[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
# .	heap	f	Heap[A] → Nat
# .	set-basic	f	Set[A] → Nat
# .	map	f	Map[A, B] → Nat
. ( . )	heap	pf	Heap[A] × Ref[A] → A with λ h, r. r ≠ null ∧ r ∈ h
. ( . )	map	pf	Map[A, B] × A → B with λ st, a. a ∈ st
. ( . := . )	map	f	Map[A, B] × A × B → Map[A, B]
. ( . := . )	heap	pf	Heap[A] × Ref[A] × A → Heap[A] with λ h, r, o. r ≠ null ∧ r ∈ h
. * .	heap-sep	f	(Heap[A] → Bool) × (Heap[A] → Bool) → Heap[A] → Bool
. + .	nat-basic	f	Nat × Nat → Nat
. ++ .	set-basic	f	Set[A] × A → Set[A]
. ++ .	heap	pf	Heap[A] × Ref[A] → Heap[A] with λ h, r. r ≠ null ∧ ¬ r ∈ h
. +1	nat-basic	f	Nat → Nat
. - .	nat	pf	Nat × Nat → Nat with λ n, m. n ≥ m
. -* .	heap-sep	f	(Heap[A] → Bool) × (Heap[A] → Bool) → Heap[A] → Bool
. -- .	set-union	f	Set[A] × A → Set[A]
. -- .	map	f	Map[A, B] × A → Map[A, B]
. -- .	heap	pf	Heap[A] × Ref[A] → Heap[A] with λ h, r. r ≠ null ∧ r ∈ h
. -> .	heap-sep	f	(Heap[A] → Bool) × (Heap[A] → Bool) → Heap[A] → Bool
. -⊗ .	heap-sep	f	(Heap[A] → Bool) × (Heap[A] → Bool) → Heap[A] → Bool
. -1	nat-basic	pf	Nat → Nat with λ n. n ≠ 0
. < .	nat-basic	p	Nat × Nat
. => .	maplet	f	Ref[A] × A → Heap[A] → Bool
. =>?	ex-maplet	f	Ref[A] → Heap[A] → Bool
. =>_	ex-maplet	f	Ref[A] → Heap[A] → Bool
. > .	nat	p	Nat × Nat
. \ .	set-union	f	Set[A] × Set[A] → Set[A]
. \ .	heapfuns	f	Heap[A] × Set[Ref[A]] → Heap[A]
. \ .	heapfuns	f	Heap[A] × Heap[A] → Heap[A]
. ∈ .	heap	p	Ref('A) × Heap('A)
. ∈ .	set-basic	p	'A × Set('A)
. ∈ .	map	p	'A × Map('A, 'B)
. ∧_ .	iter-map	f	(A × B → Heap[A] → Bool) × Map[A, B] → Heap[A] → Bool
. ∩ .	set-union	f	Set[A] × Set[A] → Set[A]
. ∪ .	set-union	f	Set[A] × Set[A] → Set[A]
. ∪ .	heapfuns	f	Heap[A] × Heap[A] → Heap[A]
. ≤ .	nat	p	Nat × Nat
. ≥ .	nat	p	Nat × Nat
. ⊆ .	set-basic	p	Set('A) × Set('A)
. ⊆ .	heapfuns	p	Heap('A) × Heap('A)
. ⊆ .	heap-sep	p	(Heap('A) → Bool) × (Heap('A) → Bool)
. ⊆ .	map	p	Map('A, 'B) × Map('A, 'B)
. ⊗ .	heap-sep	f	(Heap[A] → Bool) × (Heap[A] → Bool) → Heap[A] → Bool
. ⊗_ .	iter-map	f	(A × B → Heap[A] → Bool) × Map[A, B] → Heap[A] → Bool
. ⊥ .	heapfuns	p	Heap('A) × Heap('A)
. and .	heap-sep	f	(Heap[A] → Bool) × (Heap[A] → Bool) → Heap[A] → Bool
. exists ( . )	set-union	p	Set('A) × ('A → Bool)
. filter ( . )	set-union	f	Set[A] × (A → Bool) → Set[A]
. forall ( . )	set-union	p	Set('A) × ('A → Bool)
. map ( . )	set-union	f	Set[A] × (A → B) → Set[B]
. or .	heap-sep	f	(Heap[A] → Bool) × (Heap[A] → Bool) → Heap[A] → Bool
_∃ .	maplet	f	(B → Heap[A] → Bool) → Heap[A] → Bool
_∃ .	maplet	f	(B × C → Heap[A] → Bool) → Heap[A] → Bool
_∃ .	maplet	f	(B × C × D → Heap[A] → Bool) → Heap[A] → Bool
{ . }	set-union	f	A → Set[A]
{ . }	heap-sep	f	Heap[A] → Heap[A] → Bool
∅	heap	c	Heap[A]
∅	set-basic	c	Set[A]
∅	map	c	Map[A, B]
⌜ . ⌝	heap-sep	f	Bool → Heap[A] → Bool
Heap	heap	s
Map	map	s
Nat	nat-basic	s
Ref	polyref	s
Set	set-basic	s
a	iter-map	v	A
adP	iter-map	v	A × B → Heap[A] → Bool
alloc#	heap	pr	: Heap[A] → Ref[A] (nondeterministic)
d	iter-map	v	B
disjoint	set-union	p	Set('A) × Set('A)
dom .	heapfuns	f	Heap[A] → Set[Ref[A]]
emp	heap-sep	p	Heap('A)
false	heap-sep	p	Heap('A)
h	iter-map	v	Heap[A]
hP	iter-map	v	Heap[A] → Bool
ite	heap-sep	f	Bool × (Heap[A] → Bool) × (Heap[A] → Bool) → Heap[A] → Bool
not .	heap-sep	f	(Heap[A] → Bool) → Heap[A] → Bool
null	polyref	c	Ref[A]
precise	heap-sep	p	(Heap('A) → Bool)
st	iter-map	v	Map[A, B]
true	heap-sep	p	Heap('A)