chore: update comments in kernel/declaration.h

This file has comments that recall the data type definitions in Lean.
Most of them were still using lean3 syntax, and at least one of them was
out of date (one field missing), so I updated them.

I took the liberty to shorten the comments from the original file, or
omit them if they don’t add much over the field names.

src/kernel/declaration.h

@@ -12,10 +12,10 @@ Author: Leonardo de Moura
 
 namespace lean {
 /**
-inductive reducibility_hints
-| opaque  : reducibility_hints
-| abbrev  : reducibility_hints
-| regular : nat → reducibility_hints
+inductive ReducibilityHints where
+  | opaque  : ReducibilityHints
+  | abbrev  : ReducibilityHints
+  | regular : UInt32 → ReducibilityHints
 
 Reducibility hints are used in the convertibility checker (aka is_def_eq predicate),
 whenever checking a constraint such as
@@ -54,8 +54,10 @@ public:
 int compare(reducibility_hints const & h1, reducibility_hints const & h2);
 
 /*
-structure constant_val :=
-(id : name) (lparams : list name) (type : expr)
+structure ConstantVal where
+  name : Name
+  levelParams : List Name
+  type : Expr
 */
 class constant_val : public object_ref {
 public:
@@ -70,8 +72,8 @@ public:
 };
 
 /*
-structure axiom_val extends constant_val :=
-(is_unsafe : bool)
+structure AxiomVal extends ConstantVal where
+  isUnsafe : Bool
 */
 class axiom_val : public object_ref {
 public:
@@ -87,11 +89,17 @@ public:
     bool is_unsafe() const;
 };
 
+/*
+inductive DefinitionSafety where
+  | «unsafe» | safe | «partial»
+*/
 enum class definition_safety { unsafe, safe, partial };
 
 /*
-structure definition_val extends constant_val :=
-(value : expr) (hints : reducibility_hints) (is_unsafe : bool)
+structure DefinitionVal extends ConstantVal where
+  value  : Expr
+  hints  : ReducibilityHints
+  safety : DefinitionSafety
 */
 class definition_val : public object_ref {
 public:
@@ -131,8 +139,10 @@ public:
 };
 
 /*
-structure opaque_val extends constant_val :=
-(value : expr)
+structure OpaqueVal extends ConstantVal where
+  value : Expr
+  isUnsafe : Bool
+  all : List Name := [name]
 */
 class opaque_val : public object_ref {
 public:
@@ -150,8 +160,9 @@ public:
 };
 
 /*
-structure constructor :=
-(id : name) (type : expr)
+structure Constructor where
+  name : Name
+  type : Expr
 */
 typedef pair_ref<name, expr> constructor;
 inline name const & constructor_name(constructor const & c) { return c.fst(); }
@@ -159,8 +170,10 @@ inline expr const & constructor_type(constructor const & c) { return c.snd(); }
 typedef list_ref<constructor> constructors;
 
 /**
-structure inductive_type where
-(id : name) (type : expr) (cnstrs : list constructor)
+structure InductiveType where
+  name : Name
+  type : Expr
+  ctors : List Constructor
 */
 class inductive_type : public object_ref {
 public:
@@ -176,14 +189,14 @@ public:
 typedef list_ref<inductive_type> inductive_types;
 
 /*
-inductive declaration
-| axiom_decl       (val : axiom_val)
-| defn_decl        (val : definition_val)
-| thm_decl         (val : theorem_val)
-| opaque_decl      (val : opaque_val)
-| quot_decl        (id : name)
-| mutual_defn_decl (defns : list definition_val) -- All definitions must be marked as `unsafe`
-| induct_decl      (lparams : list name) (nparams : nat) (types : list inductive_type) (is_unsafe : bool)
+inductive Declaration where
+  | axiomDecl       (val : AxiomVal)
+  | defnDecl        (val : DefinitionVal)
+  | thmDecl         (val : TheoremVal)
+  | opaqueDecl      (val : OpaqueVal)
+  | quotDecl
+  | mutualDefnDecl  (defns : List DefinitionVal) -- All definitions must be marked as `unsafe` or `partial`
+  | inductDecl      (lparams : List Name) (nparams : Nat) (types : List InductiveType) (isUnsafe : Bool)
 */
 enum class declaration_kind { Axiom, Definition, Theorem, Opaque, Quot, MutualDefinition, Inductive };
 class declaration : public object_ref {
@@ -261,14 +274,16 @@ public:
 };
 
 /*
-structure inductive_val extends constant_val where
-(nparams : nat)       -- Number of parameters
-(nindices : nat)      -- Number of indices
-(all : list name)     -- List of all (including this one) inductive datatypes in the mutual declaration containing this one
-(cnstrs : list name)  -- List of all constructors for this inductive datatype
-(is_rec : bool)       -- `tt` iff it is recursive
-(is_unsafe : bool)
-(is_reflexive : bool)
+structure InductiveVal extends ConstantVal where
+  numParams : Nat
+  numIndices : Nat
+  all : List Name    -- List of all (including this one) inductive datatypes in the mutual
+                        declaration containing this one
+  ctors : List Name  -- List of the names of the constructors for this inductive datatype
+  isRec : Bool
+  isUnsafe : Bool
+  isReflexive : Bool
+  isNested : Bool
 */
 class inductive_val : public object_ref {
 public:
@@ -291,12 +306,12 @@ public:
 };
 
 /*
-structure constructor_val extends constant_val :=
-(induct  : name)  -- Inductive type this constructor is a member of
-(cidx    : nat)   -- Constructor index (i.e., position in the inductive declaration)
-(nparams : nat)   -- Number of parameters in inductive datatype `induct`
-(nfields : nat)   -- Number of fields (i.e., arity - nparams)
-(is_unsafe : bool)
+structure ConstructorVal extends ConstantVal where
+  induct  : Name  -- Inductive type this constructor is a member of
+  cidx    : Nat   -- Constructor index (i.e., Position in the inductive declaration)
+  numParams : Nat -- Number of parameters in inductive datatype
+  numFields : Nat -- Number of fields (i.e., arity - nparams)
+  isUnsafe : Bool
 */
 class constructor_val : public object_ref {
 public:
@@ -314,10 +329,10 @@ public:
 };
 
 /*
-structure recursor_rule :=
-(cnstr : name)  -- Reduction rule for this constructor
-(nfields : nat) -- Number of fields (i.e., without counting inductive datatype parameters)
-(rhs : expr)    -- Right hand side of the reduction rule
+structure RecursorRule where
+  ctor : Name   -- Reduction rule for this Constructor
+  nfields : Nat -- Number of fields (i.e., without counting inductive datatype parameters)
+  rhs : Expr    -- Right hand side of the reduction rule
 */
 class recursor_rule : public object_ref {
 public:
@@ -334,15 +349,15 @@ public:
 typedef list_ref<recursor_rule> recursor_rules;
 
 /*
-structure recursor_val extends constant_val :=
-(all : list name)            -- List of all inductive datatypes in the mutual declaration that generated this recursor
-(nparams : nat)              -- Number of parameters
-(nindices : nat)             -- Number of indices
-(nmotives : nat)             -- Number of motives
-(nminors : nat)              -- Number of minor premises
-(rules : list recursor_rule) -- A reduction for each constructor
-(k : bool)                   -- It supports K-like reduction
-(is_unsafe : bool)
+structure RecursorVal extends ConstantVal where
+  all : List Name  -- List of all inductive datatypes in the mutual declaration that generated this recursor
+  numParams : Nat
+  numIndices : Nat
+  numMotives : Nat
+  numMinors : Nat
+  rules : List RecursorRule
+  k : Bool         -- It supports K-like reduction.
+  isUnsafe : Bool
 */
 class recursor_val : public object_ref {
 public:
@@ -370,14 +385,14 @@ public:
 enum class quot_kind { Type, Mk, Lift, Ind };
 
 /*
-inductive quot_kind
-| type  -- `quot`
-| cnstr -- `quot.mk`
-| lift  -- `quot.lift`
-| ind   -- `quot.ind`
+inductive QuotKind where
+  | type  -- `Quot`
+  | ctor  -- `Quot.mk`
+  | lift  -- `Quot.lift`
+  | ind   -- `Quot.ind`
 
-structure quot_val extends constant_val :=
-(kind : quot_kind)
+structure QuotVal extends ConstantVal where
+  kind : QuotKind
 */
 class quot_val : public object_ref {
 public:
@@ -395,15 +410,15 @@ public:
 
 /*
 /-- Information associated with constant declarations. -/
-inductive constant_info
-| axiom_info    (val : axiom_val)
-| defn_info     (val : definition_val)
-| thm_info      (val : theorem_val)
-| opaque_info   (val : opaque_val)
-| quot_info     (val : quot_val)
-| induct_info   (val : inductive_val)
-| cnstr_info    (val : constructor_val)
-| rec_info      (val : recursor_val)
+inductive ConstantInfo where
+  | axiomInfo    (val : AxiomVal)
+  | defnInfo     (val : DefinitionVal)
+  | thmInfo      (val : TheoremVal)
+  | opaqueInfo   (val : OpaqueVal)
+  | quotInfo     (val : QuotVal)
+  | inductInfo   (val : InductiveVal)
+  | ctorInfo     (val : ConstructorVal)
+  | recInfo      (val : RecursorVal)l)
 */
 enum class constant_info_kind { Axiom, Definition, Theorem, Opaque, Quot, Inductive, Constructor, Recursor };
 class constant_info : public object_ref {