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The former is more succinct and intuitive.
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c can be non-function since c:U.
So, c c' is not typeable.
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This commit basically ajusts spaces as
- ∀x:T,t to ∀x:T,~t
- λx:T.t to λx:T.~t
- E;c:T to E;~c:T
x and T are more related than T and t.
So, T and t should not positioned closely than x and T.
Unfortunately, they are formatted that T and t are positioned closely
without "~".
(Similary, c and T are more related than E and c.)
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The former is more succinct and consistent with most of
other parts in cic.rst.
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Add :math:`...` for mathematical expressions.
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"∀Γ_P ,∀Γ_{\mathit{Arr}(t)}, \Sort" is changed to
"∀Γ_P ,∀Γ_{\mathit{Arr}(t)}, S" because
\Sort is not a term.
"S" is choosen to be consistent with the description of
Inductive Definitions.
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Exchange a closing parenthesis and a :math: closing backquote.
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In the note about η-reduction,
two lambda-abstraction used "," instead of ".".
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After #9435 (Use \mathcal instead of \cal), \Sort doesn't have
font changing effect.
So, {\Sort} is same as \Sort now and the former is changed to latter in
cic.rst.
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This corresponds to "Module TreeExample." removed at
2018-04-24 bcf5352cc7a26a672e719f7dad4021c69d723833.
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Reviewed-by: Zimmi48
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Reviewed-by: Zimmi48
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The definition of \plus and \tri in cic.rst is not effective
for HTML output.
So, move them into refman-preamble.sty.
Also, \tri is renamed to \trii to express
the suffix of "\triangleright_\iota".
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Ack-by: Zimmi48
Ack-by: anton-trunov
Ack-by: jfehrle
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\nO, \nS, \evenO, \evenS, \oddS, \length, \Nil and \cons are used.
don't use \kw in \kw{n} in Fixpoint typing rule section.
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Fix small errors in cic.rst:
* 3.4.1 Free variables: use :math: for "∀ x:T,~U".
:g: doesn't show "∀" in PDF.
"λx:T.~U" is also changed to :math: to use consistent font.
* 3.4.3 Zeta: ":U" added in "let x:=u:U in t" to be valid let-in expression.
* 3.4.3 convertibility: add :math: for u_2' to apply math formatting.
* 3.4.4.6: fix index. "n" should be "k" because they corresponds k-th
constructor.
* 3.4.5 Type constructor: I changed the section title "Type constructor" to
"Type of constructor".
"Type constructor" means a feature to construct new type.
But this section describes about a type of constructor.
* 3.4.5 Example nattree: The reason of
"``nattree`` occurs only strictly positively in ``A``" should be
bullet 1 instead of bullet 3.
The bullet 3 of strict positivity definition is about product, "∀x ∶ U , V",
but "A" is not a product.
* 3.4.5 Destructors: use :math: for "∀".
:g: doesn't show "∀" in PDF.
Also, :math: is used for expressions which has no "∀" character
for font consistency.
Note that I use \kw{has}\_\kw{length} instead of
\kw{has\_length} because the latter is formatted as has\_length in HTML.
(the backslash is retained.)
* 3.4.5 list example: curly braces added.
* 3.4.5 Fixpoint definition: add :math: for Γ_i to apply math formatting.
* 3.4.6 2nd rule of First abstracting property: use \subst.
This adds a curly brace.
Also, spacing and fonts are adjusted as follows.
* 3.4.1 let-in term: use :math: for variable x, consistent with other term
descriptions.
* 3.4.1 let-in term: use \letin command for concrete let-in term.
* 3.4.2 Note: insert spaces as ((λ x:T.~u)~t).
Since T is more closely reated to x than u, T should be positioned
close to x than u.
Since it seems most application has a space, I inserted a space here
for consistency.
* 3.4.3 beta-reduction: insert spaces as 3.4.2.
* 3.4.3 eta-expansion: insert spaces as 3.4.2.
* 3.4.5 Example: use sans-serif fonts for constructor "O" and "S".
* 3.4.5 Fixpoint definition: insert spaces around "with".
* 3.4.5 Fixpoint typing rule: fix fonts for "O" and "S" as 3.4.5 and
insert spaces as 3.4.2.
* 3.4.5 Fixpoint reduction rule: insert a space between {F} and a_1 for
consistency.
* 3.4.6 First abstracting property: insert spaces as 3.4.2.
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The previous language makes it seem as if record parameters are automatically set as implicit for the projection functions, but (per discussion with @jasongross) the omission of parameters from primitive projection only takes effect in Coq's internal AST.
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The code to generate the legacy bodies is moved to its only user in
extraction.
It almost seems like we could remove it (ie no special extraction code
for primitive projection constants) but then we run into issues with
automatic unboxing eg `Record foo := { a : nat; b : a <= 5 }.` gets
extracted to `type foo = nat` and (if we remove the special code) `let
a = a`.
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to fix all misuses.
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And a few more Sphinx fixes in passing.
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Remove objects without body from most chapters.
The remaining problems are all in the SSReflect chapter.
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This adds an optional [Subgraph] part to the Print Universes command,
eg [Print Universes Subgraph(i j)] to print only constraints related
to i and j (and Prop/Set).
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In particular, move the footnotes back to the foot of the chapter.
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Mark boolean-valued options with :flag:
Adjust tactic and command names so parameters aren't shown in the index unless
they're needed for disambiguation.
Remove references to synchronous options.
Revise doc for tables.
Correct indentation for text below :flag:
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