Data commit

Task/Variadic-function/Coq/variadic-function-1.coq

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+Fixpoint Arity (A B: Set) (n: nat): Set := match n with
+|O => B
+|S n' => A -> (Arity A B n')
+end.

Task/Variadic-function/Coq/variadic-function-2.coq

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+Definition nat_twobools (n: nat) := Arity nat (Arity bool nat (2*n)) n.

Task/Variadic-function/Coq/variadic-function-3.coq

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+Require Import List.
+Fixpoint build_list_aux {A: Set} (acc: list A) (n : nat): Arity A (list A) n := match n with
+|O => acc
+|S n' => fun (val: A) => build_list_aux (acc ++ (val :: nil)) n'
+end.

Task/Variadic-function/Coq/variadic-function-4.coq

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+Definition build_list {A: Set} := build_list_aux (@nil A).

Task/Variadic-function/Coq/variadic-function-5.coq

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+Check build_list 5 1 2 5 90 42.

Task/Variadic-function/Coq/variadic-function-6.coq

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+Lemma transparent_plus_zero: forall n, n + O = n.
+intros n; induction n.
+- reflexivity.
+- simpl; rewrite IHn; trivial.
+Defined.
+
+Lemma transparent_plus_S: forall n m, n + S m = S n + m .
+intros n; induction n; intros m.
+- reflexivity.
+- simpl; f_equal; rewrite IHn; reflexivity.
+Defined.

Task/Variadic-function/Coq/variadic-function-7.coq

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+Require Import Vector.
+
+Definition build_vector_aux {A: Set} (n: nat): forall (size_acc : nat) (acc: t A size_acc), Arity A (t A (size_acc + n)) n.
+induction n; intros size_acc acc.
+- rewrite transparent_plus_zero; apply acc. (*Just one argument, return the accumulator*)
+- intros val. rewrite transparent_plus_S. apply IHn. (*Here we use the induction hypothesis. We just have to build the new accumulator*)
+  apply shiftin; [apply val | apply acc]. (*Shiftin adds a term at the end of a vector*)

Task/Variadic-function/Coq/variadic-function-8.coq

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+Definition build_vector {A: Set} (n: nat) := build_vector_aux n O (@nil A).

Task/Variadic-function/Coq/variadic-function-9.coq

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+Require Import String.
+Eval compute in build_vector 4 "Hello" "how" "are" "you".