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[test] remove qualified-by-type constructors
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@ -54,11 +54,6 @@ inductive Empty {};
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-- An inductive type named Unit with only one constructor.
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inductive Unit { tt : Unit; };
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inductive Nat' : Type
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{ zero : Nat' ;
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suc : Nat' -> Nat' ;
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};
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-- The use of the type `Type` below is optional.
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-- The following declaration is equivalent to Nat'.
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@ -86,8 +81,8 @@ inductive Fin (n : Nat) {
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-- The type of sized vectors.
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inductive Vec (n : Nat) (A : Type)
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{
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zero : Vec Nat.zero A;
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succ : A -> Vec n A -> Vec (Nat.succ n) A;
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zero : Vec zero A;
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succ : A -> Vec n A -> Vec (succ n) A;
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};
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-- * Indexed inductive type declarations.
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@ -151,8 +146,8 @@ f' := \ {zero ↦ a ; -- We can use lambda abstractions to pattern match
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-- signature is missing.
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g : Nat -> A;
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g Nat.zero := a;
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g (Nat.suc t) := a';
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g zero := a;
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g (suc t) := a';
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-- For pattern-matching, the symbol `_` is the wildcard pattern as in
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-- Haskell or Agda. The following function definition is equivalent to
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@ -176,8 +171,8 @@ neg := A -> Empty;
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-- An equivalent type for sized vectors.
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Vec' : Nat -> Type -> Type;
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Vec' Nat.zero A := Unit;
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Vec' (Nat.suc n) A := A -> Vec' n A;
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Vec' zero A := Unit;
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Vec' (suc n) A := A -> Vec' n A;
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--------------------------------------------------------------------------------
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-- Fixity notation similarly as in Agda or Haskell.
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@ -185,8 +180,8 @@ Vec' (Nat.suc n) A := A -> Vec' n A;
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infixl 10 + ;
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+ : Nat → Nat → Nat ;
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+ Nat.zero m := m;
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+ (Nat.suc n) m := Nat.suc (n + m) ;
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+ zero m := m;
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+ (suc n) m := suc (n + m) ;
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--------------------------------------------------------------------------------
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-- Quantities for variables.
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