UPDATE: Implement the implicit Intersection Operator

The II operator takes a range and returns a single cell that is in the same column or the same row
as the present cell.

This is needed for backwards compatibility with old Excel models and as a first step towards dynamic arrays.

In the past Excel would evaluate `=A1:A10` in cell `C3` as `A3`, but today in results in an array containing all
values in the range. To be compatible with old workbooks Excel inserts the II operator
on those cases.

So this PR performs an static analysis on all formulas inserting on import automatically the II operator
where necessary. This we call the _automatic implicit operator_. When exporting to Excel the operator is striped away.
You can also manually use the II. For instance `=SUM(@A1:A10)` in cell `C3`.
This was not possible before and such a formula would break backwards compatibility with Excel. To Excel that "non automatic"
form of the II is exported as `_xlfn.SINGLE()`.

Th static analysis has to be done for all arithmetic operations and all functions.
This is a bit of a daunting task and it is not done fully in this PR. We also need to implement arrays and dynamic arrays.
My believe is that once the core operations have been implemented we can go formula by formula writing proper tests and documentation.

After this PR formulas like `=A1:A10` for instance will return `#N/IMPL!` instead of performing the implicit intersection

base/src/actions.rs

@@ -1,5 +1,6 @@
 use crate::constants::{LAST_COLUMN, LAST_ROW};
-use crate::expressions::parser::stringify::DisplaceData;
+use crate::expressions::parser::stringify::{to_string, to_string_displaced, DisplaceData};
+use crate::expressions::types::CellReferenceRC;
 use crate::model::Model;
 
 // NOTE: There is a difference with Excel behaviour when deleting cells/rows/columns
@@ -8,16 +9,45 @@ use crate::model::Model;
 // I feel this is unimportant for now.
 
 impl Model {
+    fn shift_cell_formula(
+        &mut self,
+        sheet: u32,
+        row: i32,
+        column: i32,
+        displace_data: &DisplaceData,
+    ) -> Result<(), String> {
+        if let Some(f) = self
+            .workbook
+            .worksheet(sheet)?
+            .cell(row, column)
+            .and_then(|c| c.get_formula())
+        {
+            let node = &self.parsed_formulas[sheet as usize][f as usize].clone();
+            let cell_reference = CellReferenceRC {
+                sheet: self.workbook.worksheets[sheet as usize].get_name(),
+                row,
+                column,
+            };
+            // FIXME: This is not a very performant way if the formula has changed :S.
+            let formula = to_string(node, &cell_reference);
+            let formula_displaced = to_string_displaced(node, &cell_reference, displace_data);
+            if formula != formula_displaced {
+                self.update_cell_with_formula(sheet, row, column, format!("={formula_displaced}"))?;
+            }
+        }
+        Ok(())
+    }
     /// This function iterates over all cells in the model and shifts their formulas according to the displacement data.
     ///
     /// # Arguments
     ///
     /// * `displace_data` - A reference to `DisplaceData` describing the displacement's direction and magnitude.
-    fn displace_cells(&mut self, displace_data: &DisplaceData) {
+    fn displace_cells(&mut self, displace_data: &DisplaceData) -> Result<(), String> {
         let cells = self.get_all_cells();
         for cell in cells {
-            self.shift_cell_formula(cell.index, cell.row, cell.column, displace_data);
+            self.shift_cell_formula(cell.index, cell.row, cell.column, displace_data)?;
         }
+        Ok(())
     }
 
     /// Retrieves the column indices for a specific row in a given sheet, sorted in ascending or descending order.
@@ -134,7 +164,7 @@ impl Model {
                 column,
                 delta: column_count,
             }),
-        );
+        )?;
 
         // In the list of columns:
         // * Keep all the columns to the left
@@ -214,7 +244,7 @@ impl Model {
                 column,
                 delta: -column_count,
             }),
-        );
+        )?;
         let worksheet = &mut self.workbook.worksheet_mut(sheet)?;
 
         // deletes all the column styles
@@ -338,7 +368,7 @@ impl Model {
                 row,
                 delta: row_count,
             }),
-        );
+        )?;
 
         Ok(())
     }
@@ -399,7 +429,7 @@ impl Model {
                 row,
                 delta: -row_count,
             }),
-        );
+        )?;
         Ok(())
     }
 
@@ -420,14 +450,14 @@ impl Model {
         sheet: u32,
         column: i32,
         delta: i32,
-    ) -> Result<(), &'static str> {
+    ) -> Result<(), String> {
         // Check boundaries
         let target_column = column + delta;
         if !(1..=LAST_COLUMN).contains(&target_column) {
-            return Err("Target column out of boundaries");
+            return Err("Target column out of boundaries".to_string());
         }
         if !(1..=LAST_COLUMN).contains(&column) {
-            return Err("Initial column out of boundaries");
+            return Err("Initial column out of boundaries".to_string());
         }
 
         // TODO: Add the actual displacement of data and styles
@@ -439,7 +469,7 @@ impl Model {
                 column,
                 delta,
             }),
-        );
+        )?;
 
         Ok(())
     }

base/src/cast.rs

@@ -1,7 +1,6 @@
 use crate::{
     calc_result::{CalcResult, Range},
     expressions::{parser::Node, token::Error, types::CellReferenceIndex},
-    implicit_intersection::implicit_intersection,
     model::Model,
 };
 
@@ -39,19 +38,11 @@ impl Model {
             }
             CalcResult::EmptyCell | CalcResult::EmptyArg => Ok(0.0),
             error @ CalcResult::Error { .. } => Err(error),
-            CalcResult::Range { left, right } => {
-                match implicit_intersection(&cell, &Range { left, right }) {
-                    Some(cell_reference) => {
-                        let result = self.evaluate_cell(cell_reference);
-                        self.cast_to_number(result, cell_reference)
-                    }
-                    None => Err(CalcResult::Error {
-                        error: Error::VALUE,
-                        origin: cell,
-                        message: "Invalid reference (number)".to_string(),
-                    }),
-                }
-            }
+            CalcResult::Range { .. } => Err(CalcResult::Error {
+                error: Error::NIMPL,
+                origin: cell,
+                message: "Arrays not supported yet".to_string(),
+            }),
         }
     }
 
@@ -99,19 +90,11 @@ impl Model {
             }
             CalcResult::EmptyCell | CalcResult::EmptyArg => Ok("".to_string()),
             error @ CalcResult::Error { .. } => Err(error),
-            CalcResult::Range { left, right } => {
-                match implicit_intersection(&cell, &Range { left, right }) {
-                    Some(cell_reference) => {
-                        let result = self.evaluate_cell(cell_reference);
-                        self.cast_to_string(result, cell_reference)
-                    }
-                    None => Err(CalcResult::Error {
-                        error: Error::VALUE,
-                        origin: cell,
-                        message: "Invalid reference (string)".to_string(),
-                    }),
-                }
-            }
+            CalcResult::Range { .. } => Err(CalcResult::Error {
+                error: Error::NIMPL,
+                origin: cell,
+                message: "Arrays not supported yet".to_string(),
+            }),
         }
     }
 
@@ -151,19 +134,11 @@ impl Model {
             CalcResult::Boolean(b) => Ok(b),
             CalcResult::EmptyCell | CalcResult::EmptyArg => Ok(false),
             error @ CalcResult::Error { .. } => Err(error),
-            CalcResult::Range { left, right } => {
-                match implicit_intersection(&cell, &Range { left, right }) {
-                    Some(cell_reference) => {
-                        let result = self.evaluate_cell(cell_reference);
-                        self.cast_to_bool(result, cell_reference)
-                    }
-                    None => Err(CalcResult::Error {
-                        error: Error::VALUE,
-                        origin: cell,
-                        message: "Invalid reference (bool)".to_string(),
-                    }),
-                }
-            }
+            CalcResult::Range { .. } => Err(CalcResult::Error {
+                error: Error::NIMPL,
+                origin: cell,
+                message: "Arrays not supported yet".to_string(),
+            }),
         }
     }
 

base/src/expressions/lexer/mod.rs

@@ -187,6 +187,7 @@ impl Lexer {
                     ']' => TokenType::RightBracket,
                     ':' => TokenType::Colon,
                     ';' => TokenType::Semicolon,
+                    '@' => TokenType::At,
                     ',' => {
                         if self.locale.numbers.symbols.decimal == "," {
                             match self.consume_number(',') {

base/src/expressions/lexer/test/mod.rs

@@ -1,4 +1,5 @@
 mod test_common;
+mod test_implicit_intersection;
 mod test_language;
 mod test_locale;
 mod test_ranges;

base/src/expressions/lexer/test/test_implicit_intersection.rs

@@ -0,0 +1,25 @@
+#![allow(clippy::unwrap_used)]
+
+use crate::expressions::{
+    lexer::{Lexer, LexerMode},
+    token::TokenType::*,
+};
+use crate::language::get_language;
+use crate::locale::get_locale;
+
+fn new_lexer(formula: &str) -> Lexer {
+    let locale = get_locale("en").unwrap();
+    let language = get_language("en").unwrap();
+    Lexer::new(formula, LexerMode::A1, locale, language)
+}
+
+#[test]
+fn sum_implicit_intersection() {
+    let mut lx = new_lexer("sum(@A1:A3)");
+    assert_eq!(lx.next_token(), Ident("sum".to_string()));
+    assert_eq!(lx.next_token(), LeftParenthesis);
+    assert_eq!(lx.next_token(), At);
+    assert!(matches!(lx.next_token(), Range { .. }));
+    assert_eq!(lx.next_token(), RightParenthesis);
+    assert_eq!(lx.next_token(), EOF);
+}