that are used by Agda. The theoretical foundation for Agda’s sort system are Pure Type Systems (PTS). A PTS has, besides the set of supported sorts, two parameters: 1. A set of axioms of the form s : s� (s1, s2, s3) stating that if A : s1 and B(x) : s2 then (x : A) → B(x) : s3. Agda is a functional PTS in the sense that s3 is uniquely determined by s1 and s2. Axioms are implemented internally by the once their arguments are known. univSort univSort returns the successor sort of a given sort. In PTS terminology, it implements the axioms s : univSort s. Table 1: univSort sort successor sort Prop

that are used by Agda. The theoretical foundation for Agda’s sort system are Pure Type Systems (PTS). A PTS has, besides the set of supported sorts, two parameters: 1. A set of axioms of the form s : s� : A) → B(x) : s3. 3.40. Sort System 183 Agda User Manual, Release 2.6.4.3 Agda is a functional PTS in the sense that s3 is uniquely determined by s1 and s2. Axioms are implemented internally by the Agda User Manual, Release 2.6.4.3 univSort univSort returns the successor sort of a given sort. In PTS terminology, it implements the axioms s : univSort s. Table 1: univSort sort successor sort Prop

that are used by Agda. The theoretical foundation for Agda’s sort system are Pure Type Systems (PTS). A PTS has, besides the set of supported sorts, two parameters: 1. A set of axioms of the form s : s� : A) → B(x) : s3. 3.40. Sort System 183 Agda User Manual, Release 2.6.4.2 Agda is a functional PTS in the sense that s3 is uniquely determined by s1 and s2. Axioms are implemented internally by the Agda User Manual, Release 2.6.4.2 univSort univSort returns the successor sort of a given sort. In PTS terminology, it implements the axioms s : univSort s. Table 1: univSort sort successor sort Prop

that are used by Agda. The theoretical foundation for Agda’s sort system are Pure Type Systems (PTS). A PTS has, besides the set of supported sorts, two parameters: 1. A set of axioms of the form s : s� (s1, s2, s3) stating that if A : s1 and B(x) : s2 then (x : A) → B(x) : s3. Agda is a functional PTS in the sense that s3 is uniquely determined by s1 and s2. Axioms are implemented internally by the Agda User Manual, Release 2.6.4 univSort univSort returns the successor sort of a given sort. In PTS terminology, it implements the axioms s : univSort s. Table 1: univSort sort successor sort Prop