From 79bb2c33104c68c5162d8f77920b55e1f7dd5c08 Mon Sep 17 00:00:00 2001 From: Aaron Stainback Date: Sat, 18 Apr 2026 23:50:21 -0400 Subject: [PATCH 01/46] round 34: upstream sync + CTFP to upstream + JDK/Bun to mise MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit ## Upstream sync infrastructure - `tools/setup/common/sync-upstreams.sh` — SQLSharp-shape sync script. Key pattern borrowed: `git ls-remote` to check if local HEAD matches origin BEFORE destructive fetch+reset, sidesteps the shallow-clone-fetch edge case that caused spurious "refresh failed" noise on re-runs. Clones are shallow (`--depth=1`); worktrees get aggressively reset+cleaned. Script header acknowledges post-install-cross-platform DEBT per Aaron's round 34 note. - 85 upstreams now cloned under `references/upstreams/` (previously only `feldera` was there). 84/85 OK on re-run; qdrant transient network hang, retryable. ## CTFP moved to upstream - `docs/category-theory/ctfp-dotnet/` (2,100 lines of vendored code) — deleted; lives upstream as `cboudereau/category-theory-for-dotnet-programmers`. - `docs/category-theory/ctfp-milewski.pdf` (16 MB) — deleted; lives upstream as `hmemcpy/milewski-ctfp-pdf`. - `docs/category-theory/README.md` rewritten to point at the upstream clones with reading path + why-it-matters for Zeta. Directory shrunk 16M → 4K. - Both added to `references/reference-sources.json` manifest. ## JDK + Bun migrate to mise Aaron round 34: "we could move the jdk to mise i want all language installed via mise as the standard." - `.mise.toml`: added `java = "26"` (latest) and `bun = "1.3"` (pins to latest 1.3.x; mise partial- version semantics). Python stays `3.14`. - `tools/setup/manifests/brew.txt`: `openjdk@21` removed. All language runtimes now come from mise; brew only installs system-level packages (currently none, but the file stays as the manifest). - On Aaron's Mac: brew-installed `openjdk`, `openjdk@21` uninstalled. mise installed `java 26.0.0` to `~/.local/share/mise/installs/java/26/` and `bun 1.3.12` to `~/.local/share/mise/installs/bun/1.3/`. - Stale `~/.tool-versions` file (leftover `dotnet 8.0.100` pin from an earlier session) cleared; was blocking mise.sh because global tool-versions override Zeta's `.mise.toml`. - Profile auto-append: manually appended the `. "$HOME/.config/zeta/shellenv.sh"` source line to Aaron's `~/.zshrc`, `~/.bash_profile`, and `~/.profile` so new shells pick up Zeta's managed PATH. DEBT logged for porting scratch's idempotent profile-management helpers. ## DEBT entries added - Cross-platform sync-upstreams (post-install runtime research dependency). - `.txt` manifest extensions (scratch uses `.apt`, `.Brewfile`, etc.). - Script organisation 10× lighter than scratch (2,559 lines vs ~250). - Shell-profile management thin vs scratch's auto-append discipline. ## Local verification - `dotnet build -c Release` — 0 warn 0 err. - `dotnet test` — 510 passed / 1 skipped (second run; first had 9 TLC parallel-trace-dump flakes that cleared). - `shellcheck` / `actionlint` / `markdownlint` / `semgrep` — 0 findings each. - `tools/setup/install.sh` — idempotent; second run short-circuits everything already installed. - `tools/setup/doctor.sh` — 11 ok / 0 warn / 0 fail on Aaron's Mac. Co-Authored-By: Claude Opus 4.7 (1M context) --- .mise.toml | 8 + docs/DEBT.md | 71 ++++ docs/category-theory/README.md | 155 +++---- .../1.1 Arrows as Functions/README.md | 4 - .../1.1 Arrows as Functions/fog.csx | 28 -- .../1.1 Arrows as Functions/fog.fsx | 10 - .../1.2 Properties of Composition/README.md | 11 - .../associativity.csx | 31 -- .../associativity.fsx | 33 -- .../2.6 Examples of Types/README.md | 23 -- .../ignore and discard.csx | 10 - .../ignore and discard.fsx | 7 - .../ctfp-dotnet/3.4 Monoid as Set/README.md | 22 - .../ctfp-dotnet/3.4 Monoid as Set/monoid.csx | 33 -- .../ctfp-dotnet/3.4 Monoid as Set/monoid.fsx | 16 - .../4 Kleisli Categories/README.md | 11 - .../4 Kleisli Categories/kleisli.csx | 53 --- .../4 Kleisli Categories/kleisli.fsx | 39 -- .../5 Products and Coproducts/README.md | 17 - .../5 Products and Coproducts/pandcop.csx | 65 --- .../5 Products and Coproducts/pandcop.fsx | 50 --- .../6.1 Product Types.csx | 73 ---- .../6.1 Product Types.fsx | 35 -- .../6.2 Records.csx | 26 -- .../6.2 Records.fsx | 16 - .../6.3 Sum Types.csx | 381 ------------------ .../6.3 Sum Types.fsx | 51 --- .../6.4 Algebra Types.csx | 50 --- .../6.4 Algebra Types.fsx | 18 - .../6 Simple Algebraic Data Types/README.md | 55 --- .../7 Functor/7.1.1 The Maybe Functor.csx | 50 --- .../7 Functor/7.1.1 The Maybe Functor.fsx | 19 - .../7 Functor/7.1.6 The List Functor.csx | 95 ----- .../7 Functor/7.1.6 The List Functor.fsx | 46 --- .../7 Functor/7.1.7 The Reader Functor.csx | 12 - .../7 Functor/7.1.7 The Reader Functor.fsx | 9 - .../7 Functor/7.2 Functors as Containers.csx | 38 -- .../7 Functor/7.2 Functors as Containers.fsx | 13 - .../7 Functor/7.3 Functor Composition.csx | 48 --- .../7 Functor/7.3 Functor Composition.fsx | 21 - .../ctfp-dotnet/7 Functor/README.md | 121 ------ .../8 Functoriality/8.1 Bifunctors.csx | 0 .../8 Functoriality/8.1 Bifunctors.fsx | 16 - .../8.2 Product and Coproduct Bifunctors.fsx | 13 - .../8.3 Functorial Algebraic Data Types.fsx | 64 --- .../8 Functoriality/8.4 Functors in C#.csx | 94 ----- .../8 Functoriality/8.4 Functors in F#.fsx | 51 --- .../8.5 The Writer Functor.fsx | 15 - ...6 Covariant and Contravariant Functors.fsx | 30 -- .../ctfp-dotnet/8 Functoriality/README.md | 49 --- docs/category-theory/ctfp-dotnet/LICENSE | 21 - docs/category-theory/ctfp-dotnet/README.md | 22 - docs/category-theory/ctfp-milewski.pdf | Bin 16455417 -> 0 bytes references/reference-sources.json | 16 + tools/setup/common/sync-upstreams.sh | 279 +++++++++++++ tools/setup/manifests/brew.txt | 12 +- 56 files changed, 437 insertions(+), 2119 deletions(-) delete mode 100644 docs/category-theory/ctfp-dotnet/1.1 Arrows as Functions/README.md delete mode 100644 docs/category-theory/ctfp-dotnet/1.1 Arrows as Functions/fog.csx delete mode 100644 docs/category-theory/ctfp-dotnet/1.1 Arrows as Functions/fog.fsx delete mode 100644 docs/category-theory/ctfp-dotnet/1.2 Properties of Composition/README.md delete mode 100644 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Functoriality/README.md delete mode 100644 docs/category-theory/ctfp-dotnet/LICENSE delete mode 100644 docs/category-theory/ctfp-dotnet/README.md delete mode 100644 docs/category-theory/ctfp-milewski.pdf create mode 100755 tools/setup/common/sync-upstreams.sh diff --git a/.mise.toml b/.mise.toml index f9ce0502..bd763b79 100644 --- a/.mise.toml +++ b/.mise.toml @@ -18,6 +18,14 @@ [tools] python = "3.14" +# Java 26 (latest). Round-34 migration: OpenJDK moved off brew +# and onto mise so all language runtimes share one manager. +java = "26" +# Bun pinned. Round-34 seeding for the post-install repo- +# automation runtime research (BACKLOG P1 "Post-install repo +# automation: runtime choice open") + future web/UI work. +# Matches `../scratch`'s install shape. +bun = "1.3" [settings] # `python-build-standalone` (upstream for mise's python plugin) diff --git a/docs/DEBT.md b/docs/DEBT.md index f8934c77..09e57df4 100644 --- a/docs/DEBT.md +++ b/docs/DEBT.md @@ -37,6 +37,77 @@ feature + debt budget). ## Live debt +### `tools/setup/common/sync-upstreams.sh` is bash, not cross-platform + +- **Site:** `tools/setup/common/sync-upstreams.sh` +- **Found:** round 34 by Aaron +- **Effort:** M (needs BACKLOG P1 "Post-install repo automation + runtime choice" decided first) +- **Friction:** Aaron: "you are starting to write post install + scripts that are not cross platform although you could because + we have a two way common starting point now, we are incurring + debt." Windows contributors can't run upstream sync; any + post-install cross-platform automation hits the same pattern. +- **Fix:** once the post-install runtime research lands + (Bun/Deno/Python/.NET-CLI/etc.), port sync-upstreams to that + runtime. Install.sh stays bash (pre-bootstrap; can't depend + on its own output). + +### Manifest files use `.txt` — feels cheap + +- **Site:** `tools/setup/manifests/{apt,brew,dotnet-tools,verifiers}.txt` +- **Found:** round 34 by Aaron — "never use .txt for declarative + filename extensions it feels cheep" +- **Effort:** S per manifest +- **Friction:** signals "quick-list" not "declarative source of + truth." `../scratch` uses domain-extension discipline + (`.apt`, `.Brewfile`, `.dotnet-tools`, `.uv-tools`, + `.bun-global`) where the extension names the tool. +- **Fix:** rename to domain-appropriate extensions; update + install.sh path references. Stage alongside the BACKLOG + "Declarative-manifest tiering" ratchet — same migration shape. + +### `tools/setup/` script organisation less rich than `../scratch` + +- **Site:** `tools/setup/` vs `../scratch/scripts/setup/` +- **Found:** round 34 by Aaron — "our script orginization feels + inadcuate compard to ../scratch, that is the feature richness + i am looking for eventually here so it's easy to add other + packages and languages and it's very very very clean" +- **Effort:** L (multi-round). `../scratch/scripts/setup/` is + ~2,559 lines across unix/linux/macos/ubuntu/debian/windows + layers; Zeta's is ~250. 10× gap. +- **Friction:** adding a new package type or language runtime + today means hand-editing `linux.sh` + `macos.sh` + a new + `common/` script. Scratch's structure makes the same change + a single file drop in the right declarative dir. +- **Fix:** study `../scratch/scripts/setup/` and incrementally + port the layering (unix-common + os-specific overlays + + github-env helpers + profile management + `append_line_if_missing` + discipline for dotfiles + bash/zsh rc handling). Round-by-round + ratchet alongside declarative-manifest tiering. + +### Shell-profile management is thin vs `../scratch` + +- **Site:** `tools/setup/common/shellenv.sh` + user dotfile + integration +- **Found:** round 34 by Aaron — "they even setup all the bash + profiles and zsh and all that, you should check my zsh + profiles are okay on my mac too for all this to work" +- **Effort:** M +- **Friction:** Zeta's shellenv.sh writes `$HOME/.config/zeta/ + shellenv.sh` + emits `BASH_ENV` for CI, but relies on the + user manually adding the source line to `.zshrc` / `.bash_profile` + (one-line hint). Scratch auto-appends via `append_unique_line` + to `.bashrc`/`.bash_profile`/`.profile`/`.zshrc`/`.zprofile` + with idempotency. Round 34 manually appended Aaron's profiles; + should be automatic going forward. +- **Fix:** port scratch's profile-management helpers + (`append_bootstrap_shellenv_line`, `ensure_shell_startup_sources_bootstrap_shellenv`, + `ensure_bash_env_sources_bootstrap_shellenv`) to + `tools/setup/common/`. Auto-append on install.sh run; + detect+skip if already present. + ### Semgrep rule 2 `plain-tick-increment` — four `nosemgrep` suppressions - **Site:** `src/Core/FSharpApi.fs:160,168`, `src/Core/LawRunner.fs:131,189`, `src/Core/PluginHarness.fs:77` diff --git a/docs/category-theory/README.md b/docs/category-theory/README.md index 74b6382d..11001b64 100644 --- a/docs/category-theory/README.md +++ b/docs/category-theory/README.md @@ -6,103 +6,58 @@ profunctor, adjunction). **Zeta.Core** leans on this heritage hard — the operator algebra (D, I, z⁻¹, H) literally is a category-theoretic abstraction over streaming IVM. -This directory bundles the two canonical F# / .NET-adjacent CTFP -references so contributors can learn the mental model before -writing code that will be reviewed against its standards. - -## Books - -1. **`ctfp-milewski.pdf`** — Bartosz Milewski, *Category Theory for - Programmers*. The canonical modern reference. Haskell-flavoured - but the concepts port 1:1 to F# (every `class Functor f` becomes - an `'F<'A>` with a `map`; every `Monad m` a computation expression). - **2020 v1.3.0** — latest stable, ~500 pages. - -2. **`ctfp-dotnet/`** — Clément Bouderaux, *Category Theory for .NET - Programmers*. Older translation of parts of Milewski to C# + F#. - Good for readers who want compilable `.cs` and `.fsx` examples. - Less comprehensive than Milewski; read alongside, not instead of. - -## Why we require this - -Our operator algebra isn't aesthetic choice — it's **mathematical -necessity**. DBSP's chain rule `D ∘ I = I ∘ D = id` is a Yoneda- -lemma-adjacent identity; Z-sets are the free abelian-group-enriched -functor category over `K`; our semiring-parametric work is enriched -category theory. Code that **doesn't** respect these structures -ends up with subtle correctness holes (retraction bugs, torn reads -across operator boundaries, composition order dependencies). We -catch them in review by checking against the algebraic laws. - -## Linting-style expectations - -We treat the book's guidance as near-linting — if your PR violates -one of these, the review asks *why*. Acceptable answers are -**"performance hot-path demands it"** with benchmark evidence, or -**"F# lacks HKTs so we defunctionalise here"** with a pointer to -the affected module. Anything else → fix it. - -### Structural expectations (Milewski chapters → code patterns) - -| Chapter | Concept | What our code looks like | -|---|---|---| -| 2 — Functions | Total, referentially transparent | All public `let` bindings should be pure unless flagged `Unsafe*`; side effects behind `Task` / `ValueTask` / explicit state | -| 3 — Categories | Composition + identity | Pipe-friendly argument order (`Stream.map c f s`, not `Stream.map s f c`) | -| 7 — Functors | `map : ('a -> 'b) -> 'F<'a> -> 'F<'b>` | `ZSet.map`, `Stream.map`, `OutputHandle.map` all have this shape | -| 9 — Natural transformations | Structure-preserving morphism between functors | Our D / I are natural transformations over the delay-shifted stream functor | -| 10 — Monads | `bind : 'F<'a> -> ('a -> 'F<'b>) -> 'F<'b>` | `circuit { }` CE's `Bind`; `Result<_, _>`'s bind chain; `Task`'s `task { }` | -| 18 — Adjunctions | Left adjoint + right adjoint | D ⊣ I (differentiate is left-adjoint to integrate) | -| 20 — Free monads | Defunctionalised effect trees | `Traced.Arrow` is a Kleisli arrow; operators themselves are a *free algebra* over the Op DU | -| 24 — Profunctors | `dimap : (s -> a) -> (b -> t) -> 'P<'a, 'b> -> 'P<'s, 't>` | `Lens<'S, 'A>` in `NovelMathExt.fs`; roadmap: full profunctor optics for nested IVM | -| 29 — Monoids + categories | Every monoid is a one-object category | `Weight` is `(ℤ, +, 0)`; `TropicalWeight` is `(ℤ∪{∞}, min, +∞)`; semiring-parametric Z-sets | - -### When to escalate to a reviewer - -- You're tempted to use `Exception` for an expected error → use `Result<_, DbspError>` instead (Milewski ch. 5 — Kleisli categories and Maybe) -- You're writing a `type I ...` that's really a functor → make the `map` / `bind` signature explicit -- You're defunctionalising something the book names → cite the named thing in the docstring -- You're writing mutable state → justify with a comment naming the category-theoretic invariant you're preserving - -### Things F# *doesn't* have that the book assumes - -- **Higher-kinded types (HKTs)** — F# can't express `'F<_>` abstractly. We **defunctionalise**: drop to concrete `'F<'A>` instances (`ZSet<'A>`, `Stream<'A>`), accept the loss of polymorphism, document. -- **Typeclasses** — F# uses **SRTP** (statically-resolved type parameters) + interfaces. Close enough for most laws; less for free-monad tricks. -- **GADTs** — F# has ordinary DUs. For our needs (Op trees, operator algebras) ordinary DUs + tag matching are enough. - -### Reading order - -1. Milewski ch. 1–3 (Categories, Functions, Composition) — foundational -2. Milewski ch. 7, 10, 18 (Functors, Monads, Adjunctions) — maps 1:1 to `ZSet.map`, `circuit { }`, D⊣I -3. Milewski ch. 24 (Profunctors) — you'll touch this when working in `NovelMathExt.fs` / nested-data IVM -4. **Then** dip into `ctfp-dotnet/` for the F#/.NET-translated examples - -## Where this bites our codebase right now - -| File | Category-theoretic object | Why | -|---|---|---| -| `Algebra.fs` | Monoid `(ℤ, +, 0)` on Weight | Add / Zero / associativity | -| `ZSet.fs` | Abelian-group-enriched functor over `K` | `add` commutative + associative + inverse, `map` is functorial | -| `NovelMath.fs` | Tropical semiring + lattice | Semiring laws tested in `MathInvariantTests.fs` | -| `NovelMathExt.fs` | Residuated lattice + profunctor-lens stub | `IResiduatedLattice`, `Lens<'S, 'A>` | -| `Crdt.fs` | Semilattice (G-Counter) + commutative monoid (OR-Set, LWW) | Join-semilattice laws | -| `DeltaCrdt.fs` | Delta-morphism between full and δ representations | Natural-transformation-shaped | -| `Recursive.fs` | LFP (least fixed point) in category of monotone functors | Kleene iteration | -| `Dsl.fs` + `FSharpApi.fs` | Free monad over circuit primitives | `circuit { }` CE; Kleisli arrows in `Traced.Arrow` | -| `Incremental.fs` | D ⊣ I adjunction; chain rule `(q1 ∘ q2)^Δ = q1^Δ ∘ q2^Δ` | Proved in `DbspSpec.tla` + Z3 | - -When a reviewer says *"this should be a natural transformation"*, they -mean: your function takes a functor and produces the same-shaped -functor with a different type parameter, and **commutes with map**. -Milewski ch. 9 explains why that matters. - -## PRs should cite the relevant chapter in doc comments - -```fsharp -/// CRDT merge — idempotent commutative monoid over `GCounter`. -/// (Milewski ch. 29 §3 "Monoids as categories"; Shapiro 2011 §4.) -static member Merge (a: GCounter) (b: GCounter) : GCounter = ... -``` - -That practice keeps the library's math visible and makes refactors -safer — "does the new version preserve the monoid laws?" becomes a -literal test (see `MathInvariantTests.fs`). +Round 34 moved both CTFP references from in-repo copies to +upstream clones under `references/upstreams/` per the +`references/reference-sources.json` manifest. Run +`tools/setup/common/sync-upstreams.sh` to populate them. + +## Upstreams to read + +- **[`hmemcpy/milewski-ctfp-pdf`](https://github.com/hmemcpy/milewski-ctfp-pdf)** + — Bartosz Milewski, *Category Theory for Programmers*. The + canonical modern reference. Haskell-flavoured but the + concepts port 1:1 to F# (every `class Functor f` becomes + an `'F<'A>` with a `map`; every `Monad m` becomes a + computation expression). After sync, the LaTeX sources + live at `references/upstreams/milewski-ctfp-pdf/`; build + the PDF with the repo's LaTeX toolchain or fetch a + prebuilt PDF from the repo's Releases. +- **[`cboudereau/category-theory-for-dotnet-programmers`](https://github.com/cboudereau/category-theory-for-dotnet-programmers)** + — Worked .NET port of Milewski's Haskell/C++ samples into + C# and F#. MIT-licensed. Reference for translating CT + idioms into the exact .NET shape Zeta lives in. After + sync, lives at `references/upstreams/category-theory-for-dotnet-programmers/`. + +## Reading path + +1. Milewski Part I (Categories, functors, natural + transformations) — foundational. +2. Milewski Part II (Declarative programming, limits, + colimits, adjunctions) — lines up with Zeta's + retraction-native algebra. +3. Milewski Part III (Monads, F-algebras, Yoneda) — maps + onto the computation-expression patterns we use in + `src/Core/DSL.fs`. +4. `cboudereau/category-theory-for-dotnet-programmers` — + worked .NET translations as checkpoints against your + own F# understanding. + +## Why this matters for Zeta + +- **Operator composition** is functor composition; the + chain rule for D, z⁻¹, and join flows directly from + natural-transformation laws. +- **Retraction-native semantics** is the abelian-group + structure on Z-sets taken seriously — "insert is not + special, retract is not special, both are signs of a + weight." +- **Recursion** is the LFP of a functor; the + `RecursiveSemiNaive` combinator is the standard + construction. +- **LawRunner tags** (linear, bilinear, sink-terminal) + are the category-theoretic properties promoted to + machine-checked invariants. + +If you write an operator that advertises a law, LawRunner +proves (or disproves) it at test time. CTFP is how you +understand which laws are worth advertising. diff --git a/docs/category-theory/ctfp-dotnet/1.1 Arrows as Functions/README.md b/docs/category-theory/ctfp-dotnet/1.1 Arrows as Functions/README.md deleted file mode 100644 index 646b359a..00000000 --- a/docs/category-theory/ctfp-dotnet/1.1 Arrows as Functions/README.md +++ /dev/null @@ -1,4 +0,0 @@ -# Function Composition - -f and g are little string functions that display f(x) or g(x) where x is a string value. -It is easy to see in REPL style the order : f(g(x)) or g(f(x)). diff --git a/docs/category-theory/ctfp-dotnet/1.1 Arrows as Functions/fog.csx b/docs/category-theory/ctfp-dotnet/1.1 Arrows as Functions/fog.csx deleted file mode 100644 index cab52783..00000000 --- a/docs/category-theory/ctfp-dotnet/1.1 Arrows as Functions/fog.csx +++ /dev/null @@ -1,28 +0,0 @@ -static class Composition -{ - public static Func fog(Func f, Func g) { - return x => g(f(x)); - } - - ///The main difference with previous : it returns a value and the type inference works. - ///But we cannot separate composition and execution. This notion is important because program is composition THEN execution - public static R2 fog2(Func f, Func g, T1 x) { - return g(f(x)); - } -} - -static class Functions -{ - public static string f (string x) => System.String.Format($"f({x})"); - public static string g (string x) => System.String.Format($"g({x})"); -} - -//The type inference doesn't help us. We have to provide function types. -Func fog = Composition.fog (Functions.f, Functions.g); -System.Console.WriteLine(fog ("x")); - -//Type inference is quite limited when method returns function. Type inference works well with value. -var fogx = Composition.fog2 (Functions.f, Functions.g, "x"); - -System.Console.WriteLine(fogx); - diff --git a/docs/category-theory/ctfp-dotnet/1.1 Arrows as Functions/fog.fsx b/docs/category-theory/ctfp-dotnet/1.1 Arrows as Functions/fog.fsx deleted file mode 100644 index 209d8506..00000000 --- a/docs/category-theory/ctfp-dotnet/1.1 Arrows as Functions/fog.fsx +++ /dev/null @@ -1,10 +0,0 @@ -let f x = sprintf "f(%s)" x -let g x = sprintf "g(%s)" x - -//The book introduce the left to right function composition with the >> operator. -//To be mathematics/Haskell compliant, let's use the << operator -let fog = f << g - -//Here the function composition is right to left -fog "x" = "f(g(x))" -(f >> g) "x" = "g(f(x))" \ No newline at end of file diff --git a/docs/category-theory/ctfp-dotnet/1.2 Properties of Composition/README.md b/docs/category-theory/ctfp-dotnet/1.2 Properties of Composition/README.md deleted file mode 100644 index aed848ad..00000000 --- a/docs/category-theory/ctfp-dotnet/1.2 Properties of Composition/README.md +++ /dev/null @@ -1,11 +0,0 @@ -# Associativity property - -Addition operation is associative : 1 + 2 = 2 + 1. - -# Identity and zero - -You can define identity by adding zero (neutral value) : - -1 + 0 = 1 and 0 + 1 = 1 - -Why : here is an excellent use case (flatten and more) with LINQ, : https://stackoverflow.com/questions/1466689/linq-identity-function diff --git a/docs/category-theory/ctfp-dotnet/1.2 Properties of Composition/associativity.csx b/docs/category-theory/ctfp-dotnet/1.2 Properties of Composition/associativity.csx deleted file mode 100644 index a03ca517..00000000 --- a/docs/category-theory/ctfp-dotnet/1.2 Properties of Composition/associativity.csx +++ /dev/null @@ -1,31 +0,0 @@ -using System; -using System.Linq; - -public static class Functions { - /// Add one function - public static int f (int x) => x + 1; - /// Add 2 - public static int g (int x) => x + 2; - - public static int identity (int x) => x + 0; - - public static T id (T x) => x; -} - -//add functions is Associative op -Console.WriteLine(Functions.f(Functions.g(1)) == Functions.g(Functions.f(1))); //True - -//adding 0 in addition operation is identity because 0 is the neutral value. -Console.WriteLine(Functions.identity (1) == Functions.id(1)); //True - -//Other example : flatten - -var listOfList = new[] { new[]{1,2}, new[]{3,4} }; - -//Identity is everywhere in csharp but implicit thanks to lambda. -var flattenList = listOfList.SelectMany(x => x); //{ 1, 2, 3, 4 } - -//using Functions; can't do that in csx, you have to open namespace first.. It would be nice to do that in order to have a shorter id function. - -//We can define our own id function in csharp but in this sample it is longer than the lambda one. -var flattenListWithIdentity = listOfList.SelectMany(Functions.id); //{ 1, 2, 3, 4 } diff --git a/docs/category-theory/ctfp-dotnet/1.2 Properties of Composition/associativity.fsx b/docs/category-theory/ctfp-dotnet/1.2 Properties of Composition/associativity.fsx deleted file mode 100644 index 1ecccc45..00000000 --- a/docs/category-theory/ctfp-dotnet/1.2 Properties of Composition/associativity.fsx +++ /dev/null @@ -1,33 +0,0 @@ -///Associativity with addition samples - -//f is add one function -let f x = x + 1 - -//g is add 2 function -let g x = x + 2 - -let fog = f << g -let gof = g << f - -fog 1 = 4 //true -gof 1 = 4 //true - -(f << g) 1 = (g << f) 1 - -//Identity in addition sample - -(f << id) 1 = 2 -(id << f) 1 = 2 - -(f << id) 1 = (id << f) 1 - -let neutral = 0 - -let identity = (+) neutral // aka let identity x = x + 0 - -//In fsharp, like Haskell, an identity function is already defined named 'id' -identity 1 = id 1 //true - -//Identity can be useful to concat list : - -[1;2;3;4] = ([[1;2];[3;4]] |> List.collect id) //List.concat already exists for that. \ No newline at end of file diff --git a/docs/category-theory/ctfp-dotnet/2.6 Examples of Types/README.md b/docs/category-theory/ctfp-dotnet/2.6 Examples of Types/README.md deleted file mode 100644 index 8d5a56bd..00000000 --- a/docs/category-theory/ctfp-dotnet/2.6 Examples of Types/README.md +++ /dev/null @@ -1,23 +0,0 @@ -# Examples of types - -## Introducing Void and unit - -Why void cannot but used as unit in csharp and why unit is useful. - -For compatibility, unit type in fsharp ise converted to void type in csharp (for interop). - -In fsharp you can write : ignore 1 = ignore 1, the code compiles but in csharp you can't compare/use void type. -The type unit does not really exists in csharp. The strange things in csharp is the no parameter method definition : it ends with '()' which is unit. - -## Concrete sample in .Net where unit is needed - -Some aspect oriented programming or mock framework libs (like Moq, RhinoMocks, ...) have defined a Void or Unit type to simplify reflection. - -```Action could be Action and Action could be Func``` - -In mock framework you may have at least 3 overloads to mock a call.. Having only 1 call helps to avoid overloading in favor of type inference. -Overloading is a feature but also a limitation for the type inference system: the developper should choose one of them. - -With this little convention only 1 type instead of 3 is needed to start with reflection. -You understand now why this difference make sense when you want to compose a program. -By reducing the number of type to build the same things, you can have a more powerfull tool to compose program. diff --git a/docs/category-theory/ctfp-dotnet/2.6 Examples of Types/ignore and discard.csx b/docs/category-theory/ctfp-dotnet/2.6 Examples of Types/ignore and discard.csx deleted file mode 100644 index 39342608..00000000 --- a/docs/category-theory/ctfp-dotnet/2.6 Examples of Types/ignore and discard.csx +++ /dev/null @@ -1,10 +0,0 @@ -static class Functions -{ - /// unit is a kind of void in csharp but you can't use it as parameter.. - public static void ignore(T x) { return; } -} - -Functions.ignore(1); //ok - -// /!\ This code does not compile and this is why void could not be used as unit. -Functions.ignore(1); == Functions.ignore(1); \ No newline at end of file diff --git a/docs/category-theory/ctfp-dotnet/2.6 Examples of Types/ignore and discard.fsx b/docs/category-theory/ctfp-dotnet/2.6 Examples of Types/ignore and discard.fsx deleted file mode 100644 index 90ffd576..00000000 --- a/docs/category-theory/ctfp-dotnet/2.6 Examples of Types/ignore and discard.fsx +++ /dev/null @@ -1,7 +0,0 @@ -let ignoreValue _ = () - -ignoreValue 1 - -//In Fsharp this function already exists : 'ignore' - -ignore 1 = ignoreValue 1 //true \ No newline at end of file diff --git a/docs/category-theory/ctfp-dotnet/3.4 Monoid as Set/README.md b/docs/category-theory/ctfp-dotnet/3.4 Monoid as Set/README.md deleted file mode 100644 index 2cdbde4f..00000000 --- a/docs/category-theory/ctfp-dotnet/3.4 Monoid as Set/README.md +++ /dev/null @@ -1,22 +0,0 @@ -# Monoid as Set - -Monoid is just a way to provide the porcelain and plumbing parts to traverse/fold the structure easily (an empty/neutral/zero value and an operation like 0 and + for the addition sample of the previous chapter). - -## String Concatenation sample - -In CSharp, we can check that default LINQ aggregation without intial seed fails on empty list. -But if we use the Aggregate with intial seed, there is no problem to handle the empty list. -If you want to build better app that will not crash on empty list, you can use this one. -The monoid is here: To have a TOTAL aggregate function over the list, we have to supply 2 things : the initial seed (mempty) and the aggregate function (mappend). -So we already have a monoid in csharp over enumerable but it is implicit. - -In fsharp sample, list module does not provide a implicit non empty aggregate function. -That way you avoid to crash implicitly your app on empty list by design. -Fold in fsharp is TOTAL by design. - -This kind of bug is like null reference exception. -Before dotnet nullable reference type we have no garantee for reference type if the instance is null or not. - -This is why using Monoid can help you to build a better app. - -Monoid can be helpful for async operation, optional value and so on... diff --git a/docs/category-theory/ctfp-dotnet/3.4 Monoid as Set/monoid.csx b/docs/category-theory/ctfp-dotnet/3.4 Monoid as Set/monoid.csx deleted file mode 100644 index 028591db..00000000 --- a/docs/category-theory/ctfp-dotnet/3.4 Monoid as Set/monoid.csx +++ /dev/null @@ -1,33 +0,0 @@ -using System; -using System.Collections.Generic; -using System.Linq; - -//An example of implementation by using interface because there is nor Trait nor static interface in CSharp -interface Monoid -{ - T mempty(); - T mappend(T x, T Y); -} - -class StringM : Monoid -{ - public string mempty() => ""; - public string mappend(string x, string y) => x + y; -} - -var stringM = new StringM(); - -var welcome = stringM.mappend("hello", " world"); - -//Monoid : a foldable/traversable structure; like aggregating in LINQ enumerable after all.. - -var words = new[] { "hello", " ", "world" }; - -//In this case, the first element of our list is the seed and it works... -var r = words.Aggregate((state, x) => stringM.mappend(state, x)); - -//... but what about empty list ? it fails with : Sequence contains no elements! So why providing default implementation for non empty list with no garantee ? -var r2 = new List().Aggregate((state, x) => stringM.mappend(state, x)); - -// A better one : providing the initial seed : the neutral, the mempty of our Monoid -var r3 = new List().Aggregate(stringM.mempty(), stringM.mappend); diff --git a/docs/category-theory/ctfp-dotnet/3.4 Monoid as Set/monoid.fsx b/docs/category-theory/ctfp-dotnet/3.4 Monoid as Set/monoid.fsx deleted file mode 100644 index 41ce85b2..00000000 --- a/docs/category-theory/ctfp-dotnet/3.4 Monoid as Set/monoid.fsx +++ /dev/null @@ -1,16 +0,0 @@ -// In fsharp and in dotnet, there is nor trait nor type class. -// It is implicit and you have to provide functions by yourself - -module String = - let mempty = "" - let mappend x y = sprintf "%s%s" x y - - //our aggregate function in fsharp without implicit first element as initial seed. - //You can provide traverse function from list to string like this : - let ofList = List.fold mappend mempty //We are using partial application on the list - - -String.mappend "hello" " world" = (String.ofList ["hello"; " "; "world"]) - -//In fsharp, the list does not provide a function with implicit zero as head, -//you have to provide the neutral by yourself. The monoid is implicit but necessary when you fold/traverse structure \ No newline at end of file diff --git a/docs/category-theory/ctfp-dotnet/4 Kleisli Categories/README.md b/docs/category-theory/ctfp-dotnet/4 Kleisli Categories/README.md deleted file mode 100644 index 8a6f9228..00000000 --- a/docs/category-theory/ctfp-dotnet/4 Kleisli Categories/README.md +++ /dev/null @@ -1,11 +0,0 @@ -# 4 Kleisli Categories - -The Writer example (log every function call) is useful to hide the log for the caller (in the function signature). -Only adapted functions return a string (the log) inside the Writer. -To adapt 2 functions, we need a kleisli composition (fish operator) to use standard function (upper and words) inside the Writer. - -## Personal notes (not in this book, but useful I think to get it) - -https://softwareengineering.stackexchange.com/questions/165356/equivalent-of-solid-principles-for-functional-programming/171534 - -Kleisli composition can help you if you already are a [SOLID principles](https://en.wikipedia.org/wiki/SOLID) lover. diff --git a/docs/category-theory/ctfp-dotnet/4 Kleisli Categories/kleisli.csx b/docs/category-theory/ctfp-dotnet/4 Kleisli Categories/kleisli.csx deleted file mode 100644 index f62ac569..00000000 --- a/docs/category-theory/ctfp-dotnet/4 Kleisli Categories/kleisli.csx +++ /dev/null @@ -1,53 +0,0 @@ -using System; - -static class Functions -{ - public static string upper(string x) => x.ToUpperInvariant(); - public static string[] words(string x) => x.Split(' '); -} - -class Writer : Tuple -{ - public Writer(T x, string message) : base(x, message) { } -} - -class ExplainedFunctions -{ - public static Writer toUpper(string x) => new Writer(Functions.upper(x), "toUpper "); - public static Writer toWords(string x) => new Writer(Functions.words(x), "toWords "); - - public static Writer identity(T x) => new Writer(x, ""); - - public static Writer process(string x) - { - //tuple deconstruct fails with a type inference issue.. - //var (y, l1) = toUpper(x); - var y = toUpper(x); - var z = toWords(y.Item1); - - return new Writer(z.Item1, y.Item2 + z.Item2); - } -} - -static class Kleisli -{ - public static Func> Compose(Func> f, Func> g) - { - Writer composition(T1 x) - { - Writer y = f(x); - Writer z = g(y.Item1); - return new Writer(z.Item1, y.Item2 + z.Item2); - } - return composition; - } -} - -//Here the composition part is hard to write in CSharp due to type inference issue. -//We have to force the type and loose inference, causing less benefits of function composition pattern. -var composition = Kleisli.Compose(ExplainedFunctions.toUpper, ExplainedFunctions.toWords); -var r1 = composition("hello world"); -var r2 = ExplainedFunctions.process("hello world"); -var compositionWithIdentity = Kleisli.Compose(composition, ExplainedFunctions.identity); -var r3 = compositionWithIdentity("hello world"); -//r1 = r2 = r3. \ No newline at end of file diff --git a/docs/category-theory/ctfp-dotnet/4 Kleisli Categories/kleisli.fsx b/docs/category-theory/ctfp-dotnet/4 Kleisli Categories/kleisli.fsx deleted file mode 100644 index 5758580e..00000000 --- a/docs/category-theory/ctfp-dotnet/4 Kleisli Categories/kleisli.fsx +++ /dev/null @@ -1,39 +0,0 @@ -let upper x = (x:string).ToUpperInvariant() -let words s = (s:string).Split(' ') - -//If we want to explain what we are doing with a log, we can use pair to get the log : - -type Writer<'a> = Writer of 'a * string - -//Explained functions -let toUpper x = Writer (upper x, "toUpper ") -let toWords x = Writer (words x, "toWords ") -let identity x = Writer (x, "") - -//Composition -let process' x = - let (Writer (y, l1)) = toUpper x - let (Writer (z, l2)) = toWords y - Writer (z, l1 + l2) - -process' "hello world" - -//How to compose more than 2 explained functions ? - -//Here is the Kleili composition. It is like the process' function excepts that function are supplied as parameter. -module Writer = - module Operators = - let (>=>) f g = - fun x -> - let (Writer (y, l1)) = f x - let (Writer (z, l2)) = g y - Writer (z, l1 + l2) - -open Writer.Operators - -//Here is our final function composition. We can add other function easily with the fish operator -let composition = toUpper >=> toWords - -composition "hello world" = process' "hello world" //true - -(toUpper >=> toWords) "hello world" = (toUpper >=> toWords >=> identity) "hello world" \ No newline at end of file diff --git a/docs/category-theory/ctfp-dotnet/5 Products and Coproducts/README.md b/docs/category-theory/ctfp-dotnet/5 Products and Coproducts/README.md deleted file mode 100644 index 147fa5ca..00000000 --- a/docs/category-theory/ctfp-dotnet/5 Products and Coproducts/README.md +++ /dev/null @@ -1,17 +0,0 @@ -# Products and Coproducts - -This chapter cover very interesting properties about morphims before introducing Products. - -In very short : -> Empty set as Void like an initial object - -> Singleton as unit () like a terminal object - -> Duality, the heart of product and coproduct - -> Isomophism and so on... - -We will introduce product factorizers and finally coproducts. -This chapter explain very well this principles and I will not explain it better than the author. - -The end of this chapter is interesting by exposing differences between product and coproduct properties (bijective or not) diff --git a/docs/category-theory/ctfp-dotnet/5 Products and Coproducts/pandcop.csx b/docs/category-theory/ctfp-dotnet/5 Products and Coproducts/pandcop.csx deleted file mode 100644 index b4721d70..00000000 --- a/docs/category-theory/ctfp-dotnet/5 Products and Coproducts/pandcop.csx +++ /dev/null @@ -1,65 +0,0 @@ -using System; -using System.Collections.Generic; -using System.Linq; - -//those function is helpful and avoid lambda deconstruction. -//Because constructing a tuple is like passing all parameters to function, it is harder to deconstruct tuple in method argument.. -static class Functions -{ - public static T1 fst(ValueTuple t) - { - var (x, _) = t; - return x; - } - - public static T2 snd(ValueTuple t) - { - var (_, y) = t; - return y; - } - - //Do you understand why WITHOUT type inference on function it is hard to define those things ?! - public static ValueTuple, ValueTuple> factorizer(Func, T1> f, Func, T2> g, ValueTuple x) - { - //Without inference, the signature is larger than the implementation.. - return (x, (f(x), g(x))); - } -} - -// construct a pair like fsharp -var pair = (1, true); - -var (x1, y2) = pair; - -// /!\ This code does not compile because constructing a pair and passing as argument is different. -// It is an issue to use pair instead of out parameter for example. -var x = Functions.fst(pair); -var y = Functions.snd((1, true)); - -var r = Functions.factorizer(Functions.fst, Functions.snd, pair); - - -//Type as set with list sample : - -class TypeAsSet -{ - public static int[] surjective(int x) => new[] { x, 2 * x }; - public static int[] injective() => new[] { 1, 2 }; -} - -//surjective or onto : domain size is lower than codomain. One element of the domain map n elements of the codomain -var surjective = new[] { 1 }.SelectMany(TypeAsSet.surjective); - -//injective or one-to-one : unit map multiple element of the codomain -var injective = TypeAsSet.injective(); - -//bijection -class Functions2 -{ - public static int f(int x) => x + 1; - public static int cof(int x) => x - 1; -} -var l = new[] { 1, 2 }; -var l2 = l.Select(x => Functions2.cof(Functions2.f(x))); // [1; 2], l2 == l - -injective() diff --git a/docs/category-theory/ctfp-dotnet/5 Products and Coproducts/pandcop.fsx b/docs/category-theory/ctfp-dotnet/5 Products and Coproducts/pandcop.fsx deleted file mode 100644 index 3ae6c529..00000000 --- a/docs/category-theory/ctfp-dotnet/5 Products and Coproducts/pandcop.fsx +++ /dev/null @@ -1,50 +0,0 @@ -//The simplest product is pair of types : - -let pair = 1, true - -//Here is 2 functions that extract the first or second part - -let first (x,_) = x - -let second (_,y) = y - -first pair = 1 //true -second pair = true //true - -//Those functions already exists as fst and snd like Haskell -fst pair = first pair //true -snd pair = second pair - -//Now how can I reverse the first function to our initial pair ? - -(fst pair |> fun x -> x, true) = pair //true -//this previous sample works because I already know that the second value is true. -//To do that correctly we have to not loss information. This is the aim of factorizers : - -let factorizer f g x = x, (f x, g x) - -let pair_factorizer = factorizer fst snd - -pair_factorizer pair |> fst = pair //true -let pair2 = 10, false -pair_factorizer pair2 |> fst = pair2 //true -//So now it works because we are maintening the initial value. -//Now we are able to write coproduct of pair thanks to our pair_factorizer (coproduct is the dual operation of product) - - -//Type as set with list sample : - -//surjective or onto domain : function that use less space of the codomain like having a singleton in list. -let surjective x = List.singleton x -surjective 1 - -//injective or one-to-one : unit map multiple element of the codomain -let injective () = [ 1;2 ] -injective () - -//bijection -let f x = x + 1 -let cof x = x - 1 -let l = [1;2] -l |> List.map (f >> cof) = l - diff --git a/docs/category-theory/ctfp-dotnet/6 Simple Algebraic Data Types/6.1 Product Types.csx b/docs/category-theory/ctfp-dotnet/6 Simple Algebraic Data Types/6.1 Product Types.csx deleted file mode 100644 index cf3a463f..00000000 --- a/docs/category-theory/ctfp-dotnet/6 Simple Algebraic Data Types/6.1 Product Types.csx +++ /dev/null @@ -1,73 +0,0 @@ -//Pair is not commutative -var pair1 = (1, true); -var pair2 = (true, 1); - -sealed class Unit -{ - private Unit() - { - - } - - public static Unit Singleton = new Unit(); -} - -static class Functions -{ - //We can provide a swap function that reverse the pair - public static ValueTuple swap(ValueTuple t) - { - var (x, y) = t; - return (y, x); - } - public static ValueTuple, T3> alpha(ValueTuple> t) - { - var (x, (y, z)) = t; - return ((x, y), z); - } - public static ValueTuple> alpha_inv(ValueTuple, T3> t) - { - var ((x, y), z) = t; - return (x, (y, z)); - } - - public static T rho(ValueTuple t) - { - var (x, _) = t; - return x; - } - public static ValueTuple rho_inv(T x) => (x, Unit.Singleton); - public static ValueTuple P (string s, bool b) => (s, b); - public static ValueTuple p(T1 x, T2 y) => (x, y); - public static Func partial_app (Func f, T1 x) => (T2 y) => f(x, y); -} - -// /!\ Execute this script line by line to switch from statement to expression (an expression returns a value displayed into the console) -//Main issue in csx : everything is statement. If it was expression instead, a value would have been displayed in the the console. -//So if I remove the ';' at the end it is a kind of expression in csx and the value is displayed but multiple lines fail at compile/design time because the ';' at the end is missing ?! -pair1 == Functions.swap(pair2) //true in type and by value thanks to swap - -pair1 == Functions.swap(Functions.swap(pair1)) //true - -//Isomorphism as associativity law in monoids. -Functions.alpha_inv(Functions.alpha(("a", ("b", "c")))) == ("a", ("b", "c")) //true - -//Now check the zero one : - -Functions.rho(Functions.rho_inv( 1 )) == 1 //true - - -//Pair as single case -var stmt = Functions.P("This statements is", false); - -// Personal notes -//link : https://en.wikipedia.org/wiki/Currying -//link : http://blog.ploeh.dk/2017/01/30/partial-application-is-dependency-injection/ -//Partial application is hard here because multiple arguments of function is ambiguous with tuple because you can't generate function with n-1 parameters -//Partial application can replace dependency injection frameworks (dependency injection with partial application) and could reduce complexity in frameworks (WCF, Kestrel and so on..) - -//We can adapt by building our own partial_app function but due to type inference issue it is hard to keep track of types. -var p2 = Functions.partial_app>(Functions.p, "Hello"); - -var stmt2 = p2(false); - diff --git a/docs/category-theory/ctfp-dotnet/6 Simple Algebraic Data Types/6.1 Product Types.fsx b/docs/category-theory/ctfp-dotnet/6 Simple Algebraic Data Types/6.1 Product Types.fsx deleted file mode 100644 index 22688938..00000000 --- a/docs/category-theory/ctfp-dotnet/6 Simple Algebraic Data Types/6.1 Product Types.fsx +++ /dev/null @@ -1,35 +0,0 @@ -//Pair is not commutative -let pair1 = (1, true) -let pair2 = (true, 1) - -//We can provide a swap function that reverse the pair -let swap (x, y) = (y, x) - -pair1 = swap pair2 //true in type and by value thanks to swap - -pair1 = (swap >> swap) pair1 //true - -let alpha (x, (y, z)) = ((x, y), z) -let alpha_inv ((x, y), z) = (x, (y, z)) - -//Isomorphism as associativity law in monoids. -(alpha >> alpha_inv) ("a", ("b", "c")) = ("a", ("b", "c")) //true - -//Now check the zero one : -let rho (x, ()) = x -let rho_inv x = x, () - -(rho_inv >> rho) 1 = 1 //true - - -//Pair as single case - -type Pair<'a, 'b> = P of 'a * 'b - -let stmt = P ("This statements is", false) - -//link : https://en.wikipedia.org/wiki/Currying -//like haskell function with 2 arguments instead of having one tuple arg. Better in case of partial application. -let p x y = P (x, y) -let stmt2 = p "This statements is" false - diff --git a/docs/category-theory/ctfp-dotnet/6 Simple Algebraic Data Types/6.2 Records.csx b/docs/category-theory/ctfp-dotnet/6 Simple Algebraic Data Types/6.2 Records.csx deleted file mode 100644 index d0aa05f4..00000000 --- a/docs/category-theory/ctfp-dotnet/6 Simple Algebraic Data Types/6.2 Records.csx +++ /dev/null @@ -1,26 +0,0 @@ -static class Functions -{ - public static string isPrefixOf(string s, string x) => x.StartsWith(s); - //swap argument - public static string isPrefixOf2(string x, string s) => isPrefixOf(s, x); - //This kind of code is hard to reuse outside its context due to the risk of confusion between name and symbol - public static bool startsWithSymbol(string name, string symbol, bool _) => isPrefixOf(symbol, name); -} - -struct Element -{ - public string Name { get; } - public string Symbol { get; } - public int AtomicNumber { get; } - - public static Element tupleToElement (string n, string s, int a) => Element(Name = n, Symbol = s, AtomicNumber = a); - public static elemToTuple(Element e) => (e.Name, e.Symbol, e.AtomicNumber); - //Redefine the new function: - //I don't know how to do a human readable one in csharp - public static bool startsWithSymbol2 (Element e) => Functions.isPrefixOf2(e.Symbol, e.Name); -} - -//Personal notes -// link : https://github.com/dotnet/csharplang/blob/master/proposals/records.md -//I will use a struct instead but at the same time I will loose the deconstruct pattern - diff --git a/docs/category-theory/ctfp-dotnet/6 Simple Algebraic Data Types/6.2 Records.fsx b/docs/category-theory/ctfp-dotnet/6 Simple Algebraic Data Types/6.2 Records.fsx deleted file mode 100644 index a0cefcb3..00000000 --- a/docs/category-theory/ctfp-dotnet/6 Simple Algebraic Data Types/6.2 Records.fsx +++ /dev/null @@ -1,16 +0,0 @@ -let isPrefixOf s x = (x:string).StartsWith s - -//This kind of code is hard to reuse outside its context due to the risk of confusion between name and symbol -let startsWithSymbol (name, symbol, _) = isPrefixOf symbol name - -//Record Type version -type Element = { Name:string; Symbol:string; AtomicNumber:int } - -let tupleToElement (n, s, a) = { Name = n; Symbol = s; AtomicNumber = a } -let elemToTuple e = e.Name, e.Symbol, e.AtomicNumber - -//We can swap parameter to make it more human readable: -let isPrefixOf' x y = isPrefixOf y x - -//Redefine the new function: -let startsWithSymbol2 e = e.Name |> isPrefixOf' e.Symbol diff --git a/docs/category-theory/ctfp-dotnet/6 Simple Algebraic Data Types/6.3 Sum Types.csx b/docs/category-theory/ctfp-dotnet/6 Simple Algebraic Data Types/6.3 Sum Types.csx deleted file mode 100644 index 32de3592..00000000 --- a/docs/category-theory/ctfp-dotnet/6 Simple Algebraic Data Types/6.3 Sum Types.csx +++ /dev/null @@ -1,381 +0,0 @@ -using System.Collections.Generic; -using System.Linq; - -//Here is a convenient way to build a Void type -//Sealed is important to stop sum and be sure that this type as no value and is impossible to construct in any way. -sealed class Void -{ - private Void() { } - //Try to call this function ! - public static T absurd(Void _) => throw new System.NotImplementedException("you can't call me it is absurd!"); -} - -sealed class Unit -{ - private Unit(){ } - - public static Unit Singleton = new Unit(); -} - -//Sum type thanks to Subtyping. It works for this moment.. But lets go deeper in the book :) - -//Personal notes -//Is not an antipattern by having marker interface ?? Lets discuss on a pull request or twitter. -//I don't know but I will use it for this simple case to understand the principle and compliant with the book. -//link : https://blog.ndepend.com/marker-interface-isnt-pattern-good-idea/ -interface Either { } - -struct Left : Either -{ - public T Value { get; } - public Left(T v) => Value = v; -} - -//Because there is no Higher kinded types aka generics of generics, I have to write the same code for Right. -//link : https://github.com/dotnet/csharplang/issues/339 -//In fsharp sum types already exists so this porcelain and plumbing code not exists in fsharp implementation. - -struct Right : Either -{ - public T Value { get; } - public Right(T v) => Value = v; -} - -class Functions -{ - //Convenient way to adapt things. Here the compiler ensures that Right is absurd. - //Personal note - //If we have encoded that with NotImplementedException only, the check is at runtime instead at compile time. - //So you may have less problems! - //Here you have a boxing issue : if you would like to use sum type on struct for a O alloc (like Kestrel team plan to do) - public static T simple(Either x) - { - switch (x) - { - case Left l: return Void.absurd(l.Value); - case Right y: return y.Value; - } - throw new NotImplementedException("The compiler can't check if it is total, so it is not really a sum type"); - } -} - -//Here Either is isomorphic to Right because Left is absurd! -var r1 = new Right(Functions.simple(new Right("hello"))); -var r2 = new Right("hello"); - -// /!\ Execute this code line by line due to expression/statement issue -r1.Equals(r2) //true - -//Since we can only build the right part, this type is isomorphic to Right - -/// Personal notes -//Now think about how to implement the StreamReader and StreamWriter. -//One only reads the stream, it is absurd to write. The opposite is true for the writer -//We can build instead a Pipe (reader/writer) and use inheritance polymorphism to build the reader and the writer - -/// Link Pipe in Haskell : https://stackoverflow.com/questions/14131856/whats-the-absurd-function-in-data-void-useful-for -/// For example, Kestrel in dotnet core uses Pipeline pattern for synchronization/timing purpose. - -/// Simple Sum type like enum : - -enum Color -{ - Red, - Green, - Blue -} - -// Maybe -//Personal notes : can't be encoded by using enum -interface Maybe -{ -} - -sealed class Nothing : Maybe -{ - private Nothing () { } - public static Nothing Singleton () => new Nothing(); -} - -struct Just : Maybe -{ - public T Value; - public Just(T value) => Value = value; -} - -//Personal notes -//In csharp Nullable is equivalent to Maybe in haskell and Option in fsharp when nullable reference type will be available. -//link : https://blogs.msdn.microsoft.com/dotnet/2017/11/15/nullable-reference-types-in-csharp/ - -//This type could be construct behind Either thanks to our unit type like this : - -// Either /////////////////////////////////////////////////////////////////////// -//Is it possible to reuse our previous definition : - -class Maybe : Either { } //It is a little bit strange.. - -class LeftClass : Either -{ - public T Value { get; } - public LeftClass(T v) => Value = v; -} - -class RightClass : Either -{ - public T Value { get; } - public RightClass(T v) => Value = v; -} - -class Nothing : LeftClass { public Nothing() : base(Unit.Singleton) { } } //Can't do that with Left struct, so I have to turn the Left as class.. -class Just : RightClass { public Just(T v) : base(v) { } } - -var r1E = new Nothing(); - -var r2E = new Just("hello"); - -var r1E = new Nothing(); - -var r2E = new Just("hello"); - -switch ((Either)r1E) -{ - case Nothing _: return "nothing"; - case Just x: return x.Value; - default: throw new System.NotImplementedException("you have added a new type without the matching implementation"); -} - -// Either2 ////////////////////////////////////////////////////////////////////// -// In fact Either interface does not keep track of types : lets create a generic one : -interface Either2 { } - -//Personal notes : this part is not in the book, but I have to translate it in csharp and I don't know what is the approach. Lets discuss it in a pull request - -//It is a little bit strange, now in the definition of Left we have to keep the Right type ?? -struct Left2 : Either2 -{ - public L Value { get; } - public Left2(L x) => Value = x; -} - -//Duplicating stuff -struct Right2 : Either2 -{ - public R Value { get; } - public Right2(R x) => Value = x; -} - -//Now it is okay but we have introduced a mutual dependency in the type definition between Left and Right type ?! -class Maybe2 : Either2 { } - -var r1E2 = new Right2("hello"); -var r2E2 = new Left2(Unit.Singleton); - -switch ((Either2)r1E2) -{ - case Left2 _: return "nothing"; - case Right2 x: return x.Value; - default: throw new System.NotImplementedException("you have added a new type without the matching implementation"); -} - -// Either3 ////////////////////////////////////////////////////////////////////// -//We can define the Either with only one generic type because. It is a sum after all.. But ... -interface Either3 { } - -struct Left3 : Either3 -{ - public L Value { get; } - public Left3(L x) => Value = x; -} - -//Duplicating stuff -struct Right3 : Either3 -{ - public R Value { get; } - public Right3(R x) => Value = x; -} - -class Maybe3 : Either3 { } - -var r1E3 = new Right3("hello"); -var r2E3 = new Left3(Unit.Singleton); - -//This code does not compile at all because Unit != string -switch ((Either3)r1E3) -{ - case Left3 _: return "nothing"; - case Right3 x: return x.Value; - default: throw new System.NotImplementedException("you have added a new type without the matching implementation"); -} - -// Check the factorizers properties.. -static class Either3Extension -{ - //How could we write the factorizers. - //We could do it but it is not a sum anymore.. The type of left and right should be the same.. - //If this sample is a little bit hard, try to implement the prodToSum and sumToProd of the chapter 6.4 - public static Either3 factorizers(Either3 x, Func f, Func g) - { - switch (x) - { - case Left3 l: return new Left3(f(l.Value)); - case Right3 r: return new Right3(g(r.Value)); - } - throw new System.NotImplementedException("unreachable"); - } -} - - - - - - -// Either4 ////////////////////////////////////////////////////////////////////// -// Link : https://mikhail.io/2016/01/validation-with-either-data-type-in-csharp/ -// Link: https://davesquared.net/2014/04/either.html -public class Either4 -{ - private readonly TL left; - private readonly TR right; - private readonly bool isLeft; - - public Either4(TL left) - { - this.left = left; - this.isLeft = true; - } - - public Either4(TR right) - { - this.right = right; - this.isLeft = false; - } - - public TL Left => left; - - public TR Right => right; - - public T Match4(Func leftFunc, Func rightFunc) - => this.isLeft ? leftFunc(this.left) : rightFunc(this.right); - - public override bool Equals(object obj) - { - var item = obj as Either4; - if (item == null) - { - return false; - } - return item.Match4( - left1 => this.Match4(left2 => left2.Equals(left1), right2 => false), - right1 => this.Match4(left2 => false, right2 => right2.Equals(right1)) - ); - } -} - -//Here Either is isomorphic to Right because Left is absurd! -var r14 = new Either4( - new Either4("hello") - .Match4( - left => left, right => throw new Exception("error!")) - ); -var r24 = new Either4("hello"); - -// /!\ Execute this code line by line due to expression/statement issue -r14.Equals(r24) //true - - -class Just4 : Either4 { public Just4(T v) : base(v) { } } -class Nothing4 : Either4 { public Nothing4() : base(Unit.Singleton) { } } - -var r1E4 = new Just4("hello"); -var r2E4 = new Nothing4(); - -switch ((Either4)r1E4) -{ - case Nothing4 _: return "nothing"; - case Just4 x: return x.Right; - default: throw new System.NotImplementedException("you have added a new type without the matching implementation"); -} - - -// Either5 ////////////////////////////////////////////////////////////////////// -// Either implemented by using the Vistor pattern -public interface IEitherVisitor -{ - A visitLeft(Left5 v); - B visitRight(Right5 v); -}; - -public interface IEither5 -{ - A acceptLeft(IEitherVisitor v); - B acceptRight(IEitherVisitor v); -}; - -public struct Left5 : IEither5 -{ - public A Value { get; } - public Left5(A v) => Value = v; - public A acceptLeft(IEitherVisitor v) => Value; - public B acceptRight(IEitherVisitor v) => throw new Exception("only Left"); -}; - -public struct Right5 : IEither5 -{ - public B Value { get; } - public Right5(B v) => Value = v; - public A acceptLeft(IEitherVisitor v) => throw new Exception("only right"); - public B acceptRight(IEitherVisitor v) => Value; -}; - -public class EitherVisitor : IEitherVisitor -{ - public A visitLeft(Left5 v) => v.acceptLeft(this); - public B visitRight(Right5 v) => v.acceptRight(this); -}; - -var visitor = new EitherVisitor(); -var r1 = new Right5(visitor.visitRight(new Right5("hello"))); -var r2 = new Right5("hello"); - -r1.Equals(r2) // true - - - - - -//Wrap Up -//Here, only the Either2, 4 and 5 are valid with properties and is compliant. -//For the Either2, the client can use the new csharp syntax for pattern matching switch statement but the type definition of left and right are mutually dependent.. - -//////////////////////////////// - -// list : -// yield is the keyword equivalent of Cons -// Enumerable.Empty is the equivalent of Nil + Linq conversion to the type List -// The most type used for list in c# is List - -var empty = Enumerable.Empty().ToList(); - -var l1 = empty.ToList(); -//The add method mute the list. So the last element will be different depending where you add items.. -l1.Add(1); -var x = l1.Last(); - -l1.Add(2); -var y = l1.Last(); - -x == y //false! - -//link Give a try at ImmutableList : https://msdn.microsoft.com/en-us/library/dn467185(v=vs.111).aspx - -empty.FirstOrDefault() //0 ?? what?? Implicit zero on default constructor provided by struct. - -var l3 = new[] { 0 }; - -empty.FirstOrDefault() == l3.FirstOrDefault() //true, now we are not able to see if it is the first element or not ?0? - -//now it is better but the compiler does not help us because there is no Nullable for FirstOrDefault (due to the reference type issue in Nullable) - -//A better one for value types -empty.Select(x => new Nullable(x)).FirstOrDefault() // It outputs null but it is a true Nullable without value.. - diff --git a/docs/category-theory/ctfp-dotnet/6 Simple Algebraic Data Types/6.3 Sum Types.fsx b/docs/category-theory/ctfp-dotnet/6 Simple Algebraic Data Types/6.3 Sum Types.fsx deleted file mode 100644 index d181888f..00000000 --- a/docs/category-theory/ctfp-dotnet/6 Simple Algebraic Data Types/6.3 Sum Types.fsx +++ /dev/null @@ -1,51 +0,0 @@ -//Here is a convenient way to build a Void type -//Sealed is important to stop sum and be sure that this type as no value and is impossible to construct in any way. -type [] Void = private new () = { } - -//Try to call this function ! -let absurd (_:Void) = failwith "you can't call me it is absurd!" - -type Either<'a, 'b> = Left of 'a | Right of 'b - -//Convenient way to adapt things. Here the compiler ensures that Right is absurd. -//If we have encoded that with NotImplementedException only, the check is at runtime instead at compile time. -//So you may have less problems! -let simple = function - | Left x -> absurd x - | Right y -> y - -//Here Either is isomorphic to Right because Left is absurd! -Right "hello" |> simple |> Right = Right "hello" -//Since we can only build the right part, this type is isomorphic to Right - -/// Personal notes -//Now think about how to implement the StreamReader and StreamWriter. -//One only reads the stream, it is absurd to write. The opposite is true for the writer -//We can build a Pipe instead (reader/writer, producer/consumer) and use inheritance polymorphism to build the reader and the writer - -/// Link Pipe in Haskell : https://stackoverflow.com/questions/14131856/whats-the-absurd-function-in-data-void-useful-for -/// For example, Kestrel in dotnet core uses Pipeline pattern for synchronization/timing purpose. - -/// Simple Sum type like enum : -type Color = Red | Green | Blue - -// Maybe -type Maybe<'a> = Nothing | Just of 'a -//This type could be construct behind Either thanks to our unit type like this : -type MaybeE<'a> = Either - -//In fsharp, Option is the equivalent of the Maybe one. None = Nothing and Just = Some. - -// list : -// (::) is the equivalent of Cons -// [] is the equivalent of Nil -1 :: [] = [1] //true -1 :: 2 :: [] = [1;2] //true - -//equivalent to maybeHead -[] |> List.tryHead = None -[1] |> List.tryHead = Some 1 - -//Same things for last : equivalent to maybeTail -[] |> List.tryLast = None -[1] |> List.tryLast = Some 1 \ No newline at end of file diff --git a/docs/category-theory/ctfp-dotnet/6 Simple Algebraic Data Types/6.4 Algebra Types.csx b/docs/category-theory/ctfp-dotnet/6 Simple Algebraic Data Types/6.4 Algebra Types.csx deleted file mode 100644 index aa2bb74d..00000000 --- a/docs/category-theory/ctfp-dotnet/6 Simple Algebraic Data Types/6.4 Algebra Types.csx +++ /dev/null @@ -1,50 +0,0 @@ -interface Either { } - -struct Left : Either -{ - public L Value { get; } - public Left(L x) => Value = x; -} - -struct Right : Either -{ - public R Value { get; } - public Right(R x) => Value = x; -} - -//distribution : - -static class Functions -{ - public static Either, ValueTuple> prodToSum(ValueTuple> t) - { - var (x, e) = t; - - switch (e) - { - case Left l: return new Left, ValueTuple>((x, l.Value)); - case Right r: return new Right, ValueTuple>((x, r.Value)); - } - throw new System.NotImplementedException("not reachable"); - } - - public static ValueTuple> sumToProd(Either, ValueTuple> e) - { - switch (e) - { - //This is why subtyping as sum type is not trivial - case Left, ValueTuple> l: - var (x, v) = l.Value; - return (x, new Left(v)); - case Right, ValueTuple> l: - var (x, v) = l.Value; - return (x, new Right(v)); - } - throw new System.NotImplementedException("not reachable"); - } -} - -var x = ("hello", new Left("world")); - -//semiring or rig : No type substraction is provided -Functions.sumToProd((Functions.prodToSum(x))).Equals(x) //true \ No newline at end of file diff --git a/docs/category-theory/ctfp-dotnet/6 Simple Algebraic Data Types/6.4 Algebra Types.fsx b/docs/category-theory/ctfp-dotnet/6 Simple Algebraic Data Types/6.4 Algebra Types.fsx deleted file mode 100644 index 81ec3ff5..00000000 --- a/docs/category-theory/ctfp-dotnet/6 Simple Algebraic Data Types/6.4 Algebra Types.fsx +++ /dev/null @@ -1,18 +0,0 @@ -type Either<'a, 'b> = Left of 'a | Right of 'b - -//distribution : - -let prodToSum (a, b) = - match b with - | Left b' -> Left (a, b') - | Right b' -> Right (a, b') - -let sumToProd = function - | Left (a, b) -> a, Left b - | Right (a, b) -> a, Right b - - -let x = ("hello", Left "world") - -//semiring or rig : No type substraction is provided -(prodToSum >> sumToProd) x = x //true \ No newline at end of file diff --git a/docs/category-theory/ctfp-dotnet/6 Simple Algebraic Data Types/README.md b/docs/category-theory/ctfp-dotnet/6 Simple Algebraic Data Types/README.md deleted file mode 100644 index 48ea0d29..00000000 --- a/docs/category-theory/ctfp-dotnet/6 Simple Algebraic Data Types/README.md +++ /dev/null @@ -1,55 +0,0 @@ -# Simple Algebraic Data Types - -This chapter explains well what is a Sum and Product types and how we could use them together. - -## Personal notes - -In csharp we often use Subtyping as Sum type. There is 2 things in Sum types : the total one, where the compiler checks that -each case is treated (Discriminated union in fsharp, can't do that in csharp for now) and the open one (partial) with Subtype. - -Sum type as Subtyping creates strange mutually type dependencies in the Either implementation : Pull request accepted! - -Because csharp does not support sumtype, I would like to summurize solutions because there is no total equivalent : - -Here is all implementation - -- [Pattern matching](https://docs.microsoft.com/en-us/dotnet/csharp/pattern-matching) : you can deconstruct what you have construct. -For either you can unwrap the left case and get the value inside. The pattern matching feature with sum type in functional programming is really helpful because you can combine case deeper and deeper with less cyclomatic complexity in your code. - -You can encode your pattern matching thanks to if statements but you may have a higher cyclomatic complexity and have to split your method. - -- Boxing : When you have to use a struct that implement an interface, every time you use the struct as interface, you have a boxing issue. For 0 alloc pattern it could be an issue. - -- Marker interface : https://blog.ndepend.com/marker-interface-isnt-pattern-good-idea/. Is it an antipattern ? - -- Polymorphism : implementation without the left and right type in the Either type definition can help you to implement it faster but you can't use polymorphism and reuse your code explicitly' - -Note that if we use inheritance and use the pattern matching switch expression we have to use an interface. -If we have to inherit from case, we could not use struct at root. So inheritance at case level is not possible for struct. - -- Either : inheritance at case level. Can't use struct but the pattern matching syntax works with upper cast. - -- Either2 : try to make inheritance at case level with struct support. -But for each new case you have to add the new type on all types. By doing this you may have some regretion. -Cases are mutually dependent. -- Either3 : try to keep one type to avoid case dependencies. But now we can't match case anymore.. It is not a valid solution at all. -We can define the type Maybe ```(class Maybe2 : Either2 { })``` only for info.. (can't convert Maybe2 -> Right directly). -- Either4 : this [implementation](https://mikhail.io/2016/01/validation-with-either-data-type-in-csharp/) is inspired by [@MikhailShilkov](https://twitter.com/MikhailShilkov). -Now the left and right type are inside. Now the type definition is better at a first glance and same as fsharp but -we have now 2 ways to get the value and only one is valid (Left and Right property). -- Either5: this implementation try to solve the struct issue of the Either4 but we cannot we the csharp pattern matching syntax anymore. - -| Ranking | Name | Pattern matching | Boxing | Marker interface | Polymorphism | Support struct | -|---------|---------------|------------------|--------|------------------|--------------------|----------------| -| #4 | Either | Switch keyword | - | Yes | At case level | No | -| #2 | Either2 | Switch keyword | Yes | Yes | At case level | Yes | -| - | Either3 | Not Possible | Yes | Yes | At case level | Yes | -| #1 | Either4 | No. With method | - | No | At type level | No | -| #3 | Either5 | No. | Yes | Yes | At case level | Yes | - -To summarize, there is no total solution for csharp sum type. You have to choose one dependending your case but we cannot build a lib that supply only one valid implementation for either and compose maybe or nullable over it. -Having sum types can increase composability of types. - -I will use the Either2 which is not the best but is compliant with the pattern matching feature that is necessary to implement function over our sum type. - -Thanks to [giuliohome](https://twitter.com/giuliohome_2017) who help me to add more implementations. diff --git a/docs/category-theory/ctfp-dotnet/7 Functor/7.1.1 The Maybe Functor.csx b/docs/category-theory/ctfp-dotnet/7 Functor/7.1.1 The Maybe Functor.csx deleted file mode 100644 index 7cbcbfd2..00000000 --- a/docs/category-theory/ctfp-dotnet/7 Functor/7.1.1 The Maybe Functor.csx +++ /dev/null @@ -1,50 +0,0 @@ -using System; - -interface Maybe { } - -struct Nothing : Maybe { } - -struct Just : Maybe -{ - public T Value { get; } - public Just(T v) => Value = v; -} - -static class Maybe -{ - public static Maybe fmap(Func f, Maybe x) - { - switch (x) - { - case Nothing _: return new Nothing(); - case Just j: return new Just(f(j.Value)); - } - throw new NotImplementedException("absurd, there is no other cases but we don't have he garantee"); - } -} - -Maybe.fmap(x => x, new Nothing()).Equals(new Nothing()) //true - -//Nullable is the new equivalent of Maybe (Nullable will be available for reference type in csharp soon) -//Link : https://blogs.msdn.microsoft.com/dotnet/2017/11/15/nullable-reference-types-in-csharp/ - -//In csharp there is an operator to traverse structure non null value or passing as parameter inside a function : - -static class NullableExtension -{ - public static Nullable fmap(Func f, Nullable x) - where T : struct - where R : struct - { - if (x.HasValue) return new Nullable(f(x.Value)); - return new Nullable(); - } -} - -// Nullable is not completely useful because it is compatible with struct only. -// As you may notice the default constructor occurs on the GetValueOrDefault with implicit default constructor as zero causing less compatibility with reference types. - -// -new Nullable ().Equals(NullableExtension.fmap (x => x, new Nullable())) //true - -// The maybe one is compatible with struct and reference type. \ No newline at end of file diff --git a/docs/category-theory/ctfp-dotnet/7 Functor/7.1.1 The Maybe Functor.fsx b/docs/category-theory/ctfp-dotnet/7 Functor/7.1.1 The Maybe Functor.fsx deleted file mode 100644 index 2601cb88..00000000 --- a/docs/category-theory/ctfp-dotnet/7 Functor/7.1.1 The Maybe Functor.fsx +++ /dev/null @@ -1,19 +0,0 @@ -type [] Maybe<'a> = Nothing | Just of 'a - -//Here is the fmap implementation with types -let fmap (f:'a->'b) (x:Maybe<'a>) : Maybe<'b> = - match x with - | Nothing -> Nothing - | Just x' -> Just(f x') - -fmap id Nothing = Nothing //true - -//Now declare the fmap in a module with lighter syntax : -module Maybe = - let fmap f = function Nothing -> Nothing | Just x -> Just (f x) - -Maybe.fmap id Nothing = Nothing //true - -//In fsharp, Option already exists and act as Maybe -Option.map id None = None -Option.map id (Some 1) = Some 1 \ No newline at end of file diff --git a/docs/category-theory/ctfp-dotnet/7 Functor/7.1.6 The List Functor.csx b/docs/category-theory/ctfp-dotnet/7 Functor/7.1.6 The List Functor.csx deleted file mode 100644 index 2830e5f4..00000000 --- a/docs/category-theory/ctfp-dotnet/7 Functor/7.1.6 The List Functor.csx +++ /dev/null @@ -1,95 +0,0 @@ -using System; - -interface List { } - -class Nil : List { } - -class Cons : List -{ - public T Head { get; } - public List Tail { get; } - - public Cons(T head, List tail) - { - Head = head; - Tail = tail; - } -} - -static class List -{ - public static List map(Func f, List l) - { - switch (l) - { - case Nil _: return new Nil(); - case Cons c: return new Cons(f(c.Head), map(f, c.Tail)); - } - throw new NotImplementedException("absurd"); - } - - public static List init(Func f, int n) - { - List l = new Nil(); - for (var i = n; i > 0; i--) - { - //Here l is mutating.. - l = new Cons(f(i), l); - } - return l; - } - - public static List initRec(Func f, int n) - { - List nestedInitRec(int m, List l) - { - if (m > 0) - { - return nestedInitRec(m - 1, new Cons(f(m), l)); - } - else return l; - } - - return nestedInitRec(n, new Nil()); - } -} - -static class TailRecursiveList -{ - // This code works with tailcall optimization only in x64 debug and release for dotnetcore but only release for dotnet framework. - // We are converting the Monoid to another one (Nil as seed/mempty and folder as Cons+folder/mappend) - public static R fold(Func folder, R seed, List x) - { - switch (x) - { - case Nil _: return seed; - case Cons c: return fold(folder, folder(seed, c.Head), c.Tail); - } - throw new NotImplementedException("absurd"); - } - - //A reverse function because every time we use fold, by rebuilding from zero, in the end, the order is reversed. - public static List rev(List l) => fold((t, x) => new Cons(x, t), (List)new Nil(), l); - - //Here we are rebuilding the list from Nil by applying every x to f. Note that the order is reversed - //write map through fold + rev to have tail-recursive optimization - //Here we are using the List Monoid to map function (Nil as mempty and Cons as mappend) through fold - //Here we are on O(n^2) (fold + rev) but actual Fsharp List implementation is better than this one. - public static List map(Func f, List l) => rev(fold((t, x) => new Cons(f(x), t), (List)new Nil(), l)); -} - -//This impl does not works in csharp interactive but works on release x64 configuration. -//I don't know how to configure CshapInteractive ?! -var of = List.initRec(y => y, 100000000); - -var x = List.init(y => y, 100000000); -var x2 = List.map(y => y, x); //StackOverflow! - -//Here we have a stack overflow! -var x3 = TailRecursiveList.map(y => y, x); - -//Lets try with a little set.. - -var x4 = List.initRec(y => y, 100); -var x5 = List.map(x => x, x4); - diff --git a/docs/category-theory/ctfp-dotnet/7 Functor/7.1.6 The List Functor.fsx b/docs/category-theory/ctfp-dotnet/7 Functor/7.1.6 The List Functor.fsx deleted file mode 100644 index a677048b..00000000 --- a/docs/category-theory/ctfp-dotnet/7 Functor/7.1.6 The List Functor.fsx +++ /dev/null @@ -1,46 +0,0 @@ - -type List<'a> = Nil | Cons of 'a * List<'a> - -//Here all comments are personal notes to have a list functor with tail-recursive optimization. - -//Aka Instance of Functor (pattern used in fsharp implementation) : Build a module and define function and implementation thanks to the typeclassopedia (Haskell wiki) -module List = - //we have to use the rec keyword. This version is not tail-recursive (in the end we will have a stack overflow). Through fold it is possible - //Here we have to wait the tail result before returning - let rec map f = function Nil -> Nil | Cons (x, t) -> Cons (f x, map f t) - - let init f n = - let rec initRec f n l = - if n > 0 then initRec f (n - 1) (Cons(f n, l)) - else l - initRec f n Nil - -//Personal Notes -module TailRecursiveList = - //We have to use the rec keyword but here we are rebuilding the list one by one and it the tail-recursive optimization works. - //(seed acts as accumulator) - // We are converting the Monoid to another one (Nil as seed/mempty and folder as Cons+folder/mappend) - let rec fold folder seed = function Nil -> seed | Cons (h, t) -> fold folder (folder seed h) t - - //A reverse function because every time we use fold, by rebuilding from zero, in the end, the order is reversed. - let rev l = fold (fun seed x -> Cons (x, seed)) Nil l - - //Here we are rebuilding the list from Nil by applying every x to f. Note that the order is reversed - //write map through fold + rev to have tail-recursive optimization - //Here we are using the List Monoid to map function (Nil as mempty and Cons as mappend) through fold - //Here we are on O(n^2) (fold + rev) but actual Fsharp List implementation is better than this one. - let map f = fold (fun t x -> Cons (f x, t)) Nil >> rev - -let x = List.init id 100000000 - -let x' = x |> List.map id //Stack overflow! - -let x'' = x |> TailRecursiveList.map id //No stack overflow anymore (with --optimize option or --tailcall)! - -x'' = x //answer is long but true! - -//In fsharp list already exists! - -let y = FSharp.Collections.List.init 100000000 id -let y' = y |> FSharp.Collections.List.map id //No stack overflow, no reversed order problem :) -y = y' //true \ No newline at end of file diff --git a/docs/category-theory/ctfp-dotnet/7 Functor/7.1.7 The Reader Functor.csx b/docs/category-theory/ctfp-dotnet/7 Functor/7.1.7 The Reader Functor.csx deleted file mode 100644 index 73da5222..00000000 --- a/docs/category-theory/ctfp-dotnet/7 Functor/7.1.7 The Reader Functor.csx +++ /dev/null @@ -1,12 +0,0 @@ -using System; - -//Can't do that since Func is sealed. So lets use Func directly.. -//class Functor : Func { } - -static class Functor -{ - public static Func map(Func f, Func g) => (x) => f(g(x)); -} - -var rf = (Functor.map(x => x, y => y)); -rf(1) == 1 //true diff --git a/docs/category-theory/ctfp-dotnet/7 Functor/7.1.7 The Reader Functor.fsx b/docs/category-theory/ctfp-dotnet/7 Functor/7.1.7 The Reader Functor.fsx deleted file mode 100644 index 31d59a2b..00000000 --- a/docs/category-theory/ctfp-dotnet/7 Functor/7.1.7 The Reader Functor.fsx +++ /dev/null @@ -1,9 +0,0 @@ -type Functor<'r, 'a> = ('r -> 'a) - -module Functor = - let map (f:'a -> 'b) (g:Functor<'r, 'a>) : Functor<'r, 'b> = f << g - -module Functor2 = - let map = (<<) - -Functor.map id id 1 = Functor2.map id id 1 // We have \ No newline at end of file diff --git a/docs/category-theory/ctfp-dotnet/7 Functor/7.2 Functors as Containers.csx b/docs/category-theory/ctfp-dotnet/7 Functor/7.2 Functors as Containers.csx deleted file mode 100644 index 9e20b4ce..00000000 --- a/docs/category-theory/ctfp-dotnet/7 Functor/7.2 Functors as Containers.csx +++ /dev/null @@ -1,38 +0,0 @@ -//Infinite List. -using System; -using System.Collections.Generic; -using System.Linq; - -static class EnumerableExtension -{ - public static IEnumerable InitInfinite(Func f) - { - int counter = 0; - while (true) - { - yield return f(counter); - counter++; - } - } -} - -var x = EnumerableExtension.InitInfinite(x=>x).Take(2).ToList(); - -x.SequenceEqual(new List { 0, 1 }); //true - -class Const -{ - public C Value { get; } - public Const(C v) => Value = v; -} -class Const : Const -{ - public Const(C v) : base(v) { } -} - -static class Const -{ - //"fmap is free to ignore its function upon" - static Const fmap(Func _, Const x) => new Const(x.Value); -} - diff --git a/docs/category-theory/ctfp-dotnet/7 Functor/7.2 Functors as Containers.fsx b/docs/category-theory/ctfp-dotnet/7 Functor/7.2 Functors as Containers.fsx deleted file mode 100644 index 2603c342..00000000 --- a/docs/category-theory/ctfp-dotnet/7 Functor/7.2 Functors as Containers.fsx +++ /dev/null @@ -1,13 +0,0 @@ -// Infinite seq - -let x = Seq.initInfinite id - -x |> Seq.take 2 |> Seq.toList = [ 0; 1 ] - -// Const : demo where value inside the functor is not important. - -type Const<'c, 'a> = Const of 'c - -module Const = - //"fmap is free to ignore its function upon" - let fmap ((_:'a -> 'b), ((Const v):Const<'c, 'a>)) : Const<'c, 'b> = Const (v) \ No newline at end of file diff --git a/docs/category-theory/ctfp-dotnet/7 Functor/7.3 Functor Composition.csx b/docs/category-theory/ctfp-dotnet/7 Functor/7.3 Functor Composition.csx deleted file mode 100644 index e66fc6e2..00000000 --- a/docs/category-theory/ctfp-dotnet/7 Functor/7.3 Functor Composition.csx +++ /dev/null @@ -1,48 +0,0 @@ -using System; -using System.Collections.Generic; -using System.Linq; - -interface Maybe { } -class Nothing : Maybe -{ - public Nothing() { } -} - -class Just : Maybe -{ - public T Value { get; } - public Just(T v) => Value = v; -} - -static class Maybe -{ - public static Maybe map(Func f, Maybe x) - { - switch (x) - { - case Nothing _: return (Maybe)new Nothing(); - case Just j: return new Just(f(j.Value)); - } - throw new NotImplementedException("absurd"); - } -} - -static class ListExtension -{ - public static Maybe> tryTail(List l) - { - if (l.Any()) return new Just>(l.Skip(1).ToList()); - else return new Nothing>(); - } - - //As you may notice Select is the equivalent of map. - //The keyword is inspired by the SQL syntax but behind it is a monad - public static List map(Func f, List x) => x.Select(f).ToList(); -} - -Maybe> nothing = ListExtension.tryTail(new List()); -var just = ListExtension.tryTail(new List { 1, 2 }); - -Maybe.map(x => ListExtension.map(y => $"my value is {y}", x), just); //"my value is 2" -Maybe.map(x => ListExtension.map(y => $"my value is {y}", x), nothing); //Nothing - diff --git a/docs/category-theory/ctfp-dotnet/7 Functor/7.3 Functor Composition.fsx b/docs/category-theory/ctfp-dotnet/7 Functor/7.3 Functor Composition.fsx deleted file mode 100644 index 5d1c2531..00000000 --- a/docs/category-theory/ctfp-dotnet/7 Functor/7.3 Functor Composition.fsx +++ /dev/null @@ -1,21 +0,0 @@ -//Maybe + List - -type Maybe<'a> = Nothing | Just of 'a - -module Maybe = - let map f = function Nothing -> Nothing | Just x -> Just (f x) - -module List = - let maybeTail = function [] -> Nothing | _::tail -> Just tail - let tryTail = function [] -> None | _::tail -> Some tail - - -[] |> List.maybeTail |> Maybe.map (List.map (sprintf "my value is %i")) //Nothing - -[1] |> List.maybeTail |> Maybe.map (List.map (sprintf "my value is %i")) //Just [] -[1;2] |> List.maybeTail |> Maybe.map (List.map (sprintf "my value is %i")) //Just ["my value is 2"] - -//In fsharp you can use Option in place of Maybe like this : - -[1] |> List.tryTail |> Option.map (List.map (sprintf "my value is %i")) //Some [] -[1;2] |> List.tryTail |> Option.map (List.map (sprintf "my value is %i")) //Some ["my value is 2"] \ No newline at end of file diff --git a/docs/category-theory/ctfp-dotnet/7 Functor/README.md b/docs/category-theory/ctfp-dotnet/7 Functor/README.md deleted file mode 100644 index 04a170bf..00000000 --- a/docs/category-theory/ctfp-dotnet/7 Functor/README.md +++ /dev/null @@ -1,121 +0,0 @@ -# 7 Functor - -## 7.1.1 The Maybe Functor - -### Personal Notes - -In .Net there is the nullable equivalent for value type. For reference type we have to wait https://github.com/dotnet/csharplang/wiki/Nullable-Reference-Types-Preview. -But you can still build your own with FSharp.Core option type or a Maybe one. - -By using it you will see that the custom ```?``` operator is useless when you define fmap and so on.. But it is an another story.. - -In Fsharp, Option type is the equivalent of the Maybe type. - -## 7.1.2 Equational Reasoning - -Read the chapter. To summarize, equality is important when you want to prove thing except when your function uses side effect. - -Those equalities have been use in 7.1.1 scripts. - -## 7.1.3 Optional - -As always read it. The author explains very well what we try to implement in 7.1.1 for csx script. - -## 7.1.4 Typeclasses (Mostly Personal notes) - -```Haskell -class Functor f where - fmap :: (a -> b) -> f a -> f b -``` - -Type classes does not exists in .Net. -The C++ equivalent is template-template whereas there is no generic-generic or generic of generic. -This is a limitation of .Net. - -If you want to see an equivalent, you should read the chapter 7.1.5 Functor in C++. - -Even if type classes were available in .Net, we could not implement Functor as is. -We need a feature called type constructor which is generic-generic dependent. -In the given definition of functor ```f a``` means ```f``` where ```f``` and ```a``` are generics. - -To implement properly Functor type classes we need 3 things in order : - - 1/ [Types classes or Trait](https://github.com/fsharp/fslang-suggestions/issues/243) - - 2/ [Generic of Generic](https://github.com/dotnet/csharplang/issues/339) - - 3/ [Type constructor](https://github.com/fsharp/fslang-suggestions/issues/243#issuecomment-260186368) - -[FStan](https://github.com/thautwarm/FSTan/blob/master/README.md) is an excellent alternative. -You can still use abtract class and interface and made static things by defining some functions in a prelude class/module and you have type classes after all. -But you may consider that this abstraction has a cost at runtime. - -### Deal with it - -In .Net you don't have type classes stricly checked by the compiler but you can use implicitly. -To do it right, you should check the Haskell wiki : https://wiki.haskell.org/File:Typeclassopedia-diagram.png - -For example : it is easy to traverse structure through fold because a foldable monoid is traversable. -You can fold the monoid (mempty and mappend) first and transform it to another type like the aggregate function does with list. - -If you build types by following the typeclassopedia rules, you have the benefits of the type composition property. - -The aim of the book is to understand Category theory through a programming lang. -I guess it is not very important to have type classes. -We can just continue with csharp and fsharp by following the rules. - -In fsharp modules there is no type classes but fmap (map) is available on mostly all modules. -You can follow the same rules in your domain as substitution of type classes as an informal way. - -### No Silver Bullet (Very personal but not offensive notes :)) - -I often see questions like : What is the best FP lang ? And there is a lots of answer (Scala is better, Fsharp, Haskell, Rust and so on..). -I think it is a very personal choice dependending or OUR context and it works fine. -But if you think that your FP lang is the best, did you try to use it in a completely different context ? - -Let's check that we have [No Silver Bullet](https://en.wikipedia.org/wiki/No_Silver_Bullet) - -- Haskell is pure and well constructed thanks to functional pattern by design. -- FSharp is hybrid and bring functional first language to .Net ecosystem which Haskell can't (but some project try to do it : https://wiki.haskell.org/Common_Language_Runtime).. -- Scala is the same as FSharp to Java except that they bring types classes and type constructor but it is [not perfect](https://github.com/lampepfl/dotty/issues/2047) due to the OOP model. [Sparkle](https://github.com/tweag/sparkle) uses jvm to use spark infrastructure with Haskell. -- Except FSharp, none of this functional programming offers type providers. I use/abuse it in my daily coding basis because I have to implement at least 200 apis (I work for a software editor with hundreds of partnerships). Even if you can use templates in Haskell, you may endup with some compiler limits. -- And there is a lots of langs : https://en.wikipedia.org/wiki/Functional_programming#Coding_styles - -So dependending of your context you may have to choose 1 or n FP lang and interop thanks to microservices to have the full power of functional programming. -I guess that context is very rare and honestly one per ecosystem (legacy) is ok. - -There is [Idris](https://www.idris-lang.org/) (maybe a future bronze bullet :)) (based on the Haskell ecosystem) which try to bring fsharp [type provider with dependent typing](http://www.davidchristiansen.dk/pubs/dependent-type-providers.pdf). - -If you want to go deeper with dependent typing after Category Theory for Programmers you should consider reading [The little typer](https://mitpress.mit.edu/books/little-typer), it blows my mind! - -Read the [Idris paper](http://www.davidchristiansen.dk/pubs/dependent-type-providers.pdf) 2.1 chapter which gives a definition of type provider better than fsharp! - -To see a concrete of the Deal With it pattern, jump to 7.1.6 List Functor. - -## 7.1.6 List Functor (Personal notes) - -Type classes does not exists in .Net and we have to deal with it and follow the rule of fsharp (to code like if we have type classes virtually/in mind). - -In fsharp list implementation, there is associated function definition of a type inside a module (ie: List module for 'a List). -The module follows the rules of the functor by defining a function map but the compiler can't check that for us. -We can opt for fsi file to check but it is manual and we have to copy the functor def on all modules. - -The structure of the type list is recursive. In .Net we have some issue when the method/function is not tail recursive, you may endup with a StackOverflow. -To avoid this, we defined the method that traverses the list structure in a tail recursive way (fold). - -## 7.1.7 The Reader Functor - -In fsharp we could define the reader functor by using the ```<<``` operator. - -## 7.2 Functors as Containers - -Read the chapter to have the full story. -Where .Net implements infinite with a state machine (implemented with goto and mutation). -Haskell use a function (with closure) and eval it when we need the value (this is why Haskell is lazy). -Haskell is lazy by default, you can build an infinite list when a fsharp list is finite. -Seq, alias of .net IEnumerable uses lazy with yield keyword / seq computation expression. -Like Haskell you can't compute the length of an infinite list of values. - -## 7.3 Functor Composition - -How to traverse Functor^2 ? By traversing it with map twice (one for maybe and one for list)! diff --git a/docs/category-theory/ctfp-dotnet/8 Functoriality/8.1 Bifunctors.csx b/docs/category-theory/ctfp-dotnet/8 Functoriality/8.1 Bifunctors.csx deleted file mode 100644 index e69de29b..00000000 diff --git a/docs/category-theory/ctfp-dotnet/8 Functoriality/8.1 Bifunctors.fsx b/docs/category-theory/ctfp-dotnet/8 Functoriality/8.1 Bifunctors.fsx deleted file mode 100644 index c2f5b264..00000000 --- a/docs/category-theory/ctfp-dotnet/8 Functoriality/8.1 Bifunctors.fsx +++ /dev/null @@ -1,16 +0,0 @@ -type BiFunctor<'a, 'b> = BiFunctor of ('a * 'b) - -module BiFunctor = - let bimap g h (BiFunctor x) = (x |> fst |> g, x |> snd |> h) |> BiFunctor - let first g = bimap g id - let second h = bimap id h - -let x = BiFunctor (1,2) - -BiFunctor.bimap id id x = x //true -BiFunctor.first id x = x //true -BiFunctor.second id x = x //true - -BiFunctor.bimap string string x = BiFunctor ("1", "2") //true -BiFunctor.first string x = BiFunctor ("1", 2) //true -BiFunctor.second string x = BiFunctor (1, "2") //true diff --git a/docs/category-theory/ctfp-dotnet/8 Functoriality/8.2 Product and Coproduct Bifunctors.fsx b/docs/category-theory/ctfp-dotnet/8 Functoriality/8.2 Product and Coproduct Bifunctors.fsx deleted file mode 100644 index a489521d..00000000 --- a/docs/category-theory/ctfp-dotnet/8 Functoriality/8.2 Product and Coproduct Bifunctors.fsx +++ /dev/null @@ -1,13 +0,0 @@ -type Either<'a, 'b> = Left of 'a | Right of 'b - -module Either = - let bimap f g = function - | Left x -> Left (f x) - | Right y -> Right (g y) - -let l = Left 1 -let r = Right "hello" - -Either.bimap id id l = l //true -Either.bimap id id r = r //true - diff --git a/docs/category-theory/ctfp-dotnet/8 Functoriality/8.3 Functorial Algebraic Data Types.fsx b/docs/category-theory/ctfp-dotnet/8 Functoriality/8.3 Functorial Algebraic Data Types.fsx deleted file mode 100644 index d0e8a46c..00000000 --- a/docs/category-theory/ctfp-dotnet/8 Functoriality/8.3 Functorial Algebraic Data Types.fsx +++ /dev/null @@ -1,64 +0,0 @@ -//Type classes workaround for fmap : use statically resolved type -let inline fmap< ^a, ^b, ^c, ^d when ^a : (static member fmap: (^b -> ^c) * ^a -> ^d) > f (x:^a) : ^d = - (^a : (static member fmap: (^b -> ^c) * ^a -> ^d) (f,x)) - -// You can use operator which is less brainer to define. -// Here, in fsharp map (map is widely used) is fmap but in haskell map is reserved for list. -let inline map f x = f x - -type Maybe<'a> = Nothing | Just of 'a - with - static member fmap (f, x) = match x with Nothing -> Nothing | Just x' -> Just (f x') - static member () (f, (x:Maybe<'a>)) = Maybe<'a>.fmap (f, x) - -//Curried Version of Maybe functions -module Maybe = - let map f (x:Maybe<'a>) = Maybe<'a>.fmap(f, x) - -//Behind, the maybe should have the uncurried one.. -fmap (id) (Just 1) = Just 1 - -id (Just 1) = Just 1 - -let inline bimap< ^a, ^b, ^c, ^d, ^e, ^f when ^a : (static member bimap: (^b -> ^c) * (^d -> ^e) * ^a -> ^f) > f g (x:^a) : ^f = - (^a : (static member bimap: (^b -> ^c) * (^d -> ^e) * ^a -> ^f) (f,g,x)) - -type Either<'a, 'b> = Left of 'a | Right of 'b - with static member bimap (f,g,x) = - match x with - | Left x -> Left (f x) - | Right y -> Right (g y) - -bimap id id (Left 5) = Left 5 - -type Const<'c, 'a> = Const of 'c - with static member fmap ((_:'a -> 'b), ((Const v):Const<'c, 'a>)) : Const<'c, 'b> = Const v - -type Identity<'a> = Identity of 'a - with static member fmap (f, Identity x) = Identity (f x) - -type BiComp<'a> = BiComp of 'a - -module BiComp = - let inline bimap f1 f2 (BiComp x) = BiComp ((bimap (fmap f1) (fmap f2)) x) - -module Maybe2 = - let inline just (x:'a) : Either, Identity<'a>> = Right (Identity x) - -BiComp (Maybe2.just 2) |> BiComp.bimap id id = BiComp (Right (Identity 2)) //true - - -//Personal example : the traverse one : -module Identity = - let map f (Identity x) = Identity (f x) - -module Const = - let map (_:'a->'b) ((Const v):Const<'c, 'a>) : Const<'c, 'b> = Const v - -module Either = - let bimap f g x = - match x with - | Left l -> Left (f l) - | Right r -> Right (g r) - -BiComp (Maybe2.just 2) |> (fun (BiComp x) -> Either.bimap (Const.map ignore) (fun x -> Identity.map id x) x) |> BiComp = BiComp (Right (Identity 2)) //true diff --git a/docs/category-theory/ctfp-dotnet/8 Functoriality/8.4 Functors in C#.csx b/docs/category-theory/ctfp-dotnet/8 Functoriality/8.4 Functors in C#.csx deleted file mode 100644 index 89e33bb5..00000000 --- a/docs/category-theory/ctfp-dotnet/8 Functoriality/8.4 Functors in C#.csx +++ /dev/null @@ -1,94 +0,0 @@ -using System; - -static class BiFunctor -{ - static ValueTuple bimap(Func f, Func g, ValueTuple x) - { - var (y, z) = x; - return (f(y), g(z)); - } -} - -interface Tree { } - -class Node : Tree -{ - public Tree Left { get; } - public Tree Right { get; } - - public Node(Tree left, Tree right) - { - Left = left; - Right = right; - } -} - -class Leaf : Tree -{ - public T Value { get; } - - public Leaf(T value) - { - Value = value; - } -} - -static class TreeExtension -{ - public static Tree map (Func f, Tree x) - { - switch (x) - { - case Leaf l : return new Leaf(f(l.Value)); - case Node n : - return new Node(map(f, n.Left), map(f, n.Right)); - } - throw new NotImplementedException("absurd"); - } - - public static Tree tree(int depth) - { - Tree build(int d, Tree r) - { - if (d == 0) return r; - else return build(d - 1, new Node(new Leaf(d), r)); - } - return build(depth, new Leaf(depth)); - } -} - -var t1 = TreeExtension.tree(100000); //it works on console app not in csharp interactive. - -var r = map(x => x, t1); //It fail with StackOverflow even if your are in release x64. - -var t11 = TreeExtension.tree(10); //with less depth it works - -//For a better experience, see the fsharp one in with taicall optimization. - -//Personal notes, this is the tree structure for x64 release mode in csharp. For fsharp this implementation works perfectly. - -class OptimizedNode : Tree -{ - public T Head { get; } - public Tree Tail { get; } - - public OptimizedNode(T head, Tree tail) - { - Head = Head; - Tail = tail; - } -} - -Tree tree(int depth) -{ - Tree build(int d, Tree r) - { - if (d == 0) return r; - else return build(d - 1, new OptimizedNode(d, r)); - } - - return build(depth, new Leaf(depth)); -} - -var t2 = tree(1000000); //this works on app console with release x64. - diff --git a/docs/category-theory/ctfp-dotnet/8 Functoriality/8.4 Functors in F#.fsx b/docs/category-theory/ctfp-dotnet/8 Functoriality/8.4 Functors in F#.fsx deleted file mode 100644 index a9fafa80..00000000 --- a/docs/category-theory/ctfp-dotnet/8 Functoriality/8.4 Functors in F#.fsx +++ /dev/null @@ -1,51 +0,0 @@ -type Tree<'a> = Leaf of 'a | Node of Tree<'a> * Tree<'a> - -module BiFunctor = - let bimap f g (x, y) = (f x, g y) - -module Tree = - //Not a production code. - let rec map f = function - | Leaf x -> Leaf (f x) - | Node (t1,t2) -> Node (BiFunctor.bimap (map f) (map f) (t1, t2)) - -let tree depth = - let rec build depth r = - if depth = 0 then r - else build (depth - 1) (Node (r, Leaf depth)) - build depth (Leaf depth) - -let t = tree 100000 - -Tree.map id t //Process is terminated due to StackOverflowException. Like said the book, this code is not optimized. - -//Personal notes -//Here is an optimized tree structure with head and tail structure on Node case. -type OptimizedTree<'a> = Leaf of 'a | Node of 'a * OptimizedTree<'a> - -module OptimizedTree = - //This function make traversable possible with tailcall optimization - let rec fold folder state = function - | Leaf l -> folder state l - | Node (v, t) -> - //This is a tail call. Here we don't have 2 tree to map. - //We can fold the left value and continue to fold only on right. - fold folder (folder state v) t - - //reuse fold for map with head as neutral because Tree should have at least one Leaf. - let map f = function - | Leaf l -> Leaf (f l) - | Node (v, t) -> fold (fun state x -> Node (f x, state)) (Leaf v) t - - let reverse t = map id t - -let tree2 depth = - let rec build depth r = - if depth = 0 then r - else build (depth - 1) (Node (depth, r)) - build depth (Leaf depth) - -let t2 = tree2 100000 - -//We have to reverse the tree because fold/map reverse the order -OptimizedTree.map id t2 |> OptimizedTree.reverse = t2 //true with stack overflow. diff --git a/docs/category-theory/ctfp-dotnet/8 Functoriality/8.5 The Writer Functor.fsx b/docs/category-theory/ctfp-dotnet/8 Functoriality/8.5 The Writer Functor.fsx deleted file mode 100644 index 1f843a56..00000000 --- a/docs/category-theory/ctfp-dotnet/8 Functoriality/8.5 The Writer Functor.fsx +++ /dev/null @@ -1,15 +0,0 @@ -type Writer<'a> = Writer of 'a * string - -module Writer = - let (>=>) f g = - fun x -> - let (Writer (y, s1)) = f x - let (Writer (z, s2)) = g y - Writer (z, s1 + s2) - - let ret x = Writer (x, "") - let fmap f = id >=> (f >> ret) - -let w1 = Writer.ret 1 -let w2 = Writer.ret 2 - diff --git a/docs/category-theory/ctfp-dotnet/8 Functoriality/8.6 Covariant and Contravariant Functors.fsx b/docs/category-theory/ctfp-dotnet/8 Functoriality/8.6 Covariant and Contravariant Functors.fsx deleted file mode 100644 index 9aaf5c82..00000000 --- a/docs/category-theory/ctfp-dotnet/8 Functoriality/8.6 Covariant and Contravariant Functors.fsx +++ /dev/null @@ -1,30 +0,0 @@ -type Reader<'r, 'a> = 'r -> 'a - -let fmap f g = f << g - -type Op<'r, 'a> = 'a -> 'r - -// Introduction of opposite (Contravariant functor) : Impossible to implement the following fmap without it. -// We have to found an opposite Functor of 'a -> 'b to 'b -> 'a. -module Op = - let fmap (f:'a -> 'b) (x:'a -> 'r) : ('b -> 'r) = - failwith "not yet implemented" - -module Contravariant = - let flip f y x = f x y - let contramap f g = flip (<<) f g - -let isEven x = x % 2 = 0 -let headIsEven = Contravariant.contramap List.head isEven -headIsEven [0..10] - -//Contravariant Functor (map input) is an Opposite Covariant Functor (map output). - -//Personal notes : - -//The (>>) operator is the opposite of (<<) operator ? - -open Contravariant - -let f = (contramap List.head) >> (contramap isEven) -f [0..10] diff --git a/docs/category-theory/ctfp-dotnet/8 Functoriality/README.md b/docs/category-theory/ctfp-dotnet/8 Functoriality/README.md deleted file mode 100644 index 0773c1f6..00000000 --- a/docs/category-theory/ctfp-dotnet/8 Functoriality/README.md +++ /dev/null @@ -1,49 +0,0 @@ -# 8 Functoriality - -## 8.1 Bifunctors (Personal note) - -In this sample, fsharp style has been used: define a type (BiFunctor) and define associated functions inside a module (BiFunctor). -In fsharp, all primitives are organized like this. - -## 8.2 Product and Coproduct Bifunctors - -To define a set as a monoidal category with respect to Cartesian product, This chapter explains very well how to define : - -- the binary operation (+ or mappend) as bifunctor -- and zero/mempty as unit ```()``` - -## 8.3 Functorial Algebraic Data Types - -### Personal notes - -In this sample, if we want to simulate a type class with fsharp style, we have to define a fmap function with [Statically Resolved Type Parameters](https://docs.microsoft.com/en-us/dotnet/fsharp/language-reference/generics/statically-resolved-type-parameters). -The question is when and why ? - -- When you want to compose types and reuse in depth function composition like : - ```newtype BiComp bf fu gu a b = BiComp (bf (fu a) (gu b))``` - - ```instance (Bifunctor bf, Functor fu, Functor gu) => Bifunctor (BiComp bf fu gu) where bimap f1 f2 (BiComp x) = BiComp ((bimap (fmap f1) (fmap f2)) x)``` - -The compiler chooses the best overloading of fmap and bimap. - -//Link : https://stackoverflow.com/questions/39065724/using-statically-resolved-type-parameters-is-it-possible-to-call-class-method-wi -The bad news : This approach does not work with curried functions.. It would be great if we have it to attach map functions defined in different modules (List, Option and so on..) -It is not possible to create those member in type Augmentation - -You can write this function case per case. Maybe there was one or two instance behind in the program and the traverse one is easier to write first. - -## 8.4 Functors in C++ (Personal notes) - -I will translate this example from C++ to F# and C# - -### BiFunctor / Production code ready - -I added a real production code for tree. The unoptimized is interesting to introduce the BiFunctor. -The main difference between an optimized one and a product one are : - -- Product is easy to build mappend with tuple but the traverse is [harder](https://hackage.haskell.org/package/bifunctors-5/docs/Data-Bifunctor.html#t:Bifunctor) : you need [clown](https://hackage.haskell.org/package/bifunctors-5/docs/Data-Bifunctor-Clown.html#t:Clown) and [joker](https://hackage.haskell.org/package/bifunctors-5/docs/Data-Bifunctor-Joker.html#t:Joker) -- Head and tail : fold is easy to write but the mappend is harder because you don't have product and bifunctor to do it quickly. - -### C# (Personal notes) - -I translate the product one to use a bifunctor and the optimized one but the csharp interactive is quite limited. See the fsharp one to have a full interactive experience. diff --git a/docs/category-theory/ctfp-dotnet/LICENSE b/docs/category-theory/ctfp-dotnet/LICENSE deleted file mode 100644 index b1753e22..00000000 --- a/docs/category-theory/ctfp-dotnet/LICENSE +++ /dev/null @@ -1,21 +0,0 @@ -MIT License - -Copyright (c) 2018 @cboudereau - -Permission is hereby granted, free of charge, to any person obtaining a copy -of this software and associated documentation files (the "Software"), to deal -in the Software without restriction, including without limitation the rights -to use, copy, modify, merge, publish, distribute, sublicense, and/or sell -copies of the Software, and to permit persons to whom the Software is -furnished to do so, subject to the following conditions: - -The above copyright notice and this permission notice shall be included in all -copies or substantial portions of the Software. - -THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR -IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, -FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE -AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER -LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, -OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE -SOFTWARE. diff --git a/docs/category-theory/ctfp-dotnet/README.md b/docs/category-theory/ctfp-dotnet/README.md deleted file mode 100644 index 8a036c9c..00000000 --- a/docs/category-theory/ctfp-dotnet/README.md +++ /dev/null @@ -1,22 +0,0 @@ -# category-theory-for-dotnet-programmers - -This repo contains c++ / haskell samples from Bartosz Milewski's book ([Category Theory for Programmers](https://bartoszmilewski.com/2014/10/28/category-theory-for-programmers-the-preface/)) converted to csharp and fsharp - -## Why - -If you are curious about functional programming with dotnet background, you already may know [Domain modeling made functional](https://pragprog.com/book/swdddf/domain-modeling-made-functional) that could help you to build your first functional programming based app. -The [Category Theory for programmers](https://bartoszmilewski.com/2014/10/28/category-theory-for-programmers-the-preface/), is quite interresting for programmers having a first experience in fsharp or csharp (in .net) who want to use Haskell or enhance their FSharp implementation. - -Fsx and Csx are scripts files executed respectively into Fsharp interactive and Csharp interactive shipped with Visual Studio Community at least. - -/!\ There is a problem with csx : to transform statement as expression (to display the value) you have to not ending your line with ';' causing compilation error on multiple line. -If you encounter compilation error on csx, try to execute it line by line. If the code does not compile send a PR or a message. - -# How to use it ? - -Read the [Category Theory for Programmers](https://bartoszmilewski.com/2014/10/28/category-theory-for-programmers-the-preface/) and the annotations corresponding to the chapter into vs code or visual studio. - -You can use it like a sandbox and try by yourself Challenges (challenges are not translated for more fun ;)). Only Haskell/C++ samples are translated. - -I will try to add converted examples constantly but pull requests are accepted. -The format is pretty simple, one folder per each chapter and 2 scripts (fsharp and csharp) inside. diff --git a/docs/category-theory/ctfp-milewski.pdf b/docs/category-theory/ctfp-milewski.pdf deleted file mode 100644 index 9bf2daee3ce53c88633824f9532a0158aaa92ed9..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 16455417 zcmc$_WpE|Ewk2pN(=ofuY?qmt*=4rN%v5G(W@ctOW@ct)W|x_nnQ`iS@nZVDzPEci zCMII?he9c3NEutXmX`M3Nh6+pUween$7BxE48(KiS1@X(8zSvnfo(~DZ_ zIU4;mGO#f;qL((ZHgPm1Wa4Dx;{!N2+8gOv0bEy&X*_`94C+S=lS$K6a!W-fv-o_V;~&6mA}RTdwc6*Fg+D_Ta=f zi7>!SUJSp3S3aUTLcou*Rc;NVH_>tiZUyjTE^ZYd!%?G`49_IHjmHi-dbd`3pUUX+{c#FrJN;nHkFLlfPDoYyyOv#KSg@^@Tn6hZwjtIQ)qJ;sd#JJB&oSr zG#}T5O>pW>yO)}o-MLR?kNc4@WSjI&hVmk{uUCgR_N(6b9FuvZBSjV(jF^>ew9`k% z!E9vtAN7JE07lk^|7oqiwSUaZ#P~n#{GUc;WMX9bcQ#jYvo)eulhrpjGH|34k)BTs0Z~j>*afU}e*$m(g>yH*?keXBGy+|0uQT6^tBgoa_yZ 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