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Signature symbols in this unit

Symbol	Specification	Kind	Type
# .	array	f	Array[A] → Nat
#oc	woarray	f	A × Array[A] → Nat
. ( . )	array	pf	Array[A] × Nat → A with λ ar, n. n < # ar
. ( . := . )	array	pf	Array[A] × Nat × A → Array[A] with λ ar, n, a. n < # ar
. + .	woarray	f	Array[A] × Array[A] → Array[A]
. + .	woarray	f	Array[A] × A → Array[A]
. + .	nat-basic	f	Nat × Nat → Nat
. + .	array-listops	f	A × Array[A] → Array[A]
. ++ .	woarray	f	Array[A] × A → Array[A]
. +1	nat-basic	f	Nat → Nat
. +2a .	woarray	f	A × A → Array[A]
. - .	nat	pf	Nat × Nat → Nat with λ n, m. n ≥ m
. -1	nat-basic	pf	Nat → Nat with λ n. n ≠ 0
. -1l .	woarray	f	Array[A] × A → Array[A]
. -l .	woarray	f	Array[A] × A → Array[A]
. -p .	woarray	f	Array[A] × Nat → Array[A]
. < .	nat-basic	p	Nat × Nat
. < .	array-listops	p	Array('A) × Array('A)
. < .	weakord	p	Weakord × Weakord
. > .	nat	p	Nat × Nat
. \ .	woarray	f	Array[A] × Array[A] → Array[A]
. ∈ .	woarray	p	'A × Array('A)
. ∪ .	woarray	f	Array[A] × Array[A] → Array[A]
. ≤ .	nat	p	Nat × Nat
. ≥ .	nat	p	Nat × Nat
. ⊆ .	woarray	p	Array('A) × Array('A)
. ⊆m .	woarray	p	Array('A) × Array('A)
. ⊑ .	woarray	p	Array('A) × Array('A)
. ⊒ .	woarray	p	Array('A) × Array('A)
. butlast	woarray	pf	Array[A] → Array[A] with λ x. x ≠ []
. count ( . )	woarray	f	Array[A] × (A → Bool) → Nat
. count ( . )	woarray	pf	Array[A] × Nat × Nat × (A → Bool) → Nat with λ x, m, n, p. m ≤ n ∧ n ≤ # x
. distinct	woarray	f	Array[A] → Array[A]
. drop ( . )	woarray	pf	Array[A] × Nat → Array[A] with λ x, n. n ≤ # x
. dropRight ( . )	woarray	pf	Array[A] × Nat → Array[A] with λ x, n. n ≤ # x
. filter ( . )	woarray	f	Array[A] × (A → Bool) → Array[A]
. first	array-listops	pf	Array[A] → A with λ ar. ar ≠ []
. foldLeft ( . )	woarray	f	Array[A] × B × (B × A → B) → B
. indexOf ( . )	woarray	f	Array[A] × A → Nat
. intersect .	woarray	f	Array[A] × Array[A] → Array[A]
. last	woarray	pf	Array[A] → A with λ x. x ≠ []
. map ( . )	woarray	f	Array[A] × (A → B) → Array[B]
. rest	array-listops	pf	Array[A] → Array[A] with λ ar. ar ≠ []
. sublist ( . )	woarray	pf	Array[A] × Nat × Nat → Array[A] with λ x, n, m. n + m ≤ # x
. take ( . )	woarray	pf	Array[A] × Nat → Array[A] with λ x, n. n ≤ # x
. takeRight ( . )	woarray	pf	Array[A] × Nat → Array[A] with λ x, n. n ≤ # x
. zip .	woarray	f	Array[A] × Array[B] → Array[(A, B)]
[]	array-listops	c	Array[A]
Array	array	s
Nat	nat-basic	s
Weakord	weakord	s
a	woarray	v	A
ar	woarray	v	Array[A]
cmp	array-copy	p	Array('A) × 'A
cmp	array-copy	pp	Array('A) × Nat × Array('A) × Nat × Nat with λ ar, m, ar0, m0, n. m + n ≤ # ar ∧ m0 + n ≤ # ar0
cmp	array-copy	pp	Array('A) × 'A × Nat × Nat with λ ar, a, m, n. m + n ≤ # ar
copy	array-copy	pf	Array[A] × Nat × Array[A] × Nat × Nat → Array[A] with λ ar, m, ar0, m0, n. m + n ≤ # ar ∧ m0 + n ≤ # ar0
copyAndFill#	array-copy	pr	Nat × Nat × Nat × A : Array[A] × Array[A]
disj	woarray	p	Array('A) × Array('A)
dups	woarray	p	Array('A)
fill	array-copy	f	Array[A] × A → Array[A]
fill	array-copy	pf	Array[A] × A × Nat × Nat → Array[A] with λ ar, a, n, m. n + m ≤ # ar
fillfirst	woarray	f	Nat × A × Array[A] → Array[A]
frome	woarray	f	Array[A] × A → Array[A]
id○	array-copy	p	Array('A) × Array('A) × Nat
id○	array-copy	p	Array('A) × Array('A) × Nat × Nat
idrange	array-copy	pp	Array('A) × Nat × Nat with λ ar, m, n. m + n ≤ # ar
mkar'	woarray	f	A → Array[A]
mkarray	array	f	Nat → Array[A]
mkarray	array	f	Nat × A → Array[A]
mkinitar	woarray	f	A × Nat → Array[A]
move	array-copy	pf	Array[A] × Nat × Nat × Nat → Array[A] with λ ar, m, m0, n. m + n ≤ # ar ∧ m0 + n ≤ # ar
moveAndFill#	array-copy	pr	Nat × Nat × Nat × A : Array[A]
n	woarray	v	Nat
perm	woarray	p	Array('A) × Array('A)
resize	array-copy	f	Array[A] × Nat → Array[A]
rev	woarray	f	Array[A] → Array[A]
rotateLeft	array-copy	pf	Array[A] × Nat × Nat × Nat → Array[A] with λ ar, m, n, n0. m + n ≤ # ar ∧ n0 ≤ m
rotateRight	array-copy	pf	Array[A] × Nat × Nat × Nat → Array[A] with λ ar, m, n, n0. m + n + n0 ≤ # ar
shiftLeft	array-copy	pf	Array[A] × Nat × Nat × Nat → Array[A] with λ ar, m, n, n0. m + n ≤ # ar ∧ n0 ≤ m
shiftRight	array-copy	pf	Array[A] × Nat × Nat × Nat → Array[A] with λ ar, m, n, n0. m + n + n0 ≤ # ar
subarray	array-copy	pf	Array[A] × Nat × Nat → Array[A] with λ ar, m, n. m + n ≤ # ar