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Raphaël Cauderlier
Sigmaid
Commits
a990090b
Commit
a990090b
authored
Mar 29, 2016
by
Raphaël Cauderlier
Browse files
Replace the inductive subtyping relation by incusion because it has
better transitivity properties.
parent
47be8555
Changes
2
Hide whitespace changes
Inline
Side-by-side
dk_obj.sk
View file @
a990090b
...
...
@@ -43,7 +43,7 @@ def label := string.
def type := dk_type.type. (; type := list (label * type) ;)
def Ot_nil := dk_type.tnil.
def Ot_cons := dk_type.tcons.
def Ot_st := dk_type.s
t
.
def Ot_st := dk_type.s
ub
.
def Ot_domain_subtype := dk_type.domain_subtype.
def pos := dk_type.pos.
...
...
@@ -204,17 +204,18 @@ def coerce : A : type ->
select _ (coerce A B st a)
-->
(l : label => C : type => p : pos l C B =>
select A a l C (
dk_type.domain_subtype A B
st l C p)).
select A a l C (st l C p)).
[A,B,st,a]
update _ (coerce A B st a)
-->
(l : label => C : type => p : pos l C B => m : (Expr B -> Expr C) =>
coerce A B st
(update A a l C (
dk_type.domain_subtype A B
st l C p)
(update A a l C (st l C p)
(self : Expr A =>
m (coerce A B st self)))).
[A,B,C,stAB,stBC,a]
coerce B C stBC (coerce A _ stAB a)
-->
coerce A C (dk_type.s
t
_trans A B C stAB stBC) a.
coerce A C (dk_type.s
ub
_trans A B C stAB stBC) a.
dk_type.sk
View file @
a990090b
...
...
@@ -71,38 +71,57 @@ def st_cons_tail : A : type ->
[p] st_cons_pos _ _ _ _ (st_cons _ _ _ _ p _) --> p.
[Hst] st_cons_tail _ _ _ _ (st_cons _ _ _ _ _ Hst) --> Hst.
def sub (A : type) (B : type) := l : label -> C : type -> pos l C B -> pos l C A.
def domain_subtype : A : type ->
B : type ->
Hst : st A B ->
l : label ->
C : type ->
pos l C B ->
pos l C A.
sub A B.
[
A,l,A2,B2,Hst
]
domain_subtype
A (tcons l A2 B2) Hst
_ _ (at_head _ _ _)
[
p
]
domain_subtype
_ _ (st_cons _ _ _ _ p _)
_ _ (at_head _ _ _)
-->
st_cons_pos A l A2 B2 Hst
.
p
.
[A,
l2,A2,B2,Hst
,l,H,C]
domain_subtype
A (tcons l2 A2 B2) Hst
l C (in_tail _ _ _ _ _ H)
[A,
B2,tl
,l,H,C]
domain_subtype
_ _ (st_cons A _ _ B2 _ tl)
l C (in_tail _ _ _ _ _ H)
-->
domain_subtype A B2
(st_cons_tail A l2 A2 B2 Hst)
l C H.
domain_subtype A B2
tl
l C H.
def st_trans : A : type ->
B : type ->
C : type ->
stAB :
st A B ->
stBC :
st B C ->
st A B ->
st B C ->
st A C.
[A] st_trans A _
t
nil _
_
--> st_nil A
[A,B,stAB,lC,C1,C2,
stBC
]
st_trans A
B (t
cons lC C1 C2
) stAB stBC
(;
[A] st_trans A _
_ _ (st_
nil _
)
--> st_nil A
;)
[A,B,stAB,lC,C1,C2,
p,tl
]
st_trans A
_ _ stAB (st_
cons
B
lC C1 C2
p tl)
-->
st_cons
A
lC
C1
C2
(domain_subtype A B stAB lC C1 (st_cons_pos B lC C1 C2 stBC))
(st_trans A B C2 stAB (st_cons_tail B lC C1 C2 stBC)).
(domain_subtype A B stAB lC C1 p)
(st_trans A B C2 stAB tl).
def sub_trans : A : type ->
B : type ->
C : type ->
sub A B ->
sub B C ->
sub A C.
[stAB,stBC,l,D,p,C]
sub_trans _ _ C stAB stBC -->
(l : label => (D : type => (p : pos l D C => stAB l D (stBC l D p)))).
(; [A,B,C,stAB,stBC,l,D,p] ;)
(; domain_subtype A C (st_trans _ B _ stAB stBC) l D p --> ;)
(; domain_subtype A B stAB l D (domain_subtype B C stBC l D p). ;)
(; [A,B,C,D,stAB,stBC,stCD] ;)
(; st_trans A B D stAB (st_trans _ C _ stBC stCD) --> st_trans A C D (st_trans A B C stAB stBC) stCD. ;)
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