[Imprint][Data Privacy Statement][E-Mail]

Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Signature symbols in this unit

Symbol	Specification	Kind	Type
# .	array	f	Array → Nat
# .	fsarray	f	FSArray → Nat
. ( . )	array	pf	Array × Nat → Elem with λ ar, n. n < # ar
. ( . )	fsarray	pf	FSArray × Nat → Elem with λ ar, n. n < # ar
. ( . := . )	array	pf	Array × Nat × Elem → Array with λ ar, n, a. n < # ar
. ( . := . )	fsarray	pf	FSArray × Nat × Elem → FSArray with λ ar, n, a. n < # ar
. + .	nat-basic	f	Nat × Nat → Nat
. +1	nat-basic	f	Nat → Nat
. - .	nat	pf	Nat × Nat → Nat with λ n, m. n ≥ m
. -1	nat-basic	pf	Nat → Nat with λ n. n ≠ 0
. < .	nat-basic	p	Nat × Nat
. > .	nat	p	Nat × Nat
. ≤ .	nat	p	Nat × Nat
. ≥ .	nat	p	Nat × Nat
. toArray	array-fsarray	f	FSArray → Array
. toFSArray	array-fsarray	pf	Array → FSArray with λ ar. # ar = size
Array	array	s
Elem	elem	s
FSArray	fsarray	s
Nat	nat-basic	s
a	array-fsarray	v	Elem
ar	array-fsarray	v	Array
cmp	array-copy	p	Array × Elem
cmp	fsarray-copy	p	FSArray × Elem
cmp	array-copy	pp	Array × Nat × Array × Nat × Nat with λ ar, m, ar0, m0, n. m + n ≤ # ar ∧ m0 + n ≤ # ar0
cmp	array-copy	pp	Array × Elem × Nat × Nat with λ ar, a, m, n. m + n ≤ # ar
cmp	fsarray-copy	pp	FSArray × Nat × FSArray × Nat × Nat with λ ar, m, ar0, m0, n. m + n ≤ size ∧ m0 + n ≤ size
cmp	fsarray-copy	pp	FSArray × Elem × Nat × Nat with λ ar, a, m, n. m + n ≤ size
cmp	array-fsarray	pp	FSArray × Nat × Array × Nat × Nat with λ fsar, m, ar, m0, n. m + n ≤ size ∧ m0 + n ≤ # ar
copy	array-copy	pf	Array × Nat × Array × Nat × Nat → Array with λ ar, m, ar0, m0, n. m + n ≤ # ar ∧ m0 + n ≤ # ar0
copy	fsarray-copy	pf	FSArray × Nat × FSArray × Nat × Nat → FSArray with λ ar, m, ar0, m0, n. m + n ≤ size ∧ m0 + n ≤ size
copy	array-fsarray	pf	Array × Nat × FSArray × Nat × Nat → FSArray with λ ar, m, fsar, m0, n. m + n ≤ # ar ∧ m0 + n ≤ size
copy	array-fsarray	pf	FSArray × Nat × Array × Nat × Nat → Array with λ fsar, m, ar, m0, n. m + n ≤ size ∧ m0 + n ≤ # ar
copyAndFill#	array-copy	pr	Nat × Nat × Nat × Elem : Array × Array
fill	array-copy	f	Array × Elem → Array
fill	fsarray-copy	f	FSArray × Elem → FSArray
fill	array-copy	pf	Array × Elem × Nat × Nat → Array with λ ar, a, n, m. n + m ≤ # ar
fill	fsarray-copy	pf	FSArray × Elem × Nat × Nat → FSArray with λ ar, a, n, m. n + m ≤ size
fsar	array-fsarray	v	FSArray
id○	array-copy	p	Array × Array × Nat
id○	array-copy	p	Array × Array × Nat × Nat
id○	fsarray-copy	p	FSArray × FSArray × Nat
id○	fsarray-copy	p	FSArray × FSArray × Nat × Nat
idrange	array-copy	pp	Array × Nat × Nat with λ ar, m, n. m + n ≤ # ar
idrange	fsarray-copy	pp	FSArray × Nat × Nat with λ ar, m, n. m + n ≤ size
m	array-fsarray	v	Nat
mkarray	fsarray	c	FSArray
mkarray	array	f	Nat → Array
move	array-copy	pf	Array × Nat × Nat × Nat → Array with λ ar, m, m0, n. m + n ≤ # ar ∧ m0 + n ≤ # ar
moveAndFill#	array-copy	pr	Nat × Nat × Nat × Elem : Array
n	array-fsarray	v	Nat
resize	array-copy	f	Array × Nat → Array
rotateLeft	array-copy	pf	Array × Nat × Nat × Nat → Array with λ ar, m, n, n0. m + n ≤ # ar ∧ n0 ≤ m
rotateRight	array-copy	pf	Array × Nat × Nat × Nat → Array with λ ar, m, n, n0. m + n + n0 ≤ # ar
shiftLeft	array-copy	pf	Array × Nat × Nat × Nat → Array with λ ar, m, n, n0. m + n ≤ # ar ∧ n0 ≤ m
shiftRight	array-copy	pf	Array × Nat × Nat × Nat → Array with λ ar, m, n, n0. m + n + n0 ≤ # ar
size	fsarray	c	Nat
subarray	array-copy	pf	Array × Nat × Nat → Array with λ ar, m, n. m + n ≤ # ar
subarray	array-fsarray	pf	FSArray × Nat × Nat → Array with λ fsar, m, n. m + n ≤ size