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Signature symbols in this unit

Symbol	Specification	Kind	Type
# .	array	f	Array[A] → Nat
#c .	matrix	f	Matrix[A] → Nat
#oc	list-as-arrayinstance	f	A × Array[A] → Nat
#r .	matrix	f	Matrix[A] → Nat
. ( . )	matrix	pf	Matrix[A] × Nat × Nat → A with λ mx, r, c. r < #r mx ∧ c < #c mx
. ( . )	array	pf	Array[A] × Nat → A with λ ar, n. n < # ar
. ( . := . )	matrix	pf	Matrix[A] × Nat × Nat × A → Matrix[A] with λ mx, r, c, a. r < #r mx ∧ c < #c mx
. ( . := . )	array	pf	Array[A] × Nat × A → Array[A] with λ ar, n, a. n < # ar
. * .	nat-mult	f	Nat × Nat → Nat
. + .	nat-basic	f	Nat × Nat → Nat
. + .	list-as-arrayinstance	f	Array[A] × Array[A] → Array[A]
. + .	list-as-arrayinstance	f	Array[A] × A → Array[A]
. + .	array-listops	f	A × Array[A] → Array[A]
. ++ .	list-as-arrayinstance	f	Array[A] × A → Array[A]
. +1	nat-basic	f	Nat → Nat
. +2a .	list-as-arrayinstance	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 .	list-as-arrayinstance	f	Array[A] × A → Array[A]
. -l .	list-as-arrayinstance	f	Array[A] × A → Array[A]
. -p .	list-as-arrayinstance	f	Array[A] × Nat → Array[A]
. < .	nat-basic	p	Nat × Nat
. < .	array-listops	p	Array('A) × Array('A)
. > .	nat	p	Nat × Nat
. [ . := . ]c	rowcol-upd	pf	Matrix[A] × Nat × Array[A] → Matrix[A] with λ mx, c, a. c < #c mx ∧ # a = #r mx
. [ . := . ]r	rowcol-upd	pf	Matrix[A] × Nat × Array[A] → Matrix[A] with λ mx, r, a. r < #r mx ∧ # a = #c mx
. [ . ]c	matrix+array	pf	Matrix[A] × Nat → Array[A] with λ mx, c. c < #c mx
. [ . ]r	matrix+array	pf	Matrix[A] × Nat → Array[A] with λ mx, r. r < #r mx
. \ .	list-as-arrayinstance	f	Array[A] × Array[A] → Array[A]
. ∈ .	list-as-arrayinstance	p	'A × Array('A)
. ∪ .	list-as-arrayinstance	f	Array[A] × Array[A] → Array[A]
. ≤ .	nat	p	Nat × Nat
. ≥ .	nat	p	Nat × Nat
. ⊆ .	list-as-arrayinstance	p	Array('A) × Array('A)
. ⊆m .	list-as-arrayinstance	p	Array('A) × Array('A)
. ⊑ .	list-as-arrayinstance	p	Array('A) × Array('A)
. ⊒ .	list-as-arrayinstance	p	Array('A) × Array('A)
. butlast	list-as-arrayinstance	pf	Array[A] → Array[A] with λ x. x ≠ []
. count ( . )	list-as-arrayinstance	f	Array[A] × (A → Bool) → Nat
. count ( . )	list-as-arrayinstance	pf	Array[A] × Nat × Nat × (A → Bool) → Nat with λ x, m, n, p. m ≤ n ∧ n ≤ # x
. distinct	list-as-arrayinstance	f	Array[A] → Array[A]
. drop ( . )	list-as-arrayinstance	pf	Array[A] × Nat → Array[A] with λ x, n. n ≤ # x
. dropRight ( . )	list-as-arrayinstance	pf	Array[A] × Nat → Array[A] with λ x, n. n ≤ # x
. filter ( . )	list-as-arrayinstance	f	Array[A] × (A → Bool) → Array[A]
. first	array-listops	pf	Array[A] → A with λ ar. ar ≠ []
. foldLeft ( . )	list-as-arrayinstance	f	Array[A] × B × (B × A → B) → B
. indexOf ( . )	list-as-arrayinstance	f	Array[A] × A → Nat
. intersect .	list-as-arrayinstance	f	Array[A] × Array[A] → Array[A]
. last	list-as-arrayinstance	pf	Array[A] → A with λ x. x ≠ []
. map ( . )	list-as-arrayinstance	f	Array[A] × (A → B) → Array[B]
. rest	array-listops	pf	Array[A] → Array[A] with λ ar. ar ≠ []
. sublist ( . )	list-as-arrayinstance	pf	Array[A] × Nat × Nat → Array[A] with λ x, n, m. n + m ≤ # x
. take ( . )	list-as-arrayinstance	pf	Array[A] × Nat → Array[A] with λ x, n. n ≤ # x
. takeRight ( . )	list-as-arrayinstance	pf	Array[A] × Nat → Array[A] with λ x, n. n ≤ # x
. toArc	rowcol-upd	f	Matrix[A] → Array[A]
. toArr	rowcol-upd	f	Matrix[A] → Array[A]
. zip .	list-as-arrayinstance	f	Array[A] × Array[B] → Array[(A, B)]
[]	array-listops	c	Array[A]
Array	array	s
Matrix	matrix	s
Nat	nat-basic	s
a	rowcol-upd	v	Array[A]
c	rowcol-upd	v	Nat
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	list-as-arrayinstance	p	Array('A) × Array('A)
dups	list-as-arrayinstance	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	list-as-arrayinstance	f	Nat × A × Array[A] → Array[A]
frome	list-as-arrayinstance	f	Array[A] × A → Array[A]
i	rowcol-upd	v	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
j	rowcol-upd	v	A
m	rowcol-upd	v	Nat
mkar'	list-as-arrayinstance	f	A → Array[A]
mkarray	array	f	Nat → Array[A]
mkarray	array	f	Nat × A → Array[A]
mkinitar	list-as-arrayinstance	f	A × Nat → Array[A]
mkmatrix	matrix	f	Nat × Nat × A → Matrix[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]
mx	rowcol-upd	v	Matrix[A]
n	rowcol-upd	v	Nat
perm	list-as-arrayinstance	p	Array('A) × Array('A)
r	rowcol-upd	v	Nat
resize	array-copy	f	Array[A] × Nat → Array[A]
rev	list-as-arrayinstance	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
toArc	rowcol-upd	f	Matrix[A] × Nat → Array[A]
toArr	rowcol-upd	f	Matrix[A] × Nat → Array[A]