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| author | Tanaka Akira | 2019-01-31 16:53:29 +0900 |
|---|---|---|
| committer | Tanaka Akira | 2019-01-31 16:53:29 +0900 |
| commit | 757084431407d90ee454c06a9e05a978ba4f8663 (patch) | |
| tree | 61b07d5dad99b9d7f3ce57c1e827dff025d7c9f2 | |
| parent | 631ca702f355cf96a6460682ae2d95bb7a0172b7 (diff) | |
Use "∀" and "λ" instead of \forall and \lambda.
The former is more succinct and consistent with most of
other parts in cic.rst.
| -rw-r--r-- | doc/sphinx/language/cic.rst | 30 |
1 files changed, 15 insertions, 15 deletions
diff --git a/doc/sphinx/language/cic.rst b/doc/sphinx/language/cic.rst index 26200d3b22..4553546833 100644 --- a/doc/sphinx/language/cic.rst +++ b/doc/sphinx/language/cic.rst @@ -331,7 +331,7 @@ following rules. s \in \Sort \WTE{\Gamma::(x:T)}{U}{\Prop} ----------------------------- - \WTEG{\forall~x:T,U}{\Prop} + \WTEG{∀~x:T,U}{\Prop} .. inference:: Prod-Set @@ -339,25 +339,25 @@ following rules. s \in \{\Prop, \Set\} \WTE{\Gamma::(x:T)}{U}{\Set} ---------------------------- - \WTEG{\forall~x:T,U}{\Set} + \WTEG{∀~x:T,U}{\Set} .. inference:: Prod-Type \WTEG{T}{\Type(i)} \WTE{\Gamma::(x:T)}{U}{\Type(i)} -------------------------------- - \WTEG{\forall~x:T,U}{\Type(i)} + \WTEG{∀~x:T,U}{\Type(i)} .. inference:: Lam - \WTEG{\forall~x:T,U}{s} + \WTEG{∀~x:T,U}{s} \WTE{\Gamma::(x:T)}{t}{U} ------------------------------------ - \WTEG{\lb x:T\mto t}{\forall x:T, U} + \WTEG{\lb x:T\mto t}{∀ x:T, U} .. inference:: App - \WTEG{t}{\forall~x:U,T} + \WTEG{t}{∀~x:U,T} \WTEG{u}{U} ------------------------------ \WTEG{(t\ u)}{\subst{T}{x}{u}} @@ -726,8 +726,8 @@ the sort of the inductive type :math:`t` (not to be confused with :math:`\Sort` .. math:: \ind{1}{[\List:\Set→\Set]}{\left[\begin{array}{rcl} - \Nil & : & \forall A:\Set,\List~A \\ - \cons & : & \forall A:\Set, A→ \List~A→ \List~A + \Nil & : & ∀ A:\Set,\List~A \\ + \cons & : & ∀ A:\Set, A→ \List~A→ \List~A \end{array} \right]} @@ -771,8 +771,8 @@ the sort of the inductive type :math:`t` (not to be confused with :math:`\Sort` \odd&:&\nat → \Prop \end{array}\right]} {\left[\begin{array}{rcl} \evenO &:& \even~0\\ - \evenS &:& \forall n, \odd~n → \even~(\nS~n)\\ - \oddS &:& \forall n, \even~n → \odd~(\nS~n) + \evenS &:& ∀ n, \odd~n → \even~(\nS~n)\\ + \oddS &:& ∀ n, \even~n → \odd~(\nS~n) \end{array}\right]} which corresponds to the result of the |Coq| declaration: @@ -821,8 +821,8 @@ contains an inductive declaration. E[Γ] ⊢ \even : \nat→\Prop\\ E[Γ] ⊢ \odd : \nat→\Prop\\ E[Γ] ⊢ \evenO : \even~\nO\\ - E[Γ] ⊢ \evenS : \forall~n:\nat,~\odd~n → \even~(\nS~n)\\ - E[Γ] ⊢ \oddS : \forall~n:\nat,~\even~n → \odd~(\nS~n) + E[Γ] ⊢ \evenS : ∀~n:\nat,~\odd~n → \even~(\nS~n)\\ + E[Γ] ⊢ \oddS : ∀~n:\nat,~\even~n → \odd~(\nS~n) \end{array} @@ -1450,7 +1450,7 @@ corresponding to the :math:`c:C` constructor. .. math:: \begin{array}{ll} \{c:(I~p_1\ldots p_r\ t_1 \ldots t_p)\}^P &\equiv (P~t_1\ldots ~t_p~c) \\ - \{c:\forall~x:T,C\}^P &\equiv \forall~x:T,\{(c~x):C\}^P + \{c:∀~x:T,C\}^P &\equiv ∀~x:T,\{(c~x):C\}^P \end{array} We write :math:`\{c\}^P` for :math:`\{c:C\}^P` with :math:`C` the type of :math:`c`. @@ -1477,9 +1477,9 @@ We write :math:`\{c\}^P` for :math:`\{c:C\}^P` with :math:`C` the type of :math: :nowrap: \begin{eqnarray*} - P & = & \lambda~l~.~P^\prime\\ + P & = & λ~l~.~P^\prime\\ f_1 & = & t_1\\ - f_2 & = & \lambda~(hd:\nat)~.~\lambda~(tl:\List~\nat)~.~t_2 + f_2 & = & λ~(hd:\nat)~.~λ~(tl:\List~\nat)~.~t_2 \end{eqnarray*} According to the definition: |
