In the constraints, $e, e^{'}$ means pairwise APIs, $p, p^{'}$ means pairwise parameters of pairwise functions.
In the grading, we only give the level for breaking changes on public APIs, since breaking changes on private APIs are always 🟡 Low breaking.

Module (2)

AddModule

Add a new module.

e = ⊥ \land e^{'} \in M

🟢 Compatible

RemoveModule

Remove an old module.

e \in M \land e^{'} = ⊥

🔴 High

Class (7)

AddClass

Add a new class.

e = ⊥ \land e^{'} \in C

🟢 Compatible

RemoveClass

Remove an old class.

e \in C \land e^{'} = ⊥

🔴 High

ChangeInheritance

In this case, the following basic constraint is omitted.

e, e^{'} \in C

AddBaseClass

Add a class to base classes.

b a s e s (e^{'}) \neq \subseteq b a s e s (e)

🟢 Compatible

RemoveBaseClass

Remove a class from base classes.

b a s e s (e) \neq \subseteq b a s e s (e^{'})

🔴 High

ImplementAbstractBaseClass

Implement a new (builtin) abstract base class.

a b c s (e^{'}) \neq \subseteq a b c s (e)

🟢 Compatible

DeimplementAbstractBaseClass

Deimplement a (builtin) abstract base class.

a b c s (e) \neq \subseteq a b c s (e^{'})

🔴 High

ChangeMethodResolutionOrder

Change method resolution order of a class.

m r o (e) \neq = m r o (e^{'})

🟠 Medium

Function (5)

AddFunction

In this case, the following basic constraint is omitted.

e = ⊥ \land e^{'} \in F

AddFunction

Add a new function, which is not bound to a class/instance.

s c o p e (e^{'}) = Static

🟢 Compatible

AddMethod

Add a new method, which is bound to a class/instance.

s c o p e (e^{'}) \neq = Static

🟢 Compatible

RemoveFunction

In this case, the following basic constraint is omitted.

e \in F \land e^{'} = ⊥

RemoveFunction

Remove an old function, which is not bound to a class/instance.

s c o p e (e) = Static

🔴 High

RemoveMethod

Remove an old method, which is bound to a class/instance.

s c o p e (e) \neq = Static

🔴 High

ChangeReturnType

Change type of return value for a function.

e, e^{'} \in F \land r e t u r n (e) \neq = ⊥ \land r e t u r n (e^{'}) \neq = ⊥ \land r e t u r n (e) \neq = r e t u r n (e^{'})

🟠 Medium if $r e t u r n (e^{'}) \neq \subseteq r e t u r n (e)$

Attribute (5)

AddAttribute

In this case, the following basic constraint is omitted.

e = ⊥ \land e^{'} \in A

AddAttribute

Add a new attribute, which is not bound to an instance.

s c o p e (e^{'}) \neq = Instance

🟢 Compatible

AddInstanceAttribute

Add a new attribute, which is bound to an instance.

s c o p e (e^{'}) = Instance

🟢 Compatible

RemoveAttribute

In this case, the following basic constraint is omitted.

e \in A \land e^{'} = ⊥

RemoveAttribute

Remove an old attribute, which is not bound to an instance.

s c o p e (e) \neq = Instance

🔴 High

RemoveInstanceAttribute

Remove an old attribute, which is bound to an instance.

s c o p e (e) = Instance

🔴 High

ChangeAttributeType

Change type of an attribute.

e, e^{'} \in A \land t y p e (e) \neq = ⊥ \land t y p e (e^{'}) \neq = ⊥ \land t y p e (e) \neq = t y p e (e^{'})

🟠 Medium if $t y p e (e^{'}) \neq \subseteq t y p e (e)$

Parameter (17)

AddParameter

In this case, the following basic constraint is omitted.

p = ⊥ \land p^{'} \neq = ⊥

AddRequiredParameter

Add a new required parameter.

\neg o p t i o n a l (p^{'})

🔴 High

AddOptionalParameter

Add a new optional parameter.

o p t i o n a l (p^{'})

🟠 Medium if $s c o p e (e^{'}) \neq = Static$ , i.e. the parameter is from an instance method.

AddVarPositional

Add VarPositional parameter.

k i n d (p^{'}) = VarPositional

🟢 Compatible

AddVarKeyword

Add VarKeyword parameter.

k i n d (p^{'}) = VarKeyword

🟢 Compatible

AddRequiredCandidate

Add a new required keyword candidate parameter.

k i n d (p^{'}) = VarKeywordCandidate \land \neg o p t i o n a l (p^{'})

🟠 Medium

AddOptionalCandidate

Add a new optional keyword candidate parameter.

k i n d (p^{'}) = VarKeywordCandidate \land o p t i o n a l (p^{'})

🟢 Compatible

RemoveParameter

In this case, the following basic constraint is omitted.

p \neq = ⊥ \land p^{'} = ⊥

RemoveRequiredParameter

Remove a required parameter.

\neg o p t i o n a l (p)

🔴 High

RemoveOptionalParameter

Remove an optional parameter.

o p t i o n a l (p)

🔴 High

RemoveVarPositional

Remove VarPositional parameter.

k i n d (p) = VarPositional

🔴 High

RemoveVarKeyword

Remove VarKeyword parameter.

k i n d (p) = VarKeyword

🔴 High

RemoveRequiredCandidate

Remove a required keyword candidate parameter.

k i n d (p) = VarKeywordCandidate \land \neg o p t i o n a l (p)

🟠 Medium

RemoveOptionalCandidate

Reove an optional keyword candidate parameter.

k i n d (p) = VarKeywordCandidate \land o p t i o n a l (p)

🟠 Medium

ChangeParameter

In this case, the following basic constraint is omitted.

p \neq = ⊥ \land p^{'} \neq = ⊥

AddParameterDefault

Add default value of a parameter (making it optional).

\neg o p t i o n a l (p) \land o p t i o n a l (p^{'})

🟠 Medium if $s c o p e (e^{'}) \neq = Static$ , i.e. the parameter is from an instance method.

RemoveParameterDefault

Remove default value of a parameter (making it required).

o p t i o n a l (p) \land \neg o p t i o n a l (p^{'})

🔴 High

ChangeParameterDefault

Change default value of a parameter.

o p t i o n a l (p) \land o p t i o n a l (p^{'}) \land d e f a u l t (p) \neq = d e f a u l t (p^{'})

🟠 Medium if $s c o p e (e^{'}) \neq = Static$ , i.e. the parameter is from an instance method.

MoveParameter

Change a positional parameter's position.

k i n d (p), k i n d (p^{'}) \in {Positional, PositionalOrKeyword} \land p o s i t i o n (p) \neq = p o s i t i o n (p^{'})

🔴 High

ChangeParameterType

Change type of a parameter.

t y p e (p) \neq = ⊥ \land t y p e (p^{'}) \neq = None \land t y p e (p) \neq = t y p e (p^{'})

🟠 Medium if $t y p e (p) \neq \subseteq t y p e (p^{'})$

Alias (6)

In this case, the following basic constraint is omitted.

e, e^{'} \in M \cup C

AddAlias

Add an alias to an API in the package.

\exists (n, t), t \in E \land n \in a l i a s e s (t) \land (n, t) \in (m e m b e r s (e^{'}) - m e m b e r s (e))

🟢 Compatible

AddExternalAlias

Add an alias to an API out of the package.

\exists n, (n, ⊥) \in (m e m b e r s (e^{'}) - m e m b e r s (e))

🟢 Compatible

RemoveAlias

Remove an alias from an API in the package.

\exists (n, t), t \in E \land n \in a l i a s e s (t) \land (n, t) \in (m e m b e r s (e) - m e m b e r s (e^{'}))

🔴 High

RemoveExternalAlias

Remove an alias from an API out of the package.

\exists n, (n, ⊥) \in (m e m b e r s (e) - m e m b e r s (e^{'}))

🟡 Low

ChangeAlias

Change the target in the package of an alias.

\exists n, (n, t_{1}) \in m e m b e r s (e) \land (n, t_{2}) \in m e m b e r s (e^{'}) \land t_{1} \in E \land t_{2} \in E \land t_{1} \neq = t_{2}

🟢 Compatible

ChangeExternalAlias

Change the external target of an alias.

\exists (n, t_{1}) \in m e m b e r s (e) \land (n, t_{2}) \in m e m b e r s (e^{'}) \land (t_{1} = ⊥ \lor t_{2} = ⊥) \land (t_{1} \neq = ⊥ \lor t_{2} \neq = ⊥)

🟢 Compatible