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A Simple Algorithm And Proof For Type Inference

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November 2018
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AX! #+g \] T?-/ ] YTL%Z[TVO %(A :=<4>@'^_H`3Fa14^G3Fbc:c@8E?ad5 e ] 'eX 'Tf M H L L C H L O H R R ± ² : < 9 Z , < 6 9 S , < < C ^ M @ [ S Ê 4 M @ ] ´ J = > < Z Á @ Y 6 , < S 7 4 B S 7 4 Z D , < « ¾ ] B > < Â D 7 4 B Y 6 : < Z M @ = · @ M _ ½ µ W H 6Y<®6Y:@C6¼6Y:BBf69DZ <,D»HCL 6 H <><>Z9DÒZ¥B6Y:H <6P ´#S <ÞHMPFÐ µH Z[<>47=J69= 4¹.H 6`_BÁP 6Y<>:D@CÑ647@¼B¬6Y<,69:S O < R 4JZ Z R @M<>= =7=µ ¹.6`@_ _MP ½e<>Dg ³ µ P L R H ³ # g J 4 N Z @ M @ [ S 9 6 Ê 4 M @ = B w 8 Y 6 4 B 4 Y 6 : ¾ B 7 4 9 6 < Å µ D H2O @M47B½ P P # g 7 4 h Z A @ Y 6 9 S 4 J = È < Ó [ w Õ i : > < [ S < Ç 7 4 h Z È @ ` 6 _ < Å µ @6YM4<¼6Y:D <,H2S¸O 6`_@C4JP B <>D HCL H åS R 47ZBf6`47Z¹ µ HML ½ H H H H O ² ± : h < Ê = M @ X Z ® 6 8 B D 4 Y 6 4 A B J 4 A B 9 6 : J 4 ® Z ] D , < « ¾ B 4 Y 6 4 È B J 4 Á Z Â @ 9 6 > < ; 8 : ] B J 4 · 8 C @ = B < : 7 4 ; 8 : M @ C à > < Á Z Y 6 ] : < µ P S HVHML Z²Z[=J47K2:f6Y=7_ÀB<>@C6Y<,S>½ L H H L C H L Ü ? < 9 S 4 Y 6 < S 9 S , < [ Z 9 6 9 S J 4 w 8 Y 6 , < D 6 Y 6 : < 9 S , < ¸ < C ^ M @ [ S Ê 4 M @ ] ´ J = > < Z ½ Þ ? < 9 S 7 4 9 6 < Á Ö µ µ L 6YH :]S²<6Y6`:]_ 4Ê@6Y<>D µ 4769: P R L H P O R R L ? ¼ < ] B w < 0 Ã ! 6 2 K 7 4 M ^ n < Y 6 : n < ` 6 _ 7 4 B e K S 7 = > < Z I S 9 6 : n < ` 6 _ , < 5 D J = @ # ´ « D ® @ · 8 C @ J = 8 = , Z ½ 9 6 : < M @ [ Z 9 Z > < S ¹ 6Y6Y4:H @CBÏ6 Ó :«@CZ 6`[_ÕnP 4J´S)=7<Z>Z9i :µ @M< =J=0µZ9<,S9S O 47BZ HML 6Y:< L S9<,<¼^M@CS94Ê@C´=J<,Z²4JB µ ½ ±²:<6`_ P 4JBKeS R =J<>Z L H =7= H µ 6Y:]<D]<,¾«B46Y4 H B HML ³ ³ µ :<,S9< ÁÓ FÕ ³ ³ ÞÓ +Õ ³ ³ Ó ÁÖ Ü Õ AÓ ³ Õ ³ ±6Y²::@C<Á66`476_ P 47B/Z!OQ@eP 69=J4<>H K2BÌ@M=F47B+6`_ 6YP :<Z[½ 4JZ HML 6Y:<Á=J@MZ[6nS R =7<Á4JZnD<,Z947K2B<>D¬6 H <,BZ R S9< H SÁL 6`H _ P <+47B L <>S[<>B8,<,S9B<,D P µ 4769: 6Y:]<ÂH 8 H S9L S9H <,Z P#R H BDP47BKD]<>D O R 8w6Y4 H B Ø O Z[_0:ZX476Y8;< : 69:<¼S 6`_ 'P i<474JB B L µ H S:O 478;@: 6Y4 µ H B»<5:«D@M<·Z@C= ´#<>µ <,4B56Y: <,SY6`@M_ Z[<><ÌD ³ @MZ[Z9<>SX6Y4 BZ S Bf6`_ <>D6Y<,S Z>i²47B ] ] :=@\36545N@8E?:,7 :=@&36545 a&> =: 7 :=@ Z[A d4'T 36545N@8E?:=7 T T \T d4'T S T T ] Y T T W µ TVOPW TL Z TL TL%! 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HML '½ 10 -¬TVZ HML /.!6 HH 69:<>S¥D4JZX6Y47B8,6Ú6`_ P ½ R 6 !7 *- L ' / i Y 6 : , S µ 47Z9@M=7<,=7Z>69i<Ì@M47Z²6 Z L P S <,H28>O 47¾<>'eDÂiU47B @MB@MD B @MDDÍ6 H @MBÓ9D 6 H ' ´#<BZ < Rµ PP ^M=7<>4J<,S9D 4¾«=J8·@C@6Y6Y<,4 S;H ÕzB ½ D> ?E 7 987/> 3FH :=@ ' > : I ' 7 :=7=3FH 7 N3F:,7 > :c@c> ! P? 6'T ! 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A Simple Algorithm And Proof For Type Inference

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