40 lines
1.6 KiB
Text
40 lines
1.6 KiB
Text
open tactic
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-- TODO(Leo): remove the following command.
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-- It has been added to avoid a crash in the code generator
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noncomputable theory
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inductive vector (A : Type) : nat → Type
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| nil {} : vector 0
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| cons : Π {n}, A -> vector n -> vector (nat.succ n)
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definition vmap {A B : Type} (f : A -> B) : Π {n}, vector A n -> vector B n
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| 0 vector.nil := vector.nil
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| (n+1) (vector.cons x xs) := vector.cons (f x) (vmap xs)
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noncomputable definition vappend {A} : Π {n m}, vector A n → vector A m → vector A (m + n)
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| 0 0 vector.nil vector.nil := vector.nil
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| 0 (m+1) vector.nil (vector.cons x xs) := vector.cons x xs
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| (n+1) 0 (vector.cons x xs) vector.nil := vector.cons x (vappend xs vector.nil)
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| (n+1) (m+1) (vector.cons x xs) (vector.cons y ys) := vector.cons x (vappend xs (vector.cons y ys))
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axiom Sorry : ∀ A, A
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theorem vappend_assoc :
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Π {A : Type} {n m k : nat} (v1 : vector A n) (v2 : vector A m) (v3 : vector A k),
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vappend (vappend v1 v2) v3 == vappend v1 (vappend v2 v3) :=
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by do
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intros,
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v <- get_local `v1,
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induction v,
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v2 ← get_local `v2,
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cases v2 [`m, `h2, `t2],
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trace_state, trace "------",
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-- unfold only the first occurrence (i.e., the one of the form (vappend nil nil)
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dunfold_occs_of [1] `vappend,
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trace_state, trace "------",
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mk_const `Sorry >>= apply,
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-- unfold only the first occurrence (i.e., the one of the form (vappend nil (cons ...))
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dunfold_occs_of [1] `vappend,
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trace_state, trace "------",
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repeat $ mk_const `Sorry >>= apply
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