Kind/book/testBBT.kind2

// Add_spaces
// : ∀(n: #U60)
//   (String)
// = λn
//   (U60.if #(== n #0) String (String.concat "  " (Add_spaces #(- n #1))) "")

// U60.Map_show
// : ∀(map: (U60.Map String))
//   ∀(depth: #U60)
//   (String)
// = λmap λdepth
//   let P = λx(String)
//   let bin = λsize λkey λval λlft λrgt
//     let cct = λa λb (String.concat a b)
//     let spc = λx (cct (Add_spaces depth) x)
//     let nnl = λx (cct String.newline x)
//     let key  = (U60.show key)
//     let size = (U60.show size)
//     let a = (nnl (spc (cct "key: " key)))
//     let b = (cct ", size: " size)
//     let c = (cct ", value: " val)
//     let d = (nnl (spc (cct "left: " (U60.Map_show lft #(+ #1 depth)))))
//     let e = (nnl (spc (cct "right: " (U60.Map_show rgt #(+ #1 depth)))))
//     (cct a (cct b (cct c (cct d e ))))
//   let tip = ""
//   (~map P bin tip)

// U60.Map.gen
// : ∀(V: *)
//   ∀(to_val: ∀(n: #U60) V)
//   ∀(n: #U60)
//   (U60.Map V)
// = λV λto_val λn
//   (U60.Map.gen.go V to_val n (U60.Map.new V))

// U60.Map.gen.go
// : ∀(V: *)
//   ∀(to_val: ∀(n: #U60) V)
//   ∀(n: #U60)
//   ∀(map: (U60.Map V))
//   (U60.Map V)
// = λV λto_val λn λmap
//   let P     = λx ∀(map: (U60.Map String)) (U60.Map String)
//   let true  = λmap (U60.Map.set String n (to_val n) map)
//   let false = λmap (U60.Map.gen.go V to_val #(- n #1) (U60.Map.set String n (to_val n) map))
//   ((~(U60.to_bool #(== n #0)) P true false) map)


// U60.fold
// : ∀(A: *)
//   ∀(f: ∀(n: #U60) ∀(acc: A) A)
//   ∀(nil: A)
//   ∀(n: #U60)
//   A
// = λA λf λnil λn
//   (U60.fold.go A f nil n)

// U60.fold.go
// : ∀(A: *)
//   ∀(f: ∀(n: #U60) ∀(acc: A) A)
//   ∀(acc: A)
//   ∀(n: #U60)
//   A
// = λA λf λacc λn
//   (~(U60.to_bool n) λx(A) (U60.fold.go A f (f n acc) #(- n #1)) acc)


// AscendingMap
// : (U60.Map #U60)
// = 
//   let nil = (U60.Map.new #U60)
//   let f = λn λacc (U60.Map.set #U60 #(- #11 n) #(- #11 n) acc)
//   (U60.fold (U60.Map #U60) f nil #10)

// DescendingMap
// : (U60.Map #U60)
// = 
//   let nil = (U60.Map.new #U60)
//   let f = λn λacc (U60.Map.set #U60 #(+ n #0) n acc)
//   (U60.fold (U60.Map #U60) f nil #10)

// U60.Map.sum
// : ∀(map: (U60.Map #U60))
//   (#U60)
// = λmap
//   let P = λx(#U60)
//   let bin = λsize λkey λval λlft λrgt
//     let sum = #(+ #(+ key (U60.Map.sum lft)) (U60.Map.sum rgt))
//     sum
//   let tip = #0 
//   (~map P bin tip)

// Test1
// : (Maybe String)
// = 
//   let emptyMap   = (BBT.tip #U60 String)
//   let updatedMap = (U60.Map.set String #5 "value5" emptyMap)
//   let value      = (U60.Map.get String #5 updatedMap)
//   let is_equal   = (String.equal (~value λx(String) λsome(some) "none") "value5")
//   (~is_equal λx(Maybe String) (Maybe.none String) (Maybe.some String "Test 1 Failed!"))

// Test2
// : (Maybe String)
// = 
//   let initialMap = (U60.Map.set String #10 "initialValue" (U60.Map.new String))
//   let updatedMap = (U60.Map.set String #10 "updatedValue" initialMap)
//   let value      = (U60.Map.get String #10 updatedMap)
//   let is_equal   = (String.equal (~value λx(String) λsome(some) "none") "updatedValue")
//   (~is_equal λx(Maybe String) (Maybe.none String) (Maybe.some String "Test 2 Failed!"))

// Test3
// : (Maybe String)
// = 
//   let map = (U60.Map.gen String U60.show #24)
//   let value = (U60.Map.get String #7 map)
//   let is_equal = (String.equal (~value λx(String) λsome(some) "none") "7")
//   (~is_equal λx(Maybe String) (Maybe.none String) (Maybe.some String "Test 3 Failed!"))

// Test4
// : (Maybe String)
// = 
//   let map = (U60.Map.gen String U60.show #5) 
//   let value = (U60.Map.get String #6 map) 
//   let is_none = (~value λx(Bool) λval(Bool.false) Bool.true) 
//   (~is_none λx(Maybe String) (Maybe.none String) (Maybe.some String "Test 4 Failed!"))

// Test5
// : (Maybe String)
// = 
//   let map = AscendingMap 
//   let sum = (U60.Map.sum map) 
//   let expected_sum = #55 
//   let is_equal = (U60.equal sum expected_sum) 
//   (~is_equal λx(Maybe String) (Maybe.none String) (Maybe.some String "Test 5 Failed!"))

// Test6
// : (Maybe String)
// = 
//   let map = (U60.Map.gen #U60 λx(x) #20) 
//   let new = λfirst_value λmap
//     let new = λlast_value λmap
//       let is_first_correct = (U60.equal (~first_value λx(#U60) λsome(some) #0) #3) 
//       let is_last_correct  = (U60.equal (~last_value λx(#U60) λsome(some) #0) #10) 
//       let are_both_correct = (Bool.and is_first_correct is_last_correct) 
//       (~are_both_correct λx(Maybe String) (Maybe.none String) (Maybe.some String "Test 6 Failed!"))
//     (~(U60.Map.got #U60 #10 map) λx(Maybe String) new)
//   (~(U60.Map.got #U60 #3 map) λx(Maybe String) new)


// Tests.run
// : ∀(tests: (List (Maybe String)))
//   String
// = λtests
//   let folder = (List.fold (Maybe String) tests)
//   (folder String (λhead λtail (~head λx(String) λsome(some) tail)) "All tests passed!")

// RunTests
// : (String)
// =
//   let tests = (List.nil (Maybe String))
//   let tests = (List.cons (Maybe String) Test1 tests)
//   let tests = (List.cons (Maybe String) Test2 tests)
//   let tests = (List.cons (Maybe String) Test3 tests)
//   let tests = (List.cons (Maybe String) Test4 tests)
//   let tests = (List.cons (Maybe String) Test5 tests)
//   let tests = (List.cons (Maybe String) Test6 tests)
//   let solution = (Tests.run tests)
//   solution

testBBT
: String
= 
"
File commented for backward compatibility.
To run the tests, uncomment the code on:
  testBBT.kind2
  U60.Map
"
  // RunTests