4 (and (list? t) (eq? (car t) 'abs)))
13 (char-upper-case? (string-ref (symbol->string t) 0))))
15 (define (pretty-type t)
19 (string-append "(" (pretty-type (cadr t)) ")")
20 (pretty-type (cadr t)))
22 (pretty-type (caddr t))))
23 (else (symbol->string t))))
25 (define (pretty-constraints cs)
27 (fold-left string-append
39 (define (env-lookup env n)
40 (if (null? env) (error #f "empty env" env n) ; it's a type equality
41 (if (eq? (caar env) n)
43 (env-lookup (cdr env) n))))
45 (define (env-insert env n t)
46 (cons (cons n t) env))
53 (set! cur-tvar (+ cur-tvar 1))
55 (string-append "t" (number->string (- cur-tvar 1))))))
62 (define (normalize prog) ; (+ a b) -> ((+ a) b)
65 ; (lambda (x y) (+ x y)) -> (lambda (x) (lambda (y) (+ x y)))
66 (if (> (length (lambda-args prog)) 1)
67 (list 'lambda (list (car (lambda-args prog)))
68 (normalize (list 'lambda (cdr (lambda-args prog)) (caddr prog))))
69 (list 'lambda (lambda-args prog) (normalize (caddr prog)))))
71 (if (null? (cddr prog))
72 `(,(normalize (car prog)) ,(normalize (cadr prog))) ; (f a)
73 (normalize `(,(list (normalize (car prog)) (normalize (cadr prog)))
74 ,@(cddr prog))))) ; (f a b)
77 (map (lambda (x) `(,(car x) ,(normalize (cadr x))))
79 (map normalize (let-body prog))))
80 (else (ast-traverse normalize prog))))
82 (define (builtin-type x)
84 ('+ '(abs Int (abs Int Int)))
85 ('- '(abs Int (abs Int Int)))
86 ('* '(abs Int (abs Int Int)))
88 ('= '(abs Int (abs Int Bool)))
89 ('bool->int '(abs Bool Int))
90 ('print '(abs String Void))
91 (else (error #f "Couldn't find type for builtin" x))))
93 (define (check-let env x)
95 ; acc is a pair of (env . annotated bindings)
96 (define (process-component acc comps)
98 ; create a new env with tvars for each component
100 ; scc-env = ((x . t0) (y . t1))
104 (env-insert acc c (fresh-tvar)))
106 ; typecheck each component
110 (let ([body (cadr (assoc c (let-bindings x)))])
111 (check scc-env body)))
113 ; collect all the constraints in the scc
119 ; unify with tvars from scc-env
121 (~ (env-lookup scc-env c) (cadr res))
124 '() type-results comps)]
125 ; substitute *only* the bindings in this scc
128 (if (memv (car x) comps)
129 (cons (car x) (substitute cs (cdr x)))
133 [annotated-bindings (append (cdr acc) ; the previous annotated bindings
136 (map caddr type-results)))])
137 (cons new-env annotated-bindings)))
138 ; takes in the current environment and a scc
139 ; returns new environment with scc's types added in
140 (let* ([components (reverse (sccs (graph (let-bindings x))))]
141 [results (fold-left process-component (cons env '()) components)]
142 [new-env (car results)]
143 [annotated-bindings (cdr results)]
145 [body-results (map (lambda (body) (check new-env body)) (let-body x))]
146 [let-type (cadr (last body-results))]
147 [cs (fold-left (lambda (acc cs) (constraint-merge acc cs)) '() (map car body-results))]
149 [annotated `((let ,annotated-bindings ,@(map caddr body-results)))])
150 (list cs let-type annotated)))
153 ; returns a list (constraints type annotated)
154 (define (check env x)
155 (define (make-result cs type)
156 (list cs type `(,x : ,type)))
157 ;; (display "check: ")
165 ('int-literal (make-result '() 'Int))
166 ('bool-literal (make-result '() 'Bool))
167 ('string-literal (make-result '() 'String))
168 ('builtin (make-result '() (builtin-type x)))
171 (let* ((cond-type-res (check env (cadr x)))
172 (then-type-res (check env (caddr x)))
173 (else-type-res (check env (cadddr x)))
174 (then-eq-else-cs (~ (cadr then-type-res)
175 (cadr else-type-res)))
176 (cs (constraint-merge
178 (constraint-merge (~ (cadr cond-type-res) 'Bool)
179 (constraint-merge (car else-type-res)
181 (return-type (substitute cs (cadr then-type-res)))
182 [annotated `((if ,(caddr cond-type-res)
183 ,(caddr then-type-res)
184 ,(caddr else-type-res)) : ,return-type)])
185 (list cs return-type annotated)))
187 ('var (make-result '() (env-lookup env x)))
188 ('let (check-let env x))
192 (let* ([new-env (env-insert env (lambda-arg x) (fresh-tvar))]
194 [body-type-res (check new-env (lambda-body x))]
195 [cs (car body-type-res)]
196 [subd-env (substitute-env (car body-type-res) new-env)]
197 [arg-type (env-lookup subd-env (lambda-arg x))]
198 [resolved-arg-type (substitute cs arg-type)]
200 [lambda-type `(abs ,resolved-arg-type ,(cadr body-type-res))]
202 ; TODO: do we need to annotate the lambda argument?
203 [annotated `(lambda (,(lambda-arg x)) ,(caddr body-type-res))])
205 (list (car body-type-res) ; constraints
211 (if (eqv? (car x) (cadr x))
212 ; recursive function (f f)
213 (let* ([func-type (env-lookup env (car x))]
214 [return-type (fresh-tvar)]
215 [other-func-type `(abs ,func-type ,return-type)]
216 [cs (~ func-type other-func-type)]
217 [resolved-return-type (substitute cs return-type)]
219 [annotated `(((,(car x) : ,func-type)
220 (,(cadr x) : ,func-type)) : ,resolved-return-type)])
221 (list cs resolved-return-type annotated)))
224 (let* ([arg-type-res (check env (cadr x))]
225 [arg-type (cadr arg-type-res)]
226 [func-type-res (check env (car x))]
227 [func-type (cadr func-type-res)]
231 (substitute (car arg-type-res) func-type)
232 `(abs ,arg-type ,(fresh-tvar)))]
233 [cs (constraint-merge
234 (constraint-merge func-c (car arg-type-res))
235 (car func-type-res))]
237 [resolved-func-type (substitute cs func-type)]
238 [resolved-return-type (caddr resolved-func-type)]
240 [annotated `((,(caddr func-type-res)
241 ,(caddr arg-type-res)) : ,resolved-return-type)])
243 (if (abs? resolved-func-type)
244 (let ((return-type (substitute cs (caddr resolved-func-type))))
245 (list cs return-type annotated))
246 (error #f "not a function")))))))
247 ;; (display "result of ")
250 ;; (display (pretty-type (cadr res)))
252 ;; (display (pretty-constraints (car res)))
256 (define (init-adts-env prog)
257 (flat-map data-tors-env (map data-layout (program-datas prog))))
259 ; we typecheck the lambda calculus only (only single arg lambdas)
260 (define (typecheck prog)
261 (cadr (check (init-adts-env prog) (normalize (program-body prog)))))
263 (define (annotate-types prog)
264 (caddr (check (init-adts-env prog) (normalize (program-body prog)))))
267 ; returns a list of constraints
269 (let ([res (unify? a b)])
273 (format "couldn't unify ~a ~~ ~a" a b)))))
276 (cond [(eq? a b) '()]
277 [(tvar? a) (list (cons a b))]
278 [(tvar? b) (list (cons b a))]
279 [(and (abs? a) (abs? b))
280 (let* [(arg-cs (unify? (cadr a) (cadr b)))
281 (body-cs (unify? (substitute arg-cs (caddr a))
282 (substitute arg-cs (caddr b))))]
283 (constraint-merge body-cs arg-cs))]
286 (define (substitute cs t)
292 [(abs? t) `(abs ,(substitute cs (cadr t))
293 ,(substitute cs (caddr t)))]
296 ; applies substitutions to all variables in environment
297 (define (substitute-env cs env)
298 (map (lambda (x) (cons (car x) (substitute cs (cdr x)))) env))
300 ; composes constraints a onto b and merges, i.e. applies a to b
301 ; a should be the "more important" constraints
302 (define (constraint-merge a b)
303 (define (f cs constraint)
304 (cons (car constraint)
305 (substitute cs (cdr constraint))))
307 (define (most-concrete a b)
311 [(and (abs? a) (abs? b))
312 `(abs ,(most-concrete (cadr a) (cadr b))
313 ,(most-concrete (caddr a) (caddr b)))]
318 ; for any two constraints that clash, e.g. t1 ~ abs t2 t3
319 ; and t1 ~ abs int t3
320 ; prepend the most concrete version of the type to the
321 ; list of constraints
324 (if (assoc (car x) a)
325 (cons (cons (car x) (most-concrete (cdr (assoc (car x) a))
329 (fold-left gen '() b))
332 (append (filter (lambda (x) (not (assoc (car x) p)))
335 (append (clashes) (union a (map (lambda (z) (f a z)) b))))
338 ;; ; a1 -> a2 ~ a3 -> a4;
339 ;; ; a1 -> a2 !~ Bool -> Bool
340 ;; ; basically can the tvars be renamed
341 (define (types-equal? x y)
342 (let ([cs (unify? x y)])
345 ([test (lambda (acc c)
347 (tvar? (car c)) ; the only substitutions allowed are tvar -> tvar
349 (fold-left test #t cs)))))
351 ; input: a list of binds ((x . y) (y . 3))
352 ; returns: pair of verts, edges ((x y) . (x . y))