├── .gitignore ├── Example ├── Expr.fs └── TypeEquality.Example.fsproj ├── LICENSE ├── README.md ├── Test ├── Teq.fs └── TypeEquality.Test.fsproj ├── TypeEquality.sln ├── TypeEquality ├── Teq.fs ├── Teq.fsi └── TypeEquality.fsproj └── appveyor.yml /.gitignore: -------------------------------------------------------------------------------- 1 | ## Ignore Visual Studio temporary files, build results, and 2 | ## files generated by popular Visual Studio add-ons. 3 | ## 4 | ## Get latest from https://github.com/github/gitignore/blob/master/VisualStudio.gitignore 5 | 6 | # User-specific files 7 | *.suo 8 | *.user 9 | *.userosscache 10 | *.sln.docstates 11 | 12 | # User-specific files (MonoDevelop/Xamarin Studio) 13 | *.userprefs 14 | 15 | # Build results 16 | [Dd]ebug/ 17 | [Dd]ebugPublic/ 18 | [Rr]elease/ 19 | [Rr]eleases/ 20 | x64/ 21 | x86/ 22 | bld/ 23 | [Bb]in/ 24 | [Oo]bj/ 25 | [Ll]og/ 26 | 27 | # Visual Studio 2015/2017 cache/options directory 28 | .vs/ 29 | # Uncomment if you have tasks that create the project's static files in wwwroot 30 | #wwwroot/ 31 | 32 | # Visual Studio 2017 auto generated files 33 | Generated\ Files/ 34 | 35 | # MSTest test Results 36 | [Tt]est[Rr]esult*/ 37 | [Bb]uild[Ll]og.* 38 | 39 | # NUNIT 40 | *.VisualState.xml 41 | TestResult.xml 42 | 43 | # Build Results of an ATL Project 44 | [Dd]ebugPS/ 45 | [Rr]eleasePS/ 46 | dlldata.c 47 | 48 | # Benchmark Results 49 | BenchmarkDotNet.Artifacts/ 50 | 51 | # .NET Core 52 | project.lock.json 53 | project.fragment.lock.json 54 | artifacts/ 55 | **/Properties/launchSettings.json 56 | 57 | # StyleCop 58 | StyleCopReport.xml 59 | 60 | # Files built by Visual Studio 61 | *_i.c 62 | *_p.c 63 | *_i.h 64 | *.ilk 65 | *.meta 66 | *.obj 67 | *.iobj 68 | *.pch 69 | *.pdb 70 | *.ipdb 71 | *.pgc 72 | *.pgd 73 | *.rsp 74 | *.sbr 75 | *.tlb 76 | *.tli 77 | *.tlh 78 | *.tmp 79 | *.tmp_proj 80 | *.log 81 | *.vspscc 82 | *.vssscc 83 | .builds 84 | *.pidb 85 | *.svclog 86 | *.scc 87 | 88 | # Chutzpah Test files 89 | _Chutzpah* 90 | 91 | # Visual C++ cache files 92 | ipch/ 93 | *.aps 94 | *.ncb 95 | *.opendb 96 | *.opensdf 97 | *.sdf 98 | *.cachefile 99 | *.VC.db 100 | *.VC.VC.opendb 101 | 102 | # Visual Studio profiler 103 | *.psess 104 | *.vsp 105 | *.vspx 106 | *.sap 107 | 108 | # Visual Studio Trace Files 109 | *.e2e 110 | 111 | # TFS 2012 Local Workspace 112 | $tf/ 113 | 114 | # Guidance Automation Toolkit 115 | *.gpState 116 | 117 | # ReSharper is a .NET coding add-in 118 | _ReSharper*/ 119 | *.[Rr]e[Ss]harper 120 | *.DotSettings.user 121 | 122 | # JustCode is a .NET coding add-in 123 | .JustCode 124 | 125 | # TeamCity is a build add-in 126 | _TeamCity* 127 | 128 | # DotCover is a Code Coverage Tool 129 | *.dotCover 130 | 131 | # AxoCover is a Code Coverage Tool 132 | .axoCover/* 133 | !.axoCover/settings.json 134 | 135 | # Visual Studio code coverage results 136 | *.coverage 137 | *.coveragexml 138 | 139 | # NCrunch 140 | _NCrunch_* 141 | .*crunch*.local.xml 142 | nCrunchTemp_* 143 | 144 | # MightyMoose 145 | *.mm.* 146 | AutoTest.Net/ 147 | 148 | # Web workbench (sass) 149 | .sass-cache/ 150 | 151 | # Installshield output folder 152 | [Ee]xpress/ 153 | 154 | # DocProject is a documentation generator add-in 155 | DocProject/buildhelp/ 156 | DocProject/Help/*.HxT 157 | DocProject/Help/*.HxC 158 | DocProject/Help/*.hhc 159 | DocProject/Help/*.hhk 160 | DocProject/Help/*.hhp 161 | DocProject/Help/Html2 162 | DocProject/Help/html 163 | 164 | # Click-Once directory 165 | publish/ 166 | 167 | # Publish Web Output 168 | *.[Pp]ublish.xml 169 | *.azurePubxml 170 | # Note: Comment the next line if you want to checkin your web deploy settings, 171 | # but database connection strings (with potential passwords) will be unencrypted 172 | *.pubxml 173 | *.publishproj 174 | 175 | # Microsoft Azure Web App publish settings. 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We also recommend that a 185 | file or class name and description of purpose be included on the 186 | same "printed page" as the copyright notice for easier 187 | identification within third-party archives. 188 | 189 | Copyright [yyyy] [name of copyright owner] 190 | 191 | Licensed under the Apache License, Version 2.0 (the "License"); 192 | you may not use this file except in compliance with the License. 193 | You may obtain a copy of the License at 194 | 195 | http://www.apache.org/licenses/LICENSE-2.0 196 | 197 | Unless required by applicable law or agreed to in writing, software 198 | distributed under the License is distributed on an "AS IS" BASIS, 199 | WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 200 | See the License for the specific language governing permissions and 201 | limitations under the License. 202 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # TypeEquality 2 | 3 | [![NuGet latest release](https://badgen.net/nuget/v/TypeEquality)](https://www.nuget.org/packages/TypeEquality) 4 | [![NuGet latest pre-release](https://badgen.net/nuget/v/TypeEquality/pre)](https://www.nuget.org/packages/TypeEquality) 5 | [![Build status](https://ci.appveyor.com/api/projects/status/xk2mp8igycy4avxd?svg=true)](https://ci.appveyor.com/project/G-Research/typeequality) 6 | 7 | ## Type equalities for F# 8 | 9 | This library contains type equalities (Teqs) for F#. These equalities 10 | allow us to create type-safe abstractions by allowing us to encode 11 | Generalised Algebraic Data Types (GADTs), as found in languages like 12 | Haskell. 13 | 14 | Ralf Hinze explains the concepts of GADTs and phantom types in 15 | [_Fun with phantom types_](https://www.cs.ox.ac.uk/ralf.hinze/publications/With.pdf). 16 | In particular, _Section 7, "A type equality type"_, covers the role of a type 17 | equality in the encoding of GADTs. 18 | 19 | ## Usage 20 | 21 | To use Teqs in your projects, you'll want to reference the main TypeEquality 22 | project. The project is available as a nuget package - https://www.nuget.org/packages/TypeEquality. 23 | This project provides a type `Teq<'a,'b>` of proofs that `'a` 24 | and `'b` are the same type. By including these in the declaration of a 25 | generic discriminated union, you can constrain the types each case 26 | applies to, encoding a GADT. 27 | An example of this may be found in the Example folder. 28 | 29 | For more advanced usage, TypeEquality also allows you to reason about Teqs 30 | using the functions in the Teq and Teq.Cong (congruence) modules. 31 | 32 | The library has some unit tests in the Test/TypeEquality.Test.fsproj project. 33 | 34 | ## Contributing 35 | 36 | We welcome new contributors! We'll happily receive PRs for bug fixes 37 | or small changes. If you're contemplating something larger please get 38 | in touch first by opening a GitHub Issue describing the problem and 39 | how you propose to solve it. 40 | 41 | ## License 42 | 43 | Copyright 2018 G-Research 44 | 45 | Licensed under the Apache License, Version 2.0 (the "License"); you may not use these files except in compliance with the License. 46 | You may obtain a copy of the License at 47 | 48 | http://www.apache.org/licenses/LICENSE-2.0 49 | 50 | Unless required by applicable law or agreed to in writing, software 51 | distributed under the License is distributed on an "AS IS" BASIS, 52 | WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 53 | See the License for the specific language governing permissions and 54 | limitations under the License. 55 | -------------------------------------------------------------------------------- /Test/Teq.fs: -------------------------------------------------------------------------------- 1 | namespace TypeEquality.Test 2 | 3 | open TypeEquality 4 | 5 | open NUnit.Framework 6 | open FsUnitTyped 7 | 8 | [] 9 | module TestTeq = 10 | 11 | [] 12 | let ``Casting with Teq.refl is id`` () = 13 | let value = 42 14 | let t = Teq.refl 15 | Teq.cast t value 16 | |> shouldEqual value 17 | Teq.castFrom t value 18 | |> shouldEqual value 19 | 20 | [] 21 | let ``Cong.list does not throw`` () = 22 | let t : Teq = Teq.refl 23 | Assert.DoesNotThrow(fun () -> Teq.Cong.list t |> ignore) 24 | 25 | [] 26 | let ``Teq.tryRefl returns a Teq when the types match`` () = 27 | let t = Teq.tryRefl 28 | t |> Option.isSome |> shouldEqual true 29 | 30 | [] 31 | let ``Teq.tryRefl returns None when the types differ`` () = 32 | let t = Teq.tryRefl 33 | t |> Option.isSome |> shouldEqual false 34 | -------------------------------------------------------------------------------- /Test/TypeEquality.Test.fsproj: -------------------------------------------------------------------------------- 1 |  2 | 3 | netcoreapp2.1;net461 4 | true 5 | 4 6 | true 7 | full 8 | true 9 | portable 10 | true 11 | true 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | -------------------------------------------------------------------------------- /TypeEquality.sln: -------------------------------------------------------------------------------- 1 |  2 | Microsoft Visual Studio Solution File, Format Version 12.00 3 | Project("{F2A71F9B-5D33-465A-A702-920D77279786}") = "TypeEquality", "TypeEquality/TypeEquality.fsproj", "{AFC054F9-8300-494F-A959-6ABABEB4C4B6}" 4 | EndProject 5 | Project("{F2A71F9B-5D33-465A-A702-920D77279786}") = "TypeEquality.Test", "Test\TypeEquality.Test.fsproj", "{4152B8C3-1F28-45EB-92C2-CED0D990B603}" 6 | EndProject 7 | Project("{F2A71F9B-5D33-465A-A702-920D77279786}") = "TypeEquality.Example", "Example\TypeEquality.Example.fsproj", "{B5D3307D-D216-4723-9151-A5F1B1015DDB}" 8 | EndProject 9 | Global 10 | GlobalSection(SolutionConfigurationPlatforms) = preSolution 11 | Debug|Any CPU = Debug|Any CPU 12 | Release|Any CPU = Release|Any CPU 13 | EndGlobalSection 14 | GlobalSection(ProjectConfigurationPlatforms) = postSolution 15 | {AFC054F9-8300-494F-A959-6ABABEB4C4B6}.Debug|Any CPU.ActiveCfg = Debug|Any CPU 16 | {AFC054F9-8300-494F-A959-6ABABEB4C4B6}.Debug|Any CPU.Build.0 = Debug|Any CPU 17 | {AFC054F9-8300-494F-A959-6ABABEB4C4B6}.Release|Any CPU.ActiveCfg = Release|Any CPU 18 | {AFC054F9-8300-494F-A959-6ABABEB4C4B6}.Release|Any CPU.Build.0 = Release|Any CPU 19 | {4152B8C3-1F28-45EB-92C2-CED0D990B603}.Debug|Any CPU.ActiveCfg = Debug|Any CPU 20 | {4152B8C3-1F28-45EB-92C2-CED0D990B603}.Debug|Any CPU.Build.0 = Debug|Any CPU 21 | {4152B8C3-1F28-45EB-92C2-CED0D990B603}.Release|Any CPU.ActiveCfg = Release|Any CPU 22 | {4152B8C3-1F28-45EB-92C2-CED0D990B603}.Release|Any CPU.Build.0 = Release|Any CPU 23 | {B5D3307D-D216-4723-9151-A5F1B1015DDB}.Debug|Any CPU.ActiveCfg = Debug|Any CPU 24 | {B5D3307D-D216-4723-9151-A5F1B1015DDB}.Debug|Any CPU.Build.0 = Debug|Any CPU 25 | {B5D3307D-D216-4723-9151-A5F1B1015DDB}.Release|Any CPU.ActiveCfg = Release|Any CPU 26 | {B5D3307D-D216-4723-9151-A5F1B1015DDB}.Release|Any CPU.Build.0 = Release|Any CPU 27 | EndGlobalSection 28 | EndGlobal 29 | -------------------------------------------------------------------------------- /TypeEquality/Teq.fs: -------------------------------------------------------------------------------- 1 | namespace TypeEquality 2 | 3 | /// A type for witnessing type equality between 'a and 'b 4 | type Teq<'a, 'b> = private Teq of ('a -> 'b) * ('b -> 'a) 5 | 6 | /// Module for creating and using type equalities, primarily useful for Generalised Algebraic Data Types (GADTs) 7 | /// Invariant: If you use this module (without reflection shenanigans) and the 8 | /// code builds, it will be correct. 9 | [] 10 | module Teq = 11 | 12 | /// The single constructor for Teq - witnesses equality between 'a and 'a 13 | /// It would be nice to accept any isomorphism (i.e. 1-1 mapping between 14 | /// values, but Refl is the only provably correct constructor we can create 15 | /// in F#, so we choose soundness over completeness here). 16 | let refl<'a> : Teq<'a, 'a> = Teq (id, id) 17 | 18 | /// Returns a Teq when the two type parameters have the same value, 19 | /// otherwise returns None. 20 | let tryRefl<'a, 'b> : Teq<'a, 'b> option = 21 | if typeof<'a> = typeof<'b> then 22 | refl<'a> |> unbox |> Some 23 | else 24 | None 25 | 26 | /// Order isn't important 27 | /// a = b => b = a 28 | /// If you always do this followed by a cast, you may as well just use castFrom 29 | let symmetry (Teq (ab, ba)) = Teq (ba, ab) 30 | 31 | /// Let's compose two type-equalities: a = b && b = c => a = c 32 | let transitivity (Teq (ab, ba) : Teq<'a, 'b>) (Teq (bc, cb) : Teq<'b, 'c>) : Teq<'a, 'c> = 33 | // Obviously more efficient with a believeMe as below, but we like type 34 | // safety and this *can* be proven in the F# type system 35 | Teq (ab >> bc, cb >> ba) 36 | 37 | /// Converts an 'a to a 'b 38 | let cast (Teq (f, _)) a = f a 39 | 40 | /// Converts an 'a to a 'b 41 | /// Alias for cast 42 | let castTo teq a = cast teq a 43 | 44 | /// Converts a 'b to an 'a 45 | /// Equivalent to symmetry >> cast, but more efficient 46 | let castFrom (Teq (_, g)) b = g b 47 | 48 | /// Utility function to map an object of one type using a mapping function 49 | /// for a different type when we have a type equality between the two types 50 | let mapAs (Teq (f, g)) h a = a |> f |> h |> g 51 | 52 | /// The Cong module (short for congruence) contains functions that 53 | /// allow you safely transform Teqs into other Teqs that logically follow. 54 | /// 55 | /// Congruence: if x = y then f x = f y 56 | /// From a type-level perspective, this means, for example, 57 | /// iff 'a = 'b, then 'a list = 'b list. 58 | /// 59 | /// We do the munging below since we don't have type-level functions, so there 60 | /// is no such thing as, for example, Teq.cong List, to raise a 61 | /// Teq<'a, 'b> to a Teq<'a list, 'b list>. Instead we must create a function for 62 | /// any functor (wrapping type) we might want, e.g. list, option, array. 63 | /// 64 | /// More efficient than mapping the application of the teq across the functor. 65 | /// i.e. Use Teq.Cong.list in preference to List.map (Teq.cast) 66 | /// 67 | /// If you need to make your own Teq.Cong.foo for your own functor 'Foo<_>' using believeMe, 68 | /// then the onus is on you to verify that doing that is sane. 69 | [] 70 | module Cong = 71 | 72 | /// Clearly unsafe in general, but safe if we know 'a = 'b (which the Teq proves), 73 | /// and that there is some f such that f 'a = 'a2 = f 'b = 'b2, which we assume (and 74 | /// this assumption is why we don't make this public). Examples of valid values for 75 | /// f include list, array and option. 76 | let believeMe<'a, 'b, 'a2, 'b2> (teq : Teq<'a, 'b>) : Teq<'a2, 'b2> = 77 | unbox <| (refl : Teq<'a2, 'a2>) 78 | 79 | /// Given a type equality between two types, returns the type equality on the corresponding array types. 80 | let array<'a, 'b> (prf : Teq<'a, 'b>) : Teq<'a array, 'b array> = 81 | believeMe prf 82 | 83 | /// Given a type equality between two array types, returns the type equality on the corresponding element types. 84 | let arrayOf<'a, 'b> (prf : Teq<'a array, 'b array>) : Teq<'a, 'b> = 85 | believeMe prf 86 | 87 | /// Given a type equality between two types, returns the type equality on the corresponding list types. 88 | let list<'a, 'b> (prf : Teq<'a, 'b>) : Teq<'a list, 'b list> = 89 | believeMe prf 90 | 91 | /// Given a type equality between two list types, returns the type equality on the corresponding element types. 92 | let listOf<'a, 'b> (prf : Teq<'a list, 'b list>) : Teq<'a, 'b> = 93 | believeMe prf 94 | 95 | /// Given a type equality between two types, returns the type equality on the corresponding option types. 96 | let option<'a, 'b> (prf : Teq<'a, 'b>) : Teq<'a option, 'b option> = 97 | believeMe prf 98 | 99 | /// Given a type equality between two option types, returns the type equality on the corresponding element types. 100 | let optionOf<'a, 'b> (prf : Teq<'a option, 'b option>) : Teq<'a, 'b> = 101 | believeMe prf 102 | 103 | /// Given a type equality between two types 'domain1 and 'domain2, returns the type equality 104 | /// on the function types ('domain1 -> 'range) and ('domain2 -> 'range), for any arbitrary 'range. 105 | let domain<'domain1, 'domain2, 'range> (prf : Teq<'domain1, 'domain2>) : Teq<'domain1 -> 'range, 'domain2 -> 'range> = 106 | believeMe prf 107 | 108 | /// Given a type equality between two function types, returns the type equality on their corresponding domains. 109 | let domainOf<'domain1, 'domain2, 'range1, 'range2> (prf: Teq<'domain1 -> 'range1, 'domain2 -> 'range2>) : Teq<'domain1, 'domain2> = 110 | believeMe prf 111 | 112 | /// Given a type equality between two types 'range1 and 'range2, returns the type equality 113 | /// on the function types ('domain -> 'range1) and ('domain -> 'range2), for any arbitrary 'domain. 114 | let range<'domain, 'range1, 'range2> (prf : Teq<'range1, 'range2>) : Teq<'domain -> 'range1, 'domain -> 'range2> = 115 | believeMe prf 116 | 117 | /// Given a type equality between two function types, returns the type equality on their corresponding ranges. 118 | let rangeOf<'domain1, 'domain2, 'range1, 'range2> (prf: Teq<'domain1 -> 'range1, 'domain2 -> 'range2>) : Teq<'range1, 'range2> = 119 | believeMe prf 120 | 121 | /// Given a pair of type equalities, one for domains and one for ranges, returns the type equality for the corresponding function types. 122 | let func<'domain1, 'range1, 'domain2, 'range2> (domainPrf : Teq<'domain1, 'domain2>) (rangePrf : Teq<'range1, 'range2>) : Teq<'domain1 -> 'range1, 'domain2 -> 'range2> = 123 | transitivity 124 | (domain domainPrf) 125 | (range rangePrf) 126 | 127 | /// Given a type equality between two types 'fst1 and 'fst2, returns the type equality 128 | /// on the pair types ('fst1 * 'snd) and ('fst2 * 'snd), for any arbitrary 'snd. 129 | let fst<'fst1, 'fst2, 'snd> (prf : Teq<'fst1, 'fst2>) : Teq<'fst1 * 'snd, 'fst2 * 'snd> = 130 | believeMe prf 131 | 132 | /// Given a type equality between two types 'snd1 and 'snd2, returns the type equality 133 | /// on the pair types ('fst * 'snd1) and ('fst * 'snd2), for any arbitrary 'fst. 134 | let snd<'snd1, 'snd2, 'fst> (prf : Teq<'snd1, 'snd2>) : Teq<'fst * 'snd1, 'fst * 'snd2> = 135 | believeMe prf 136 | 137 | /// Given a pair of type equalities, one for the first element of a pair and one for the second element of a pair, 138 | /// returns the type equality for the corresponding pair types. 139 | let pair<'fst1, 'snd1, 'fst2, 'snd2> (fstPrf : Teq<'fst1, 'fst2>) (sndPrf : Teq<'snd1, 'snd2>) : Teq<'fst1 * 'snd1, 'fst2 * 'snd2> = 140 | transitivity 141 | (fst fstPrf) 142 | (snd sndPrf) 143 | -------------------------------------------------------------------------------- /TypeEquality/Teq.fsi: -------------------------------------------------------------------------------- 1 | namespace TypeEquality 2 | 3 | /// A type for witnessing type equality between 'a and 'b 4 | type Teq<'a, 'b> 5 | 6 | /// Module for creating and using type equalities, primarily useful for Generalised Algebraic Data Types (GADTs) 7 | /// Invariant: If you use this module (without reflection shenanigans) and the 8 | /// code builds, it will be correct. 9 | [] 10 | module Teq = 11 | 12 | /// The single constructor for Teq - witnesses equality between 'a and 'a 13 | /// It would be nice to accept any isomorphism (i.e. 1-1 mapping between 14 | /// values, but Refl is the only provably correct constructor we can create 15 | /// in F#, so we choose soundness over completeness here). 16 | val refl<'a> : Teq<'a, 'a> 17 | 18 | /// Returns a Teq when the two type parameters have the same value, 19 | /// otherwise returns None. 20 | val tryRefl<'a, 'b> : Teq<'a, 'b> option 21 | 22 | /// Order isn't important 23 | /// a = b => b = a 24 | /// If you always do this followed by a cast, you may as well just use castFrom 25 | val symmetry : Teq<'a, 'b> -> Teq<'b, 'a> 26 | 27 | /// Let's compose two type-equalities: a = b && b = c => a = c 28 | val transitivity : Teq<'a, 'b> -> Teq<'b, 'c> -> Teq<'a, 'c> 29 | 30 | /// Converts an 'a to a 'b 31 | val cast : Teq<'a, 'b> -> 'a -> 'b 32 | 33 | /// Converts an 'a to a 'b 34 | /// Alias for cast 35 | val castTo : Teq<'a, 'b> -> 'a -> 'b 36 | 37 | /// Converts a 'b to an 'a 38 | /// Equivalent to symmetry >> cast, but more efficient 39 | val castFrom : Teq<'a, 'b> -> 'b -> 'a 40 | 41 | /// Utility function to map an object of one type using a mapping function 42 | /// for a different type when we have a type equality between the two types 43 | val mapAs : Teq<'a, 'b> -> ('b -> 'b) -> 'a -> 'a 44 | 45 | /// The Cong module (short for congruence) contains functions that 46 | /// allow you safely transform Teqs into other Teqs that logically follow. 47 | /// 48 | /// Congruence: if x = y then f x = f y 49 | /// From a type-level perspective, this means, for example, 50 | /// iff 'a = 'b, then 'a list = 'b list. 51 | /// 52 | /// We do the munging below since we don't have type-level functions, so there 53 | /// is no such thing as, for example, Teq.cong List, to raise a 54 | /// Teq<'a, 'b> to a Teq<'a list, 'b list>. Instead we must create a function for 55 | /// any functor (wrapping type) we might want, e.g. list, option, array. 56 | /// 57 | /// More efficient than mapping the application of the teq across the functor. 58 | /// i.e. Use Teq.Cong.list in preference to List.map (Teq.cast) 59 | /// 60 | /// If you need to make your own Teq.Cong.foo for your own functor 'Foo<_>' using believeMe, 61 | /// then the onus is on you to verify that doing that is sane. 62 | [] 63 | module Cong = 64 | 65 | /// Clearly unsafe in general, but safe if we know 'a = 'b (which the Teq proves), 66 | /// and that there is some f such that f 'a = 'a2 = f 'b = 'b2, which we assume (and 67 | /// this assumption is why we don't make this public). Examples of valid values for 68 | /// f include list, array and option. 69 | val believeMe<'a, 'b, 'a2, 'b2> : Teq<'a, 'b> -> Teq<'a2, 'b2> 70 | 71 | /// Given a type equality between two types, returns the type equality on the corresponding array types. 72 | val array<'a, 'b> : Teq<'a, 'b> -> Teq<'a array, 'b array> 73 | 74 | /// Given a type equality between two array types, returns the type equality on the corresponding element types. 75 | val arrayOf<'a, 'b> : Teq<'a array, 'b array> -> Teq<'a, 'b> 76 | 77 | /// Given a type equality between two types, returns the type equality on the corresponding list types. 78 | val list<'a, 'b> : Teq<'a, 'b> -> Teq<'a list, 'b list> 79 | 80 | /// Given a type equality between two list types, returns the type equality on the corresponding element types. 81 | val listOf<'a, 'b> : Teq<'a list, 'b list> -> Teq<'a, 'b> 82 | 83 | /// Given a type equality between two types, returns the type equality on the corresponding option types. 84 | val option<'a, 'b> : Teq<'a, 'b> -> Teq<'a option, 'b option> 85 | 86 | /// Given a type equality between two option types, returns the type equality on the corresponding element types. 87 | val optionOf<'a, 'b> : Teq<'a option, 'b option> -> Teq<'a, 'b> 88 | 89 | /// Given a type equality between two types 'domain1 and 'domain2, returns the type equality 90 | /// on the function types ('domain1 -> 'range) and ('domain2 -> 'range), for any arbitrary 'range. 91 | val domain<'domain1, 'domain2, 'range> : Teq<'domain1, 'domain2> -> Teq<'domain1 -> 'range, 'domain2 -> 'range> 92 | 93 | /// Given a type equality between two function types, returns the type equality on their corresponding domains. 94 | val domainOf<'domain1, 'domain2, 'range1, 'range2> : Teq<'domain1 -> 'range1, 'domain2 -> 'range2> -> Teq<'domain1, 'domain2> 95 | 96 | /// Given a type equality between two types 'range1 and 'range2, returns the type equality 97 | /// on the function types ('domain -> 'range1) and ('domain -> 'range2), for any arbitrary 'domain. 98 | val range<'domain, 'range1, 'range2> : Teq<'range1, 'range2> -> Teq<'domain -> 'range1, 'domain -> 'range2> 99 | 100 | /// Given a type equality between two function types, returns the type equality on their corresponding ranges. 101 | val rangeOf<'domain1, 'domain2, 'range1, 'range2> : Teq<'domain1 -> 'range1, 'domain2 -> 'range2> -> Teq<'range1, 'range2> 102 | 103 | /// Given a pair of type equalities, one for domains and one for ranges, returns the type equality for the corresponding function types. 104 | val func<'domain1, 'range1, 'domain2, 'range2> : Teq<'domain1, 'domain2> -> Teq<'range1, 'range2> -> Teq<'domain1 -> 'range1, 'domain2 -> 'range2> 105 | 106 | /// Given a type equality between two types 'fst1 and 'fst2, returns the type equality 107 | /// on the pair types ('fst1 * 'snd) and ('fst2 * 'snd), for any arbitrary 'snd. 108 | val fst<'fst1, 'fst2, 'snd> : Teq<'fst1, 'fst2> -> Teq<'fst1 * 'snd, 'fst2 * 'snd> 109 | 110 | /// Given a type equality between two types 'snd1 and 'snd2, returns the type equality 111 | /// on the pair types ('fst * 'snd1) and ('fst * 'snd2), for any arbitrary 'fst. 112 | val snd<'snd1, 'snd2, 'fst> : Teq<'snd1, 'snd2> -> Teq<'fst * 'snd1, 'fst * 'snd2> 113 | 114 | /// Given a pair of type equalities, one for the first element of a pair and one for the second element of a pair, 115 | /// returns the type equality for the corresponding pair types. 116 | val pair<'fst1, 'snd1, 'fst2, 'snd2> : Teq<'fst1, 'fst2> -> Teq<'snd1, 'snd2> -> Teq<'fst1 * 'snd1, 'fst2 * 'snd2> 117 | -------------------------------------------------------------------------------- /TypeEquality/TypeEquality.fsproj: -------------------------------------------------------------------------------- 1 |  2 | 3 | netstandard2.0;net461 4 | true 5 | 4 6 | full 7 | true 8 | portable 9 | true 10 | true 11 | 0.3.0 12 | G-Research 13 | G-Research 14 | TypeEquality 15 | Type equalities for F#. These equalities allow us to create type-safe abstractions by allowing us to encode Generalised Algebraic Data Types (GADTs), as found in languages like Haskell. 16 | Copyright G-Research 2018 17 | https://github.com/G-Research/Teq 18 | Apache-2.0 19 | gresearch g-research .net f# 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | -------------------------------------------------------------------------------- /appveyor.yml: -------------------------------------------------------------------------------- 1 | version: 0.0.{build} 2 | build_script: 3 | - cmd: dotnet build TypeEquality.sln 4 | test_script: 5 | - cmd: cd Test 6 | - cmd: nuget install Appveyor.TestLogger -Version 2.0.0 7 | - cmd: cd .. 8 | - cmd: dotnet test --no-build --no-restore --test-adapter-path:. --logger:Appveyor Test 9 | --------------------------------------------------------------------------------