From 6bce3de10ec1cd18c60e1ce3b5af33350ec4ac86 Mon Sep 17 00:00:00 2001 From: Timothy Bourke Date: Sat, 21 Jul 2018 18:11:25 +0200 Subject: Docs: Fix p values in CIC Inductive Defs examples It seems that p is a natural number, so why not write it as 0 rather than the empty list for tree and forest? And, if I understand correctly, odd and even have p = 0 and Arr(even) = Arr(odd) = 1. --- doc/sphinx/language/cic.rst | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/doc/sphinx/language/cic.rst b/doc/sphinx/language/cic.rst index 98e81ebc65..9f932ae78f 100644 --- a/doc/sphinx/language/cic.rst +++ b/doc/sphinx/language/cic.rst @@ -745,7 +745,7 @@ the sort of the inductive type t (not to be confused with :math:`\Sort` which is is: .. math:: - \ind{~}{\left[\begin{array}{rcl}\tree&:&\Set\\\forest&:&\Set\end{array}\right]} + \ind{0}{\left[\begin{array}{rcl}\tree&:&\Set\\\forest&:&\Set\end{array}\right]} {\left[\begin{array}{rcl} \node &:& \forest → \tree\\ \emptyf &:& \forest\\ @@ -766,7 +766,7 @@ the sort of the inductive type t (not to be confused with :math:`\Sort` which is The declaration for a mutual inductive definition of even and odd is: .. math:: - \ind{1}{\left[\begin{array}{rcl}\even&:&\nat → \Prop \\ + \ind{0}{\left[\begin{array}{rcl}\even&:&\nat → \Prop \\ \odd&:&\nat → \Prop \end{array}\right]} {\left[\begin{array}{rcl} \evenO &:& \even~0\\ -- cgit v1.2.3 From f25c1d252ad61b4dc4321e3a11f33b1e6d4e3dff Mon Sep 17 00:00:00 2001 From: Timothy Bourke Date: Sun, 22 Jul 2018 07:43:32 +0200 Subject: Docs: minor typo in W-Ind relative to text The rule uses s'_j, the text refers to s_j, the latter is simpler in the absence of any other constraints. --- doc/sphinx/language/cic.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/doc/sphinx/language/cic.rst b/doc/sphinx/language/cic.rst index 9f932ae78f..b670305389 100644 --- a/doc/sphinx/language/cic.rst +++ b/doc/sphinx/language/cic.rst @@ -961,7 +961,7 @@ such that :math:`Γ_I` is :math:`[I_1 :∀ Γ_P ,A_1 ;…;I_k :∀ Γ_P ,A_k]`, .. inference:: W-Ind \WFE{Γ_P} - (E[Γ_P ] ⊢ A_j : s_j' )_{j=1… k} + (E[Γ_P ] ⊢ A_j : s_j )_{j=1… k} (E[Γ_I ;Γ_P ] ⊢ C_i : s_{q_i} )_{i=1… n} ------------------------------------------ \WF{E;\ind{p}{Γ_I}{Γ_C}}{Γ} -- cgit v1.2.3 From 80883ddf89949afa82081ba80ccb4934320e6ee3 Mon Sep 17 00:00:00 2001 From: Timothy Bourke Date: Sun, 22 Jul 2018 10:56:23 +0200 Subject: Docs: minor typo in "Template Polymorphism" --- doc/sphinx/language/cic.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/doc/sphinx/language/cic.rst b/doc/sphinx/language/cic.rst index b670305389..721dc80b18 100644 --- a/doc/sphinx/language/cic.rst +++ b/doc/sphinx/language/cic.rst @@ -1019,7 +1019,7 @@ Template polymorphism +++++++++++++++++++++ Inductive types declared in :math:`\Type` are polymorphic over their arguments -in :math:`\Type`. If :math:`A` is an arity of some sort and math:`s` is a sort, we write :math:`A_{/s}` +in :math:`\Type`. If :math:`A` is an arity of some sort and :math:`s` is a sort, we write :math:`A_{/s}` for the arity obtained from :math:`A` by replacing its sort with :math:`s`. Especially, if :math:`A` is well-typed in some global environment and local context, then :math:`A_{/s}` is typable by typability of all products in the -- cgit v1.2.3