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=\bot\wedge e'\in M

🟢 Compatible

RemoveModule

Remove an old module.

e\in M\wedge e'=\bot

🔴 High

Class (7)

AddClass

Add a new class.

e=\bot\wedge e'\in C

🟢 Compatible

RemoveClass

Remove an old class.

e\in C\wedge e'=\bot

🔴 High

ChangeInheritance

In this case, the following basic constraint is omitted.

e,e'\in C

AddBaseClass

Add a class to base classes.

\mathbf{bases}(e')\not\subseteq\mathbf{bases}(e)

🟢 Compatible

RemoveBaseClass

Remove a class from base classes.

\mathbf{bases}(e)\not\subseteq\mathbf{bases}(e')

🔴 High

ImplementAbstractBaseClass

Implement a new (builtin) abstract base class.

\mathbf{abcs}(e')\not\subseteq\mathbf{abcs}(e)

🟢 Compatible

DeimplementAbstractBaseClass

Deimplement a (builtin) abstract base class.

\mathbf{abcs}(e)\not\subseteq\mathbf{abcs}(e')

🔴 High

ChangeMethodResolutionOrder

Change method resolution order of a class.

\mathbf{mro}(e)\ne\mathbf{mro}(e')

🟠 Medium

Function (5)

AddFunction

In this case, the following basic constraint is omitted.

e=\bot\wedge e'\in F

AddFunction

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

\mathbf{scope}(e')=\text{Static}

🟢 Compatible

AddMethod

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

\mathbf{scope}(e')\ne\text{Static}

🟢 Compatible

RemoveFunction

In this case, the following basic constraint is omitted.

e\in F\wedge e'=\bot

RemoveFunction

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

\mathbf{scope}(e)=\text{Static}

🔴 High

RemoveMethod

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

\mathbf{scope}(e)\ne\text{Static}

🔴 High

ChangeReturnType

Change type of return value for a function.

e,e'\in F\wedge \mathbf{return}(e)\ne \bot\wedge\mathbf{return}(e')\ne \bot\wedge\mathbf{return}(e)\ne\mathbf{return}(e')

🟠 Medium if \mathbf{return}(e')\not\subseteq\mathbf{return}(e)

Attribute (5)

AddAttribute

In this case, the following basic constraint is omitted.

e=\bot\wedge e'\in A

AddAttribute

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

\mathbf{scope}(e')\ne\text{Instance}

🟢 Compatible

AddInstanceAttribute

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

\mathbf{scope}(e')=\text{Instance}

🟢 Compatible

RemoveAttribute

In this case, the following basic constraint is omitted.

e\in A\wedge e'=\bot

RemoveAttribute

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

\mathbf{scope}(e)\ne\text{Instance}

🔴 High

RemoveInstanceAttribute

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

\mathbf{scope}(e)=\text{Instance}

🔴 High

ChangeAttributeType

Change type of an attribute.

e,e'\in A\wedge\mathbf{type}(e)\ne \bot\wedge\mathbf{type}(e')\ne \bot\wedge\mathbf{type}(e)\ne\mathbf{type}(e')

🟠 Medium if \mathbf{type}(e')\not\subseteq\mathbf{type}(e)

Parameter (17)

AddParameter

In this case, the following basic constraint is omitted.

p=\bot\wedge p'\ne\bot

AddRequiredParameter

Add a new required parameter.

\neg\mathbf{optional}(p')

🔴 High

AddOptionalParameter

Add a new optional parameter.

\mathbf{optional}(p')

🟠 Medium if \mathbf{scope}(e')\ne\text{Static}, i.e. the parameter is from an instance method.

AddVarPositional

Add VarPositional parameter.

\mathbf{kind}(p')=\text{VarPositional}

🟢 Compatible

AddVarKeyword

Add VarKeyword parameter.

\mathbf{kind}(p')=\text{VarKeyword}

🟢 Compatible

AddRequiredCandidate

Add a new required keyword candidate parameter.

\mathbf{kind}(p')=\text{VarKeywordCandidate}\wedge \neg\mathbf{optional}(p')

🟠 Medium

AddOptionalCandidate

Add a new optional keyword candidate parameter.

\mathbf{kind}(p')=\text{VarKeywordCandidate}\wedge \mathbf{optional}(p')

🟢 Compatible

RemoveParameter

In this case, the following basic constraint is omitted.

p\ne\bot\wedge p'=\bot

RemoveRequiredParameter

Remove a required parameter.

\neg\mathbf{optional}(p)

🔴 High

RemoveOptionalParameter

Remove an optional parameter.

\mathbf{optional}(p)

🔴 High

RemoveVarPositional

Remove VarPositional parameter.

\mathbf{kind}(p)=\text{VarPositional}

🔴 High

RemoveVarKeyword

Remove VarKeyword parameter.

\mathbf{kind}(p)=\text{VarKeyword}

🔴 High

RemoveRequiredCandidate

Remove a required keyword candidate parameter.

\mathbf{kind}(p)=\text{VarKeywordCandidate}\wedge \neg\mathbf{optional}(p)

🟠 Medium

RemoveOptionalCandidate

Reove an optional keyword candidate parameter.

\mathbf{kind}(p)=\text{VarKeywordCandidate}\wedge \mathbf{optional}(p)

🟠 Medium

ChangeParameter

In this case, the following basic constraint is omitted.

p\ne\bot\wedge p'\ne\bot

AddParameterDefault

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

\neg\mathbf{optional}(p) \wedge \mathbf{optional}(p')

🟠 Medium if \mathbf{scope}(e')\ne\text{Static}, i.e. the parameter is from an instance method.

RemoveParameterDefault

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

\mathbf{optional}(p) \wedge \neg\mathbf{optional}(p')

🔴 High

ChangeParameterDefault

Change default value of a parameter.

\mathbf{optional}(p) \wedge \mathbf{optional}(p')\wedge \mathbf{default}(p)\ne\mathbf{default}(p')

🟠 Medium if \mathbf{scope}(e')\ne\text{Static}, i.e. the parameter is from an instance method.

MoveParameter

Change a positional parameter's position.

\mathbf{kind}(p),\mathbf{kind}(p')\in\{\text{Positional},\text{PositionalOrKeyword}\}\wedge\mathbf{position}(p)\ne \mathbf{position}(p')

🔴 High

ChangeParameterType

Change type of a parameter.

\mathbf{type}(p)\ne \bot\wedge\mathbf{type}(p')\ne \text{None}\wedge\mathbf{type}(p)\ne\mathbf{type}(p')

🟠 Medium if \mathbf{type}(p)\not\subseteq\mathbf{type}(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 \wedge n \in \mathbf{aliases}(t)\wedge (n,t) \in (\mathbf{members}(e') - \mathbf{members}(e))

🟢 Compatible

AddExternalAlias

Add an alias to an API out of the package.

\exists n, (n,\bot)\in (\mathbf{members}(e') - \mathbf{members}(e))

🟢 Compatible

RemoveAlias

Remove an alias from an API in the package.

\exists (n, t), t\in E \wedge n \in \mathbf{aliases}(t)\wedge (n,t) \in (\mathbf{members}(e) - \mathbf{members}(e'))

🔴 High

RemoveExternalAlias

Remove an alias from an API out of the package.

\exists n, (n,\bot)\in (\mathbf{members}(e) - \mathbf{members}(e'))

🟡 Low

ChangeAlias

Change the target in the package of an alias.

\exists n, (n,t_1)\in \mathbf{members}(e)\wedge (n,t_2)\in \mathbf{members}(e') \wedge t_1\in E\wedge t_2\in E\wedge t_1\ne t_2

🟢 Compatible

ChangeExternalAlias

Change the external target of an alias.

\exists (n,t_1)\in \mathbf{members}(e)\wedge (n,t_2)\in \mathbf{members}(e') \wedge (t_1=\bot\vee t_2=\bot)\wedge(t_1\ne\bot\vee t_2\ne\bot)

🟢 Compatible