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Signature symbols in this unit

Symbol	Specification	Kind	Type
# .	map	f	Map[A, B] → Nat
# .	set-basic	f	Set[A] → Nat
# .	list-data	f	List[A] → Nat
. '	list	f	A → List[A]
. ( . )	map	pf	Map[A, B] × A → B with λ st, a. a ∈ st
. ( . := . )	map	f	Map[A, B] × A × B → Map[A, B]
. * .	map-sep	f	(Map[A, B] → Bool) × (Map[A, B] → Bool) → Map[A, B] → Bool
. + .	nat-basic	f	Nat × Nat → Nat
. + .	list-data	f	A × List[A] → List[A]
. + .	list	f	List[A] × List[A] → List[A]
. + .	list	f	List[A] × A → List[A]
. ++ .	set-basic	f	Set[A] × A → Set[A]
. ++ .	list-dup	f	List[A] × A → List[A]
. +1	nat-basic	f	Nat → Nat
. +2 .	list	f	A × A → List[A]
. - .	nat	pf	Nat × Nat → Nat with λ n, m. n ≥ m
. -* .	map-sep	f	(Map[A, B] → Bool) × (Map[A, B] → Bool) → Map[A, B] → Bool
. -- .	map	f	Map[A, B] × A → Map[A, B]
. -- .	set-union	f	Set[A] × A → Set[A]
. -> .	map-sep	f	(Map[A, B] → Bool) × (Map[A, B] → Bool) → Map[A, B] → Bool
. -⊗ .	map-sep	f	(Map[A, B] → Bool) × (Map[A, B] → Bool) → Map[A, B] → Bool
. -1	nat-basic	pf	Nat → Nat with λ n. n ≠ 0
. < .	nat-basic	p	Nat × Nat
. < .	list-data	p	List('A) × List('A)
. => .	refmap-maplet	f	Ref[A] × A → Map[Ref[A], A] → Bool
. =>?	refmap-ex-maplet	f	Ref[A] → Map[Ref[A], A] → Bool
. =>_	refmap-ex-maplet	f	Ref[A] → Map[Ref[A], A] → Bool
. > .	nat	p	Nat × Nat
. \ .	set-union	f	Set[A] × Set[A] → Set[A]
. \ .	heapfuns-map	f	Map[A, B] × Set[A] → Map[A, B]
. \ .	heapfuns-map	f	Map[A, B] × Map[A, B] → Map[A, B]
. × .	cell	f	A × Ref[Cell[A]] → Cell[A]
. ∈ .	map	p	'A × Map('A, 'B)
. ∈ .	set-basic	p	'A × Set('A)
. ∈ .	list	p	'A × List('A)
. ∩ .	set-union	f	Set[A] × Set[A] → Set[A]
. ∪ .	set-union	f	Set[A] × Set[A] → Set[A]
. ∪ .	heapfuns-map	f	Map[A, B] × Map[A, B] → Map[A, B]
. ≡ .	refmap-separation	p	Map(Ref('A), 'A) × Map(Ref('A), 'A)
. ≤ .	nat	p	Nat × Nat
. ≥ .	nat	p	Nat × Nat
. ⊆ .	map	p	Map('A, 'B) × Map('A, 'B)
. ⊆ .	set-basic	p	Set('A) × Set('A)
. ⊆ .	map-sep	p	(Map('A, 'B) → Bool) × (Map('A, 'B) → Bool)
. ⊑ .	list-last	p	List('A) × List('A)
. ⊒ .	list-last	p	List('A) × List('A)
. ⊗ .	map-sep	f	(Map[A, B] → Bool) × (Map[A, B] → Bool) → Map[A, B] → Bool
. ⊥ .	heapfuns-map	p	Map('A, 'B) × Map('A, 'B)
. and .	map-sep	f	(Map[A, B] → Bool) × (Map[A, B] → Bool) → Map[A, B] → Bool
. butlast	list-last	pf	List[A] → List[A] with λ x. x ≠ []
. distinct	list-dup	f	List[A] → List[A]
. dropRight ( . )	list-last	pf	List[A] × Nat → List[A] with λ x, n. n ≤ # x
. exists ( . )	set-union	p	Set('A) × ('A → Bool)
. filter ( . )	set-union	f	Set[A] × (A → Bool) → Set[A]
. foldLeft ( . )	list	f	List[A] × B × (B × A → B) → B
. forall ( . )	set-union	p	Set('A) × ('A → Bool)
. head	list-data	pf	List[A] → A with λ x. x ≠ []
. last	list-last	pf	List[A] → A with λ x. x ≠ []
. map ( . )	set-union	f	Set[A] × (A → B) → Set[B]
. map ( . )	list	f	List[A] × (A → B) → List[B]
. nxt	cell	f	Cell[A] → Ref[Cell[A]]
. nxt:= .	cell	f	Cell[A] × Ref[Cell[A]] → Cell[A]
. or .	map-sep	f	(Map[A, B] → Bool) × (Map[A, B] → Bool) → Map[A, B] → Bool
. tail	list-data	pf	List[A] → List[A] with λ x. x ≠ []
. val	cell	f	Cell[A] → A
. val:= .	cell	f	Cell[A] × A → Cell[A]
[]	list-data	c	List[A]
_∃ .	refmap-maplet	f	(B → Map[Ref[A], A] → Bool) → Map[Ref[A], A] → Bool
_∃ .	refmap-maplet	f	(B × C → Map[Ref[A], A] → Bool) → Map[Ref[A], A] → Bool
{ . }	set-union	f	A → Set[A]
{ . }	map-sep	f	Map[A, B] → Map[A, B] → Bool
∅	map	c	Map[A, B]
∅	set-basic	c	Set[A]
⌜ . ⌝	map-sep	f	Bool → Map[A, B] → Bool
Cell	cell	s
List	list-data	s
Map	map	s
Nat	nat-basic	s
Ref	polyref	s
Set	set-basic	s
True	refmap-separation	p	Bool
a	linked-maplist-seg	v	A
b	linked-maplist-seg	v	A
ce	linked-maplist-seg	v	Cell[A]
disj	list-dup	p	List('A) × List('A)
disjoint	set-union	p	Set('A) × Set('A)
dom .	heapfuns-map	f	Map[A, B] → Set[A]
dups	list-dup	p	List('A)
emp	map-sep	p	Map('A, 'B)
false	map-sep	p	Map('A, 'B)
fillfirst	list-last	f	Nat × A × List[A] → List[A]
h	linked-maplist-seg	v	Map[Ref[Cell[A]], Cell[A]]
hP	linked-maplist-seg	v	Map[Ref[Cell[A]], Cell[A]] → Bool
ite	map-sep	f	Bool × (Map[A, B] → Bool) × (Map[A, B] → Bool) → Map[A, B] → Bool
ll-trav	linked-maplist-seg	f	Ref[Cell[A]] × Ref[Cell[A]] × List[A] → Map[Ref[Cell[A]], Cell[A]] → Bool
ll-trav	linked-maplist-seg	f	Ref[Cell[A]] × Ref[Cell[A]] × Ref[Cell[A]] × List[A] → Map[Ref[Cell[A]], Cell[A]] → Bool
lls	linked-maplist-seg	f	Ref[Cell[A]] × Ref[Cell[A]] × List[A] → Map[Ref[Cell[A]], Cell[A]] → Bool
ls	linked-maplist	f	Ref[Cell[A]] × List[A] → Map[Ref[Cell[A]], Cell[A]] → Bool
mklist	list-last	f	A × Nat → List[A]
not .	map-sep	f	(Map[A, B] → Bool) → Map[A, B] → Bool
null	polyref	c	Ref[A]
precise	map-sep	p	(Map('A, 'B) → Bool)
r	linked-maplist-seg	v	Ref[Cell[A]]
rev	list-last	f	List[A] → List[A]
true	map-sep	p	Map('A, 'B)
x	linked-maplist-seg	v	List[A]
y	linked-maplist-seg	v	List[A]