module NamedArguments;

axiom A : Type;

axiom B : Type;

axiom C : Type;

axiom D : Type;

axiom E : Type;

axiom F : Type;

axiom G : Type;

axiom H : Type;

type Unit := unit : Unit;

axiom fun1 : (a : Type) -> (b : Type) -> {c : Type} -> Type;

-- all provided by name
t1 : Type :=
  fun1@?{
    a := A;
    b := B;
    c := C
  };

-- skip implicit at the end
t1' : {_ : Type} -> Type :=
  fun1@?{
    b := B;
    a := A
  };

axiom fun2 : (a : Type)
  -> (b : Type)
  -> {c : Type}
  -> {d : Type}
  -> Type;

-- skip implicit in implicit group
t2 : {_ : Type} -> Type :=
  fun2@?{
    a := A;
    b := B;
    c := D
  };

axiom fun3 : (a : Type)
  -> (b : Type)
  -> {c : Type}
  -> {d : c}
  -> Type;

-- skip implicit in the middle
t3 : Type :=
  fun3@?{
    a := A;
    b := B;
    d := unit
  };

axiom fun4 : (a : Type)
  -> (b : Type)
  -> {c : Type}
  -> (d : c)
  -> Type;

-- skip implicit in the middle
t4 : Type :=
  fun4@?{
    a := A;
    b := B;
    d := unit
  };

axiom fun5 : (a : Type)
  -> (b : Type)
  -> {c c' : Type}
  -> (d : c)
  -> (d' : c')
  -> Type;

t5 : Type :=
  fun5@?{
    a := A;
    b := B;
    d' := unit;
    d := unit
  };

t5' : Type :=
  fun5@?{
    a := A;
    b := B;
    d' := unit;
    d := unit
  };

axiom fun6 : {a : Type}
  -> (b : Type)
  -> {c c' : Type}
  -> (d : c)
  -> (d' : c')
  -> (a' : a)
  -> Type;

t6 : Type :=
  fun6@?{
    b := B;
    d' := unit;
    d := unit;
    a' := unit
  };

t6' : Type :=
  fun6@?{
    d' := unit;
    d := unit;
    a' := unit;
    b := B
  };

module FakeRecord;
  type Pair (A B : Type) :=
    mkPair : (fst : A) -> (snd : B) -> Pair A B;

  pp
    : Pair@?{
      B := Unit;
      A := Type
    } :=
    mkPair@?{
      snd := unit;
      fst := Type
    };

  pp2
    : Pair@?{
      B := Unit;
      A := Type
    } := mkPair@?{fst := Type} (unit);
end;