References Telescopes Termination Checking With-functions Universe Levels With-Abstraction Usage Technical details Without K Abstract definitions Definitions can be marked as abstract, for the purpose abstraction Rewrite The inspect idiom Alternatives to with-abstraction Performance considerations Technical details Examples Ill-typed with-abstractions With abstraction was first introduced by Conor McBride type and the type of the original arguments are generalised over the value of the scrutinee. See Technical details below for the details. This generalisation is important when you have to prove properties

Termination Checking With-functions Pragmas and Options Universe Levels With-Abstraction Usage Technical details Without K Abstract definitions Definitions can be marked as abstract, for the purpose repetition Rewrite The inspect idiom Alternatives to with-abstraction Performance considerations Technical details Examples Ill-typed with-abstractions With abstraction was first introduced by Conor McBride type and the type of the original arguments are generalised over the value of the scrutinee. See Technical details below for the details. This generalisation is important when you have to prove properties

Termination Checking With-functions Pragmas and Options Universe Levels With-Abstraction Usage Technical details Without K Abstract definitions Definitions can be marked as abstract, for the purpose repetition Rewrite The inspect idiom Alternatives to with-abstraction Performance considerations Technical details Examples Ill-typed with-abstractions With-abstraction was first introduced by Conor McBride type and the type of the original arguments are generalised over the value of the scrutinee. See Technical details below for the details. This generalisation is important when you have to prove properties

Termination Checking With-functions Pragmas and Options Universe Levels With-Abstraction Usage Technical details Without K Abstract definitions Definitions can be marked as abstract, for the purpose repetition Rewrite The inspect idiom Alternatives to with-abstraction Performance considerations Technical details Examples Ill-typed with-abstractions With-abstraction was first introduced by Conor McBride type and the type of the original arguments are generalised over the value of the scrutinee. See Technical details below for the details. This generalisation is important when you have to prove properties

Termination Checking With-functions Pragmas and Options Universe Levels With-Abstraction Usage Technical details Without K Abstract definitions Definitions can be marked as abstract, for the purpose repetition Rewrite The inspect idiom Alternatives to with-abstraction Performance considerations Technical details Examples Ill-typed with-abstractions With-abstraction was first introduced by Conor McBride type and the type of the original arguments are generalised over the value of the scrutinee. See Technical details below for the details. This generalisation is important when you have to prove properties

Rewrite – The inspect idiom – Alternatives to with-abstraction – Performance considerations • Technical details – Examples – Ill-typed with-abstractions With abstraction was first introduced by Conor type and the type of the original arguments are generalised over the value of the scrutinee. See Technical details below for the details. This generalisation is important when you have to prove properties patterns. Helper functions Internally with-abstractions are translated to auxiliary functions (see Technical details below) and you can always1 write these functions manually. The downside is that the type

References Universe Levels Introduction to universes Universe polymorphism With-Abstraction Usage Technical details Without K Restrictions on pattern matching Restrictions on termination checking Restrictions repetition Rewrite The inspect idiom Alternatives to with-abstraction Performance considerations Technical details Examples Ill-typed with-abstractions With-abstraction was first introduced by Conor McBride type and the type of the original arguments are generalised over the value of the scrutinee. See Technical details below for the details. This generalisation is important when you have to prove properties

References Universe Levels Introduction to universes Universe polymorphism With-Abstraction Usage Technical details Without K Restrictions on pattern matching Restrictions on termination checking Restrictions repetition Rewrite The inspect idiom Alternatives to with-abstraction Performance considerations Technical details Examples Ill-typed with-abstractions With-abstraction was first introduced by Conor McBride type and the type of the original arguments are generalised over the value of the scrutinee. See Technical details below for the details. This generalisation is important when you have to prove properties

Rewrite – The inspect idiom – Alternatives to with-abstraction – Performance considerations • Technical details – Examples 3.31. Universe Levels 81 Agda Documentation, Release 2.5.3 – Ill-typed with-abstractions type and the type of the original arguments are generalised over the value of the scrutinee. See Technical details below for the details. This generalisation is important when you have to prove properties patterns. Helper functions Internally with-abstractions are translated to auxiliary functions (see Technical details below) and you can always1 write these functions manually. The downside is that the type

properties forall notation Expressions of sort Setω Pragmas and options With-Abstraction Usage Technical details Without K Restrictions on pattern matching Restrictions on termination checking Restrictions to substitute the indices of an indexed inductive type. A handful of definitions (satisfying a technical restriction on their pattern matching) will compute when applied to a transport along indices. As With-abstraction equality Alternatives to with-abstraction Termination checking Performance considerations Technical details Examples Ill-typed with-abstractions With-abstraction was first introduced by Conor McBride