Add absolute values and convert to Minion

Add support for absolute values, in particular:

* Parsing from JSON.
* The `Abs` expression variant.
* The `FlatAbsEq` Minion constraint.
* Flattening and conversion to Minion.

As part of this change, a division domain bug is fixed. In our domain
calculation we use truncating division, the default Rust integer
division operator. However, the semantics of Essence Prime specify floor
division.

Truncating division has the effect of rounding towards 0.

Truncating division does `-5 / 2 =-2` and `5/2 = 2`. However, we want
`-5/2 = -3` and `5/2 = 2`.

This caused the domains of variables containing negative divisions to
sometimes be one too high. For abs-03, this caused Oxide to give
different solutions than Conjure.

conjure_oxide/tests/integration/basic/abs/0-simple/config.toml

@@ -0,0 +1 @@
+use_native_parser=false

conjure_oxide/tests/integration/basic/abs/0-simple/input-expected-rule-trace-human.txt

@@ -0,0 +1,24 @@
+Model before rewriting:
+
+find x: int(-2..3)
+
+such that
+
+(|x| = 1)
+
+--
+
+(|x| = 1), 
+   ~~> introduce_abseq ([("Minion", 4400)]) 
+AbsEq(1,x) 
+
+--
+
+Final model:
+
+find x: int(-2..3)
+
+such that
+
+AbsEq(1,x)
+

conjure_oxide/tests/integration/basic/abs/0-simple/input.eprime

@@ -0,0 +1,6 @@
+language ESSENCE' 1.0
+
+find x : int(-2..3) 
+
+such that 
+|x| = 1 

conjure_oxide/tests/integration/basic/abs/0-simple/input.expected-minion.solutions.json

@@ -0,0 +1,8 @@
+[
+  {
+    "x": -1
+  },
+  {
+    "x": 1
+  }
+]

conjure_oxide/tests/integration/basic/abs/0-simple/input.expected-parse.serialised.json

@@ -0,0 +1,66 @@
+{
+  "constraints": [
+    {
+      "Eq": [
+        {
+          "clean": false,
+          "etype": null
+        },
+        {
+          "Abs": [
+            {
+              "clean": false,
+              "etype": null
+            },
+            {
+              "Atomic": [
+                {
+                  "clean": false,
+                  "etype": null
+                },
+                {
+                  "Reference": {
+                    "UserName": "x"
+                  }
+                }
+              ]
+            }
+          ]
+        },
+        {
+          "Atomic": [
+            {
+              "clean": false,
+              "etype": null
+            },
+            {
+              "Literal": {
+                "Int": 1
+              }
+            }
+          ]
+        }
+      ]
+    }
+  ],
+  "next_var": 0,
+  "variables": [
+    [
+      {
+        "UserName": "x"
+      },
+      {
+        "domain": {
+          "IntDomain": [
+            {
+              "Bounded": [
+                -2,
+                3
+              ]
+            }
+          ]
+        }
+      }
+    ]
+  ]
+}

conjure_oxide/tests/integration/basic/abs/0-simple/input.expected-rewrite.serialised.json

@@ -0,0 +1,42 @@
+{
+  "constraints": [
+    {
+      "FlatAbsEq": [
+        {
+          "clean": false,
+          "etype": null
+        },
+        {
+          "Literal": {
+            "Int": 1
+          }
+        },
+        {
+          "Reference": {
+            "UserName": "x"
+          }
+        }
+      ]
+    }
+  ],
+  "next_var": 0,
+  "variables": [
+    [
+      {
+        "UserName": "x"
+      },
+      {
+        "domain": {
+          "IntDomain": [
+            {
+              "Bounded": [
+                -2,
+                3
+              ]
+            }
+          ]
+        }
+      }
+    ]
+  ]
+}

conjure_oxide/tests/integration/basic/abs/01-simple/config.toml

@@ -0,0 +1,2 @@
+run_solver=true
+use_native_parser=false

conjure_oxide/tests/integration/basic/abs/01-simple/input-expected-rule-trace-human.txt

@@ -0,0 +1,65 @@
+Model before rewriting:
+
+find x: int(-5..5)
+find y: int(-5..5)
+
+such that
+
+(Sum([|x|, |y|]) = 10)
+
+--
+
+Sum([|x|, |y|]), 
+   ~~> flatten_vecop ([("Minion", 4200)]) 
+Sum([__0, __1]) 
+new variables:
+  __0: int(0..5)
+  __1: int(0..5)
+new constraints:
+  __0 =aux |x|
+  __1 =aux |y|
+--
+
+__0 =aux |x|, 
+   ~~> introduce_abseq ([("Minion", 4400)]) 
+AbsEq(__0,x) 
+
+--
+
+__1 =aux |y|, 
+   ~~> introduce_abseq ([("Minion", 4400)]) 
+AbsEq(__1,y) 
+
+--
+
+(Sum([__0, __1]) = 10), 
+   ~~> sum_eq_to_inequalities ([("Minion", 4100)]) 
+And([(Sum([__0, __1]) <= 10), (Sum([__0, __1]) >= 10)]) 
+
+--
+
+(Sum([__0, __1]) <= 10), 
+   ~~> introduce_sumleq ([("Minion", 4400)]) 
+SumLeq([__0, __1], 10) 
+
+--
+
+(Sum([__0, __1]) >= 10), 
+   ~~> introduce_sumgeq ([("Minion", 4400)]) 
+SumGeq([__0, __1], 10) 
+
+--
+
+Final model:
+
+find x: int(-5..5)
+find y: int(-5..5)
+find __0: int(0..5)
+find __1: int(0..5)
+
+such that
+
+And([SumLeq([__0, __1], 10), SumGeq([__0, __1], 10)]),
+AbsEq(__0,x),
+AbsEq(__1,y)
+

conjure_oxide/tests/integration/basic/abs/01-simple/input.eprime

@@ -0,0 +1,5 @@
+language ESSENCE' 1.0
+
+find x,y: int(-5..5)
+
+such that  |x| + |y| = 10

conjure_oxide/tests/integration/basic/abs/01-simple/input.expected-minion.solutions.json

@@ -0,0 +1,26 @@
+[
+  {
+    "__0": 5,
+    "__1": 5,
+    "x": -5,
+    "y": -5
+  },
+  {
+    "__0": 5,
+    "__1": 5,
+    "x": -5,
+    "y": 5
+  },
+  {
+    "__0": 5,
+    "__1": 5,
+    "x": 5,
+    "y": -5
+  },
+  {
+    "__0": 5,
+    "__1": 5,
+    "x": 5,
+    "y": 5
+  }
+]

conjure_oxide/tests/integration/basic/abs/01-simple/input.expected-parse.serialised.json

@@ -0,0 +1,114 @@
+{
+  "constraints": [
+    {
+      "Eq": [
+        {
+          "clean": false,
+          "etype": null
+        },
+        {
+          "Sum": [
+            {
+              "clean": false,
+              "etype": null
+            },
+            [
+              {
+                "Abs": [
+                  {
+                    "clean": false,
+                    "etype": null
+                  },
+                  {
+                    "Atomic": [
+                      {
+                        "clean": false,
+                        "etype": null
+                      },
+                      {
+                        "Reference": {
+                          "UserName": "x"
+                        }
+                      }
+                    ]
+                  }
+                ]
+              },
+              {
+                "Abs": [
+                  {
+                    "clean": false,
+                    "etype": null
+                  },
+                  {
+                    "Atomic": [
+                      {
+                        "clean": false,
+                        "etype": null
+                      },
+                      {
+                        "Reference": {
+                          "UserName": "y"
+                        }
+                      }
+                    ]
+                  }
+                ]
+              }
+            ]
+          ]
+        },
+        {
+          "Atomic": [
+            {
+              "clean": false,
+              "etype": null
+            },
+            {
+              "Literal": {
+                "Int": 10
+              }
+            }
+          ]
+        }
+      ]
+    }
+  ],
+  "next_var": 0,
+  "variables": [
+    [
+      {
+        "UserName": "x"
+      },
+      {
+        "domain": {
+          "IntDomain": [
+            {
+              "Bounded": [
+                -5,
+                5
+              ]
+            }
+          ]
+        }
+      }
+    ],
+    [
+      {
+        "UserName": "y"
+      },
+      {
+        "domain": {
+          "IntDomain": [
+            {
+              "Bounded": [
+                -5,
+                5
+              ]
+            }
+          ]
+        }
+      }
+    ]
+  ]
+}