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 dls 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 dls 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 dls 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)) : ,let-type)])
150 (list cs let-type annotated)))
152 (define (check-app dls env x)
153 (if (eqv? (car x) (cadr x))
154 ; recursive function (f f)
155 ; TODO: what about ((f a) f)????
156 (let* ([func-type (env-lookup env (car x))]
157 [return-type (fresh-tvar)]
158 [other-func-type `(abs ,func-type ,return-type)]
159 [cs (~ func-type other-func-type)]
160 [resolved-return-type (substitute cs return-type)]
162 [annotated `(((,(car x) : ,func-type)
163 (,(cadr x) : ,func-type)) : ,resolved-return-type)])
164 (list cs resolved-return-type annotated)))
167 (let* ([arg-type-res (check dls env (cadr x))]
168 [arg-type (cadr arg-type-res)]
169 [func-type-res (check dls env (car x))]
170 [func-type (cadr func-type-res)]
174 (substitute (car arg-type-res) func-type)
175 `(abs ,arg-type ,(fresh-tvar)))]
176 [cs (constraint-merge
177 (constraint-merge func-c (car arg-type-res))
178 (car func-type-res))]
180 [resolved-func-type (substitute cs func-type)]
181 [resolved-return-type (caddr resolved-func-type)]
183 [annotated `((,(caddr func-type-res)
184 ,(caddr arg-type-res)) : ,resolved-return-type)])
186 (if (abs? resolved-func-type)
187 (let ((return-type (substitute cs (caddr resolved-func-type))))
188 (list cs return-type annotated))
189 (error #f "not a function"))))
191 (define (check-case dls env x)
193 (define (check-match switch-type x)
194 (let ([pattern (car x)]
196 (if (eqv? (ast-type pattern) 'app)
197 ; a pattern match with bindings
198 (let ([sum (assoc (car pattern) (cdr (assoc switch-type dls)))])
199 (unless sum (error #f "can't pattern match ~a with ~a" switch-type pattern))
200 (let* ([names (cdr pattern)]
202 [new-env (fold-left env-insert env names types)])
203 (check dls new-env expr)))
204 ; a pattern match without bindings
205 (check dls env expr))))
207 (let* ([switch-type-res (check dls env (case-switch x))]
208 [switch-type (cadr switch-type-res)]
210 [case-expr-type-res (map (lambda (x) (check-match switch-type x)) (case-cases x))]
211 [case-expr-types (map cadr case-expr-type-res)]
213 [case-expr-equality-cs (fold-left constraint-merge '()
214 (map (lambda (t) (~ t (car case-expr-types)))
215 (cdr case-expr-types)))]
217 [resolved-type (substitute case-expr-equality-cs (car case-expr-types))]
219 [annotated `((case (,(case-expr x) : ,switch-type)
220 ,(map (lambda (c e et)
222 (map car (case-cases x))
223 (map cadr (case-cases x))
224 case-expr-types)) : ,resolved-type)]
226 [cs (fold-left constraint-merge '()
227 (cons (car switch-type-res) case-expr-equality-cs))])
228 (list cs resolved-type annotated)))
230 ; returns a list (constraints type annotated)
231 (define (check dls env x)
232 (define (make-result cs type)
233 (list cs type `(,x : ,type)))
234 ;; (display "check: ")
242 ('int-literal (make-result '() 'Int))
243 ('bool-literal (make-result '() 'Bool))
244 ('string-literal (make-result '() 'String))
245 ('builtin (make-result '() (builtin-type x)))
248 (let* ((cond-type-res (check dls env (cadr x)))
249 (then-type-res (check dls env (caddr x)))
250 (else-type-res (check dls env (cadddr x)))
251 (then-eq-else-cs (~ (cadr then-type-res)
252 (cadr else-type-res)))
253 (cs (constraint-merge
255 (constraint-merge (~ (cadr cond-type-res) 'Bool)
256 (constraint-merge (car else-type-res)
258 (return-type (substitute cs (cadr then-type-res)))
259 [annotated `((if ,(caddr cond-type-res)
260 ,(caddr then-type-res)
261 ,(caddr else-type-res)) : ,return-type)])
262 (list cs return-type annotated)))
264 ('var (make-result '() (env-lookup env x)))
265 ('let (check-let dls env x))
269 (let* ([new-env (env-insert env (lambda-arg x) (fresh-tvar))]
271 [body-type-res (check dls new-env (lambda-body x))]
272 [cs (car body-type-res)]
273 [subd-env (substitute-env (car body-type-res) new-env)]
274 [arg-type (env-lookup subd-env (lambda-arg x))]
275 [resolved-arg-type (substitute cs arg-type)]
277 [lambda-type `(abs ,resolved-arg-type ,(cadr body-type-res))]
279 [annotated `((lambda (,(lambda-arg x)) ,(caddr body-type-res)) : ,lambda-type)])
281 (list (car body-type-res) ; constraints
286 ('app (check-app dls env x))
287 ['case (check-case dls env x)])))
290 ;; (display "result of ")
293 ;; (display (pretty-type (cadr res)))
295 ;; (display (pretty-constraints (car res)))
299 (define (init-adts-env prog)
300 (flat-map data-tors-type-env (program-data-layouts prog)))
302 ; we typecheck the lambda calculus only (only single arg lambdas)
303 (define (typecheck prog)
304 (let ([expanded (expand-pattern-matches prog)])
305 (cadr (check (program-data-layouts prog)
306 (init-adts-env expanded)
307 (normalize (program-body expanded))))))
310 ; before passing annotated types onto codegen
311 ; we need to restore the pre-normalization structure
312 ; (this is important for function arity etc)
313 (define (denormalize orig normed)
315 (define (collapse-lambdas n x)
319 (let* ([inner-lambda (lambda-body (ann-expr x))]
320 [arg (lambda-arg (ann-expr x))]
321 [inner-collapsed (ann-expr (collapse-lambdas (- n 1) inner-lambda))])
322 `((lambda ,(cons arg (lambda-args inner-collapsed))
323 ,(lambda-body inner-collapsed)) : ,(ann-type x)))]))
325 (define (collapse-apps n x)
327 [-1 (error #f "nullary functions not handled yet")]
330 (let* ([inner-app (car (ann-expr x))]
331 [inner-collapsed (collapse-apps (- n 1) inner-app)])
332 `(,(append (ann-expr inner-collapsed) (cdr (ann-expr x))) : ,(ann-type x)))]))
334 (case (ast-type orig)
336 (let ([collapsed (collapse-lambdas (- (length (lambda-args orig)) 1) normed)])
337 `((lambda ,(lambda-args (ann-expr collapsed))
338 ,(denormalize (lambda-body orig)
339 (lambda-body (ann-expr collapsed)))) : ,(ann-type collapsed)))]
341 (let ([collapsed (collapse-apps (- (length orig) 2) normed)])
342 `(,(map (lambda (o n) (denormalize o n)) orig (ann-expr collapsed))
343 : ,(ann-type collapsed)))]
345 `((let ,(map (lambda (o n) (list (car o) (denormalize (cadr o) (cadr n))))
347 (let-bindings (ann-expr normed)))
348 ,@(map (lambda (o n) (denormalize o n))
350 (let-body (ann-expr normed)))) : ,(ann-type normed))]
351 ['if `((if ,@(map denormalize (cdr orig) (cdr (ann-expr normed))))
352 : (ann-type normed))]
355 (define ann-expr car)
356 (define ann-type caddr)
358 ; prerequisites: expand-pattern-matches
359 (define (annotate-types prog)
362 (caddr (check (init-adts-env prog) (normalize (program-body prog))))))
365 ; returns a list of constraints
367 (let ([res (unify? a b)])
371 (format "couldn't unify ~a ~~ ~a" a b)))))
374 (cond [(eq? a b) '()]
375 [(tvar? a) (list (cons a b))]
376 [(tvar? b) (list (cons b a))]
377 [(and (abs? a) (abs? b))
378 (let* [(arg-cs (unify? (cadr a) (cadr b)))
379 (body-cs (unify? (substitute arg-cs (caddr a))
380 (substitute arg-cs (caddr b))))]
381 (constraint-merge body-cs arg-cs))]
384 (define (substitute cs t)
390 [(abs? t) `(abs ,(substitute cs (cadr t))
391 ,(substitute cs (caddr t)))]
394 ; applies substitutions to all variables in environment
395 (define (substitute-env cs env)
396 (map (lambda (x) (cons (car x) (substitute cs (cdr x)))) env))
398 ; composes constraints a onto b and merges, i.e. applies a to b
399 ; a should be the "more important" constraints
400 (define (constraint-merge a b)
401 (define (f cs constraint)
402 (cons (car constraint)
403 (substitute cs (cdr constraint))))
405 (define (most-concrete a b)
409 [(and (abs? a) (abs? b))
410 `(abs ,(most-concrete (cadr a) (cadr b))
411 ,(most-concrete (caddr a) (caddr b)))]
416 ; for any two constraints that clash, e.g. t1 ~ abs t2 t3
417 ; and t1 ~ abs int t3
418 ; prepend the most concrete version of the type to the
419 ; list of constraints
422 (if (assoc (car x) a)
423 (cons (cons (car x) (most-concrete (cdr (assoc (car x) a))
427 (fold-left gen '() b))
430 (append (filter (lambda (x) (not (assoc (car x) p)))
433 (append (clashes) (union a (map (lambda (z) (f a z)) b))))
436 ;; ; a1 -> a2 ~ a3 -> a4;
437 ;; ; a1 -> a2 !~ Bool -> Bool
438 ;; ; basically can the tvars be renamed
439 (define (types-equal? x y)
440 (let ([cs (unify? x y)])
443 ([test (lambda (acc c)
445 (tvar? (car c)) ; the only substitutions allowed are tvar -> tvar
447 (fold-left test #t cs)))))
449 ; input: a list of binds ((x . y) (y . 3))
450 ; returns: pair of verts, edges ((x y) . (x . y))