( I Cf j(I j ~ -- __ 0 -)1 ltyl shy
) I t shyI lt5 (12c1 1 JSl- 15- Art t c C
C- I middot Jd2 )- -J I-~J Co d l
(t 1
--1 ~ T
c-r -r
v- ~
A I - -I VCJ) e r J 5~f
I L
- L~1 CPu -~ c -=~+ Of ~Ic j of 1 u-J~ I -ZLLence cor (e5 poJj I - ~ ~ -t I
) UIJ - )( [J - X -1 - J(U) J
XI r tlj ~ y ~ - no J - ~ 1 shy) I Jshy
I
-shyJ= --
-+i~ jAJQ(Cll
-j L J == I I r) n ( [n-(1J XI [(J ~ ~ ( -(I 0 J
f D+S~--L r - ( 1- ( ) (lo
l Ll -
) -J C1 Jj Jshy(v rvJ VI [ 1 J
Y2 [ (I
L YI () b I bullJj
I
IIJ c - -
CD
ovA
~ x ll -I (J I Xl Cmiddot)J 1~= ~a Co 2 Ii jJ(L +(11() bull a)(~ [It)
~() -Iil1(~J - laquo x[1J-Iei2A (oj ~f~
nv) ~ (J == )( [IlJ -~ C -tJ
j(J +Jl-IJ= )( [~j
jlvJ =- Alj - JL -J
I
)
- 1 ~
l J _-I
-- v 7 - ~
- 1 1 r shy
-----
C) - d~[J ~ C( Al -+ Cl f1
--- shy-- ~laquo(- y -+ C-z(4)
IL
ZeJ -ip4 V-l)OISR CC- ~ obfoAIl cl ~ -- hO-P-lSlC(s s o (JA
bj ~ vc-IAcJi AJ JluL (cYS~~ J1AIlA- ~ li~ (ol1~1rlCgtU
~ [- j gt 1 [-1J gt
~ [ 0 J == 3 JL0 J t- lJ J [- 2J =- S J L- tJ -I 4 J [- 2)
~ Lmiddot - -3 ~ [ 1- J 4 ~ ( - lJ =- 3 J [0 J -I- q J[- J I )
d Go ~~- CD j(o) - C -Cz
(j(t) = - Ct -f 4C2
C -l CL ~ 3 jl-fJ -f -I J(-2J = 3x5 +~xo-=15
-C -+4Cz = 3)LoJ -f~J(-iJ -315 +1Y5= 65
~LnJ -= XlA ) - X(tl-]
(0) YC=e-) X=t) - 7-i Xt~
(b) Y(C)[iJ = X[J [I - 2J - i
1 -r
(c) F (2~AIl(j res pOflUL 15
HkJ~)= I~Ci) _ _jLv
I - e l = ~ltv
H (-e J I I
shyli
Jr1 2 J ) - (a L~ -+
) 2
1 7I I I - v_ J )J2 ( cJ -gt ~ bull bull I
)
~ - r- gt~) -+
1i I)j _ 2--2
I t IH[e ) -
w
bull
+ I
I ~ I I - v
w
(d) Ik e-IeA IS ~
~Nk~ ~
~ ~ l-nliJ _ cDmiddot
--
o d~iN~
271 ttLshy 3 7T efLr3 - ) Ii - Jz eXL~J~ L X (11) e - 2 x [~J
0 gt1=0
X[0J == - -e cgt + 2 -e 0 -t- 2 e v t
- J I- -JrrrX[J =- -f e +2 e + 2 e -t
X[2J - -l eO - 2 ej~ 2 e~ )ofT -+ r
r - - ]3~ -JiIFXl3) - - I e -t 2 e T 2 -e -z
I) - z-
0 rz [ I --y 2shyQ
-- () 7- 0I --
-~- ----I
o i l I 2shyI
I -e ~ It - )~
I e- = -( - J- 2fJ = -J-J
e) 3V _ i - 2 +2- ~- I 2shy
_r)11Tfz -t- I ~ = _(-4 2j _2 -j=--rj
( I - 2 j L - I shy
J-I J) bull I 0
J I ~ - ~ j_Jshy
~ l I - - -t l 1 J - shy
A ( - 0 J L f) - L I
shy
v)( C CcuV lX hI L) jAshy
MATLAi3
ro belYl 5
~ ~ - -gt rX - rxX [) = L
ltgt
J z - y z f-l = 2- ~r
I r I n - 2 r~ - 2 l - 2shy -=l-i I bull
2shy 2 2Z clt1 _shyI
I - ~ I - 0( ~-I 8
) I
- l ~
-3 -3
I I
~ ~
r- -=- A bull bull J
I fn 0lt- r
kshy I~I- 3 r+3 0 - t
- 3 ~ ~
- -2 0( zy ( ~ ~) shy lJ shy L
0 0
-3 ~ z ~
~ I --- ell SljJ ~ll
-- i t
I
lf I I ~ I -3 ~3
0lt pound I C 0
ovA
~ x ll -I (J I Xl Cmiddot)J 1~= ~a Co 2 Ii jJ(L +(11() bull a)(~ [It)
~() -Iil1(~J - laquo x[1J-Iei2A (oj ~f~
nv) ~ (J == )( [IlJ -~ C -tJ
j(J +Jl-IJ= )( [~j
jlvJ =- Alj - JL -J
I
)
- 1 ~
l J _-I
-- v 7 - ~
- 1 1 r shy
-----
C) - d~[J ~ C( Al -+ Cl f1
--- shy-- ~laquo(- y -+ C-z(4)
IL
ZeJ -ip4 V-l)OISR CC- ~ obfoAIl cl ~ -- hO-P-lSlC(s s o (JA
bj ~ vc-IAcJi AJ JluL (cYS~~ J1AIlA- ~ li~ (ol1~1rlCgtU
~ [- j gt 1 [-1J gt
~ [ 0 J == 3 JL0 J t- lJ J [- 2J =- S J L- tJ -I 4 J [- 2)
~ Lmiddot - -3 ~ [ 1- J 4 ~ ( - lJ =- 3 J [0 J -I- q J[- J I )
d Go ~~- CD j(o) - C -Cz
(j(t) = - Ct -f 4C2
C -l CL ~ 3 jl-fJ -f -I J(-2J = 3x5 +~xo-=15
-C -+4Cz = 3)LoJ -f~J(-iJ -315 +1Y5= 65
~LnJ -= XlA ) - X(tl-]
(0) YC=e-) X=t) - 7-i Xt~
(b) Y(C)[iJ = X[J [I - 2J - i
1 -r
(c) F (2~AIl(j res pOflUL 15
HkJ~)= I~Ci) _ _jLv
I - e l = ~ltv
H (-e J I I
shyli
Jr1 2 J ) - (a L~ -+
) 2
1 7I I I - v_ J )J2 ( cJ -gt ~ bull bull I
)
~ - r- gt~) -+
1i I)j _ 2--2
I t IH[e ) -
w
bull
+ I
I ~ I I - v
w
(d) Ik e-IeA IS ~
~Nk~ ~
~ ~ l-nliJ _ cDmiddot
--
o d~iN~
271 ttLshy 3 7T efLr3 - ) Ii - Jz eXL~J~ L X (11) e - 2 x [~J
0 gt1=0
X[0J == - -e cgt + 2 -e 0 -t- 2 e v t
- J I- -JrrrX[J =- -f e +2 e + 2 e -t
X[2J - -l eO - 2 ej~ 2 e~ )ofT -+ r
r - - ]3~ -JiIFXl3) - - I e -t 2 e T 2 -e -z
I) - z-
0 rz [ I --y 2shyQ
-- () 7- 0I --
-~- ----I
o i l I 2shyI
I -e ~ It - )~
I e- = -( - J- 2fJ = -J-J
e) 3V _ i - 2 +2- ~- I 2shy
_r)11Tfz -t- I ~ = _(-4 2j _2 -j=--rj
( I - 2 j L - I shy
J-I J) bull I 0
J I ~ - ~ j_Jshy
~ l I - - -t l 1 J - shy
A ( - 0 J L f) - L I
shy
v)( C CcuV lX hI L) jAshy
MATLAi3
ro belYl 5
~ ~ - -gt rX - rxX [) = L
ltgt
J z - y z f-l = 2- ~r
I r I n - 2 r~ - 2 l - 2shy -=l-i I bull
2shy 2 2Z clt1 _shyI
I - ~ I - 0( ~-I 8
) I
- l ~
-3 -3
I I
~ ~
r- -=- A bull bull J
I fn 0lt- r
kshy I~I- 3 r+3 0 - t
- 3 ~ ~
- -2 0( zy ( ~ ~) shy lJ shy L
0 0
-3 ~ z ~
~ I --- ell SljJ ~ll
-- i t
I
lf I I ~ I -3 ~3
0lt pound I C 0
-----
C) - d~[J ~ C( Al -+ Cl f1
--- shy-- ~laquo(- y -+ C-z(4)
IL
ZeJ -ip4 V-l)OISR CC- ~ obfoAIl cl ~ -- hO-P-lSlC(s s o (JA
bj ~ vc-IAcJi AJ JluL (cYS~~ J1AIlA- ~ li~ (ol1~1rlCgtU
~ [- j gt 1 [-1J gt
~ [ 0 J == 3 JL0 J t- lJ J [- 2J =- S J L- tJ -I 4 J [- 2)
~ Lmiddot - -3 ~ [ 1- J 4 ~ ( - lJ =- 3 J [0 J -I- q J[- J I )
d Go ~~- CD j(o) - C -Cz
(j(t) = - Ct -f 4C2
C -l CL ~ 3 jl-fJ -f -I J(-2J = 3x5 +~xo-=15
-C -+4Cz = 3)LoJ -f~J(-iJ -315 +1Y5= 65
~LnJ -= XlA ) - X(tl-]
(0) YC=e-) X=t) - 7-i Xt~
(b) Y(C)[iJ = X[J [I - 2J - i
1 -r
(c) F (2~AIl(j res pOflUL 15
HkJ~)= I~Ci) _ _jLv
I - e l = ~ltv
H (-e J I I
shyli
Jr1 2 J ) - (a L~ -+
) 2
1 7I I I - v_ J )J2 ( cJ -gt ~ bull bull I
)
~ - r- gt~) -+
1i I)j _ 2--2
I t IH[e ) -
w
bull
+ I
I ~ I I - v
w
(d) Ik e-IeA IS ~
~Nk~ ~
~ ~ l-nliJ _ cDmiddot
--
o d~iN~
271 ttLshy 3 7T efLr3 - ) Ii - Jz eXL~J~ L X (11) e - 2 x [~J
0 gt1=0
X[0J == - -e cgt + 2 -e 0 -t- 2 e v t
- J I- -JrrrX[J =- -f e +2 e + 2 e -t
X[2J - -l eO - 2 ej~ 2 e~ )ofT -+ r
r - - ]3~ -JiIFXl3) - - I e -t 2 e T 2 -e -z
I) - z-
0 rz [ I --y 2shyQ
-- () 7- 0I --
-~- ----I
o i l I 2shyI
I -e ~ It - )~
I e- = -( - J- 2fJ = -J-J
e) 3V _ i - 2 +2- ~- I 2shy
_r)11Tfz -t- I ~ = _(-4 2j _2 -j=--rj
( I - 2 j L - I shy
J-I J) bull I 0
J I ~ - ~ j_Jshy
~ l I - - -t l 1 J - shy
A ( - 0 J L f) - L I
shy
v)( C CcuV lX hI L) jAshy
MATLAi3
ro belYl 5
~ ~ - -gt rX - rxX [) = L
ltgt
J z - y z f-l = 2- ~r
I r I n - 2 r~ - 2 l - 2shy -=l-i I bull
2shy 2 2Z clt1 _shyI
I - ~ I - 0( ~-I 8
) I
- l ~
-3 -3
I I
~ ~
r- -=- A bull bull J
I fn 0lt- r
kshy I~I- 3 r+3 0 - t
- 3 ~ ~
- -2 0( zy ( ~ ~) shy lJ shy L
0 0
-3 ~ z ~
~ I --- ell SljJ ~ll
-- i t
I
lf I I ~ I -3 ~3
0lt pound I C 0
~LnJ -= XlA ) - X(tl-]
(0) YC=e-) X=t) - 7-i Xt~
(b) Y(C)[iJ = X[J [I - 2J - i
1 -r
(c) F (2~AIl(j res pOflUL 15
HkJ~)= I~Ci) _ _jLv
I - e l = ~ltv
H (-e J I I
shyli
Jr1 2 J ) - (a L~ -+
) 2
1 7I I I - v_ J )J2 ( cJ -gt ~ bull bull I
)
~ - r- gt~) -+
1i I)j _ 2--2
I t IH[e ) -
w
bull
+ I
I ~ I I - v
w
(d) Ik e-IeA IS ~
~Nk~ ~
~ ~ l-nliJ _ cDmiddot
--
o d~iN~
271 ttLshy 3 7T efLr3 - ) Ii - Jz eXL~J~ L X (11) e - 2 x [~J
0 gt1=0
X[0J == - -e cgt + 2 -e 0 -t- 2 e v t
- J I- -JrrrX[J =- -f e +2 e + 2 e -t
X[2J - -l eO - 2 ej~ 2 e~ )ofT -+ r
r - - ]3~ -JiIFXl3) - - I e -t 2 e T 2 -e -z
I) - z-
0 rz [ I --y 2shyQ
-- () 7- 0I --
-~- ----I
o i l I 2shyI
I -e ~ It - )~
I e- = -( - J- 2fJ = -J-J
e) 3V _ i - 2 +2- ~- I 2shy
_r)11Tfz -t- I ~ = _(-4 2j _2 -j=--rj
( I - 2 j L - I shy
J-I J) bull I 0
J I ~ - ~ j_Jshy
~ l I - - -t l 1 J - shy
A ( - 0 J L f) - L I
shy
v)( C CcuV lX hI L) jAshy
MATLAi3
ro belYl 5
~ ~ - -gt rX - rxX [) = L
ltgt
J z - y z f-l = 2- ~r
I r I n - 2 r~ - 2 l - 2shy -=l-i I bull
2shy 2 2Z clt1 _shyI
I - ~ I - 0( ~-I 8
) I
- l ~
-3 -3
I I
~ ~
r- -=- A bull bull J
I fn 0lt- r
kshy I~I- 3 r+3 0 - t
- 3 ~ ~
- -2 0( zy ( ~ ~) shy lJ shy L
0 0
-3 ~ z ~
~ I --- ell SljJ ~ll
-- i t
I
lf I I ~ I -3 ~3
0lt pound I C 0
--
o d~iN~
271 ttLshy 3 7T efLr3 - ) Ii - Jz eXL~J~ L X (11) e - 2 x [~J
0 gt1=0
X[0J == - -e cgt + 2 -e 0 -t- 2 e v t
- J I- -JrrrX[J =- -f e +2 e + 2 e -t
X[2J - -l eO - 2 ej~ 2 e~ )ofT -+ r
r - - ]3~ -JiIFXl3) - - I e -t 2 e T 2 -e -z
I) - z-
0 rz [ I --y 2shyQ
-- () 7- 0I --
-~- ----I
o i l I 2shyI
I -e ~ It - )~
I e- = -( - J- 2fJ = -J-J
e) 3V _ i - 2 +2- ~- I 2shy
_r)11Tfz -t- I ~ = _(-4 2j _2 -j=--rj
( I - 2 j L - I shy
J-I J) bull I 0
J I ~ - ~ j_Jshy
~ l I - - -t l 1 J - shy
A ( - 0 J L f) - L I
shy
v)( C CcuV lX hI L) jAshy
MATLAi3
ro belYl 5
~ ~ - -gt rX - rxX [) = L
ltgt
J z - y z f-l = 2- ~r
I r I n - 2 r~ - 2 l - 2shy -=l-i I bull
2shy 2 2Z clt1 _shyI
I - ~ I - 0( ~-I 8
) I
- l ~
-3 -3
I I
~ ~
r- -=- A bull bull J
I fn 0lt- r
kshy I~I- 3 r+3 0 - t
- 3 ~ ~
- -2 0( zy ( ~ ~) shy lJ shy L
0 0
-3 ~ z ~
~ I --- ell SljJ ~ll
-- i t
I
lf I I ~ I -3 ~3
0lt pound I C 0
ro belYl 5
~ ~ - -gt rX - rxX [) = L
ltgt
J z - y z f-l = 2- ~r
I r I n - 2 r~ - 2 l - 2shy -=l-i I bull
2shy 2 2Z clt1 _shyI
I - ~ I - 0( ~-I 8
) I
- l ~
-3 -3
I I
~ ~
r- -=- A bull bull J
I fn 0lt- r
kshy I~I- 3 r+3 0 - t
- 3 ~ ~
- -2 0( zy ( ~ ~) shy lJ shy L
0 0
-3 ~ z ~
~ I --- ell SljJ ~ll
-- i t
I
lf I I ~ I -3 ~3
0lt pound I C 0
![arXiv:2002.08874v1 [cs.LO] 20 Feb 2020Fig.1. Sort inference rules. 2.1 Syntax c:: = j j k j x j j j j (1) j j k j x j j j j (2) j j jc c jc;c (3) The syntax of the calculus, generated](https://static.documents.pub/doc/80x56/5f1dc7e7e96ebd77263b89bc/arxiv200208874v1-cslo-20-feb-2020-fig1-sort-inference-rules-21-syntax-c.jpg)
