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Version 3.0

The library has been tested using Agda 2.8.0.

Highlights

  • Modules that previously used --cubical-compatible once again use --without-K.

  • The notation for Decidable relations has been (partially) standardised: thus

    • _≡?_ (at infix 4) for DecidableEquality
    • _≈?_ (ditto.) for the general IsDecEquivalence

    At present, the old fieldname _≟_ has been retained, in order to avoid a non-backwards compatible/breaking change of fieldname, which will plan to do in Version 3.0, with accompanying deprecation of that name, against its eventual removal in subsequent versions.

    The change leads to a number of (trivial) renamings/deprecations, others more substantive in Data.{Nat|Fin}.Properties for the concrete datatypes, which are summarised below, but are not each documented for all affected modules.

Bug-fixes

  • Fix a bug in Data.List.Base's linesBy (the last empty line would be dropped).

Non-backwards compatible changes

  • issue #2547 The names of the implicit binders in the following definitions have been rectified to be consistent with the rest of Relation.Binary.Definitions: Transitive, Antisym, and Antisymmetric.

  • Issue #2548 Consistent with other names (such as ∙-cong, ε-homo etc.) in Algebra.*, the field name of the basic homomorphism property homo in Algebra.Morphism.Structures.IsMagmaHomomorphism has been renamed to ∙-homo.

Minor improvements

  • In Induction.WellFoudned, the final parameter of Acc has been changed to an index.

Deprecated modules

Deprecated names

  • In Algebra.Morphism.Structures:

    homo  ↦  ∙-homo

  • In Data.Fin.Properties:

    _≟_      ↦  _≡?_
inj⇒≟    ↦  inj⇒≡?
≟-≡      ↦  ≡?-≡
≟-≡-refl ↦  ≡?-≡-refl
≟-≢     ↦  ≡?-≢

  • In Data.Integer.GCD:

    gcd[0,0]≡0 ↦ gcd[i,i]≡∣i∣

  • In Data.Nat.GCD:

    gcd[0,0]≡0 ↦ gcd[n,n]≡n

  • In Data.Nat.Properties:

    _≟_       ↦   _≡?_
≟-diag    ↦   ≡?-≡
≟-≡       ↦   ≡?-≢
≟?-≡-refl ↦ ≡?-≡-refl

  • In Effect.Monad.Partiality:

    _≟-Kind_     ↦   _≡?-Kind_

  • In Reflection.AST.AlphaEquality:

    ≟⇒α     ↦   ≡?⇒α

  • In Relation.Binary.PropositionalEquality:

    ≡-≟-identity     ↦   ≡-≡?-identity
≢-≟-identity     ↦   ≢-≡?-identity

  • In Relation.Nary:

    ≟-mapₙ     ↦   ≡?-mapₙ

New modules

  • Codata.Guarded.Stream.Relation.Unary.Linked for a proof that each pair of consecutive elements of a stream are related.

  • Data.Bool.ListAction.Properties for properties of conjunction and disjunction of lists.

  • A new type of lists that grow on the right. This is typically useful to model contexts of typing rules or type accumulators that need to be reversed in the base case.

    Data.SnocList.Base

Additions to existing modules

  • In Data.Integer.GCD:

    gcd[i,i]≡∣i∣ : ∀ i → gcd i i ≡ + ∣i∣

  • In Data.Nat.GCD:

    gcd[n,n]≡n : ∀ n → gcd n n ≡ n

  • In Data.Rational.Properties:

    ↥[i/1]≡i  : (i : ℤ) → ↥ (i / 1) ≡ i
↧ₙ[i/1]≡1 : (i : ℤ) → ↧ₙ (i / 1) ≡ 1
n/n≡1 : ∀ (n : ℕ) .{{_ : ℕ.NonZero n}} → + n / n ≡ 1ℚ
-i/n≡-[i/n] : ∀ (i : ℤ) (n : ℕ) .{{_ : ℕ.NonZero n}} →
              ℤ.- i / n ≡ - (i / n)
*-cancelˡ-/ : ∀ p {q r} .{{_ : ℕ.NonZero r}} .{{_ : ℕ.NonZero (p ℕ.* r)}} →
              (+ p ℤ.* q) / (p ℕ.* r) ≡ q / r
*-cancelʳ-/ : ∀ p {q r} .{{_ : ℕ.NonZero r}} .{{_ : ℕ.NonZero (r ℕ.* p)}} →
              (q ℤ.* + p) / (r ℕ.* p) ≡ q / r
i/n+j/n≡[i+j]/n : ∀ (i j : ℤ) (n : ℕ) .{{_ : ℕ.NonZero n }} →
                  i / n + j / n ≡ (i ℤ.+ j) / n