Interpreter

appveyor.yml

@@ -5,7 +5,7 @@ init:
 
 environment:
   matrix:
-  - solution: Semester4/NetworkModel/NetworkModel.sln
+  - solution: Semester4/Interpreter/Interpreter.sln
 
 before_build:
   - nuget restore %solution%

semester4/Interpreter/Interpreter.sln

@@ -0,0 +1,22 @@
+
+Microsoft Visual Studio Solution File, Format Version 12.00
+Project("{F2A71F9B-5D33-465A-A702-920D77279786}") = "Interpreter", "Interpreter\Interpreter.fsproj", "{F4AC6C26-010E-4A43-9A7E-DE86E607064B}"
+EndProject
+Project("{F2A71F9B-5D33-465A-A702-920D77279786}") = "InterpreterTests", "InterpreterTests\InterpreterTests.fsproj", "{B0759521-85A7-4058-A22F-DAC2B0BC2EAE}"
+EndProject
+Global
+	GlobalSection(SolutionConfigurationPlatforms) = preSolution
+		Debug|Any CPU = Debug|Any CPU
+		Release|Any CPU = Release|Any CPU
+	EndGlobalSection
+	GlobalSection(ProjectConfigurationPlatforms) = postSolution
+		{F4AC6C26-010E-4A43-9A7E-DE86E607064B}.Debug|Any CPU.ActiveCfg = Debug|Any CPU
+		{F4AC6C26-010E-4A43-9A7E-DE86E607064B}.Debug|Any CPU.Build.0 = Debug|Any CPU
+		{F4AC6C26-010E-4A43-9A7E-DE86E607064B}.Release|Any CPU.ActiveCfg = Release|Any CPU
+		{F4AC6C26-010E-4A43-9A7E-DE86E607064B}.Release|Any CPU.Build.0 = Release|Any CPU
+		{B0759521-85A7-4058-A22F-DAC2B0BC2EAE}.Debug|Any CPU.ActiveCfg = Debug|Any CPU
+		{B0759521-85A7-4058-A22F-DAC2B0BC2EAE}.Debug|Any CPU.Build.0 = Debug|Any CPU
+		{B0759521-85A7-4058-A22F-DAC2B0BC2EAE}.Release|Any CPU.ActiveCfg = Release|Any CPU
+		{B0759521-85A7-4058-A22F-DAC2B0BC2EAE}.Release|Any CPU.Build.0 = Release|Any CPU
+	EndGlobalSection
+EndGlobal

semester4/Interpreter/Interpreter/Interpreter.fs

@@ -0,0 +1,54 @@
+module Interpreter
+
+/// Лямбда-терм, бывает трёх видов
+type Term =
+    | Variable of char
+    | Abstraction of char * Term
+    | Application of Term * Term
+
+/// Свободна переменная в выражении или нет
+let rec isFree expression variable =
+    match expression with
+    | Variable var -> var = variable
+    | Abstraction (var, term) -> var <> variable && isFree term variable
+    | Application (left, right) -> isFree left variable || isFree right variable
+
+/// Замена переменной в выражении
+let rec substitution oldVariable newVariable expression =
+    let vars = [ 'a' .. 'z' ]
+    match expression with
+    | Variable var when var = oldVariable -> newVariable
+    | Variable _ -> expression
+    | Abstraction (var, _) when var = oldVariable -> expression
+    | Abstraction (var, term) when not <| isFree newVariable var ->
+        Abstraction(var, substitution oldVariable newVariable term)
+    | Abstraction (var, term) ->
+        let newSymbol =
+            vars
+            |> List.filter (not << isFree newVariable)
+            |> List.head
+
+        Abstraction
+            (newSymbol,
+             substitution oldVariable newVariable
+             <| substitution var (Variable newSymbol) term)
+    | Application (left, right) ->
+        Application(substitution oldVariable newVariable left, substitution oldVariable newVariable right)
+
+/// Бета-редукция выражения
+let betaReduction (term: Term) =
+    let rec betaReductionRec term =
+        match term with
+        | Variable var -> Variable(var)
+        | Abstraction (var, term) -> Abstraction(var, betaReductionRec <| term)
+        | Application (Abstraction (var, leftTerm), rightTerm) ->
+            leftTerm
+            |> substitution var rightTerm
+            |> betaReductionRec
+        | Application (left, right) ->
+            let leftReduce = betaReductionRec left
+            match leftReduce with
+            | Abstraction (_) -> Application(leftReduce, right) |> betaReductionRec
+            | _ -> Application(leftReduce, betaReductionRec right)
+
+    betaReductionRec term

semester4/Interpreter/Interpreter/Interpreter.fsproj

@@ -0,0 +1,11 @@
+<Project Sdk="Microsoft.NET.Sdk">
+
+    <PropertyGroup>
+        <TargetFramework>netcoreapp3.1</TargetFramework>
+    </PropertyGroup>
+
+    <ItemGroup>
+        <Compile Include="Interpreter.fs" />
+    </ItemGroup>
+
+</Project>

semester4/Interpreter/InterpreterTests/InterpreterTest.fs

@@ -0,0 +1,44 @@
+module InterpreterTests
+
+open NUnit.Framework
+open FsUnit
+open Interpreter
+
+[<Test>]
+let ``simple variable test`` () =
+    Variable('x')
+    |> betaReduction
+    |> should equal (Variable('x'))
+
+[<Test>]
+let ``simple abstraction test`` () =
+    Abstraction('x', Variable('x'))
+    |> betaReduction
+    |> should equal (Abstraction('x', Variable('x')))
+
+[<Test>]
+let ``simple application test`` () =
+    Application(Variable('x'), Variable('y'))
+    |> betaReduction
+    |> should equal (Application(Variable('x'), Variable('y')))
+
+// (λx.x y)
+[<Test>]
+let ``simple test`` () =
+    Application(Abstraction('x', Variable('x')), Variable('y'))
+    |> betaReduction
+    |> should equal (Variable('y'))
+
+// λx.(x y) z
+[<Test>]
+let ``simple test two`` () =
+    Application(Abstraction('x', Application(Variable('x'), Variable('y'))), Variable('z'))
+    |> betaReduction
+    |> should equal (Application(Variable('z'), Variable('y')))
+
+// (λx.y z) (λa.(a z) b)
+[<Test>]
+let ``simple test three`` () =
+    Application(Application(Abstraction('x', Variable('y')), Variable('z')), Application(Abstraction('a', Application(Variable('a'), Variable('z'))), Variable('b')))
+    |> betaReduction
+    |> should equal (Application(Variable('y'), Application(Variable('b'), Variable('z'))))

semester4/Interpreter/InterpreterTests/InterpreterTests.fsproj

@@ -0,0 +1,25 @@
+<Project Sdk="Microsoft.NET.Sdk">
+
+    <PropertyGroup>
+        <TargetFramework>netcoreapp3.1</TargetFramework>
+
+        <IsPackable>true</IsPackable>
+        <GenerateProgramFile>true</GenerateProgramFile>
+    </PropertyGroup>
+
+    <ItemGroup>
+        <PackageReference Include="FsUnit" Version="4.0.1" />
+        <PackageReference Include="nunit" Version="3.12.0" />
+        <PackageReference Include="NUnit3TestAdapter" Version="3.15.1" />
+        <PackageReference Include="Microsoft.NET.Test.Sdk" Version="16.4.0" />
+    </ItemGroup>
+
+    <ItemGroup>
+        <Compile Include="InterpreterTest.fs" />
+    </ItemGroup>
+
+    <ItemGroup>
+      <ProjectReference Include="..\Interpreter\Interpreter.fsproj" />
+    </ItemGroup>
+
+</Project>