diff options
author | Chloe Brown <chloe.brown.00@outlook.com> | 2025-05-06 16:00:11 +0100 |
---|---|---|
committer | Chloe Brown <chloe.brown.00@outlook.com> | 2025-05-06 16:00:11 +0100 |
commit | de463fdc28ca9e32627818f508509d870c8a948b (patch) | |
tree | dc9ff5da85b3f31d40c011c6d2129e6946f19cb2 /sec/lang.ltx | |
parent | 27d17d272cb291ca3838565bb0f1c2dfbe630983 (diff) |
Change signature of `\casetm`.
Diffstat (limited to 'sec/lang.ltx')
-rw-r--r-- | sec/lang.ltx | 6 |
1 files changed, 3 insertions, 3 deletions
diff --git a/sec/lang.ltx b/sec/lang.ltx index 3b0134a..1ad22d4 100644 --- a/sec/lang.ltx +++ b/sec/lang.ltx @@ -104,7 +104,7 @@ unrepresentable in some models of System~T}. \begin{prooftree} \hypo{\judgement{\Gamma}{t}{\sum_i A_i}} \hypo{\rangeover{\judgement{\Gamma, x_i : A_i}{t_i}{B}}{i}} - \infer2{\judgement{\Gamma}{\casetm{t}{x_i}{t_i}{i}}{B}} + \infer2{\judgement{\Gamma}{\casetm{t}{\tuple{i,x_i}}{t_i}{i}}{B}} \end{prooftree} \\\\ \multicolumn{2}{c}{ @@ -156,7 +156,7 @@ derivation \(\jdgmnt{ty}{\Psi}{A}\), with our chosen variable \(X \in \Psi\). \maptm{X}{A \to B} &\coloneq \lambda f, x. x \\ \maptm{X}{\prod_i A_i} &\coloneq \lambda f, x. \tuple{\rangeover{\maptm{X}{A_i}~f~x.i}{i}} \\ \maptm{X}{\sum_i A_i} &\coloneq - \lambda f, x. \casetm{x}{x_i}{\tuple{i, \maptm{X}{A_i}~f~x_i}}{i} \\ + \lambda f, x. \casetm{x}{\tuple{i,x_i}}{\tuple{i, \maptm{X}{A_i}~f~x_i}}{i} \\ \maptm{X}{\mu Y. A} &\coloneq \lambda f, x. \dofold{x}{y}{\roll~(\maptm{X}{\sub{A}{Y/\mu Y. \sub{A}{X/C}}}~f~y)} @@ -193,7 +193,7 @@ do not accidentally depend on an equation that does not hold. \begin{align*} (\lambda x. t)~u &\coloneq \sub{t}{x/u} & - \casetm{\tuple{k, t}}{x_i}{u_i}{i} &\coloneq \sub{u_k}{x_k/t} + \casetm{\tuple{k, t}}{\tuple{i,x_i}}{u_i}{i} &\coloneq \sub{u_k}{x_k/t} \\ \tuple{\rangeover{t_i}{i}}.k &\coloneq t_k & |