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(use-modules (ice-9 match)
(srfi srfi-1)
(srfi srfi-9))
(define-record-type <named-type>
(make-named-type name)
named-type?
(name named-type-name))
(define-record-type <variable-type>
(make-variable-type name)
variable-type?
(name variable-type-name))
(define-record-type <function-type>
(make-function-type from to)
function-type?
(from function-type-from)
(to function-type-to))
(define (make-function-type* . types)
(reduce-right make-function-type #f types))
(define int (make-named-type 'int))
(define bool (make-named-type 'bool))
(define unique-counter (make-parameter 0))
(define (unique-number)
(let ((n (unique-counter)))
(unique-counter (+ n 1))
n))
(define* (unique-identifier #:optional (prefix 'T))
(string->symbol
(format #f "~a~a" prefix (unique-number))))
(define (make-fresh-variable-type)
(make-variable-type (unique-identifier)))
(define (substitute-type subs type)
(cond
((named-type? type)
type)
((variable-type? type)
(or (assq-ref subs type) type))
((function-type? type)
(let* ((from (function-type-from type))
(to (function-type-to type))
(from* (substitute-type subs from))
(to* (substitute-type subs to)))
(if (and (eq? from from*) (eq? to to*))
type
(make-function-type from* to*))))))
(define (substitute-env subs env)
(map (match-lambda
((name . type)
(cons name (substitute-type subs type))))
env))
(define (substitute-constraints subs constraints)
(map (match-lambda
((a . b)
(cons (substitute-type subs a) (substitute-type subs b))))
constraints))
(define (contains? a b)
(cond
((variable-type? a)
(eq? a b))
((named-type? a) #f)
((function-type? a)
(or (contains? (function-type-from a) b)
(contains? (function-type-to a) b)))))
(define (make-constraints exp env)
(match exp
((and (? number?) (? exact-integer?))
(values (list (cons exp int)) '()))
((? boolean?)
(values (list (cons exp bool)) '()))
((? symbol?)
(values (list (cons exp
(or (assq-ref env exp)
(error "unbound variable" exp))))
'()))
(('lambda (arg) body)
(define arg-type (make-fresh-variable-type))
(define-values (body-env body-constraints)
(make-constraints body (alist-cons arg arg-type env)))
(values (cons* (cons exp (make-function-type arg-type
(assq-ref body-env body)))
(cons arg arg-type)
body-env)
body-constraints))
(('if test consequent alternate)
(define-values (test-env test-constraints)
(make-constraints test env))
(define-values (consequent-env consequent-constraints)
(make-constraints consequent env))
(define-values (alternate-env alternate-constraints)
(make-constraints alternate env))
(values (cons (cons exp (assq-ref consequent-env consequent))
(append test-env
consequent-env
alternate-env
env))
(append (list (cons (assq-ref test-env test) bool)
(cons (assq-ref consequent-env consequent)
(assq-ref alternate-env alternate)))
test-constraints
consequent-constraints
alternate-constraints)))
((proc args ...)
(define-values (%arg-envs %arg-constraints)
(unzip2
(map (lambda (arg)
(call-with-values (lambda ()
(make-constraints arg env))
list))
args)))
(define arg-env (concatenate %arg-envs))
(define arg-constraints (concatenate %arg-constraints))
(define-values (proc-env proc-constraints)
(make-constraints proc env))
(define return-type (make-fresh-variable-type))
(define call-type
(fold-right make-function-type return-type
(map (lambda (arg)
(assq-ref arg-env arg))
args)))
(values (append (list (cons exp return-type))
proc-env
arg-env)
(append (list (cons (assq-ref proc-env proc) call-type))
proc-constraints
arg-constraints)))
(_
(error "invalid expression" exp))))
(define %default-env
`((not . ,(make-function-type bool bool))
(add1 . ,(make-function-type int int))
(sub1 . ,(make-function-type int int))
(+ . ,(make-function-type* int int int))
(- . ,(make-function-type* int int int))
(* . ,(make-function-type* int int int))
(/ . ,(make-function-type* int int int))
(= . ,(make-function-type* int int bool))
(< . ,(make-function-type* int int bool))
(<= . ,(make-function-type* int int bool))
(> . ,(make-function-type* int int bool))
(>= . ,(make-function-type* int int bool))))
(define (make-constraints* exp)
(parameterize ((unique-counter 0))
(define-values (env constraints)
(make-constraints exp %default-env))
(values (delete-duplicates env) constraints)))
(define (unify a b)
(define (sub-var var type)
(cond
;; Type is also a variable, so we can't do anything.
((eq? var type)
'())
;; Variable appears within type, which is not allowed.
((contains? type var)
(error "circular reference" var type))
(else
(list (cons var type)))))
(cond
;; A and B are the same simple type (like int or bool.)
((and (named-type? a) (named-type? b) (eq? a b))
'())
;; A or B is a type variable.
((variable-type? a)
(sub-var a b))
((variable-type? b)
(sub-var b a))
;; A and B are function types.
((and (function-type? a) (function-type? b))
(let* ((a-subs (unify (function-type-from a) (function-type-from b)))
(b-subs (unify (substitute-type a-subs (function-type-to a))
(substitute-type a-subs (function-type-to b)))))
(append a-subs b-subs)))
;; Oh no.
(else
(error "type mismtach" a b))))
;; Successively transform the type environment by applying
;; constraints. If there are no type mismatches or other errors then
;; a new type environment in which all type variables have been
;; removed is returned.
(define (solve-constraints env constraints)
(match constraints
(() env)
(((a . b) . rest)
;; First, attempt to unify the 2 types in the constraint and get
;; the substitutions that unification creates. Subsitutions need
;; to be applied to the type environment *and* the remaining
;; constraints.
(let* ((new-subs (unify a b)))
(solve-constraints (substitute-env new-subs env)
(substitute-constraints new-subs rest))))))
(define (infer exp)
(define-values (env constraints)
(make-constraints* exp))
(assq-ref (solve-constraints env constraints) exp))
(define (test-equal a b)
(unless (equal? a b)
(error "fail:" a b)))
(test-equal (infer 6) int)
(test-equal (infer #t) bool)
(test-equal (infer #f) bool)
(test-equal (false-if-exception (infer 'x)) #f)
(test-equal (infer '(lambda (x) (not x))) (make-function-type bool bool))
(test-equal (infer '((lambda (x) x) 6)) int)
(test-equal (infer '((lambda (x) (if (not #t) (add1 x) (sub1 x))) 1)) int)
(test-equal (false-if-exception (infer '((lambda (x) (if #t 1 x)) #f))) #f)
(test-equal (infer '((lambda (x) (+ 1 x)) 2)) int)
(test-equal (infer '((lambda (x) (= 1 x)) 2)) bool)
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