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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,231 @@ | ||
| { | ||
| "displayName": "Coq", | ||
| "fileTypes": [ | ||
| "v" | ||
| ], | ||
| "name": "coq", | ||
| "patterns": [ | ||
| { | ||
| "comment": "Vernacular import keywords", | ||
| "match": "\\b(From|Require|Import|Export|Local|Global|Include)\\b", | ||
| "name": "keyword.control.import.coq" | ||
| }, | ||
| { | ||
| "comment": "Vernacular scope keywords", | ||
| "match": "\\b((Open|Close|Delimit|Undelimit|Bind)\\s+Scope)\\b", | ||
| "name": "keyword.control.import.coq" | ||
| }, | ||
| { | ||
| "captures": { | ||
| "1": { | ||
| "name": "keyword.source.coq" | ||
| }, | ||
| "2": { | ||
| "name": "entity.name.function.theorem.coq" | ||
| } | ||
| }, | ||
| "comment": "Theorem declarations", | ||
| "match": "(Theorem|Lemma|Remark|Fact|Corollary|Property|Proposition|Goal)\\s+((\\p{L}|[_\\u00A0])(\\p{L}|[0-9_\\u00A0'])*)" | ||
| }, | ||
| { | ||
| "captures": { | ||
| "1": { | ||
| "name": "keyword.source.coq" | ||
| }, | ||
| "2": { | ||
| "name": "keyword.source.coq" | ||
| }, | ||
| "3": { | ||
| "name": "entity.name.assumption.coq" | ||
| } | ||
| }, | ||
| "comment": "Assumptions", | ||
| "match": "\\b(Parameters?|Axioms?|Conjectures?|Variables?|Hypothesis|Hypotheses)(\\s+Inline)?\\b\\s*\\(?\\s*((\\p{L}|[_\\u00A0])(\\p{L}|[0-9_\\u00A0'])*)" | ||
| }, | ||
| { | ||
| "captures": { | ||
| "1": { | ||
| "name": "keyword.source.coq" | ||
| }, | ||
| "3": { | ||
| "name": "entity.name.assumption.coq" | ||
| } | ||
| }, | ||
| "comment": "Context", | ||
| "match": "\\b(Context)\\b\\s*`?\\s*(\\(|\\{)?\\s*((\\p{L}|[_\\u00A0])(\\p{L}|[0-9_\\u00A0'])*)" | ||
| }, | ||
| { | ||
| "captures": { | ||
| "1": { | ||
| "name": "keyword.source.coq" | ||
| }, | ||
| "2": { | ||
| "name": "keyword.source.coq" | ||
| }, | ||
| "3": { | ||
| "name": "entity.name.function.coq" | ||
| } | ||
| }, | ||
| "comment": "Definitions", | ||
| "match": "(\\b(?:Program|Local)\\s+)?\\b(Definition|Fixpoint|CoFixpoint|Function|Example|Let(?:\\s+Fixpoint|\\s+CoFixpoint)?|Instance|Equations|Equations?)\\s+((\\p{L}|[_\\u00A0])(\\p{L}|[0-9_\\u00A0'])*)" | ||
| }, | ||
| { | ||
| "captures": { | ||
| "1": { | ||
| "name": "keyword.source.coq" | ||
| } | ||
| }, | ||
| "comment": "Obligations", | ||
| "match": "\\b((Show\\s+)?Obligation\\s+Tactic|Obligations\\s+of|Obligation|Next\\s+Obligation(\\s+of)?|Solve\\s+Obligations(\\s+of)?|Solve\\s+All\\s+Obligations|Admit\\s+Obligations(\\s+of)?|Instance)\\b" | ||
| }, | ||
| { | ||
| "captures": { | ||
| "1": { | ||
| "name": "keyword.source.coq" | ||
| }, | ||
| "3": { | ||
| "name": "entity.name.type.coq" | ||
| } | ||
| }, | ||
| "comment": "Type declarations", | ||
| "match": "(CoInductive|Inductive|Variant|Record|Structure|Class)\\s+(>\\s*)?((\\p{L}|[_\\u00A0])(\\p{L}|[0-9_\\u00A0'])*)" | ||
| }, | ||
| { | ||
| "captures": { | ||
| "1": { | ||
| "name": "keyword.source.coq" | ||
| }, | ||
| "2": { | ||
| "name": "entity.name.function.ltac" | ||
| } | ||
| }, | ||
| "comment": "Ltac declarations", | ||
| "match": "(Ltac)\\s+((\\p{L}|[_\\u00A0])(\\p{L}|[0-9_\\u00A0'])*)" | ||
| }, | ||
| { | ||
| "comment": "Vernacular keywords", | ||
| "match": "\\b(Hint|Constructors|Resolve|Rewrite|Ltac|Implicit(\\s+Types)?|Set|Unset|Remove\\s+Printing|Arguments|Tactic\\s+Notation|Notation|Infix|Reserved\\s+Notation|Section|Module\\s+Type|Module|End|Check|Print|Eval|Search|Universe|Coercions?|Generalizable\\s+All|Generalizable\\s+Variable?|Existing\\s+Instance|Existing\\s+Class|Canonical|About|Locate|Collection|Typeclasses\\s+(Opaque|Transparent))\\b", | ||
| "name": "keyword.source.coq" | ||
| }, | ||
| { | ||
| "comment": "Proof keywords", | ||
| "match": "\\b(Proof|Qed|Defined|Save|Abort(\\s+All)?|Undo(\\s+To)?|Restart|Focus|Unfocus|Unfocused|Show\\s+Proof|Show\\s+Existentials|Show|Unshelve)\\b", | ||
| "name": "keyword.source.coq" | ||
| }, | ||
| { | ||
| "comment": "Vernacular Debug keywords", | ||
| "match": "\\b(Quit|Drop|Time|Redirect|Timeout|Fail)\\b", | ||
| "name": "keyword.debug.coq" | ||
| }, | ||
| { | ||
| "comment": "Admits are bad", | ||
| "match": "\\b(admit|Admitted)\\b", | ||
| "name": "invalid.illegal.admit.coq" | ||
| }, | ||
| { | ||
| "comment": "Operators", | ||
| "match": ":|\\||=|<|>|\\*|\\+|-|\\{|\\}|≠|∨|∧|↔|¬|→|≤|≥", | ||
| "name": "keyword.operator.coq" | ||
| }, | ||
| { | ||
| "comment": "Type keywords", | ||
| "match": "\\b(forall|exists|Type|Set|Prop|nat|bool|option|list|unit|sum|prod|comparison|Empty_set)\\b|∀|∃", | ||
| "name": "support.type.coq" | ||
| }, | ||
| { | ||
| "comment": "Ltac keywords", | ||
| "match": "\\b(try|repeat|rew|progress|fresh|solve|now|first|tryif|at|once|do|only)\\b", | ||
| "name": "keyword.control.ltac" | ||
| }, | ||
| { | ||
| "comment": "Common Ltac connectors", | ||
| "match": "\\b(into|with|eqn|by|move|as|using)\\b", | ||
| "name": "keyword.control.ltac" | ||
| }, | ||
| { | ||
| "comment": "Gallina keywords", | ||
| "match": "\\b(match|lazymatch|multimatch|fun|with|return|end|let|in|if|then|else|fix|for|where|and)\\b|λ", | ||
| "name": "keyword.control.gallina" | ||
| }, | ||
| { | ||
| "comment": "Ltac builtins", | ||
| "match": "\\b(intro|intros|revert|induction|destruct|auto|eauto|tauto|eassumption|apply|eapply|assumption|constructor|econstructor|reflexivity|inversion|injection|assert|split|esplit|omega|fold|unfold|specialize|rewrite|erewrite|change|symmetry|refine|simpl|intuition|firstorder|generalize|idtac|exist|exists|eexists|elim|eelim|rename|subst|congruence|trivial|left|right|set|pose|discriminate|clear|clearbody|contradict|contradiction|exact|dependent|remember|case|easy|unshelve|pattern|transitivity|etransitivity|f_equal|exfalso|replace|abstract|cycle|swap|revgoals|shelve|unshelve)\\b", | ||
| "name": "support.function.builtin.ltac" | ||
| }, | ||
| { | ||
| "applyEndPatternLast": 1, | ||
| "begin": "\\(\\*(?!#)", | ||
| "end": "\\*\\)", | ||
| "name": "comment.block.coq", | ||
| "patterns": [ | ||
| { | ||
| "include": "#block_comment" | ||
| }, | ||
| { | ||
| "include": "#block_double_quoted_string" | ||
| } | ||
| ] | ||
| }, | ||
| { | ||
| "match": "\\b((0(x|X)[0-9a-fA-F]+)|([0-9]+(\\.[0-9]+)?))\\b", | ||
| "name": "constant.numeric.gallina" | ||
| }, | ||
| { | ||
| "comment": "Gallina builtin constructors", | ||
| "match": "\\b(True|False|tt|false|true|Some|None|nil|cons|pair|inl|inr|O|S|Eq|Lt|Gt|id|ex|all|unique)\\b", | ||
| "name": "constant.language.constructor.gallina" | ||
| }, | ||
| { | ||
| "match": "\\b_\\b", | ||
| "name": "constant.language.wildcard.coq" | ||
| }, | ||
| { | ||
| "begin": "\"", | ||
| "beginCaptures": { | ||
| "0": { | ||
| "name": "punctuation.definition.string.begin.coq" | ||
| } | ||
| }, | ||
| "end": "\"", | ||
| "endCaptures": { | ||
| "0": { | ||
| "name": "punctuation.definition.string.end.coq" | ||
| } | ||
| }, | ||
| "name": "string.quoted.double.coq" | ||
| } | ||
| ], | ||
| "repository": { | ||
| "block_comment": { | ||
| "applyEndPatternLast": 1, | ||
| "begin": "\\(\\*(?!#)", | ||
| "end": "\\*\\)", | ||
| "name": "comment.block.coq", | ||
| "patterns": [ | ||
| { | ||
| "include": "#block_comment" | ||
| }, | ||
| { | ||
| "include": "#block_double_quoted_string" | ||
| } | ||
| ] | ||
| }, | ||
| "block_double_quoted_string": { | ||
| "applyEndPatternLast": 1, | ||
| "begin": "\"", | ||
| "beginCaptures": { | ||
| "0": { | ||
| "name": "punctuation.definition.string.begin.coq" | ||
| } | ||
| }, | ||
| "end": "\"", | ||
| "endCaptures": { | ||
| "0": { | ||
| "name": "punctuation.definition.string.end.coq" | ||
| } | ||
| }, | ||
| "name": "string.quoted.double.coq" | ||
| } | ||
| }, | ||
| "scopeName": "source.coq" | ||
| } |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,36 @@ | ||
| From Coq Require Import ssreflect. | ||
|
|
||
| (* ensure proofs are well-structured *) | ||
| Set Default Goal Selector "!". | ||
| #[global] Open Scope general_if_scope. | ||
|
|
||
| Module list_playground. | ||
| (* Let's do a typical proof by induction: we'll define [list] as an inductive, | ||
| [app] (list append) as a recursive function, and prove that [app] is | ||
| associative. *) | ||
| Inductive list (A: Type) := | ||
| | nil | ||
| | cons (x: A) (l: list A). | ||
|
|
||
| (* Fix up implicit arguments. *) | ||
| Arguments nil {A}. | ||
| Arguments cons {A} x l. | ||
| Notation "[]" := nil. | ||
| Infix "::" := cons. | ||
|
|
||
| Fixpoint app {A} (l1 l2: list A): list A := | ||
| match l1 with | ||
| | [] => l2 | ||
| | x :: l1 => x :: app l1 l2 | ||
| end. | ||
|
|
||
| Infix "++" := app. | ||
|
|
||
| Theorem app_assoc {A} (l1 l2 l3: list A) : | ||
| (l1 ++ l2) ++ l3 = l1 ++ (l2 ++ l3). | ||
| Proof. | ||
| induction l1 as [|x l1]; simpl. | ||
| - reflexivity. | ||
| - by rewrite IHl1. | ||
| Qed. | ||
| End list_playground. |
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