4 (and (list? t) (eq? (car t) 'abs)))
7 (and (not (list? t)) (not (concrete? t)) (symbol? t)))
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))))
26 (define (env-lookup env n)
27 (if (null? env) (error #f "empty env") ; it's a type equality
28 (if (eq? (caar env) n)
30 (env-lookup (cdr env) n))))
32 (define (env-insert env n t)
33 (cons (cons n t) env))
40 (set! cur-tvar (+ cur-tvar 1))
42 (string-append "t" (number->string (- cur-tvar 1))))))
50 (define (normalize prog) ; (+ a b) -> ((+ a) b)
52 ; (lambda (x y) (+ x y)) -> (lambda (x) (lambda (y) (+ x y)))
54 (if (> (length (lambda-args prog)) 1)
55 (list 'lambda (list (car (lambda-args prog)))
56 (normalize (list 'lambda (cdr (lambda-args prog)) (caddr prog))))
57 (list 'lambda (lambda-args prog) (normalize (caddr prog)))))
59 (if (null? (cddr prog))
60 (cons (normalize (car prog)) (normalize (cdr prog))) ; (f a)
61 (list (list (normalize (car prog)) (normalize (cadr prog))) (normalize (caddr prog))))) ; (f a b)
64 (map (lambda (x) (cons (car x) (normalize (cdr x))))
66 (map normalize (let-body prog))))
69 (define (builtin-type x)
71 ('+ '(abs int (abs int int)))
72 ('- '(abs int (abs int int)))
73 ('* '(abs int (abs int int)))
75 ('bool->int '(abs bool int))
78 ; we typecheck the lambda calculus only (only single arg lambdas)
79 (define (typecheck prog)
81 ;; (display "check: ")
89 ((integer? x) (list '() 'int))
90 ((boolean? x) (list '() 'bool))
91 ((builtin-type x) (list '() (builtin-type x)))
92 ((symbol? x) (list '() (env-lookup env x)))
94 (let ((new-env (fold-left
97 (env-insert acc (car bind) (fresh-tvar))
99 (env-insert acc (car bind) (cadr t))))
100 env (let-bindings x))))
101 (check new-env (last (let-body x)))))
105 (let* ((new-env (env-insert env (lambda-arg x) (fresh-tvar)))
106 (body-type-res (check new-env (lambda-body x)))
107 (cs (car body-type-res))
108 (subd-env (substitute-env (car body-type-res) new-env))
109 (arg-type (env-lookup subd-env (lambda-arg x)))
110 (resolved-arg-type (substitute cs arg-type)))
111 ;; (display "lambda:\n\t")
116 ;; (display resolved-arg-type)
118 (list (car body-type-res)
121 (cadr body-type-res)))))
124 (let* ((arg-type-res (check env (cadr x)))
125 (arg-type (cadr arg-type-res))
126 (func-type-res (check env (car x)))
127 (func-type (cadr func-type-res))
130 (func-c (unify func-type
135 (consolidate func-c (car arg-type-res))
136 (car func-type-res)))
138 (resolved-func-type (substitute cs func-type))
139 (resolved-return-type (caddr resolved-func-type)))
140 ;; (display "app:\n")
143 ;; (display func-type)
145 ;; (display resolved-func-type)
147 ;; (display arg-type-res)
149 (if (abs? resolved-func-type)
150 (let ((return-type (substitute cs (caddr resolved-func-type))))
151 (list cs return-type))
152 (error #f "not a function")))))))
153 ;; (display "result of ")
156 ;; (display (cadr res))
158 ;; (display (car res))
161 (cadr (check '() (normalize prog))))
163 ; returns a list of pairs of constraints
165 (cond ((eq? a b) '())
166 ((or (tvar? a) (tvar? b)) (~ a b))
167 ((and (abs? a) (abs? b))
168 (consolidate (unify (cadr a) (cadr b))
169 (unify (caddr a) (caddr b))))
170 (else (error #f "could not unify"))))
172 ; TODO: what's the most appropriate substitution?
173 ; should all constraints just be limited to a pair?
174 (define (substitute cs t)
175 ; gets the first concrete type
176 ; otherwise returns the last type variable
178 (define (get-concrete c)
179 (let ((last (null? (cdr c))))
180 (if (not (tvar? (car c)))
182 (substitute cs (car c))
186 (get-concrete (cdr c))))))
189 (substitute cs (cadr t))
190 (substitute cs (caddr t))))
199 (define (substitute-env cs env)
200 (map (lambda (x) (cons (car x) (substitute cs (cdr x)))) env))
205 (define (consolidate x y)
209 (else (if (member (car b) a)
211 (cons (car b) (merge a (cdr b)))))))
212 (define (overlap? a b)
213 (if (or (null? a) (null? b))
215 (if (fold-left (lambda (acc v)
216 (or acc (eq? v (car a))))
219 (overlap? (cdr a) b))))
223 (else (let* ((a (car y))
233 (filter (lambda (b) (not (eq? b (cdr merged)))) x)
236 (consolidate removed (cons (car merged) (cdr y)))
237 (consolidate (cons a x) (cdr y)))))))