diff options
Diffstat (limited to 'sec/encoding.ltx')
| -rw-r--r-- | sec/encoding.ltx | 9 |
1 files changed, 5 insertions, 4 deletions
diff --git a/sec/encoding.ltx b/sec/encoding.ltx index b697150..b93ca8f 100644 --- a/sec/encoding.ltx +++ b/sec/encoding.ltx @@ -491,10 +491,11 @@ At this point, the only type former not present in System~T is the union type.\@ \textcite{oleg} gives an inductive encoding for binary unions. We instead use an encoding for unions derived from the argument form of types. Given we have a family of types \(A_i\) in -argument form, their union is the concatenation \(A_1 ++ A_2 ++ \cdots ++ -A_n\). To inject type \(A_k\) into the union, we ignore the function -arguments for all the other type constructors. To project type \(A_k\) -out of the union, we pass \(\mathsf{arb}\) to all the other arguments. +argument form, their union is the concatenation \(A_1 \append A_2 +\append \cdots \append A_n\). To inject type \(A_k\) into the union, we +ignore the function arguments for all the other type constructors. To +project type \(A_k\) out of the union, we pass \(\mathsf{arb}\) to all +the other arguments. Using this argument-form union, we remove the need to perform induction on types, and only have to iterate over the number of types |