diff options
Diffstat (limited to 'doc')
8 files changed, 97 insertions, 5 deletions
diff --git a/doc/changelog/02-specification-language/12121-master+fix11903-warn-non-truly-fixpoint.rst b/doc/changelog/02-specification-language/12121-master+fix11903-warn-non-truly-fixpoint.rst new file mode 100644 index 0000000000..d69a94205f --- /dev/null +++ b/doc/changelog/02-specification-language/12121-master+fix11903-warn-non-truly-fixpoint.rst @@ -0,0 +1,5 @@ +- **Added:** + New warning on using :cmd:`Fixpoint` or :cmd:`CoFixpoint` for + definitions which are not recursive + (`#12121 <https://github.com/coq/coq/pull/12121>`_, + by Hugo Herbelin) diff --git a/doc/changelog/09-coqide/12068-master+coqide-completion-no-matched.rst b/doc/changelog/09-coqide/12068-master+coqide-completion-no-matched.rst new file mode 100644 index 0000000000..dbb4bdecab --- /dev/null +++ b/doc/changelog/09-coqide/12068-master+coqide-completion-no-matched.rst @@ -0,0 +1,5 @@ +- **Fixed:** + New patch presumably fixing the random Coq 8.11 segfault issue with CoqIDE completion + (`#12068 <https://github.com/coq/coq/pull/12068>`_, + by Hugo Herbelin, presumably fixing + `#11943 <https://github.com/coq/coq/pull/11943>`_). diff --git a/doc/changelog/10-standard-library/12121-master+fix11903-warn-non-truly-fixpoint.rst b/doc/changelog/10-standard-library/12121-master+fix11903-warn-non-truly-fixpoint.rst new file mode 100644 index 0000000000..f22fff0736 --- /dev/null +++ b/doc/changelog/10-standard-library/12121-master+fix11903-warn-non-truly-fixpoint.rst @@ -0,0 +1,5 @@ +- **Fixed:** + :cmd:`Fixpoint`\s of the standard library without a recursive call turned + into ordinary :cmd:`Definition`\s + (`#12121 <https://github.com/coq/coq/pull/12121>`_, + by Hugo Herbelin; fixes `#11903 <https://github.com/coq/coq/pull/11903>`_). diff --git a/doc/changelog/10-standard-library/12263-fix-haskell-extraction.rst b/doc/changelog/10-standard-library/12263-fix-haskell-extraction.rst new file mode 100644 index 0000000000..c80a070181 --- /dev/null +++ b/doc/changelog/10-standard-library/12263-fix-haskell-extraction.rst @@ -0,0 +1,9 @@ +- **Fixed:** + In Haskell extraction with ``ExtrHaskellString``, equality comparisons on + strings and characters are now guaranteed to be uniquely well-typed, even in + very polymorphic contexts under ``unsafeCoerce``; this is achieved by adding + type annotations to the extracted code, and by making ``ExtrHaskellString`` + export ``ExtrHaskellBasic`` (`#12263 + <https://github.com/coq/coq/pull/12263>`_, fixes `#12257 + <https://github.com/coq/coq/issues/12257>`_ and `#12258 + <https://github.com/coq/coq/issues/12258>`_, by Jason Gross). diff --git a/doc/sphinx/language/cic.rst b/doc/sphinx/language/cic.rst index e5af39c8fb..b125d21a3c 100644 --- a/doc/sphinx/language/cic.rst +++ b/doc/sphinx/language/cic.rst @@ -1108,6 +1108,75 @@ between universes for inductive types in the Type hierarchy. Check infinite_loop (lam (@id Lam)) : False. +.. example:: Non strictly positive occurrence + + It is less obvious why inductive type definitions with occurences + that are positive but not strictly positive are harmful. + We will see that in presence of an impredicative type they + are unsound: + + .. coqtop:: all + + Fail Inductive A: Type := introA: ((A -> Prop) -> Prop) -> A. + + If we were to accept this definition we could derive a contradiction + by creating an injective function from :math:`A → \Prop` to :math:`A`. + + This function is defined by composing the injective constructor of + the type :math:`A` with the function :math:`λx. λz. z = x` injecting + any type :math:`T` into :math:`T → \Prop`. + + .. coqtop:: none + + Unset Positivity Checking. + Inductive A: Type := introA: ((A -> Prop) -> Prop) -> A. + Set Positivity Checking. + + .. coqtop:: all + + Definition f (x: A -> Prop): A := introA (fun z => z = x). + + .. coqtop:: in + + Lemma f_inj: forall x y, f x = f y -> x = y. + Proof. + unfold f; intros ? ? H; injection H. + set (F := fun z => z = y); intro HF. + symmetry; replace (y = x) with (F y). + + unfold F; reflexivity. + + rewrite <- HF; reflexivity. + Qed. + + The type :math:`A → \Prop` can be understood as the powerset + of the type :math:`A`. To derive a contradiction from the + injective function :math:`f` we use Cantor's classic diagonal + argument. + + .. coqtop:: all + + Definition d: A -> Prop := fun x => exists s, x = f s /\ ~s x. + Definition fd: A := f d. + + .. coqtop:: in + + Lemma cantor: (d fd) <-> ~(d fd). + Proof. + split. + + intros [s [H1 H2]]; unfold fd in H1. + replace d with s. + * assumption. + * apply f_inj; congruence. + + intro; exists d; tauto. + Qed. + + Lemma bad: False. + Proof. + pose cantor; tauto. + Qed. + + This derivation was first presented by Thierry Coquand and Christine + Paulin in :cite:`CP90`. + .. _Template-polymorphism: Template polymorphism diff --git a/doc/sphinx/proof-engine/proof-handling.rst b/doc/sphinx/proof-engine/proof-handling.rst index 3b5233502d..cf4d432f64 100644 --- a/doc/sphinx/proof-engine/proof-handling.rst +++ b/doc/sphinx/proof-engine/proof-handling.rst @@ -90,9 +90,7 @@ list of assertion commands is given in :ref:`Assertions`. The command .. cmd:: Save @ident :name: Save - Forces the name of the original goal to be :token:`ident`. This - command can only be used if the original goal - was opened using the :cmd:`Goal` command. + Forces the name of the original goal to be :token:`ident`. .. cmd:: Admitted @@ -821,7 +819,7 @@ in compacted hypotheses: .. .. image:: ../_static/diffs-coqide-compacted.png - :alt: coqide with Set Diffs on with compacted hyptotheses + :alt: coqide with Set Diffs on with compacted hypotheses Controlling the effect of proof editing commands ------------------------------------------------ diff --git a/doc/sphinx/proof-engine/ssreflect-proof-language.rst b/doc/sphinx/proof-engine/ssreflect-proof-language.rst index 28c5359a04..4be18ccda9 100644 --- a/doc/sphinx/proof-engine/ssreflect-proof-language.rst +++ b/doc/sphinx/proof-engine/ssreflect-proof-language.rst @@ -286,7 +286,7 @@ example, the null and all list function(al)s can be defined as follows: .. coqtop:: all Variable d: Set. - Fixpoint null (s : list d) := + Definition null (s : list d) := if s is nil then true else false. Variable a : d -> bool. Fixpoint all (s : list d) : bool := diff --git a/doc/stdlib/Library.tex b/doc/stdlib/Library.tex index 44a0b1d361..1a9d4d738f 100644 --- a/doc/stdlib/Library.tex +++ b/doc/stdlib/Library.tex @@ -5,6 +5,7 @@ \usepackage[T1]{fontenc} \usepackage{fullpage} \usepackage{amsfonts} +\usepackage{amssymb} \usepackage{url} \usepackage[color]{../../coqdoc} |