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ocaml-hm-ctor-env registers None/Some : 'a -> 'a option, Ok/Error :
'a -> ('a, 'b) result. :con NAME instantiates the scheme; :pcon NAME
ARG-PATS walks arg patterns through the constructor's arrow type,
unifying each.
Pretty-printer renders 'Int option' and '(Int, 'b) result'.
Examples now infer:
fun x -> Some x : 'a -> 'a option
match Some 5 with | None -> 0 | Some n -> n : Int
fun o -> match o with | None -> 0 | Some n -> n : Int option -> Int
Ok 1 : (Int, 'b) result
Error "oops" : ('a, String) result
User type-defs would extend the registry — pending.
447 lines
19 KiB
Plaintext
447 lines
19 KiB
Plaintext
;; lib/ocaml/infer.sx — Algorithm W type inference for OCaml-on-SX.
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;;
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;; Consumes lib/guest/hm.sx (algebra) and lib/guest/match.sx (unify) per
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;; the Phase 5 sequencing. The kit ships fresh-tv, generalize,
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;; instantiate, and substitution composition; this file assembles the
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;; lambda / app / let / if rules of Algorithm W against the OCaml AST.
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;;
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;; Coverage in this slice (atoms + core forms):
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;; :int :float :string :char :bool :unit :var :fun :app :let :if
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;; :op (with builtin signatures for +, -, *, /, mod, comparisons, &&, ||)
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;;
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;; Out of scope: pattern matching, tuples, lists (need product/list types
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;; first), records, modules, ADTs, let-rec.
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;;
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;; Inference state:
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;; env — dict: name → scheme
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;; counter — one-element list (mutable cell) used by hm-fresh-tv
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;;
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;; Returned value: {:subst S :type T}.
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(define ocaml-hm-counter (fn () (list 0)))
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(define ocaml-hm-empty-subst (fn () {}))
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;; A registry of constructor types so :con / :pcon can be inferred.
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;; OCaml's stdlib ctors are seeded here; user type-defs would extend
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;; this in a future iteration.
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(define ocaml-hm-ctor-env
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(fn ()
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(let ((a (hm-tv "a")) (b (hm-tv "b")))
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(let ((opt-of-a (hm-con "option" (list a)))
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(res-of-ab (hm-con "result" (list a b))))
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{"None" (hm-scheme (list "a") opt-of-a)
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"Some" (hm-scheme (list "a") (hm-arrow a opt-of-a))
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"Ok" (hm-scheme (list "a" "b") (hm-arrow a res-of-ab))
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"Error" (hm-scheme (list "a" "b") (hm-arrow b res-of-ab))
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"true" (hm-monotype (hm-bool))
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"false" (hm-monotype (hm-bool))}))))
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(define ocaml-hm-builtin-env
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(fn ()
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(let ((int-int-int (hm-arrow (hm-int) (hm-arrow (hm-int) (hm-int))))
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(int-int-bool (hm-arrow (hm-int) (hm-arrow (hm-int) (hm-bool))))
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(bool-bool-bool (hm-arrow (hm-bool) (hm-arrow (hm-bool) (hm-bool))))
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(str-str-str (hm-arrow (hm-string) (hm-arrow (hm-string) (hm-string))))
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(any-any-bool
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(let ((a (hm-tv "a")))
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(hm-scheme (list "a")
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(hm-arrow a (hm-arrow a (hm-bool))))))
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(a->a
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(let ((a (hm-tv "a")))
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(hm-scheme (list "a") (hm-arrow a a)))))
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{"+" (hm-monotype int-int-int)
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"-" (hm-monotype int-int-int)
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"*" (hm-monotype int-int-int)
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"/" (hm-monotype int-int-int)
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"mod" (hm-monotype int-int-int)
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"%" (hm-monotype int-int-int)
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"**" (hm-monotype int-int-int)
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"<" (hm-monotype int-int-bool)
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">" (hm-monotype int-int-bool)
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"<=" (hm-monotype int-int-bool)
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">=" (hm-monotype int-int-bool)
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"=" any-any-bool
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"<>" any-any-bool
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"&&" (hm-monotype bool-bool-bool)
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"||" (hm-monotype bool-bool-bool)
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"^" (hm-monotype str-str-str)
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"not" (hm-monotype (hm-arrow (hm-bool) (hm-bool)))
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"succ" (hm-monotype (hm-arrow (hm-int) (hm-int)))
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"pred" (hm-monotype (hm-arrow (hm-int) (hm-int)))
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"abs" (hm-monotype (hm-arrow (hm-int) (hm-int)))})))
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(define ocaml-infer (fn (expr env counter) nil))
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;; Unify two types; raise on failure. The match.sx unify returns nil on
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;; failure so we wrap it for clearer errors.
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(define ocaml-hm-unify
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(fn (t1 t2 subst)
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(let ((s2 (unify t1 t2 subst)))
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(cond
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((= s2 nil)
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(error (str "ocaml-infer: cannot unify " t1 " with " t2)))
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(else s2)))))
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;; Look up name; instantiate scheme to a fresh monotype.
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(define ocaml-infer-var
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(fn (name env counter)
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(cond
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((has-key? env name)
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(let ((scheme (get env name)))
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(let ((t (hm-instantiate scheme counter)))
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{:subst {} :type t})))
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(else (error (str "ocaml-infer: unbound variable " name))))))
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(define ocaml-infer-app
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(fn (fn-expr arg-expr env counter)
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(let ((r1 (ocaml-infer fn-expr env counter)))
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(let ((s1 (get r1 :subst)) (t1 (get r1 :type)))
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(let ((env2 (hm-apply-env s1 env)))
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(let ((r2 (ocaml-infer arg-expr env2 counter)))
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(let ((s2 (get r2 :subst)) (t2 (get r2 :type)))
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(let ((tv (hm-fresh-tv counter)))
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(let ((s3 (ocaml-hm-unify
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(hm-apply s2 t1)
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(hm-arrow t2 tv)
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(hm-compose s2 s1))))
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{:subst s3 :type (hm-apply s3 tv)})))))))))
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(define ocaml-infer-fun
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(fn (params body env counter)
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(cond
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((= (len params) 0)
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(error "ocaml-infer: fun without params"))
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((= (len params) 1)
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(let ((tv (hm-fresh-tv counter)))
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(let ((env2 (assoc env (first params) (hm-monotype tv))))
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(let ((r (ocaml-infer body env2 counter)))
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(let ((s (get r :subst)) (t-body (get r :type)))
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{:subst s
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:type (hm-arrow (hm-apply s tv) t-body)})))))
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(else
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;; Curry: fun x y -> e ≡ fun x -> fun y -> e
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(let ((tv (hm-fresh-tv counter)))
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(let ((env2 (assoc env (first params) (hm-monotype tv))))
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(let ((r (ocaml-infer-fun (rest params) body env2 counter)))
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(let ((s (get r :subst)) (t-rest (get r :type)))
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{:subst s
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:type (hm-arrow (hm-apply s tv) t-rest)}))))))))
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(define ocaml-infer-let
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(fn (name params rhs body env counter)
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(let ((rhs-expr (cond
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((= (len params) 0) rhs)
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(else (list :fun params rhs)))))
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(let ((r1 (ocaml-infer rhs-expr env counter)))
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(let ((s1 (get r1 :subst)) (t1 (get r1 :type)))
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(let ((env2 (hm-apply-env s1 env)))
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(let ((scheme (hm-generalize t1 env2)))
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(let ((env3 (assoc env2 name scheme)))
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(let ((r2 (ocaml-infer body env3 counter)))
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(let ((s2 (get r2 :subst)) (t2 (get r2 :type)))
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{:subst (hm-compose s2 s1) :type t2}))))))))))
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(define ocaml-infer-if
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(fn (c-ast t-ast e-ast env counter)
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(let ((rc (ocaml-infer c-ast env counter)))
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(let ((sc (get rc :subst)) (tc (get rc :type)))
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(let ((sc2 (ocaml-hm-unify tc (hm-bool) sc)))
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(let ((env2 (hm-apply-env sc2 env)))
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(let ((rt (ocaml-infer t-ast env2 counter)))
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(let ((st (get rt :subst)) (tt (get rt :type)))
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(let ((env3 (hm-apply-env st env2)))
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(let ((re (ocaml-infer e-ast env3 counter)))
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(let ((se (get re :subst)) (te (get re :type)))
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(let ((sf (ocaml-hm-unify
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(hm-apply se tt)
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te
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(hm-compose se (hm-compose st sc2)))))
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{:subst sf
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:type (hm-apply sf te)}))))))))))))
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;; Tuple type: (hm-con "*" (list T1 T2 ...)).
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(define ocaml-hm-tuple
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(fn (types) (hm-con "*" types)))
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;; List type: (hm-con "list" (list ELEM)).
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(define ocaml-hm-list
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(fn (elem) (hm-con "list" (list elem))))
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(define ocaml-infer-tuple
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(fn (items env counter)
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(let ((subst {}) (types (list)))
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(begin
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(define loop
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(fn (xs env-cur)
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(when (not (= xs (list)))
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(let ((r (ocaml-infer (first xs) env-cur counter)))
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(let ((s (get r :subst)) (t (get r :type)))
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(begin
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(set! subst (hm-compose s subst))
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(append! types t)
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(loop (rest xs) (hm-apply-env s env-cur))))))))
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(loop items env)
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{:subst subst
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:type (ocaml-hm-tuple
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(map (fn (t) (hm-apply subst t)) types))}))))
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;; Pattern type inference. Returns {:type T :env ENV2 :subst S} where
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;; ENV2 is the original env extended with any names the pattern binds.
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;; Constructor patterns aren't supported here yet (need a type-def
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;; registry) — :pcon falls through to a fresh tv so they don't break
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;; inference of mixed clauses.
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(define ocaml-infer-pcon
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(fn (name arg-pats env counter)
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(cond
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((has-key? ocaml-hm-ctors name)
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(let ((ctor-type (hm-instantiate (get ocaml-hm-ctors name) counter))
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(env-cur env) (subst {}))
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(let ((cur-type (list nil)))
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(begin
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(set-nth! cur-type 0 ctor-type)
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(define loop
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(fn (xs)
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(when (not (= xs (list)))
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(let ((rp (ocaml-infer-pat (first xs) env-cur counter)))
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(let ((arg-tv (hm-fresh-tv counter))
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(res-tv (hm-fresh-tv counter)))
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(let ((s1 (ocaml-hm-unify
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(nth cur-type 0)
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(hm-arrow arg-tv res-tv)
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(hm-compose (get rp :subst) subst))))
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(let ((s2 (ocaml-hm-unify
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(hm-apply s1 arg-tv)
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(hm-apply s1 (get rp :type))
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s1)))
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(begin
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(set! subst s2)
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(set-nth! cur-type 0 (hm-apply s2 res-tv))
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(set! env-cur (get rp :env))
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(loop (rest xs))))))))))
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(loop arg-pats)
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{:type (hm-apply subst (nth cur-type 0))
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:env env-cur
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:subst subst}))))
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(else
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(let ((tv (hm-fresh-tv counter)))
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{:type tv :env env :subst {}})))))
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(define ocaml-infer-pat
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(fn (pat env counter)
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(let ((tag (nth pat 0)))
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(cond
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((= tag "pwild")
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(let ((tv (hm-fresh-tv counter)))
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{:type tv :env env :subst {}}))
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((= tag "pvar")
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(let ((nm (nth pat 1)) (tv (hm-fresh-tv counter)))
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{:type tv :env (assoc env nm (hm-monotype tv)) :subst {}}))
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((= tag "plit")
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(let ((r (ocaml-infer (nth pat 1) env counter)))
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{:type (get r :type) :env env :subst (get r :subst)}))
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((= tag "pcons")
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(let ((rh (ocaml-infer-pat (nth pat 1) env counter)))
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(let ((rt (ocaml-infer-pat (nth pat 2) (get rh :env) counter)))
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(let ((s (ocaml-hm-unify
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(ocaml-hm-list (get rh :type))
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(get rt :type)
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(hm-compose (get rt :subst) (get rh :subst)))))
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{:type (hm-apply s (ocaml-hm-list (get rh :type)))
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:env (get rt :env)
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:subst s}))))
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((= tag "plist")
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(let ((items (rest pat)) (tv (hm-fresh-tv counter)) (env-cur env) (subst {}))
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(begin
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(define loop
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(fn (xs)
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(when (not (= xs (list)))
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(let ((rp (ocaml-infer-pat (first xs) env-cur counter)))
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(let ((s (ocaml-hm-unify
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(hm-apply (get rp :subst) tv)
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(get rp :type)
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(hm-compose (get rp :subst) subst))))
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(begin
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(set! subst s)
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(set! env-cur (get rp :env))
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(loop (rest xs))))))))
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(loop items)
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{:type (hm-apply subst (ocaml-hm-list tv))
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:env env-cur
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:subst subst})))
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((= tag "ptuple")
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(let ((items (rest pat)) (env-cur env) (subst {}) (types (list)))
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(begin
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(define loop
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(fn (xs)
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(when (not (= xs (list)))
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(let ((rp (ocaml-infer-pat (first xs) env-cur counter)))
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(begin
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(set! subst (hm-compose (get rp :subst) subst))
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(append! types (get rp :type))
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(set! env-cur (get rp :env))
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(loop (rest xs)))))))
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(loop items)
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{:type (ocaml-hm-tuple
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(map (fn (t) (hm-apply subst t)) types))
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:env env-cur
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:subst subst})))
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((= tag "pas")
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(let ((rp (ocaml-infer-pat (nth pat 1) env counter)))
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(let ((alias (nth pat 2)))
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{:type (get rp :type)
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:env (assoc (get rp :env) alias (hm-monotype (get rp :type)))
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:subst (get rp :subst)})))
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((= tag "pcon")
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(ocaml-infer-pcon (nth pat 1) (rest (rest pat)) env counter))
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(else
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(let ((tv (hm-fresh-tv counter)))
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{:type tv :env env :subst {}}))))))
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(define ocaml-infer-match
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(fn (scrut clauses env counter)
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(let ((rs (ocaml-infer scrut env counter)))
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(let ((s (get rs :subst)) (st (get rs :type)) (result-tv (hm-fresh-tv counter)))
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(let ((subst s))
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(begin
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(define loop
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(fn (cs)
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(when (not (= cs (list)))
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(let ((clause (first cs)))
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(let ((ctag (nth clause 0)))
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(let ((p (nth clause 1))
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(body (cond
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((= ctag "case") (nth clause 2))
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(else (nth clause 3)))))
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(let ((rp (ocaml-infer-pat p (hm-apply-env subst env) counter)))
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(let ((s1 (ocaml-hm-unify
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(hm-apply (get rp :subst) st)
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(get rp :type)
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(hm-compose (get rp :subst) subst))))
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(let ((rb (ocaml-infer body
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(hm-apply-env s1 (get rp :env)) counter)))
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(let ((s2 (ocaml-hm-unify
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(hm-apply (get rb :subst) result-tv)
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(get rb :type)
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(hm-compose (get rb :subst) s1))))
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(begin
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(set! subst s2)
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(loop (rest cs)))))))))))))
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(loop clauses)
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{:subst subst :type (hm-apply subst result-tv)}))))))
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(define ocaml-infer-list
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(fn (items env counter)
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(cond
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((= (len items) 0)
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{:subst {} :type (ocaml-hm-list (hm-fresh-tv counter))})
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(else
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(let ((subst {}) (elem-tv (hm-fresh-tv counter)))
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(begin
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(define loop
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(fn (xs env-cur)
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(when (not (= xs (list)))
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(let ((r (ocaml-infer (first xs) env-cur counter)))
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(let ((s (get r :subst)) (t (get r :type)))
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(let ((s2 (ocaml-hm-unify
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(hm-apply s elem-tv)
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t
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(hm-compose s subst))))
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(begin
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(set! subst s2)
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(loop (rest xs) (hm-apply-env s2 env-cur)))))))))
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(loop items env)
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{:subst subst
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:type (ocaml-hm-list (hm-apply subst elem-tv))}))))))
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(define ocaml-hm-ctors (ocaml-hm-ctor-env))
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(set! ocaml-infer
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(fn (expr env counter)
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(let ((tag (nth expr 0)))
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(cond
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((= tag "con")
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;; (:con NAME) — look up constructor type, instantiate fresh.
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(let ((name (nth expr 1)))
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(cond
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((has-key? ocaml-hm-ctors name)
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{:subst {}
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:type (hm-instantiate (get ocaml-hm-ctors name) counter)})
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(else
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;; Unknown ctor — treat as a fresh polymorphic type.
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{:subst {} :type (hm-fresh-tv counter)}))))
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((= tag "int") {:subst {} :type (hm-int)})
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((= tag "float") {:subst {} :type (hm-int)}) ;; treat float as int for now
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((= tag "string") {:subst {} :type (hm-string)})
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((= tag "char") {:subst {} :type (hm-string)})
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((= tag "bool") {:subst {} :type (hm-bool)})
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((= tag "unit") {:subst {} :type (hm-con "Unit" (list))})
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((= tag "var") (ocaml-infer-var (nth expr 1) env counter))
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((= tag "fun") (ocaml-infer-fun (nth expr 1) (nth expr 2) env counter))
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((= tag "app") (ocaml-infer-app (nth expr 1) (nth expr 2) env counter))
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((= tag "let") (ocaml-infer-let (nth expr 1) (nth expr 2)
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(nth expr 3) (nth expr 4) env counter))
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((= tag "if") (ocaml-infer-if (nth expr 1) (nth expr 2)
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(nth expr 3) env counter))
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((= tag "tuple") (ocaml-infer-tuple (rest expr) env counter))
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((= tag "list") (ocaml-infer-list (rest expr) env counter))
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((= tag "match") (ocaml-infer-match (nth expr 1) (nth expr 2) env counter))
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((= tag "neg")
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(let ((r (ocaml-infer (nth expr 1) env counter)))
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(let ((s (get r :subst)) (t (get r :type)))
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(let ((s2 (ocaml-hm-unify t (hm-int) s)))
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{:subst s2 :type (hm-int)}))))
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((= tag "not")
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(let ((r (ocaml-infer (nth expr 1) env counter)))
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(let ((s (get r :subst)) (t (get r :type)))
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(let ((s2 (ocaml-hm-unify t (hm-bool) s)))
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{:subst s2 :type (hm-bool)}))))
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((= tag "op")
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;; Treat (:op OP L R) as (:app (:app (:var OP) L) R) — same rule.
|
|
(ocaml-infer
|
|
(list :app (list :app (list :var (nth expr 1)) (nth expr 2)) (nth expr 3))
|
|
env counter))
|
|
(else (error (str "ocaml-infer: unsupported tag " tag)))))))
|
|
|
|
;; Top-level convenience: parse + infer + render the type.
|
|
(define ocaml-type-of
|
|
(fn (src)
|
|
(let ((expr (ocaml-parse src))
|
|
(env (ocaml-hm-builtin-env))
|
|
(counter (ocaml-hm-counter)))
|
|
(let ((r (ocaml-infer expr env counter)))
|
|
(ocaml-hm-format-type (hm-apply (get r :subst) (get r :type)))))))
|
|
|
|
;; Pretty-print a type as an OCaml-style string for testing. Only handles
|
|
;; the constructors we use: Int / Bool / String / Unit / -> / type-vars.
|
|
(define ocaml-hm-format-type
|
|
(fn (t)
|
|
(cond
|
|
((is-var? t) (str "'" (var-name t)))
|
|
((is-ctor? t)
|
|
(let ((head (ctor-head t)) (args (ctor-args t)))
|
|
(cond
|
|
((= head "->")
|
|
(let ((a (nth args 0)) (b (nth args 1)))
|
|
(str
|
|
(cond
|
|
((and (is-ctor? a) (= (ctor-head a) "->"))
|
|
(str "(" (ocaml-hm-format-type a) ")"))
|
|
(else (ocaml-hm-format-type a)))
|
|
" -> " (ocaml-hm-format-type b))))
|
|
((= head "*")
|
|
(let ((parts (map ocaml-hm-format-type args)))
|
|
(join " * " parts)))
|
|
((= head "list")
|
|
(let ((elem (ocaml-hm-format-type (nth args 0))))
|
|
(str elem " list")))
|
|
((= head "option")
|
|
(let ((elem (ocaml-hm-format-type (nth args 0))))
|
|
(str elem " option")))
|
|
((= head "result")
|
|
(let ((a (ocaml-hm-format-type (nth args 0)))
|
|
(b (ocaml-hm-format-type (nth args 1))))
|
|
(str "(" a ", " b ") result")))
|
|
(else head))))
|
|
(else (str t)))))
|