19ee270c60
Reason: vector in in init folder was introducing an overload (`::`) for all Lean users. The workaround (use `local infix ::`) was counterintuitive. We currently have no special support for bitvectors in the code generator. Thus, there is no need to have vector and bitvec in the init folder right now. Moreover, the new parser and elaborator (issue #1674) should provide better ways of managing overloaded symbols.
41 lines
1.3 KiB
Text
41 lines
1.3 KiB
Text
import data.vector namespace Ex
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universe u
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-- def vector (α : Type u) (n : ℕ) := { l : list α // l.length = n }
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namespace vector
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variables {α : Type u} {n : ℕ}
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@[pattern] def cons : α → vector α n → vector α (nat.succ n)
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| a ⟨ v, h ⟩ := ⟨ a::v, congr_arg nat.succ h ⟩
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def to_list' (v : vector α n) : list α := v.1
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def drop (i : ℕ) : vector α n → vector α (n - i)
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| ⟨l, p⟩ := ⟨ list.drop i l, by simp * ⟩
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protected axiom eq {n : ℕ} : ∀ (a1 a2 : vector α n), to_list' a1 = to_list' a2 → a1 = a2
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@[simp] axiom to_list'_cons (a : α) (v : vector α n) : to_list' (cons a v) = list.cons a (to_list' v)
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@[simp] axiom to_list'_drop {n m : ℕ} (v : vector α m) : to_list' (drop n v) = list.drop n (to_list' v)
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end vector
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open Ex.vector
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@[reducible] def bitvec (n : ℕ) := vector bool n
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def byte_type := bitvec 8
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-- A byte is formed from concatenating two bits and a 6-bit field.
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def mk_byte (a b : bool) (l : bitvec 6) : byte_type := cons a (cons b l)
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-- Get the third component
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def get_data (byte : byte_type) : bitvec 6 := vector.drop 2 byte
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lemma get_data_mk_byte {a b : bool} {l : bitvec 6} : get_data (mk_byte a b l) = l :=
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begin
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apply vector.eq,
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unfold mk_byte,
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unfold get_data,
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simp [to_list'_drop],
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simp [to_list'_cons]
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end
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end Ex
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