] ...) body ...)
@ -384,6 +161,8 @@
#:with ((begin deftype+ ...) ...) (stx-map expand/df/module-ctx #'(deftype ...))
#:with (structdef ...) (stx-flatten #'((deftype+ ...) ...))
#:with (structdef+:strct ...) (stx-map expand/df/module-ctx #'(structdef ...))
;; <----- everything before here gets called twice (eg try inserting printf)
;; (the expand on the previous line must be calling module begin?)
#:with (def-val:def-val ...) #'(structdef+.def-val ...)
#:with (def-val-lhs ...) #'(def-val.lhs ...)
#:with (def-val-rhs ...) #'(def-val.rhs ...)
@ -403,8 +182,44 @@
#,(expand/df #'(let-values ([def-val-lhs def-val-rhs] ...)
(let-syntax ([def-syn-lhs def-syn-rhs] ...)
(letrec/tc ([f : τ v] ...) e ... (void)))))
(define #,(datum->syntax stx 'runtime-env)
#;(define #,(datum->syntax stx 'runtime-env)
(for/hash ([x:τ '#,(map (λ () (cons (car ) (syntax->datum (cdr ))))
(hash->list (do-subst (Γ))))])
(values (car x:τ) (cdr x:τ))))
))]))
;; testing fns ----------------------------------------------------------------
;; for now, these are duplicated from stlc.rkt: 2014-08-14
;; type checking testing: -----------------------------------------------------
(require rackunit)
(require (for-syntax rackunit "typecheck.rkt"))
(provide check-equal?)
(provide check-type-error check-type check-type-and-result check-not-type)
(define-syntax (check-type-error stx)
(syntax-parse stx
[(_ e)
#:when (check-exn exn:fail? (λ () (expand/df #'e)))
#'(void)]))
(define-syntax (check-type stx)
(syntax-parse stx #:datum-literals (:)
[(_ e : τ)
#:with e+ (expand/df #'e)
#:when (check-true (assert-type #'e+ #'τ)
(format "Expected type ~a but got type ~a" #'τ (typeof #'e)))
#'(void)]))
(define-syntax (check-not-type stx)
(syntax-parse stx #:datum-literals (:)
[(_ e : τ)
#:with e+ (expand/df #'e)
#:when (check-false (type=? (typeof #'e+) #'τ)
(format "Expected type to not be ~a but got type ~a" #'τ (typeof #'e)))
#'(void)]))
(define-syntax (check-type-and-result stx)
(syntax-parse stx #:datum-literals (: =>)
[(_ e : τ => v)
#'(begin (check-type e : τ)
(check-equal? e v))]))