Better primitive type support in custom string and numeral notations.

- float and array values are now supported for printing and parsing in custom notations (and in notations defined using the ocaml API)
- the three constants bound to the primitive float, int and array type are now allowed anywhere inside a term to print, to handle them similar to `real` type constructors
- Grants #13484: String notations for primitive arrays
- Fixes #13517: String notation printing fails with primitive integers inside lists

2 files changed, 159 insertions, 0 deletions

diff --git a/test-suite/output/StringSyntaxPrimitive.out b/test-suite/output/StringSyntaxPrimitive.out
new file mode 100644
index 0000000000..131975c760
--- /dev/null
+++ b/test-suite/output/StringSyntaxPrimitive.out
@@ -0,0 +1,20 @@
+"abc"
+     : intList
+"abc"
+     : intList
+mk_intList [97%int63; 98%int63; 99%int63]
+     : intList
+"abc"
+     : intArray
+"abc"
+     : intArray
+     = "abc"
+     : nestArray
+"abc"
+     : nestArray
+"100"
+     : floatList
+"100"
+     : floatList
+mk_floatList [1%float; 0%float; 0%float]
+     : floatList
diff --git a/test-suite/output/StringSyntaxPrimitive.v b/test-suite/output/StringSyntaxPrimitive.v
new file mode 100644
index 0000000000..23ef082013
--- /dev/null
+++ b/test-suite/output/StringSyntaxPrimitive.v
@@ -0,0 +1,139 @@
+Require Import Coq.Lists.List.
+Require Import Coq.Strings.String Coq.Strings.Byte Coq.Strings.Ascii.
+Require Coq.Array.PArray Coq.Floats.PrimFloat.
+Require Import Coq.Numbers.BinNums Coq.Numbers.Cyclic.Int63.Int63.
+
+Set Printing Depth 100000.
+Set Printing Width 1000.
+
+Close Scope char_scope.
+Close Scope string_scope.
+
+(* Notations for primitive integers inside polymorphic datatypes *)
+Module Test1.
+  Inductive intList := mk_intList (_ : list int).
+  Definition i63_from_byte (b : byte) : int := Int63.of_Z (BinInt.Z.of_N (Byte.to_N b)).
+  Definition i63_to_byte (i : int) : byte :=
+      match Byte.of_N (BinInt.Z.to_N (Int63.to_Z i)) with Some x => x | None => x00%byte end.
+
+  Definition to_byte_list '(mk_intList a) := List.map i63_to_byte a.
+
+  Definition from_byte_list (xs : list byte) : intList:=
+    mk_intList (List.map i63_from_byte xs).
+
+  Declare Scope intList_scope.
+  Delimit Scope intList_scope with intList.
+
+  String Notation intList from_byte_list to_byte_list : intList_scope.
+
+  Open Scope intList_scope.
+  Import List.ListNotations.
+  Check mk_intList [97; 98; 99]%int63%list.
+  Check "abc"%intList.
+
+  Definition int' := int.
+  Check mk_intList (@cons int' 97 [98; 99])%int63%list.
+End Test1.
+
+Import PArray.
+
+(* Notations for primitive arrays *)
+Module Test2.
+  Inductive intArray := mk_intArray (_ : array int).
+
+  Definition i63_from_byte (b : byte) : Int63.int := Int63.of_Z (BinInt.Z.of_N (Byte.to_N b)).
+  Definition i63_to_byte (i : Int63.int) : byte :=
+  match Byte.of_N (BinInt.Z.to_N (Int63.to_Z i)) with Some x => x | None => x00%byte end.
+
+  Definition i63_to_nat x := BinInt.Z.to_nat (Int63.to_Z x).
+  Local Definition nat_length {X} (x : array X) :nat := i63_to_nat (length x).
+
+  Local Fixpoint list_length_i63 {A} (xs : list A) :int :=
+            match xs with
+            | nil => 0
+            | cons _ xs => 1 + list_length_i63 xs
+            end.
+
+  Definition to_byte_list '(mk_intArray a) :=
+    ((fix go (n : nat) (i : Int63.int) (acc : list byte) :=
+        match n with
+        | 0 => acc
+        | S n => go n (i - 1) (cons (i63_to_byte a.[i]) acc)
+        end) (nat_length a) (length a - 1) nil)%int63.
+
+  Definition from_byte_list (xs : list byte) :=
+    (let arr := make (list_length_i63 xs) 0 in
+    mk_intArray ((fix go i xs acc :=
+        match xs with
+        | nil => acc
+        | cons x xs => go (i + 1) xs (acc.[i <- i63_from_byte x])
+        end) 0 xs arr))%int63.
+
+  Declare Scope intArray_scope.
+  Delimit Scope intArray_scope with intArray.
+
+  String Notation intArray from_byte_list to_byte_list : intArray_scope.
+
+  Open Scope intArray_scope.
+  Check mk_intArray ( [| 97; 98; 99 | 0|])%int63%array.
+  Check "abc"%intArray.
+
+End Test2.
+
+(* Primitive arrays inside primitive arrays *)
+Module Test3.
+
+  Inductive nestArray := mk_nestArray (_ : array (array int)).
+  Definition to_byte_list '(mk_nestArray a) :=
+    ((fix go (n : nat) (i : Int63.int) (acc : list byte) :=
+        match n with
+        | 0 => acc
+        | S n => go n (i - 1) (cons (Test2.i63_to_byte a.[i].[0]) acc)
+        end) (Test2.nat_length a) (length a - 1) nil)%int63.
+
+  Definition from_byte_list (xs : list byte) :=
+    (let arr := make (Test2.list_length_i63 xs) (make 0 0) in
+    mk_nestArray ((fix go i xs acc :=
+        match xs with
+        | nil => acc
+        | cons x xs => go (i + 1) xs (acc.[i <- make 1 (Test2.i63_from_byte x)])
+        end) 0 xs arr))%int63.
+
+  Declare Scope nestArray_scope.
+  Delimit Scope nestArray_scope with nestArray.
+
+  String Notation nestArray from_byte_list to_byte_list : nestArray_scope.
+
+  Open Scope nestArray_scope.
+  Eval cbv in mk_nestArray ( [| make 1 97; make 1 98; make 1 99 | make 0 0|])%int63%array.
+  Check "abc"%nestArray.
+End Test3.
+
+
+
+(* Notations for primitive floats inside polymorphic datatypes *)
+Module Test4.
+  Import PrimFloat.
+  Inductive floatList := mk_floatList (_ : list float).
+  Definition float_from_byte (b : byte) : float :=
+    if Byte.eqb b "0"%byte then PrimFloat.zero else PrimFloat.one.
+  Definition float_to_byte (f : float) : byte :=
+    if PrimFloat.is_zero f then "0" else "1".
+  Definition to_byte_list '(mk_floatList a) := List.map float_to_byte a.
+
+  Definition from_byte_list (xs : list byte) : floatList:=
+    mk_floatList (List.map float_from_byte xs).
+
+  Declare Scope floatList_scope.
+  Delimit Scope floatList_scope with floatList.
+
+  String Notation floatList from_byte_list to_byte_list : floatList_scope.
+
+  Open Scope floatList_scope.
+  Import List.ListNotations.
+  Check mk_floatList [97; 0; 0]%float%list.
+  Check "100"%floatList.
+
+  Definition float' := float.
+  Check mk_floatList (@cons float' 1 [0; 0])%float%list.
+End Test4.