Quickcheck properties

gistfile1.txt

Tests
  basics
    arbitrary instance: wf(l):                                OK (0.04s)
      +++ OK, passed 5000 tests.
  take, drop
    take
      commutativity: take n ∘ take m ≡ take m ∘ take n:       OK (1.57s)
        +++ OK, passed 5000 tests.
      accumulativity: take m ∘ take n ≡ take (m ⊓ n):         OK (1.54s)
        +++ OK, passed 5000 tests.
      bounds length: length (take m t) ≡ length t ⊓ m:        OK (0.02s)
        +++ OK, passed 5000 tests.
      data refinement: take n ∘ fromList ≡ fromList ∘ take n: OK (1.15s)
        +++ OK, passed 5000 tests.
      data abstraction: toList ∘ take n ≡ take n ∘ toList:    OK (0.80s)
        +++ OK, passed 5000 tests.
      identity: take (length t) t ≡ t:                        OK (2.91s)
        +++ OK, passed 5000 tests.
      empty-neutral: take n ε ≡ ε:                            OK (0.01s)
        +++ OK, passed 5000 tests.
      wellformedness invariant: wf(take n t):                 OK
        +++ OK, passed 5000 tests.
    drop
      commutativity: drop n ∘ drop m ≡ drop m ∘ drop n:       OK (0.31s)
        +++ OK, passed 5000 tests.
      accumulativity: drop n ∘ drop m ≡ drop (m + n):         OK (0.28s)
        +++ OK, passed 5000 tests.
      reduces length: length (drop n t) ≡ length t ∸ n:       OK (0.02s)
        +++ OK, passed 5000 tests.
      unappending: drop (length t) (t ∙ u) ≡ u:               OK (2.95s)
        +++ OK, passed 5000 tests.
      data refinement: drop n ∘ fromList ≡ fromList ∘ drop n: OK (2.12s)
        +++ OK, passed 5000 tests.
      data abstraction: toList ∘ drop n ≡ drop n ∘ toList:    OK (1.62s)
        +++ OK, passed 5000 tests.
      identity: drop 0 ≡ id:                                  OK (2.93s)
        +++ OK, passed 5000 tests.
      empty-neutral: drop n ε ≡ ε:                            OK
        +++ OK, passed 5000 tests.
      wellformedness invariant: wf(drop n t):                 OK (0.03s)
        +++ OK, passed 5000 tests.
    take-drop: take n t ∙ drop n t ≡ t:                       OK (3.08s)
      +++ OK, passed 5000 tests.
  monoid operations
    left identity: ε ∙ t ≡ t:                                 OK (2.90s)
      +++ OK, passed 5000 tests.
    right identity: t ∙ ε ≡ t:                                OK (2.92s)
      +++ OK, passed 5000 tests.
    associativity: t ∙ (u ∙ v) ≡ (t ∙ u) ∙ v:                 OK (10.17s)
      +++ OK, passed 5000 tests.
    data refinement: fromList is a monoid morphism
      identity: fromList [] ≡ ε:                              OK
        +++ OK, passed 5000 tests.
      append: fromList (a ++ b) ≡ fromList a ∙ fromList b:    OK (6.51s)
        +++ OK, passed 5000 tests.
    data abstraction: toList is a monoid morphism
      identity: toList ε ≡ []:                                OK
        +++ OK, passed 5000 tests.
      append: toList (a ∙ b) ≡ toList a ++ toList b:          OK (4.65s)
        +++ OK, passed 5000 tests.
    length is a monoid morphism
      identity: length ε ≡ 0:                                 OK
        +++ OK, passed 5000 tests.
      append: length (a ∙ b) = length a + length b:           OK (0.03s)
        +++ OK, passed 5000 tests.
    wellformedness invariant
      identity: wf(ε):                                        OK
        +++ OK, passed 5000 tests.
      append: wf(a ∙ b):                                      OK (0.05s)
        +++ OK, passed 5000 tests.
  composed
    data refinement: composed ∘ fromList ≡ mconcat:           OK (2.79s)
      +++ OK, passed 5000 tests.
    data abstraction: composed ≡ mconcat ∘ toList:            OK (3.06s)
      +++ OK, passed 5000 tests.
    composed is a monoid morphism
      identity: composed ε ≡ ε:                               OK
        +++ OK, passed 5000 tests.
      append: composed (t ∙ u) ≡ composed t ∙ composed u:     OK (6.55s)
        +++ OK, passed 5000 tests.
  (fromList, toList) is an isomorphism
    fromList ∘ toList ≡ id:                                   OK (3.23s)
      +++ OK, passed 5000 tests.
    toList ∘ fromList ≡ id:                                   OK (2.31s)
      +++ OK, passed 5000 tests.

All 36 tests passed (66.77s)