Add symbols

FicroKanSharp.Test/Arithmetic.fs

@@ -0,0 +1,89 @@
+namespace FicroKanSharp.Test
+
+open FicroKanSharp
+open FsUnitTyped
+open Xunit
+
+module Arithmetic =
+
+    type Nat = Nat
+
+    [<Fact>]
+    let ``Arithmetic example`` () =
+        let zero : Term<Nat> = Term.Symbol ("zero", [])
+
+        let succ (x : Term<Nat>) : Term<Nat> =
+            Term.Symbol ("succ", [ TypedTerm.make x ])
+
+        let rec ofInt (n : int) : Term<Nat> =
+            if n = 0 then
+                zero
+            else
+                succ (ofInt (n - 1))
+
+        // "pluso x y z" is "x + y == z".
+        let rec pluso (x : Term<Nat>) (y : Term<Nat>) (z : Term<Nat>) : Goal =
+            let succCase =
+                Goal.callFresh (fun n ->
+                    let n = Term.Variable n
+
+                    Goal.callFresh (fun m ->
+                        let m = Term.Variable m
+
+                        Goal.conj
+                            (Goal.equiv x (succ n))
+                            (Goal.conj (Goal.equiv z (succ m)) (Goal.delay (fun () -> pluso n y m)))
+                    )
+                )
+
+            let zeroCase =
+                Goal.conj (Goal.equiv x zero) (Goal.equiv y z)
+
+            Goal.disj zeroCase succCase
+
+        Goal.evaluate (Goal.callFresh (fun z -> Goal.equiv<Nat> (Term.Variable z) (Term.Variable z))) State.empty
+        |> Stream.toList
+        |> shouldEqual [ Map.empty ]
+
+        // Evaluate 1 + 1
+        Goal.evaluate (Goal.callFresh (fun z -> pluso (ofInt 1) (ofInt 1) (Term.Variable z))) State.empty
+        |> Stream.toList
+        |> List.exactlyOne
+        |> shouldEqual (
+            Map.ofList
+                [
+                    VariableCount 0, TypedTerm.make (succ (Term.Variable (VariableCount 2)))
+                    VariableCount 1, TypedTerm.make (ofInt 0)
+                    VariableCount 2, TypedTerm.make (ofInt 1)
+                ]
+        )
+
+        // Evaluate 2 + 2
+        Goal.evaluate (Goal.callFresh (fun z -> pluso (ofInt 2) (ofInt 2) (Term.Variable z))) State.empty
+        |> Stream.toList
+        |> List.exactlyOne
+        |> shouldEqual (
+            Map.ofList
+                [
+                    VariableCount 0, TypedTerm.make (succ (Term.Variable (VariableCount 2)))
+                    VariableCount 1, TypedTerm.make (ofInt 1)
+                    VariableCount 2, TypedTerm.make (succ (Term.Variable (VariableCount 4)))
+                    VariableCount 3, TypedTerm.make zero
+                    VariableCount 4, TypedTerm.make (ofInt 2)
+                ]
+        )
+
+        // Find n such that n + n = 4
+        Goal.evaluate (Goal.callFresh (fun z -> pluso (Term.Variable z) (Term.Variable z) (ofInt 4))) State.empty
+        |> Stream.toList
+        |> List.exactlyOne
+        |> shouldEqual (
+            Map.ofList
+                [
+                    VariableCount 0, TypedTerm.make (succ (Term.Variable (VariableCount 1)))
+                    VariableCount 1, TypedTerm.make (succ (Term.Variable (VariableCount 3)))
+                    VariableCount 2, TypedTerm.make (ofInt 3)
+                    VariableCount 3, TypedTerm.make zero
+                    VariableCount 4, TypedTerm.make (ofInt 2)
+                ]
+        )

FicroKanSharp.Test/FicroKanSharp.Test.fsproj

@@ -6,6 +6,7 @@
 
     <ItemGroup>
         <Compile Include="TestExamples.fs" />
+        <Compile Include="Arithmetic.fs" />
     </ItemGroup>
 
     <ItemGroup>