Proof Assistant Projects
Collection
Digesting proof assistant libraries for AI ingestion. • 84 items • Updated
• 3
fact stringlengths 3 3.37k | type stringclasses 3 values | library stringclasses 3 values | imports listlengths 0 65 | filename stringlengths 31 124 | symbolic_name stringlengths 1 66 | docstring stringclasses 1 value |
|---|---|---|---|---|---|---|
AlltokenSpec(i: int) requires Valid() decreases |allTokens| requires 0 <= i < |allTokens| ensures allTokens == allTokens[..i] + allTokens[i].allTokens | lemma | Source | [
"System"
] | Source/DafnyCore/AST/DafnyInterface.dfy | AlltokenSpec | |
TokenNextIsIPlus1(middle: Token, i: int) requires Valid() requires 0 <= i < |allTokens| requires allTokens[i] == middle requires middle.Next != null ensures 0 <= i + 1 < |allTokens| && allTokens[i+1] == middle.Next | lemma | Source | [
"System"
] | Source/DafnyCore/AST/DafnyInterface.dfy | TokenNextIsIPlus1 | |
TokenNextIsNullImpliesLastToken(middle: Token, i: int) requires middle.Valid() && this.Valid() requires 0 <= i < |allTokens| requires middle == allTokens[i] requires middle.Next == null ensures i == |allTokens|-1 | lemma | Source | [
"System"
] | Source/DafnyCore/AST/DafnyInterface.dfy | TokenNextIsNullImpliesLastToken | |
Valid() | predicate | Source | [
"System"
] | Source/DafnyCore/AST/DafnyInterface.dfy | Valid | |
EndsWithNewline(input: CsString) | predicate | Source | [
"System"
] | Source/DafnyCore/AST/DafnyInterface.dfy | EndsWithNewline | |
GetNewLeadingTrivia(token: Token) : CsString | function | Source | [
"MicrosoftDafny",
"System"
] | Source/DafnyCore/AST/Formatting.dfy | GetNewLeadingTrivia | |
GetNewTrailingTrivia(token: Token) : CsString | function | Source | [
"MicrosoftDafny",
"System"
] | Source/DafnyCore/AST/Formatting.dfy | GetNewTrailingTrivia | |
IsAllocated(x: T) ensures allocated(x) | lemma | Source | [
"MicrosoftDafny",
"System"
] | Source/DafnyCore/AST/Formatting.dfy | IsAllocated | |
ContainsTransitive(other: CsString, needle: CsString) requires Contains(other) && other.Contains(needle) ensures Contains(needle) } lemma ContainsTransitive() ensures forall s1: CsString, s2: CsString, s3: CsString | s1.Contains(s2) && s2.Contains(s3) :: s1.Contains(s3) | lemma | Source | [] | Source/DafnyCore/AST/System.dfy | ContainsTransitive | |
BelowIsNonStrictLess(a: Box, b: Box) ensures Below(a, b) <==> Less(a, b) || a == b | lemma | Source | [] | Source/DafnyCore/Prelude/Boxes.dfy | BelowIsNonStrictLess | |
LessIrreflexive(a: Box) ensures !Less(a, a) | lemma | Source | [] | Source/DafnyCore/Prelude/Boxes.dfy | LessIrreflexive | |
LessAsymmetric(a: Box, b: Box) requires Less(a, b) && Less(b, a) ensures false | lemma | Source | [] | Source/DafnyCore/Prelude/Boxes.dfy | LessAsymmetric | |
LessBelowAsymmetric(a: Box, b: Box) requires Less(a, b) && Below(b, a) ensures false | lemma | Source | [] | Source/DafnyCore/Prelude/Boxes.dfy | LessBelowAsymmetric | |
NotLess(a: Box, b: Box) ensures !Less(a, b) <==> Below(b, a) | lemma | Source | [] | Source/DafnyCore/Prelude/Boxes.dfy | NotLess | |
LessTransitive(a: Box, b: Box, c: Box) requires Less(a, b) && Less(b, c) ensures Less(a, c) | lemma | Source | [] | Source/DafnyCore/Prelude/Boxes.dfy | LessTransitive | |
LessBelowTransitive(a: Box, b: Box, c: Box) requires || (Less(a, b) && Below(b, c)) || (Below(a, b) && Less(b, c)) ensures Less(a, c) | lemma | Source | [] | Source/DafnyCore/Prelude/Boxes.dfy | LessBelowTransitive | |
Connected(a: Box, b: Box) ensures a != b ==> Less(a, b) || Less(b, a) | lemma | Source | [] | Source/DafnyCore/Prelude/Boxes.dfy | Connected | |
Less(a: Box, b: Box) | predicate | Source | [] | Source/DafnyCore/Prelude/Boxes.dfy | Less | |
Length() : nat | function | Source | [] | Source/DafnyCore/Prelude/Lists.dfy | Length | |
Append(xs: List<X>) : List<X> | function | Source | [] | Source/DafnyCore/Prelude/Lists.dfy | Append | |
At(i: nat) : X | function | Source | [] | Source/DafnyCore/Prelude/Lists.dfy | At | |
Take(n: nat) : List<X> | function | Source | [] | Source/DafnyCore/Prelude/Lists.dfy | Take | |
Drop(n: nat) : List<X> | function | Source | [] | Source/DafnyCore/Prelude/Lists.dfy | Drop | |
Split(n: nat) : (split: (List<X>, List<X>)) | function | Source | [] | Source/DafnyCore/Prelude/Lists.dfy | Split | |
LengthAppend(xs: List<X>) ensures Append(xs).Length() == Length() + xs.Length() | lemma | Source | [] | Source/DafnyCore/Prelude/Lists.dfy | LengthAppend | |
HeadTailAt() requires Cons? ensures head == At(0) ensures forall i :: 0 <= i < tail.Length() ==> tail.At(i) == At(i + 1) | lemma | Source | [] | Source/DafnyCore/Prelude/Lists.dfy | HeadTailAt | |
ContainsAt(x: X) requires Contains(x) ensures i < Length() && At(i) == x | lemma | Source | [] | Source/DafnyCore/Prelude/Lists.dfy | ContainsAt | |
AtContains(i: nat, x: X) requires i < Length() && At(i) == x ensures Contains(x) | lemma | Source | [] | Source/DafnyCore/Prelude/Lists.dfy | AtContains | |
ConsAt(x: X, i: nat) requires i < Cons(x, this).Length() ensures Cons(x, this).At(i) == if i == 0 then x else At(i - 1) | lemma | Source | [] | Source/DafnyCore/Prelude/Lists.dfy | ConsAt | |
AppendAt(xs: List<X>, i: nat) requires i < Append(xs).Length() ensures Append(xs).At(i) == if i < Length() then At(i) else (LengthAppend(xs); xs.At(i - Length())) | lemma | Source | [] | Source/DafnyCore/Prelude/Lists.dfy | AppendAt | |
AboutDrop(n: nat) requires n < Length() ensures Drop(n).Cons? | lemma | Source | [] | Source/DafnyCore/Prelude/Lists.dfy | AboutDrop | |
AppendTake(xs: List<X>) ensures (LengthAppend(xs); Append(xs).Take(Length()) == this) | lemma | Source | [] | Source/DafnyCore/Prelude/Lists.dfy | AppendTake | |
TakeFromAppend(xs: List<X>, n: nat) requires n <= Length() + xs.Length() ensures (LengthAppend(xs); Append(xs).Take(n) == if n <= Length() then Take(n) else Append(xs.Take(n - Length()))) | lemma | Source | [] | Source/DafnyCore/Prelude/Lists.dfy | TakeFromAppend | |
AppendDrop(xs: List<X>) ensures (LengthAppend(xs); Append(xs).Drop(Length()) == xs) | lemma | Source | [] | Source/DafnyCore/Prelude/Lists.dfy | AppendDrop | |
DropFromAppend(xs: List<X>, n: nat) requires n <= Length() + xs.Length() ensures (LengthAppend(xs); Append(xs).Drop(n) == if n <= Length() then Drop(n).Append(xs) else xs.Drop(n - Length())) | lemma | Source | [] | Source/DafnyCore/Prelude/Lists.dfy | DropFromAppend | |
AppendTakeDrop(i: nat) requires i <= Length() ensures Take(i).Append(Drop(i)) == this | lemma | Source | [] | Source/DafnyCore/Prelude/Lists.dfy | AppendTakeDrop | |
LengthTakeDrop(i: nat) requires i <= Length() ensures Take(i).Length() == i && Drop(i).Length() == Length() - i | lemma | Source | [] | Source/DafnyCore/Prelude/Lists.dfy | LengthTakeDrop | |
Contains(x: X) | predicate | Source | [] | Source/DafnyCore/Prelude/Lists.dfy | Contains | |
BoolInt(b: bool) : nat | function | Source | [
"Boxes",
"Lists",
"Math",
"Sets",
"Sequences"
] | Source/DafnyCore/Prelude/Multisets.dfy | BoolInt | |
Update(m: List<Box>, o: Box, n: nat) : List<Box> | function | Source | [
"Boxes",
"Lists",
"Math",
"Sets",
"Sequences"
] | Source/DafnyCore/Prelude/Multisets.dfy | Update | |
RemoveOne(a: Multiset, x: Box) : Multiset | function | Source | [
"Boxes",
"Lists",
"Math",
"Sets",
"Sequences"
] | Source/DafnyCore/Prelude/Multisets.dfy | RemoveOne | |
MultiplicityWrapper(a: Multiset, o: Box) : int | function | Source | [
"Boxes",
"Lists",
"Math",
"Sets",
"Sequences"
] | Source/DafnyCore/Prelude/Multisets.dfy | MultiplicityWrapper | |
TailIncreasing(s: List<Box>) requires Increasing(s) && s.Cons? ensures Increasing(s.tail) | lemma | Source | [
"Boxes",
"Lists",
"Math",
"Sets",
"Sequences"
] | Source/DafnyCore/Prelude/Multisets.dfy | TailIncreasing | |
MultiplicityUpdateSame(m: Multiset, o: Box, n: int) requires 0 <= n ensures (UpdatePreservesIncreasing(m, o, n); Multiplicity(Update(m, o, n), o) == n) | lemma | Source | [
"Boxes",
"Lists",
"Math",
"Sets",
"Sequences"
] | Source/DafnyCore/Prelude/Multisets.dfy | MultiplicityUpdateSame | |
MultiplicityUpdateDifferent(m: Multiset, o: Box, n: int, p: Box) requires 0 <= n && o != p ensures (UpdatePreservesIncreasing(m, o, n); Multiplicity(Update(m, o, n), p) == Multiplicity(m, p)) | lemma | Source | [
"Boxes",
"Lists",
"Math",
"Sets",
"Sequences"
] | Source/DafnyCore/Prelude/Multisets.dfy | MultiplicityUpdateDifferent | |
ElementsOfUpdate(m: List<Box>, o: Box, n: nat, m': List<Box>) requires m' == Update(m, o, n) ensures forall i :: 0 <= i < m'.Length() ==> m'.At(i) == o || m.Contains(m'.At(i)) | lemma | Source | [
"Boxes",
"Lists",
"Math",
"Sets",
"Sequences"
] | Source/DafnyCore/Prelude/Multisets.dfy | ElementsOfUpdate | |
HeadIsLeast(x: Box, m: List<Box>) requires Increasing(m) requires m == Nil || Below(x, m.head) ensures forall i :: 0 <= i < m.Length() ==> Below(x, m.At(i)) | lemma | Source | [
"Boxes",
"Lists",
"Math",
"Sets",
"Sequences"
] | Source/DafnyCore/Prelude/Multisets.dfy | HeadIsLeast | |
ConsUpdatePreservesIncreasing(x: Box, m: List<Box>, o: Box, n: nat) requires Increasing(m) requires Increasing(Update(m, o, n)) requires forall i :: 0 <= i < m.Length() ==> Below(x, m.At(i)) requires Below(x, o) ensures Increasing(Cons(x, Update(m, o, n))) | lemma | Source | [
"Boxes",
"Lists",
"Math",
"Sets",
"Sequences"
] | Source/DafnyCore/Prelude/Multisets.dfy | ConsUpdatePreservesIncreasing | |
UpdatePreservesIncreasing(m: List<Box>, o: Box, n: nat) requires Increasing(m) ensures Increasing(Update(m, o, n)) | lemma | Source | [
"Boxes",
"Lists",
"Math",
"Sets",
"Sequences"
] | Source/DafnyCore/Prelude/Multisets.dfy | UpdatePreservesIncreasing | |
PrependPreservesIncreasingAll(o: Box, m: List<Box>) requires Increasing(m) requires forall i :: 0 <= i < m.Length() ==> Below(o, m.At(i)) ensures Increasing(Cons(o, m)) | lemma | Source | [
"Boxes",
"Lists",
"Math",
"Sets",
"Sequences"
] | Source/DafnyCore/Prelude/Multisets.dfy | PrependPreservesIncreasingAll | |
PrependPreservesIncreasing(o: Box, m: List<Box>) requires Increasing(m) requires m == Nil || Below(o, m.head) ensures Increasing(Cons(o, m)) | lemma | Source | [
"Boxes",
"Lists",
"Math",
"Sets",
"Sequences"
] | Source/DafnyCore/Prelude/Multisets.dfy | PrependPreservesIncreasing | |
MultiplicityCard(m: Multiset, x: Box) ensures 0 <= Multiplicity(m, x) <= Card(m) | lemma | Source | [
"Boxes",
"Lists",
"Math",
"Sets",
"Sequences"
] | Source/DafnyCore/Prelude/Multisets.dfy | MultiplicityCard | |
ZeroMultiplicityForLargerElements(s: Multiset, x: Box) requires s == Nil || Less(x, s.head) ensures Multiplicity(s, x) == 0 | lemma | Source | [
"Boxes",
"Lists",
"Math",
"Sets",
"Sequences"
] | Source/DafnyCore/Prelude/Multisets.dfy | ZeroMultiplicityForLargerElements | |
ZeroMultiplicityForNonElements(s: Multiset, o: Box) requires !s.Contains(o) ensures Multiplicity(s, o) == 0 | lemma | Source | [
"Boxes",
"Lists",
"Math",
"Sets",
"Sequences"
] | Source/DafnyCore/Prelude/Multisets.dfy | ZeroMultiplicityForNonElements | |
NonZeroMultiplicityForElements(s: Multiset, o: Box) ensures s.Contains(o) <==> Multiplicity(s, o) != 0 | lemma | Source | [
"Boxes",
"Lists",
"Math",
"Sets",
"Sequences"
] | Source/DafnyCore/Prelude/Multisets.dfy | NonZeroMultiplicityForElements | |
UnionOneContains(a: Multiset, x: Box, o: Box) ensures UnionOne(a, x).Contains(o) <==> o == x || a.Contains(o) | lemma | Source | [
"Boxes",
"Lists",
"Math",
"Sets",
"Sequences"
] | Source/DafnyCore/Prelude/Multisets.dfy | UnionOneContains | |
MultiplicityDelta(a: Multiset, x: Box, y: Box) ensures Multiplicity(UnionOne(a, x), y) == BoolInt(x == y) + Multiplicity(a, y) | lemma | Source | [
"Boxes",
"Lists",
"Math",
"Sets",
"Sequences"
] | Source/DafnyCore/Prelude/Multisets.dfy | MultiplicityDelta | |
RemoveOnePreservesBelow(a: Multiset, x: Box, o: Box) requires a.Contains(x) requires forall i :: 0 <= i < a.Length() ==> Below(o, a.At(i)) ensures forall i :: 0 <= i < RemoveOne(a, x).Length() ==> Below(o, RemoveOne(a, x).At(i)) decreases a | lemma | Source | [
"Boxes",
"Lists",
"Math",
"Sets",
"Sequences"
] | Source/DafnyCore/Prelude/Multisets.dfy | RemoveOnePreservesBelow | |
MultiplicityRemoveOne(a: Multiset, x: Box, o: Box) requires a.Contains(x) ensures Multiplicity(RemoveOne(a, x), o) == Multiplicity(a, o) - BoolInt(x == o) | lemma | Source | [
"Boxes",
"Lists",
"Math",
"Sets",
"Sequences"
] | Source/DafnyCore/Prelude/Multisets.dfy | MultiplicityRemoveOne | |
ZeroMinMultiplicity(a: Multiset, o: Box) ensures Math.Min(0, Multiplicity(a, o)) == 0 == Math.Min(Multiplicity(a, o), 0) | lemma | Source | [
"Boxes",
"Lists",
"Math",
"Sets",
"Sequences"
] | Source/DafnyCore/Prelude/Multisets.dfy | ZeroMinMultiplicity | |
RevealMin() ensures forall a, b :: Math.Min(a, b) == if a < b then a else b | lemma | Source | [
"Boxes",
"Lists",
"Math",
"Sets",
"Sequences"
] | Source/DafnyCore/Prelude/Multisets.dfy | RevealMin | |
MinDistribution(a: int, b: int, c: int) ensures Math.Min(a - c, b - c) == Math.Min(a, b) - c | lemma | Source | [
"Boxes",
"Lists",
"Math",
"Sets",
"Sequences"
] | Source/DafnyCore/Prelude/Multisets.dfy | MinDistribution | |
ClipNonPos(i: int) requires i <= 0 ensures Math.Clip(i) == 0 | lemma | Source | [
"Boxes",
"Lists",
"Math",
"Sets",
"Sequences"
] | Source/DafnyCore/Prelude/Multisets.dfy | ClipNonPos | |
ClipDistribution(a: nat, b: nat) ensures Math.Clip(a) + b == Math.Clip(a + b) | lemma | Source | [
"Boxes",
"Lists",
"Math",
"Sets",
"Sequences"
] | Source/DafnyCore/Prelude/Multisets.dfy | ClipDistribution | |
ClipMultiplicity(a: Multiset, o: Box) ensures Math.Clip(Multiplicity(a, o)) == Multiplicity(a, o) | lemma | Source | [
"Boxes",
"Lists",
"Math",
"Sets",
"Sequences"
] | Source/DafnyCore/Prelude/Multisets.dfy | ClipMultiplicity | |
ExhibitSubsetDifference(a: Multiset, b: Multiset) requires !Subset(a, b) ensures Multiplicity(a, o) > Multiplicity(b, o) | lemma | Source | [
"Boxes",
"Lists",
"Math",
"Sets",
"Sequences"
] | Source/DafnyCore/Prelude/Multisets.dfy | ExhibitSubsetDifference | |
ExhibitDifference(a: Multiset, b: Multiset) requires a != b ensures Multiplicity(a, o) != Multiplicity(b, o) decreases a != Nil, a.Cons? && b.Cons? && !Less(a.head, b.head), a | lemma | Source | [
"Boxes",
"Lists",
"Math",
"Sets",
"Sequences"
] | Source/DafnyCore/Prelude/Multisets.dfy | ExhibitDifference | |
MultiplicityFromSetIsBinary(s: Sets.Set, o: Box) ensures 0 <= Multiplicity(FromSet(s), o) <= 1 | lemma | Source | [
"Boxes",
"Lists",
"Math",
"Sets",
"Sequences"
] | Source/DafnyCore/Prelude/Multisets.dfy | MultiplicityFromSetIsBinary | |
MultiplicityFromSeqAppend(a: Sequences.Seq, b: Sequences.Seq, o: Box) ensures Multiplicity(FromSeq(Sequences.Append(a, b)), o) == Multiplicity(FromSeq(a), o) + Multiplicity(FromSeq(b), o) | lemma | Source | [
"Boxes",
"Lists",
"Math",
"Sets",
"Sequences"
] | Source/DafnyCore/Prelude/Multisets.dfy | MultiplicityFromSeqAppend | |
MultiplicityFromSeqContainment(s: Sequences.Seq, v: Box, x: Box) requires s.Contains(v) ensures Multiplicity(Singleton(v), x) <= Multiplicity(FromSeq(s), x) | lemma | Source | [
"Boxes",
"Lists",
"Math",
"Sets",
"Sequences"
] | Source/DafnyCore/Prelude/Multisets.dfy | MultiplicityFromSeqContainment | |
MultiplicityFromSeqCons(s: Sequences.Seq, x: Box) requires s.Cons? ensures Multiplicity(FromSeq(s), x) == Multiplicity(FromSeq(s.tail), x) + BoolInt(s.head == x) | lemma | Source | [
"Boxes",
"Lists",
"Math",
"Sets",
"Sequences"
] | Source/DafnyCore/Prelude/Multisets.dfy | MultiplicityFromSeqCons | |
SequenceAndMultisetContainment(s: Sequences.Seq, o: Box) ensures Sequences.Contains(s, o) <==> FromSeq(s).Contains(o) | lemma | Source | [
"Boxes",
"Lists",
"Math",
"Sets",
"Sequences"
] | Source/DafnyCore/Prelude/Multisets.dfy | SequenceAndMultisetContainment | |
Increasing(m: List<Box>) | predicate | Source | [
"Boxes",
"Lists",
"Math",
"Sets",
"Sequences"
] | Source/DafnyCore/Prelude/Multisets.dfy | Increasing | |
TailContains(s: Seq, val: Box) requires s.Cons? ensures Contains(s, val) <==> s.head == val || Contains(s.tail, val) | lemma | Source | [
"Lists",
"Boxes"
] | Source/DafnyCore/Prelude/Sequences.dfy | TailContains | |
DatatypeEquality(s0: Seq, s1: Seq) requires s0.Length() == s1.Length() requires forall j :: 0 <= j < s0.Length() ==> s0.At(j) == s1.At(j) ensures s0 == s1 | lemma | Source | [
"Lists",
"Boxes"
] | Source/DafnyCore/Prelude/Sequences.dfy | DatatypeEquality | |
UnionOneRaw(s: List<Box>, o: Box) : List<Box> | function | Source | [
"Boxes",
"Lists"
] | Source/DafnyCore/Prelude/Sets.dfy | UnionOneRaw | |
IntersectionRaw(a: List<Box>, b: List<Box>) : List<Box> | function | Source | [
"Boxes",
"Lists"
] | Source/DafnyCore/Prelude/Sets.dfy | IntersectionRaw | |
DifferenceRaw(a: List<Box>, b: List<Box>) : List<Box> | function | Source | [
"Boxes",
"Lists"
] | Source/DafnyCore/Prelude/Sets.dfy | DifferenceRaw | |
TailStrictlyIncreasing(s: List<Box>) requires StrictlyIncreasing(s) && s.Cons? ensures StrictlyIncreasing(s.tail) | lemma | Source | [
"Boxes",
"Lists"
] | Source/DafnyCore/Prelude/Sets.dfy | TailStrictlyIncreasing | |
UnionOneRawSame(s: List<Box>, o: Box) requires StrictlyIncreasing(s) && s.Contains(o) ensures s == UnionOneRaw(s, o) | lemma | Source | [
"Boxes",
"Lists"
] | Source/DafnyCore/Prelude/Sets.dfy | UnionOneRawSame | |
UnionOnePreservesStrictlyIncreasing(s: List<Box>, o: Box) requires StrictlyIncreasing(s) ensures StrictlyIncreasing(UnionOneRaw(s, o)) | lemma | Source | [
"Boxes",
"Lists"
] | Source/DafnyCore/Prelude/Sets.dfy | UnionOnePreservesStrictlyIncreasing | |
PrependIncreasing(o: Box, s: List<Box>) requires StrictlyIncreasing(s) requires s != Nil && Less(o, s.head) ensures StrictlyIncreasing(Cons(o, s)) | lemma | Source | [
"Boxes",
"Lists"
] | Source/DafnyCore/Prelude/Sets.dfy | PrependIncreasing | |
UnionCommutative(a: Set, b: Set) ensures Union(a, b) == Union(b, a) | lemma | Source | [
"Boxes",
"Lists"
] | Source/DafnyCore/Prelude/Sets.dfy | UnionCommutative | |
DisjointDifferenceAux(a: Set, b: Set) requires Disjoint(a, b) ensures Difference(Union(a, b), a) == b | lemma | Source | [
"Boxes",
"Lists"
] | Source/DafnyCore/Prelude/Sets.dfy | DisjointDifferenceAux | |
IntersectionRawElements(a: List<Box>, b: List<Box>, o: Box) ensures In(IntersectionRaw(a, b), o) <==> In(a, o) && In(b, o) | lemma | Source | [
"Boxes",
"Lists"
] | Source/DafnyCore/Prelude/Sets.dfy | IntersectionRawElements | |
IntersectionRawPreservesStrictlyIncreasing(a: List<Box>, b: List<Box>) requires StrictlyIncreasing(a) && StrictlyIncreasing(b) ensures StrictlyIncreasing(IntersectionRaw(a, b)) | lemma | Source | [
"Boxes",
"Lists"
] | Source/DafnyCore/Prelude/Sets.dfy | IntersectionRawPreservesStrictlyIncreasing | |
IntersectionCommutative(a: Set, b: Set) ensures Intersection(a, b) == Intersection(b, a) | lemma | Source | [
"Boxes",
"Lists"
] | Source/DafnyCore/Prelude/Sets.dfy | IntersectionCommutative | |
CardUnion(a: Set, b: Set) requires a != Nil ensures (TailStrictlyIncreasing(a); var m, n := Card(Union(a, b)), Card(Union(a.tail, b)); m == if In(b, a.head) then n else n + 1) | lemma | Source | [
"Boxes",
"Lists"
] | Source/DafnyCore/Prelude/Sets.dfy | CardUnion | |
DifferenceRawElements(a: List<Box>, b: List<Box>, o: Box) ensures In(DifferenceRaw(a, b), o) <==> In(a, o) && !In(b, o) | lemma | Source | [
"Boxes",
"Lists"
] | Source/DafnyCore/Prelude/Sets.dfy | DifferenceRawElements | |
DifferenceRawPreservesStrictlyIncreasing(a: List<Box>, b: List<Box>) requires StrictlyIncreasing(a) && StrictlyIncreasing(b) ensures StrictlyIncreasing(DifferenceRaw(a, b)) | lemma | Source | [
"Boxes",
"Lists"
] | Source/DafnyCore/Prelude/Sets.dfy | DifferenceRawPreservesStrictlyIncreasing | |
CardOfDisjoint(a: Set, b: Set) requires Disjoint(a, b) ensures Card(Union(a, b)) == Card(a) + Card(b) | lemma | Source | [
"Boxes",
"Lists"
] | Source/DafnyCore/Prelude/Sets.dfy | CardOfDisjoint | |
HeadIsSmallest(s: List<Box>, o: Box) requires StrictlyIncreasing(s) && s.Contains(o) ensures Below(s.head, o) | lemma | Source | [
"Boxes",
"Lists"
] | Source/DafnyCore/Prelude/Sets.dfy | HeadIsSmallest | |
NothingIsSmallerThanHead(s: List<Box>, o: Box) requires StrictlyIncreasing(s) && s != Nil && Less(o, s.head) ensures !s.Contains(o) | lemma | Source | [
"Boxes",
"Lists"
] | Source/DafnyCore/Prelude/Sets.dfy | NothingIsSmallerThanHead | |
TailDoesNotContainHead(s: List<Box>) requires StrictlyIncreasing(s) && s != Nil ensures !s.tail.Contains(s.head) | lemma | Source | [
"Boxes",
"Lists"
] | Source/DafnyCore/Prelude/Sets.dfy | TailDoesNotContainHead | |
StrictlyIncreasing(s: List<Box>) | predicate | Source | [
"Boxes",
"Lists"
] | Source/DafnyCore/Prelude/Sets.dfy | StrictlyIncreasing | |
In(s: List<Box>, o: Box) | predicate | Source | [
"Boxes",
"Lists"
] | Source/DafnyCore/Prelude/Sets.dfy | In | |
SeqToHeight(s: seq<T>, f: T --> nat) : (r: nat) | function | Source | [
"Std.Wrappers",
"Std"
] | Source/DafnyCore/Backends/Dafny/AST.dfy | SeqToHeight | |
name() : Name | function | Source | [
"Std.Wrappers",
"Std"
] | Source/DafnyCore/Backends/Dafny/AST.dfy | name | |
attributes() : seq<Attribute> | function | Source | [
"Std.Wrappers",
"Std"
] | Source/DafnyCore/Backends/Dafny/AST.dfy | attributes | |
Replace(mapping: map<Type, Type>) : Type | function | Source | [
"Std.Wrappers",
"Std"
] | Source/DafnyCore/Backends/Dafny/AST.dfy | Replace |
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Dafny
A structured dataset of functions, lemmas, and predicates from Dafny, a verification-aware programming language.
Source
- Repository: https://github.com/dafny-lang/dafny
- Website: https://dafny.org
- License: MIT
Statistics
| Property | Value |
|---|---|
| Total Entries | 9,572 |
| Functions | 4,849 |
| Predicates | 2,468 |
| Lemmas | 2,255 |
| Source Files | 2,155 |
Schema
| Column | Type | Description |
|---|---|---|
fact |
string | Declaration signature with specs |
type |
string | "function", "predicate", or "lemma" |
library |
string | Dafny module/directory |
imports |
list[string] | Import statements |
filename |
string | Source .dfy file |
symbolic_name |
string | Declaration name |
About Dafny
Dafny combines:
- Imperative programming (methods, loops)
- Functional programming (functions)
- Built-in verification (preconditions, postconditions, loop invariants)
- SMT-based automated proving (Z3)
Creator
Charles Norton (phanerozoic)
- Downloads last month
- 15
Size of downloaded dataset files:
257 kB
Size of the auto-converted Parquet files:
257 kB
Number of rows:
9,572