A function definition package for Coq
See the release notes for Equations 1.3
This is a new major release of Equations, working with Coq 8.18. This version adds an improved syntax (less ;
-separation), integration with the Coq-HoTT library and numerous bug fixes. See the reference manual for details.
This version introduces minor breaking changes along with the following features:
Enhancements of pattern interpretation
No explicit shadowing of pattern variables is allowed anymore. This fixes numerous bugs where generated implicit names introduced by the elaboration of patterns could shadow user-given names, leading to incorrect names in right-hand sides and confusing environments.
Improved syntax for "concise" clauses separated by |
, at top-level or inside with
subprograms.
We no longer require to separate them by ;
. For example, the following definition is now accepted:
Equations foo : nat -> nat :=
| 0 => 1
| S n => S (foo n).
The old syntax is however still supported for backwards compatibility.
Multiple patterns can be separated by ,
in addition to |
, as in:
Equations trans {A} {x y z : A} (e : x = y) (e' : y = z) : x = z := | 1, 1 => 1.
Require Import Equations.Equations.
does not work anymore.
One has to use Require Import Equations.Prop.Equations
to load the plugin's default instance where equality is in Prop
. From Equations Require Import Equations
is unaffected.
Use Require Import Equations.HoTT.All
to use the HoTT variant of the library compatible with the Coq HoTT library
The plugin then reuses the definition of paths
from the HoTT library and all its constructions are universe polymorphic. As for the HoTT library alone, coq must be passed the arguments -noinit -indices-matter
to use the library and plugin. The coq-equations
opam package depends optionally on coq-hott
, so if coq-hott
is installed before it, coq-equations
will automatically install the HoTT
library variant in addition to the standard one. This variant of Equations allows to write very concise dependent pattern-matchings on equality:
Require Import Equations.HoTT.All.
Equations sym {A} {x y : A} (e : x = y) : y = x := | 1 => 1.
New attribute #[tactic=tac]
to set locally the default tactic to solve remaining holes.
The goals on which the tactic applies are now always of the form Γ |- τ
where Γ is the context where the hole was introduced and τ the expected type, even when using the Obligation
machinery to solve them, resulting in a possible incompatibility if the obligation tactic treated the context differently than the conclusion. By default, the program_simpl
tactic performs a simpl
call before introducing the hypotheses, so you might need to add a simpl in *
to your tactics.
New attributes #[derive(equations=yes,no, eliminator=yes|no)]
can be used in place of the (noeqns, noind)
flags which are deprecated.
Qed
or Defined
(similarly to Coq’s #[refine] Instance
command).funelim
applied to a partial application failingSProp
This is a new major release of Equations, working with Coq 8.17. This version adds an improved syntax (less ;
-separation), integration with the Coq-HoTT library and numerous bug fixes. See the reference manual for details.
This version introduces minor breaking changes along with the following features:
Enhancements of pattern interpretation
No explicit shadowing of pattern variables is allowed anymore. This fixes numerous bugs where generated implicit names introduced by the elaboration of patterns could shadow user-given names, leading to incorrect names in right-hand sides and confusing environments.
Improved syntax for "concise" clauses separated by |
, at top-level or inside with
subprograms.
We no longer require to separate them by ;
. For example, the following definition is now accepted:
Equations foo : nat -> nat :=
| 0 => 1
| S n => S (foo n).
The old syntax is however still supported for backwards compatibility.
Multiple patterns can be separated by ,
in addition to |
, as in:
Equations trans {A} {x y z : A} (e : x = y) (e' : y = z) : x = z := | 1, 1 => 1.
Require Import Equations.Equations.
does not work anymore.
One has to use Require Import Equations.Prop.Equations
to load the plugin's default instance where equality is in Prop
. From Equations Require Import Equations
is unaffected.
Use Require Import Equations.HoTT.All
to use the HoTT variant of the library compatible with the Coq HoTT library
The plugin then reuses the definition of paths
from the HoTT library and all its constructions are universe polymorphic. As for the HoTT library alone, coq must be passed the arguments -noinit -indices-matter
to use the library and plugin. The coq-equations
opam package depends optionally on coq-hott
, so if coq-hott
is installed before it, coq-equations
will automatically install the HoTT
library variant in addition to the standard one. This variant of Equations allows to write very concise dependent pattern-matchings on equality:
Require Import Equations.HoTT.All.
Equations sym {A} {x y : A} (e : x = y) : y = x := | 1 => 1.
New attribute #[tactic=tac]
to set locally the default tactic to solve remaining holes.
The goals on which the tactic applies are now always of the form Γ |- τ
where Γ is the context where the hole was introduced and τ the expected type, even when using the Obligation
machinery to solve them, resulting in a possible incompatibility if the obligation tactic treated the context differently than the conclusion. By default, the program_simpl
tactic performs a simpl
call before introducing the hypotheses, so you might need to add a simpl in *
to your tactics.
New attributes #[derive(equations=yes,no, eliminator=yes|no)]
can be used in place of the (noeqns, noind)
flags which are deprecated.
Qed
or Defined
(similarly to Coq’s #[refine] Instance
command).funelim
applied to a partial application failingSProp
This is a new major release of Equations, working with Coq 8.16. This version adds an improved syntax (less ;
-separation), integration with the Coq-HoTT library and numerous bug fixes. See the reference manual for details.
This version introduces minor breaking changes along with the following features:
Enhancements of pattern interpretation
No explicit shadowing of pattern variables is allowed anymore. This fixes numerous bugs where generated implicit names introduced by the elaboration of patterns could shadow user-given names, leading to incorrect names in right-hand sides and confusing environments.
Improved syntax for "concise" clauses separated by |
, at top-level or inside with
subprograms.
We no longer require to separate them by ;
. For example, the following definition is now accepted:
Equations foo : nat -> nat :=
| 0 => 1
| S n => S (foo n).
The old syntax is however still supported for backwards compatibility.
Multiple patterns can be separated by ,
in addition to |
, as in:
Equations trans {A} {x y z : A} (e : x = y) (e' : y = z) : x = z := | 1, 1 => 1.
Require Import Equations.Equations.
does not work anymore.
One has to use Require Import Equations.Prop.Equations
to load the plugin's default instance where equality is in Prop
. From Equations Require Import Equations
is unaffected.
Use Require Import Equations.HoTT.All
to use the HoTT variant of the library compatible with the Coq HoTT library
The plugin then reuses the definition of paths
from the HoTT library and all its constructions are universe polymorphic. As for the HoTT library alone, coq must be passed the arguments -noinit -indices-matter
to use the library and plugin. The coq-equations
opam package depends optionally on coq-hott
, so if coq-hott
is installed before it, coq-equations
will automatically install the HoTT
library variant in addition to the standard one. This variant of Equations allows to write very concise dependent pattern-matchings on equality:
Require Import Equations.HoTT.All.
Equations sym {A} {x y : A} (e : x = y) : y = x := | 1 => 1.
New attribute #[tactic=tac]
to set locally the default tactic to solve remaining holes.
The goals on which the tactic applies are now always of the form Γ |- τ
where Γ is the context where the hole was introduced and τ the expected type, even when using the Obligation
machinery to solve them, resulting in a possible incompatibility if the obligation tactic treated the context differently than the conclusion. By default, the program_simpl
tactic performs a simpl
call before introducing the hypotheses, so you might need to add a simpl in *
to your tactics.
New attributes #[derive(equations=yes,no, eliminator=yes|no)]
can be used in place of the (noeqns, noind)
flags which are deprecated.
Qed
or Defined
(similarly to Coq’s #[refine] Instance
command).funelim
applied to a partial application failingSProp
This is a new major release of Equations, working with Coq 8.15. This version adds an improved syntax (less ;
-separation), integration with the Coq-HoTT library and numerous bug fixes. See the reference manual for details.
This version introduces minor breaking changes along with the following features:
Enhancements of pattern interpretation
No explicit shadowing of pattern variables is allowed anymore. This fixes numerous bugs where generated implicit names introduced by the elaboration of patterns could shadow user-given names, leading to incorrect names in right-hand sides and confusing environments.
Improved syntax for "concise" clauses separated by |
, at top-level or inside with
subprograms.
We no longer require to separate them by ;
. For example, the following definition is now accepted:
Equations foo : nat -> nat :=
| 0 => 1
| S n => S (foo n).
The old syntax is however still supported for backwards compatibility.
Multiple patterns can be separated by ,
in addition to |
, as in:
Equations trans {A} {x y z : A} (e : x = y) (e' : y = z) : x = z := | 1, 1 => 1.
Require Import Equations.Equations.
does not work anymore.
One has to use Require Import Equations.Prop.Equations
to load the plugin's default instance where equality is in Prop
. From Equations Require Import Equations
is unaffected.
Use Require Import Equations.HoTT.All
to use the HoTT variant of the library compatible with the Coq HoTT library
The plugin then reuses the definition of paths
from the HoTT library and all its constructions are universe polymorphic. As for the HoTT library alone, coq must be passed the arguments -noinit -indices-matter
to use the library and plugin. The coq-equations
opam package depends optionally on coq-hott
, so if coq-hott
is installed before it, coq-equations
will automatically install the HoTT
library variant in addition to the standard one. This variant of Equations allows to write very concise dependent pattern-matchings on equality:
Require Import Equations.HoTT.All.
Equations sym {A} {x y : A} (e : x = y) : y = x := | 1 => 1.
New attribute #[tactic=tac]
to set locally the default tactic to solve remaining holes.
The goals on which the tactic applies are now always of the form Γ |- τ
where Γ is the context where the hole was introduced and τ the expected type, even when using the Obligation
machinery to solve them, resulting in a possible incompatibility if the obligation tactic treated the context differently than the conclusion. By default, the program_simpl
tactic performs a simpl
call before introducing the hypotheses, so you might need to add a simpl in *
to your tactics.
New attributes #[derive(equations=yes,no, eliminator=yes|no)]
can be used in place of the (noeqns, noind)
flags which are deprecated.
Qed
or Defined
(similarly to Coq’s #[refine] Instance
command).funelim
applied to a partial application failingSProp
This is a new major release of Equations, working with Coq 8.13. This version adds an improved syntax (less ;
-separation), integration with the Coq-HoTT library and numerous bug fixes. See the reference manual for details.
This version introduces minor breaking changes along with the following features:
Enhancements of pattern interpretation
No explicit shadowing of pattern variables is allowed anymore. This fixes numerous bugs where generated implicit names introduced by the elaboration of patterns could shadow user-given names, leading to incorrect names in right-hand sides and confusing environments.
Improved syntax for "concise" clauses separated by |
, at top-level or inside with
subprograms.
We no longer require to separate them by ;
. For example, the following definition is now accepted:
Equations foo : nat -> nat :=
| 0 => 1
| S n => S (foo n).
The old syntax is however still supported for backwards compatibility.
Multiple patterns can be separated by ,
in addition to |
, as in:
Equations trans {A} {x y z : A} (e : x = y) (e' : y = z) : x = z := | 1, 1 => 1.
Require Import Equations.Equations.
does not work anymore.
One has to use Require Import Equations.Prop.Equations
to load the plugin's default instance where equality is in Prop
. From Equations Require Import Equations
is unaffected.
Use Require Import Equations.HoTT.All
to use the HoTT variant of the library compatible with the Coq HoTT library
The plugin then reuses the definition of paths
from the HoTT library and all its constructions are universe polymorphic. As for the HoTT library alone, coq must be passed the arguments -noinit -indices-matter
to use the library and plugin. The coq-equations
opam package depends optionally on coq-hott
, so if coq-hott
is installed before it, coq-equations
will automatically install the HoTT
library variant in addition to the standard one. This variant of Equations allows to write very concise dependent pattern-matchings on equality:
Require Import Equations.HoTT.All.
Equations sym {A} {x y : A} (e : x = y) : y = x := | 1 => 1.
New attribute #[tactic=tac]
to set locally the default tactic to solve remaining holes.
The goals on which the tactic applies are now always of the form Γ |- τ
where Γ is the context where the hole was introduced and τ the expected type, even when using the Obligation
machinery to solve them, resulting in a possible incompatibility if the obligation tactic treated the context differently than the conclusion. By default, the program_simpl
tactic performs a simpl
call before introducing the hypotheses, so you might need to add a simpl in *
to your tactics.
New attributes #[derive(equations=yes,no, eliminator=yes|no)]
can be used in place of the (noeqns, noind)
flags which are deprecated.
Qed
or Defined
(similarly to Coq’s #[refine] Instance
command).funelim
applied to a partial application failingSProp
This is a new major release of Equations, working with Coq 8.14. This version adds an improved syntax (less ;
-separation), integration with the Coq-HoTT library and numerous bug fixes. See the reference manual for details.
This version introduces minor breaking changes along with the following features:
Enhancements of pattern interpretation
No explicit shadowing of pattern variables is allowed anymore. This fixes numerous bugs where generated implicit names introduced by the elaboration of patterns could shadow user-given names, leading to incorrect names in right-hand sides and confusing environments.
Improved syntax for "concise" clauses separated by |
, at top-level or inside with
subprograms.
We no longer require to separate them by ;
. For example, the following definition is now accepted:
Equations foo : nat -> nat :=
| 0 => 1
| S n => S (foo n).
The old syntax is however still supported for backwards compatibility.
Multiple patterns can be separated by ,
in addition to |
, as in:
Equations trans {A} {x y z : A} (e : x = y) (e' : y = z) : x = z := | 1, 1 => 1.
Require Import Equations.Equations.
does not work anymore.
One has to use Require Import Equations.Prop.Equations
to load the plugin's default instance where equality is in Prop
. From Equations Require Import Equations
is unaffected.
Use Require Import Equations.HoTT.All
to use the HoTT variant of the library compatible with the Coq HoTT library
The plugin then reuses the definition of paths
from the HoTT library and all its constructions are universe polymorphic. As for the HoTT library alone, coq must be passed the arguments -noinit -indices-matter
to use the library and plugin. The coq-equations
opam package depends optionally on coq-hott
, so if coq-hott
is installed before it, coq-equations
will automatically install the HoTT
library variant in addition to the standard one. This variant of Equations allows to write very concise dependent pattern-matchings on equality:
Require Import Equations.HoTT.All.
Equations sym {A} {x y : A} (e : x = y) : y = x := | 1 => 1.
New attribute #[tactic=tac]
to set locally the default tactic to solve remaining holes.
The goals on which the tactic applies are now always of the form Γ |- τ
where Γ is the context where the hole was introduced and τ the expected type, even when using the Obligation
machinery to solve them, resulting in a possible incompatibility if the obligation tactic treated the context differently than the conclusion. By default, the program_simpl
tactic performs a simpl
call before introducing the hypotheses, so you might need to add a simpl in *
to your tactics.
New attributes #[derive(equations=yes,no, eliminator=yes|no)]
can be used in place of the (noeqns, noind)
flags which are deprecated.
Qed
or Defined
(similarly to Coq’s #[refine] Instance
command).funelim
applied to a partial application failingSProp
This is a new major release of Equations, working with Coq 8.13. This version adds an improved syntax (less ;
-separation), integration with the Coq-HoTT library and numerous bug fixes. See the reference manual for details.
This version introduces minor breaking changes along with the following features:
Enhancements of pattern interpretation
No explicit shadowing of pattern variables is allowed anymore. This fixes numerous bugs where generated implicit names introduced by the elaboration of patterns could shadow user-given names, leading to incorrect names in right-hand sides and confusing environments.
Improved syntax for "concise" clauses separated by |
, at top-level or inside with
subprograms.
We no longer require to separate them by ;
. For example, the following definition is now accepted:
Equations foo : nat -> nat :=
| 0 => 1
| S n => S (foo n).
The old syntax is however still supported for backwards compatibility.
Multiple patterns can be separated by ,
in addition to |
, as in:
Equations trans {A} {x y z : A} (e : x = y) (e' : y = z) : x = z := | 1, 1 => 1.
Require Import Equations.Equations.
does not work anymore.
One has to use Require Import Equations.Prop.Equations
to load the plugin's default instance where equality is in Prop
. From Equations Require Import Equations
is unaffected.
Use Require Import Equations.HoTT.All
to use the HoTT variant of the library compatible with the Coq HoTT library
The plugin then reuses the definition of paths
from the HoTT library and all its constructions are universe polymorphic. As for the HoTT library alone, coq must be passed the arguments -noinit -indices-matter
to use the library and plugin. The coq-equations
opam package depends optionally on coq-hott
, so if coq-hott
is installed before it, coq-equations
will automatically install the HoTT
library variant in addition to the standard one. This variant of Equations allows to write very concise dependent pattern-matchings on equality:
Require Import Equations.HoTT.All.
Equations sym {A} {x y : A} (e : x = y) : y = x := | 1 => 1.
New attribute #[tactic=tac]
to set locally the default tactic to solve remaining holes.
The goals on which the tactic applies are now always of the form Γ |- τ
where Γ is the context where the hole was introduced and τ the expected type, even when using the Obligation
machinery to solve them, resulting in a possible incompatibility if the obligation tactic treated the context differently than the conclusion. By default, the program_simpl
tactic performs a simpl
call before introducing the hypotheses, so you might need to add a simpl in *
to your tactics.
New attributes #[derive(equations=yes,no, eliminator=yes|no)]
can be used in place of the (noeqns, noind)
flags which are deprecated.
Qed
or Defined
(similarly to Coq’s #[refine] Instance
command).funelim
applied to a partial application failingSProp
This is a new major release of Equations, working with Coq 8.13. This version adds an improved syntax (less ;
-separation), integration with the Coq-HoTT library and numerous bug fixes. See the reference manual for details.
This version introduces minor breaking changes along with the following features:
|
, at top-level or inside with
subprograms.
We no longer require to separate them by ;
. For example, the following definition is now accepted:
Equations foo : nat -> nat :=
| 0 => 1
| S n => S (foo n).
The old syntax is however still supported for backwards compatibility.,
in addition to |
, as in:
Equations trans {A} {x y z : A} (e : x = y) (e' : y = z) : x = z := | 1, 1 => 1.
Require Import Equations.Equations.
does not work anymore.
One has to use Require Import Equations.Prop.Equations
to load the plugin's default instance where equality is in Prop
. From Equations Require Import Equations
is unaffected.Require Import Equations.HoTT.All
to use the HoTT variant of the library compatible with the Coq HoTT library
The plugin then reuses the definition of paths
from the HoTT library and all its constructions are universe polymorphic. As for the HoTT library alone, coq must be passed the arguments -noinit -indices-matter
to use the library and plugin. The coq-equations
opam package depends optionally on coq-hott
, so if coq-hott
is installed before it, coq-equations
will automatically install the HoTT
library variant in addition to the standard one. This variant of Equations allows to write very concise dependent pattern-matchings on equality:
Require Import Equations.HoTT.All.
Equations sym {A} {x y : A} (e : x = y) : y = x := | 1 => 1.
#[tactic=tac]
to set locally the default tactic to solve remaining holes.
The goals on which the tactic applies are now always of the form Γ |- τ
where Γ is the context where the hole was introduced and τ the expected type, even when using the Obligation
machinery to solve them, resulting in a possible incompatibility if the obligation tactic treated the context differently than the conclusion. By default, the program_simpl
tactic performs a simpl
call before introducing the hypotheses, so you might need to add a simpl in *
to your tactics.#[derive(equations=yes,no, eliminator=yes|no)]
can be used in place of the (noeqns, noind)
flags which are deprecated.∗ #329: improved strengthening avoiding to abstract over recursive definitions which would not pass the guardness checker. This can simplify the produced terms, avoiding unnecessary "commutative cuts".
∗ #321: warn rather than error when using Equations? and no subgoals are left. This will leave a proof state with no subgoals, that must be closed using a Qed
or Defined
(similarly to Coq’s #[refine] Instance
command).
∗ #372, #194: funelim
applied to a partial application failing
∗ #354: support for building values in SProp
∗ #353: name capture problem in presence of modules
∗ #335: provide an alias Equations Derive to not conflict with QuickChick’s Derive
∗ #325: properly inline all Equations helper constants during Extraction
This is a bugfix release of version 1.2 working with Coq 8.13, 8.12 and 8.11 See https://mattam82.github.io/Coq-Equations/equations/2019/05/17/1.2.html for the 1.2 release notes. Fixed in this version:
Require Import Equations
for compatibility and ease of use).