(define (inner y) (ast-collect f y))
(case (ast-type x)
['let (append (f x)
- (fold-map inner (let-bindings x))
- (fold-map inner (let-body x)))]
+ (flat-map inner (let-bindings x))
+ (flat-map inner (let-body x)))]
['app (append (f x)
- (fold-map inner x))]
+ (flat-map inner x))]
['lambda (append (f x)
(inner (lambda-body x)))]
['if (append (f x)
- (fold-map inner (cdr x)))]
+ (flat-map inner (cdr x)))]
[else (f x)]))
(define (ast-find p x)
['if (either (p x) (any inner (cdr x)))]
[else (p x)]))
-(define let-bindings cadr)
+(define (let-bindings e)
+ (define (pattern-match x body)
+ (if (eqv? (ast-type x) 'var)
+ (cons x body)
+ (let* ([constructor (car x)]
+ [destructor (lambda (i) `(destruct ,i ,constructor))])
+ (flat-map (lambda (y i)
+ (pattern-match y (list (destructor i) body)))
+ (cdr x)
+ (range 0 (length (cdr x)))))))
+ (flat-map (lambda (x) (pattern-match (car x) (cdr x))) (cadr e)))
(define let-body cddr)
(define (lambda? x)
(and (list? x) (eq? (car x) 'lambda)))
+
+(define (statement-type x)
+ (cond
+ [(and (list? x)
+ (eqv? (car x) 'data)) 'data]
+ [(and (list? x)
+ (eqv? (car x) 'define)) 'define]
+ [else 'expr]))
+
+(define (program-datas program)
+ (filter (lambda (x) (eqv? (statement-type x) 'data))
+ program))
+
+(define (program-defines program)
+ (filter (lambda (x) (eqv? (statement-type x) 'defines))
+ program))
+
+(define (program-body program)
+ `(let ()
+ ,@(filter (lambda (x) (eqv? (statement-type x) 'expr))
+ program)))
+
; for use in normalized form
(define lambda-arg caadr)
; for use elsewhere
(define lambda-body caddr)
; utils
-(define (fold-map f x) (fold-left append '() (map f x)))
+(define (range s n)
+ (if (= 0 n) '()
+ (append (range s (- n 1))
+ (list (+ s (- n 1))))))
+
+(define (flat-map f . xs) (fold-left append '() (map f xs)))
(define (repeat x n) (if (<= n 0) '()
(cons x (repeat x (- n 1)))))
expected actual))))
(define (test . xs) (apply test-f (cons equal? xs)))
-(define (test-types . xs) (apply test-f (cons types-equal? xs)))
+
+(define-syntax test-types
+ (syntax-rules ()
+ ((_ a e)
+ (begin
+ (display (quote a))
+ (newline)
+ (test-f types-equal? a e)))))
(define (read-file file)
(call-with-input-file file
(compile-to-binary prog "/tmp/test-prog" host-os)
(test (system "/tmp/test-prog") exit-code))
+(define (test-expr prog exit-code)
+ (test-prog (list prog) exit-code))
+
(define (test-prog-stdout prog output)
(display prog)
(newline)
(let ((str (read-file "/tmp/test-output.txt")))
(test str output)))
-(test-types (typecheck '(lambda (x) (+ ((lambda (y) (x y 3)) 5) 2)))
- '(abs (abs int (abs int int)) int))
+(test-types (typecheck '((lambda (x) (+ ((lambda (y) (x y 3)) 5) 2))))
+ '(abs (abs Int (abs Int Int)) Int))
; recursive types
-(test-types (substitute '((t1 (abs t1 t10))) 't1) '(abs t1 t10))
+(test-types (substitute '((t1 . (abs t1 t10))) 't1) '(abs t1 t10))
-(test-types (typecheck '(let ([bar (lambda (y) y)]
+(test-types (typecheck '((let ([bar (lambda (y) y)]
[foo (lambda (x) (foo (bar #t)))])
- foo))
- '(abs bool a))
+ foo)))
+ '(abs Bool a))
-(test-types (typecheck '(let ([bar (lambda (y) y)]
+(test-types (typecheck '((let ([bar (lambda (y) y)]
[foo (lambda (x) (foo (bar #t)))])
- bar))
+ bar)))
'(abs a a))
-(test-types (typecheck '(let ([foo 3]
+(test-types (typecheck '((let ([foo 3]
[bar (+ foo baz)]
[baz (- bar 1)])
- bar))
- 'int)
+ bar)))
+ 'Int)
-(test-types (typecheck '(let ([foo 3]
+(test-types (typecheck '((let ([foo 3]
[bar (baz foo)]
[baz (lambda (x) x)])
- baz))
+ baz)))
'(abs a a))
-(test-types (typecheck '(let ([foo 3]
+(test-types (typecheck '((let ([foo 3]
[bar (baz foo)]
[baz (lambda (x) x)])
- bar))
- 'int)
+ bar)))
+ 'Int)
-(test-prog '(+ 1 2) 3)
-(test-prog '(bool->int (= 2 0)) 0)
-(test-prog '((lambda (x) ((lambda (y) (+ x y)) 42)) 100) 142)
-
-(test-prog '(* 10 5) 50)
+ ; mutual recursion
+(test-types (typecheck '((let ([f (lambda (n) (if (= n 0)
+ 0
+ (+ 1 (g (- n 1)))))]
+ [g (lambda (m) (f m))])
+ (f 10))))
+ 'Int)
-(test-prog '(let ((x (+ 1 32))
+(test-types (typecheck '((let ([pow (lambda (p y)
+ (let ([go (lambda (n x)
+ (if (= n 0)
+ x
+ (go (- n 1) (* x y))))])
+ (go p 1)))])
+ (pow 4 2))))
+ 'Int)
+
+(test-types
+ (typecheck
+ '((data A
+ [foo Int]
+ [bar Bool])
+ (let ([x (foo 42)]
+ [(foo y) x])
+ x)))
+ 'A)
+
+(test-types
+ (typecheck
+ '((data A
+ [foo Int]
+ [bar Bool])
+ (let ([x (foo 42)]
+ [(foo y) x])
+ y)))
+ 'Int)
+
+(test-expr '(+ 1 2) 3)
+(test-expr '(bool->int (= 2 0)) 0)
+(test-expr '((lambda (x) ((lambda (y) (+ x y)) 42)) 100) 142)
+
+(test-expr '(* 10 5) 50)
+
+(test-expr '(let ((x (+ 1 32))
(y x))
((lambda (z) (+ 2 z)) (* y x)))
67) ; exit code modulos at 256
-(test-prog '(if ((lambda (x) (= x 2)) 1) 0 (- 32 1)) 31)
+(test-expr '(if ((lambda (x) (= x 2)) 1) 0 (- 32 1)) 31)
-(test-prog-stdout '(if (= 3 2) 1 (let () (print "hello world!") 0)) "hello world!")
+(test-prog-stdout '((if (= 3 2) 1 (let () (print "hello world!") 0))) "hello world!")
-(test-prog '((lambda (x y) (+ x y)) 1 2) 3)
-(test-prog '((lambda (x) (+ ((lambda (y) (+ y 1)) 3) x)) 2) 6)
+(test-expr '((lambda (x y) (+ x y)) 1 2) 3)
+(test-expr '((lambda (x) (+ ((lambda (y) (+ y 1)) 3) x)) 2) 6)
; passing closures about
-(test-prog '((lambda (z) ((lambda (x) (x 1)) (lambda (y) (+ z y)))) 2) 3)
+(test-expr '((lambda (z) ((lambda (x) (x 1)) (lambda (y) (+ z y)))) 2) 3)
; passing builtins about
-(test-prog '((lambda (x) ((lambda (a b) (a b 3)) + x)) 3) 6)
-(test-prog '(bool->int ((lambda (x) (x #f)) !)) 1)
-(test-prog '((lambda (f) (f #t)) bool->int) 1)
-(test-prog-stdout '(let () ((lambda (f) (f "foo")) print) 0) "foo")
-(test-prog '((lambda (f) (f 3 3)) (lambda (x y) (bool->int (= x y)))) 1)
-(test-prog '(bool->int ((lambda (f) (! (f 2 3))) =)) 1)
+(test-expr '((lambda (x) ((lambda (a b) (a b 3)) + x)) 3) 6)
+(test-expr '(bool->int ((lambda (x) (x #f)) !)) 1)
+(test-expr '((lambda (f) (f #t)) bool->int) 1)
+(test-prog-stdout '((let () ((lambda (f) (f "foo")) print) 0)) "foo")
+(test-expr '((lambda (f) (f 3 3)) (lambda (x y) (bool->int (= x y)))) 1)
+(test-expr '(bool->int ((lambda (f) (! (f 2 3))) =)) 1)
; recursion
-(test-prog '(let [(inc (lambda (f n x)
+(test-expr '(let [(inc (lambda (f n x)
(if (= n 0)
x
(f f (- n 1) (+ x 1)))))]
(inc inc 3 2))
5)
-(test-prog '(let ([go (lambda (n m x)
+(test-expr '(let ([go (lambda (n m x)
(if (= n 0)
x
(go (- n 1) m (* x m))))]
(pow 3 2))
8)
-(test-prog '(let ([pow (lambda (p y)
+(test-expr '(let ([pow (lambda (p y)
(let ([go (lambda (n x)
(if (= n 0)
x
(and (list? t) (eq? (car t) 'abs)))
(define (tvar? t)
- (and (not (list? t)) (not (concrete? t)) (symbol? t)))
+ (and (not (list? t))
+ (not (concrete? t))
+ (symbol? t)))
(define (concrete? t)
- (case t
- ('int #t)
- ('bool #t)
- ('void #t)
- (else #f)))
+ (and (symbol? t)
+ (char-upper-case? (string-ref (symbol->string t) 0))))
(define (pretty-type t)
(cond ((abs? t)
(pretty-type (caddr t))))
(else (symbol->string t))))
+(define (pretty-constraints cs)
+ (string-append "{"
+ (fold-left string-append
+ ""
+ (map (lambda (c)
+ (string-append
+ (pretty-type (car c))
+ ": "
+ (pretty-type (cdr c))
+ ", "))
+ cs))
+ "}"))
+
; ('a, ('b, 'a))
(define (env-lookup env n)
(if (null? env) (error #f "empty env") ; it's a type equality
(define (builtin-type x)
(case x
- ('+ '(abs int (abs int int)))
- ('- '(abs int (abs int int)))
- ('* '(abs int (abs int int)))
- ('! '(abs bool bool))
- ('= '(abs int (abs int bool)))
- ('bool->int '(abs bool int))
- ('print '(abs string void))
- (else #f)))
-
-; we typecheck the lambda calculus only (only single arg lambdas)
-(define (typecheck prog)
- (define (check env x)
- ;; (display "check: ")
- ;; (display x)
- ;; (display "\n\t")
- ;; (display env)
- ;; (newline)
- (let
- ((res
- (case (ast-type x)
- ('int-literal (list '() 'int))
- ('bool-literal (list '() 'bool))
- ('string-literal (list '() 'string))
- ('builtin (list '() (builtin-type x)))
-
- ('if
- (let* ((cond-type-res (check env (cadr x)))
- (then-type-res (check env (caddr x)))
- (else-type-res (check env (cadddr x)))
- (then-eq-else-cs (~ (cadr then-type-res)
- (cadr else-type-res)))
- (cs (consolidate
- (car then-type-res)
- (consolidate (car else-type-res)
- then-eq-else-cs)))
- (return-type (substitute cs (cadr then-type-res))))
- (when (not (eqv? (cadr cond-type-res) 'bool))
- (error #f "if condition isn't bool"))
- (list cs return-type)))
-
- ('var (list '() (env-lookup env x)))
- ('let
+ ('+ '(abs Int (abs Int Int)))
+ ('- '(abs Int (abs Int Int)))
+ ('* '(abs Int (abs Int Int)))
+ ('! '(abs Bool Bool))
+ ('= '(abs Int (abs Int Bool)))
+ ('bool->int '(abs Bool Int))
+ ('print '(abs String Void))
+ (else (error #f "Couldn't find type for builtin" x))))
+
+(define (check-let env x)
; takes in the current environment and a scc
; returns new environment with scc's types added in
(let* ([components (reverse (sccs (graph (let-bindings x))))]
[cs
(fold-left
(lambda (acc res c)
- (consolidate
- acc
- (consolidate (car res)
+ (constraint-merge
+ (constraint-merge
; unify with tvars from scc-env
; result ~ tvar
- (~ (cadr res) (env-lookup scc-env c)))))
+ (~ (env-lookup scc-env c) (cadr res))
+ (car res))
+ acc))
'() type-results comps)]
; substitute *only* the bindings in this scc
[new-env
[new-env (fold-left process-component env components)])
(check new-env (last (let-body x)))))
+(define (check env x)
+ (display "check: ")
+ (display x)
+ (display "\n\t")
+ (display env)
+ (newline)
+ (let
+ ((res
+ (case (ast-type x)
+ ('int-literal (list '() 'Int))
+ ('bool-literal (list '() 'Bool))
+ ('string-literal (list '() 'String))
+ ('builtin (list '() (builtin-type x)))
+
+ ('if
+ (let* ((cond-type-res (check env (cadr x)))
+ (then-type-res (check env (caddr x)))
+ (else-type-res (check env (cadddr x)))
+ (then-eq-else-cs (~ (cadr then-type-res)
+ (cadr else-type-res)))
+ (cs (constraint-merge
+ (car then-type-res)
+ (constraint-merge (~ (cadr cond-type-res) 'Bool)
+ (constraint-merge (car else-type-res)
+ then-eq-else-cs))))
+ (return-type (substitute cs (cadr then-type-res))))
+ (list cs return-type)))
+
+ ('var (list '() (env-lookup env x)))
+ ('let (check-let env x))
+
+
('lambda
(let* [(new-env (env-insert env (lambda-arg x) (fresh-tvar)))
;; (display "\n\t")
;; (display cs)
;; (display "\n\t")
+ ;; (display (format "subd-env: ~a\n" subd-env))
;; (display resolved-arg-type)
;; (newline)
(list (car body-type-res)
(other-func-type `(abs ,func-type ,return-type))
(cs (~ func-type other-func-type))
(resolved-return-type (substitute cs return-type))]
- (list cs resolved-return-type))
+ (list cs resolved-return-type)))
; regular function
(let* ((arg-type-res (check env (cadr x)))
; f ~ a -> t0
(func-c (~
- func-type
- (list 'abs
- arg-type
- (fresh-tvar))))
- (cs (consolidate
- (consolidate func-c (car arg-type-res))
+ (substitute (car arg-type-res) func-type)
+ `(abs ,arg-type ,(fresh-tvar))))
+ (cs (constraint-merge
+ (constraint-merge func-c (car arg-type-res))
(car func-type-res)))
(resolved-func-type (substitute cs func-type))
(if (abs? resolved-func-type)
(let ((return-type (substitute cs (caddr resolved-func-type))))
(list cs return-type))
- (error #f "not a function"))))))))
- ;; (display "result of ")
- ;; (display x)
- ;; (display ":\n\t")
- ;; (display (pretty-type (cadr res)))
- ;; (display "\n\t[")
- ;; (display (car res))
- ;; (display "]\n")
+ (error #f "not a function")))))))
+ (display "result of ")
+ (display x)
+ (display ":\n\t")
+ (display (pretty-type (cadr res)))
+ (display "\n\t[")
+ (display (pretty-constraints (car res)))
+ (display "]\n")
res))
- (cadr (check '() (normalize prog))))
- ; returns a list of pairs of constraints
+ ; we typecheck the lambda calculus only (only single arg lambdas)
+(define (typecheck prog)
+ (define (constructor-type t ctr)
+ (fold-left (lambda (acc x) `(abs ,x ,acc)) t (cdr ctr)))
+ (define (constructors data-def)
+ (let ([type-name (cadr data-def)]
+ [ctrs (cddr data-def)])
+ (fold-left (lambda (acc ctr)
+ (cons (cons (car ctr) (constructor-type type-name ctr))
+ acc))
+ '()
+ ctrs)))
+ (let ([init-env (flat-map constructors (program-datas prog))])
+ (display init-env)
+ (cadr (check init-env (normalize (program-body prog))))))
+
+ ; returns a list of constraints
(define (~ a b)
(let ([res (unify? a b)])
(if res
(define (unify? a b)
(cond [(eq? a b) '()]
- [(or (tvar? a) (tvar? b)) (list (list a b))]
+ [(tvar? a) (list (cons a b))]
+ [(tvar? b) (list (cons b a))]
[(and (abs? a) (abs? b))
(let* [(arg-cs (unify? (cadr a) (cadr b)))
(body-cs (unify? (substitute arg-cs (caddr a))
(substitute arg-cs (caddr b))))]
- (consolidate arg-cs body-cs))]
+ (constraint-merge body-cs arg-cs))]
[else #f]))
- ; TODO: what's the most appropriate substitution?
- ; should all constraints just be limited to a pair?
- ; this is currently horrific and i don't know what im doing.
- ; should probably use ast-find here or during consolidation
- ; to detect substitutions more than one layer deep
- ; e.g. (abs t1 int) ~ (abs bool int)
- ; substituting these constraints with t1 should resolve t1 with bool
(define (substitute cs t)
- ; gets the first concrete type
- ; otherwise returns the last type variable
-
- ; removes t itself from cs, to prevent infinite recursion
- (define cs-without-t
- (map (lambda (c)
- (filter (lambda (x) (not (eqv? t x))) c))
- cs))
-
- (define (get-concrete c)
- (let [(last (null? (cdr c)))]
- (if (not (tvar? (car c)))
- (if (abs? (car c))
- (substitute cs-without-t (car c))
- (car c))
- (if last
- (car c)
- (get-concrete (cdr c))))))
-
(cond
- ((abs? t) (list 'abs
- (substitute cs (cadr t))
- (substitute cs (caddr t))))
- (else
- (fold-left
- (lambda (t c)
- (if (member t c)
- (get-concrete c)
- t))
- t cs))))
-
+ [(tvar? t)
+ (if (assoc t cs)
+ (cdr (assoc t cs))
+ t)]
+ [(abs? t) `(abs ,(substitute cs (cadr t))
+ ,(substitute cs (caddr t)))]
+ [else t]))
+
+ ; applies substitutions to all variables in environment
(define (substitute-env cs env)
(map (lambda (x) (cons (car x) (substitute cs (cdr x)))) env))
-(define (consolidate x y)
- (define (merge a b)
- (cond ((null? a) b)
- ((null? b) a)
- (else (if (member (car b) a)
- (merge a (cdr b))
- (cons (car b) (merge a (cdr b)))))))
- (define (overlap? a b)
- (if (or (null? a) (null? b))
- #f
- (if (fold-left (lambda (acc v)
- (or acc (eq? v (car a))))
- #f b)
- #t
- (overlap? (cdr a) b))))
-
- (cond ((null? y) x)
- ((null? x) y)
- (else
- (let* ((a (car y))
- (merged (fold-left
- (lambda (acc b)
- (if acc
- acc
- (if (overlap? a b)
- (cons (merge a b) b)
- #f)))
- #f x))
- (removed (if merged
- (filter (lambda (b) (not (eq? b (cdr merged)))) x)
- x)))
- (if merged
- (consolidate removed (cons (car merged) (cdr y)))
- (consolidate (cons a x) (cdr y)))))))
-
- ; a1 -> a2 ~ a3 -> a4;
- ; a1 -> a2 !~ bool -> bool
- ; basically can the tvars be renamed
+ ; composes constraints a onto b and merges, i.e. applies a to b
+ ; a should be the "more important" constraints
+(define (constraint-merge a b)
+ (define (f cs constraint)
+ (cons (car constraint)
+ (substitute cs (cdr constraint))))
+
+ (define (most-concrete a b)
+ (cond
+ [(tvar? a) b]
+ [(tvar? b) a]
+ [(and (abs? a) (abs? b))
+ `(abs ,(most-concrete (cadr a) (cadr b))
+ ,(most-concrete (caddr a) (caddr b)))]
+ [(abs? a) b]
+ [(abs? b) a]
+ [else a]))
+
+ ; for any two constraints that clash, e.g. t1 ~ abs t2 t3
+ ; and t1 ~ abs int t3
+ ; prepend the most concrete version of the type to the
+ ; list of constraints
+ (define (clashes)
+ (define (gen acc x)
+ (if (assoc (car x) a)
+ (cons (cons (car x) (most-concrete (cdr (assoc (car x) a))
+ (cdr x)))
+ acc)
+ acc))
+ (fold-left gen '() b))
+
+ (define (union p q)
+ (append (filter (lambda (x) (not (assoc (car x) p)))
+ q)
+ p))
+ (append (clashes) (union a (map (lambda (z) (f a z)) b))))
+
+
+;; ; a1 -> a2 ~ a3 -> a4;
+;; ; a1 -> a2 !~ Bool -> Bool
+;; ; basically can the tvars be renamed
(define (types-equal? x y)
(let ([cs (unify? x y)])
(if (not cs) #f
(let*
- ([test-kind
- (lambda (acc c)
- (if (tvar? c) acc #f))]
- [test (lambda (acc c)
+ ([test (lambda (acc c)
(and acc
- (fold-left test-kind #t c) ; check only tvar substitutions
- (<= (length c) 2)))]) ; check maximum 2 subs per equality group
+ (tvar? (car c)) ; the only substitutions allowed are tvar -> tvar
+ (tvar? (cdr c))))])
(fold-left test #t cs)))))
; input: a list of binds ((x . y) (y . 3))
projects / scheme.git / commitdiff