├── .gitignore
├── CNAME
├── dune-project
├── styles
├── _intro.scss
├── _canvas.scss
├── _aside.scss
├── _status.scss
├── _list.scss
├── _footer.scss
├── _semantics.scss
├── _resources.scss
├── _om.scss
├── _code.scss
├── _header.scss
├── _index.scss
├── mathjax.js
├── _stack.scss
├── _exe.scss
├── _types.scss
└── main.scss
├── dune
├── TODO
├── src
├── dune
├── error.ml
├── parser.mly
├── expr.ml
├── lexer.mll
├── alonzo.ml
└── stlc.ml
├── .gitattributes
├── CHANGELOG
├── lib
├── bool.alonzo
└── nat.alonzo
├── footer.pug
├── alonzo.opam
├── README.md
├── package.json
├── highlight.js
├── LICENSE
├── framework.js
├── header.pug
├── index.pug
├── main.css
└── bundle.js
/.gitignore:
--------------------------------------------------------------------------------
1 | _build/
2 |
--------------------------------------------------------------------------------
/CNAME:
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1 | alonzo.groupoid.space
2 |
--------------------------------------------------------------------------------
/dune-project:
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1 | (lang dune 2.9)
2 | (using menhir 2.1)
3 |
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/styles/_intro.scss:
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1 | .intro {
2 | width: 650px;
3 | max-width: 100%;
4 | margin: auto;
5 | }
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/styles/_canvas.scss:
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1 | canvas {
2 | max-width: 100%;
3 | position: absolute;
4 | z-index: -10;
5 | }
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/dune:
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1 | (env (dev (flags (:standard -warn-error -A))))
2 | (install (files lib/bool.alonzo lib/nat.alonzo) (section share) (package alonzo))
3 |
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/TODO:
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1 | # TODO
2 |
3 | * Better Errors
4 | * Function Equality
5 | * Empty, Unit, Product
6 | * Bool, Nat
7 | * Semantics (CCC)
8 | * PDF paper
9 |
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/src/dune:
--------------------------------------------------------------------------------
1 | (ocamllex lexer)
2 | (menhir (modules parser))
3 | (executable (name alonzo) (libraries dynlink zarith unix) (package alonzo) (public_name alonzo))
4 |
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/styles/_aside.scss:
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1 | aside {
2 | max-width: 650px;
3 | margin: auto;
4 | padding: 8px;
5 | font-size: 20px;
6 | text-align: right;
7 | time, div {
8 | margin-bottom: 20px;
9 | display: block;
10 | }
11 | }
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/.gitattributes:
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1 | *.js linguist-detectable=false
2 | *.pug linguist-detectable=false
3 | *.css linguist-detectable=false
4 | *.scss linguist-detectable=false
5 | *.tex linguist-detectable=false
6 | *.sh linguist-detectable=false
7 | *.html linguist-detectable=false
8 | *.htm linguist-detectable=false
9 |
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/styles/_status.scss:
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1 | .status {
2 | text-align: left;
3 | display: inline-block;
4 | padding-left: 32px;
5 |
6 | ol {
7 | line-height: 1.5;
8 | font-size: 18px;
9 | @media(min-width: 768px) {
10 | font-size: 22px;
11 | }
12 | }
13 |
14 | }
--------------------------------------------------------------------------------
/CHANGELOG:
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1 | Changelog
2 | =========
3 |
4 | 5 APR 2022 Version 0.4.0 Church Encoding:
5 |
6 | * Bool and Nat terms
7 | * Pure Core of Simply Typed Lambda Calculus in 100 LOC
8 | * Parser in 15 LOC
9 | * Lexer in 35 LOC
10 |
11 | 2 JUN 2025 Version 3.6.0 STLC Implementation
12 |
13 | * Added stlc.ml as alternative implementation
14 |
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/styles/_list.scss:
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1 | .list {
2 | h1 {
3 | color: #7D8A96;
4 | font-size: 32px;
5 | text-transform: uppercase;
6 | border-bottom: 1px solid rgba(0, 0 , 0,0.3);
7 | display: inline-block;
8 | margin: 42px 8px 10px;
9 | @media(min-width: 768px) {
10 | font-size: 40px;
11 | }
12 | }
13 | }
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/lib/bool.alonzo:
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1 | -- STLC
2 |
3 | #eval λ (x: T), x : T → T
4 | #eval (λ (x: T → T),x) (λ (y: T), y) : T → T
5 |
6 | abbrev bool := T → T → T
7 | abbrev bool_to_bool := bool → bool
8 | def true : bool := λ (x: T), λ (y:T), x
9 | def false : bool := λ (x: T) (y: T), y
10 |
11 | #eval λ (t: T) (f: T), true t f : bool
12 | #eval λ (t: T) (f: T), false t f : bool
13 | #eval (λ (x: bool_to_bool), x) (λ (y: bool), y) : bool_to_bool
14 |
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/footer.pug:
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1 | link(rel='stylesheet' href='https://groupoid.space/main.css')
2 |
3 | footer.footer
4 | a(href='https://5HT.co/license/')
5 | img.footer__logo(src='https://longchenpa.guru/seal.png',width=50)
6 | span.footer__copy 2015—2025 © Олег Мараховський
7 | script(src='https://groupoid.space/highlight.js?v=1')
8 | script(src='https://groupoid.space/bundle.js')
9 |
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/styles/_footer.scss:
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1 | .footer {
2 | width: 100%;
3 | padding: 15px;
4 | background: #7F8C8D;
5 | color: white;
6 | text-align: center;
7 |
8 | &__logo {
9 | width: 50px;
10 | margin: 20px;
11 | }
12 |
13 | &__copy {
14 | font-size: 16px;
15 | white-space: pre;
16 | }
17 | @media(min-width: 768px) {
18 | &__copy {
19 | font-size: 24px;
20 | }
21 | }
22 | }
23 |
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/lib/nat.alonzo:
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1 | -- STLC
2 |
3 | def zero : (T → T) → T → T := λ (s: T → T) (z: T),z
4 | def one : (T → T) → T → T := λ (s: T → T) (z: T), s z
5 | def two : (T → T) → T → T := λ (s: T → T) (z: T), s (s z)
6 | def three : (T → T) → T → T := λ (s: T → T) (z: T), s (s (s z))
7 |
8 | def succ : ((T → T) → T → T) → ((T → T) → T → T)
9 | := λ (w: (T → T) → T → T) (y: T → T) (x: T), y (w y x)
10 |
11 | #eval succ zero : (T → T) → T → T
12 | #eval succ one : (T → T) → T → T
13 | #eval succ two : (T → T) → T → T
14 |
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/alonzo.opam:
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1 | opam-version: "2.0"
2 | name: "alonzo"
3 | version: "0.4.0"
4 | maintainer: "Namdak Tönpa "
5 | authors: [ "Oleh Marakhovskyi @jealrock" ]
6 | homepage: "https://github.com/groupoid/alonzo"
7 | bug-reports: "https://github.com/groupoid/alonzo/issues"
8 | dev-repo: "git+https://github.com/groupoid/alonzo"
9 | synopsis: "STLC type system"
10 | license: "ISC"
11 | depends: [
12 | "dune" {>= "2.9"}
13 | "zarith" {>= "1.12"}
14 | "ocaml" {>= "4.14.0"}
15 | "menhir" {>= "20220210"}
16 | ]
17 | build: [ ["dune" "build" "-p" name "-j" jobs] ]
18 |
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/styles/_semantics.scss:
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1 | .semantics {
2 | text-align: center;
3 |
4 | figure {
5 | display: inline-block;
6 | max-width: min-content;
7 | font-size: 13px;
8 | @media(min-width:800px) {
9 | font-size: 16px;
10 | }
11 | }
12 |
13 | h1 {
14 | color: #7D8A96;
15 | font-size: 32px;
16 | text-transform: uppercase;
17 | border-bottom: 1px solid rgba(0, 0 , 0,0.3);
18 | display: inline-block;
19 | margin-bottom: 8px;
20 | }
21 |
22 | section {
23 | margin-top: 40px;
24 | }
25 | }
26 |
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/styles/_resources.scss:
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1 | .resources {
2 |
3 | max-width: 650px;
4 | margin: 32px auto 0;
5 | text-align: left;
6 | padding: 8px;
7 |
8 | &__title {
9 | display: inline-block;
10 | margin-bottom: 10px;
11 | color: #7D8A96;
12 | font-size: 32px;
13 | text-transform: uppercase;
14 | border-bottom: 1px solid rgba(0, 0 , 0,0.3);
15 | @media(min-width: 768px) {
16 | font-size: 40px;
17 | }
18 | }
19 | &__list {
20 | padding-left: 32px;
21 | line-height: 1.5;
22 | font-size: 18px;
23 | @media(min-width: 768px) {
24 | font-size: 22px;
25 | }
26 | }
27 | }
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/README.md:
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1 | # Alonzo
2 |
3 | 
4 |
5 | Alonzo is a STLC type system written in OCaml.
6 |
7 | ## Build
8 |
9 | ```shell
10 | $ dune build
11 | $ dune exec alonzo lib/nat.alonzo
12 | ```
13 |
14 | ## STLC
15 |
16 | * A Formulation of the Simple Theory of Types [Church]
17 | * An Overview of Type Theories [Guallart]
18 | * Category Theory and Lambda Calculus [García]
19 |
20 | ## Credits
21 |
22 | * Oleh Marakhovskyi
23 |
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/styles/_om.scss:
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1 | .om {
2 |
3 | figure {
4 | max-width: inherit;
5 | }
6 |
7 | section {
8 | h1 {
9 | margin-top: 50px;
10 | }
11 | }
12 |
13 | h1 {
14 | color: #7D8A96;
15 | font-size: 32px;
16 | text-transform: uppercase;
17 | border-bottom: 1px solid rgba(0, 0 , 0,0.3);
18 | display: inline-block;
19 | margin-bottom: 32px;
20 | @media(min-width: 768px) {
21 | font-size: 40px;
22 | }
23 | }
24 |
25 | h1 + h2 {
26 | margin-top: 20px;
27 | }
28 |
29 | h3 {
30 | max-width: 100%;
31 | margin: auto;
32 | width: 600px;
33 | padding: 16px 8px 0;
34 | }
35 | }
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/src/error.ml:
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1 | open Expr
2 |
3 | exception Parser of int * int * string
4 | exception UnboundVariable of name
5 | exception Type of typexp * typexp
6 | exception Application of exp * typexp * exp * typexp
7 |
8 | let print_error : exn -> unit = function
9 | | UnboundVariable var -> Printf.printf "Unbound variable: %s\n" var
10 | | Type (expected, actual) -> Printf.printf "Types don't match.\n Expected: %s\nActual: %s\n" (t_to_s expected) (t_to_s actual)
11 | | Application (e1, te1, e2, te2) -> Printf.printf "Can't apply %s:%s\nto %s:%s.\n" (e_to_s e1) (t_to_s te1) (e_to_s e2) (t_to_s te2)
12 | | ex -> Printf.printf "Uncaught exception: %s\n" (Printexc.to_string ex)
13 |
14 | let handle_errors (f : 'a -> 'b) (arg : 'a) : unit =
15 | try f arg with ex -> print_error ex; ()
16 |
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/package.json:
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1 | {
2 | "name": "alonzo",
3 | "version": "1.0.1",
4 | "description": "Groupoid Infinity Institute",
5 | "main": "",
6 | "scripts": {
7 | "start": "node-sass ./styles -o ./ && pug -O ./framework.js index.pug ",
8 | "test": "echo \"Error: no test specified\" && exit 1"
9 | },
10 | "repository": {
11 | "type": "git",
12 | "url": "https://github.com/groupoid/alonzo"
13 | },
14 | "author": "Namdak Tonpa",
15 | "license": "DHARMA",
16 | "preinstall": "npm i -g node-sass && npm i -g pug-cli",
17 | "dependencies": {
18 | "mathjax-full": "^3.2.0",
19 | "npm": "^8.12.1",
20 | "pug": "^3.0.2",
21 | "pug-cli": "^1.0.0-alpha6",
22 | "sass": "^1.52.2"
23 | },
24 | "devDependencies": {
25 | "node-sass": "^7.0.3"
26 | }
27 | }
28 |
--------------------------------------------------------------------------------
/src/parser.mly:
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1 | %{ open Expr %}
2 |
3 | %token IDENT
4 | %token LPARENS RPARENS
5 | %token COLON COMMA LAM ARROW DEF DEFEQ EVAL ABBREV
6 | %token EOF
7 |
8 | %right ARROW
9 | %start main
10 |
11 | %%
12 |
13 | typexp: IDENT { TVar $1 } | typexp ARROW typexp { TFun ($1, $3) } | LPARENS typexp RPARENS { $2 }
14 | param: LPARENS IDENT COLON typexp RPARENS { PVar ($2, $4) }
15 | params: param params { $1 :: $2 } | param { [$1] }
16 | exp: IDENT { EVar $1 } | LAM params COMMA exp { lam $2 $4 } | exp2 exp2+ { app $1 $2 } | LPARENS exp RPARENS { $2 }
17 | exp2: IDENT { EVar $1 } | LPARENS exp RPARENS { $2 }
18 | command: DEF IDENT COLON typexp DEFEQ exp { Decl ($2, $4, $6) } | ABBREV IDENT DEFEQ typexp { Abbr ($2, $4) } | EVAL exp COLON typexp { Eval ($2, $4) }
19 | main: command main { $1 :: $2 } | EOF { [] }
20 |
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/styles/_code.scss:
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1 | code {
2 | display: inline-block;
3 | overflow-x: auto;
4 | max-width: 100%;
5 | padding: 12px;
6 | margin: 8px 0;
7 | white-space: pre;
8 | text-align: left;
9 | border-radius: 4px;
10 | font-size: 14px;
11 | color: #00259c;
12 | background: white;
13 | box-shadow: 0 1px 4px #f1f0f0, inset 0 0 0 1px #e7e6e5;
14 | @media (min-width: 768px) {
15 | font-size: 17px;
16 | }
17 | }
18 |
19 | pre {
20 | white-space: normal;
21 | max-width: 100%;
22 | width: 650px;
23 | padding: 12px;
24 | margin: 8px auto;
25 | text-align: left;
26 | border-radius: 4px;
27 | font-size: 14px;
28 | color: #00259c;
29 | background: white;
30 | box-shadow: 0 1px 4px #f1f0f0, inset 0 0 0 1px #e7e6e5;
31 | @media (min-width: 768px) {
32 | font-size: 17px;
33 | }
34 | }
35 |
36 | .h__name {
37 | color: #00259c;
38 | font-weight: bold;
39 | }
40 |
41 | .h__keyword {
42 | color: #ca30d4;
43 | }
44 |
45 | .h__symbol {
46 | color: #9f9fa3;
47 | }
--------------------------------------------------------------------------------
/highlight.js:
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1 | function highlight() {
2 | var code = document.getElementsByTagName('code');
3 | for (var i = 0; i < code.length; i++) {
4 | code[i].innerHTML = code[i].innerHTML
5 | .replace(/([(){}→=]+|:|:=)/g,
6 | '$1')
7 | .replace(/\b(data|transp|∀|Π|Σ|λ|glue|unglue|Glue|hcomp|where|def|mutual|begin|end|module|import|option|false|true|indᵂ|sup|.1|.2|Σ|Π|Pi|Sigma|W|𝟎|𝟏|𝟐|ind₂|ind₁|ind₀|★|0₂|1₂|Path|PathP|Type|Prop|inductive|record|forall|fun|match|let|axiom|type|theorem|lemma|in|U|S|V)\b(?!:)/g,
8 | '$1');
9 | }
10 | }
11 |
12 | highlight();
13 |
14 | var lastScrollPosition = 0;
15 | var ticking = false;
16 |
17 | var titles = document.querySelector('.header__titles');
18 | var logo = document.querySelector('.header__logo');
19 | function doSomething(scrollPos) {
20 | titles.style.transform = 'translate3d(0px, ' + (scrollPos/2) + 'px, 0px)';
21 | logo.style.transform = 'translate3d(0px, ' + (scrollPos/2) + 'px, 0px)';
22 | }
23 |
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/src/expr.ml:
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1 | type name = string
2 |
3 | type typexp =
4 | | TVar of name
5 | | TFun of typexp * typexp
6 |
7 | type param =
8 | | PVar of name * typexp
9 |
10 | type exp =
11 | | ELam of param * exp
12 | | EApp of exp * exp
13 | | EVar of name
14 |
15 | type command =
16 | | Decl of name * typexp * exp
17 | | Abbr of name * typexp
18 | | Eval of exp * typexp
19 |
20 | let rec lam params exp =
21 | match params with
22 | | [] -> exp
23 | | x :: xs -> ELam (x, lam xs exp)
24 |
25 | let rec app f = function
26 | | [] -> f
27 | | x :: xs -> app (EApp (f, x)) xs
28 |
29 | let rec t_to_s (t : typexp): name :> string =
30 | match t with
31 | | TVar n -> n
32 | | TFun (t1, t2) -> Printf.sprintf "(%s→%s)" (t_to_s t1) (t_to_s t2)
33 |
34 | let p_to_s (p : param): name :> string =
35 | match p with
36 | | PVar (n, t) -> Printf.sprintf "(%s: %s)" n (t_to_s t)
37 |
38 | let rec e_to_s (exp: exp): name :> string =
39 | match exp with
40 | | ELam (p, e) -> Printf.sprintf "(λ%s,%s)" (p_to_s p) (e_to_s e)
41 | | EApp (e1, e2) -> Printf.sprintf "(%s %s)" (e_to_s e1) (e_to_s e2)
42 | | EVar v -> v
43 |
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/styles/_header.scss:
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1 | .header {
2 | background: black;
3 | color: white;
4 | position: relative;
5 | min-height: 450px;
6 | padding: 16px 8px;
7 | display: flex;
8 | text-align: center;
9 | flex-direction: column;
10 | justify-content: center;
11 | align-items: center;
12 | width: 100%;
13 | z-index: 5;
14 |
15 | &__logo {
16 | width: 130px;
17 | position: relative;
18 | }
19 |
20 | &__titles {
21 | position: relative;
22 | max-width: 800px;
23 | margin: 20px;
24 | text-shadow: 1px 1px 7px #56CCF2;
25 | }
26 |
27 | &__title {
28 | font-size: 48px;
29 | line-height: 1.1;
30 | }
31 |
32 | &__subtitle {
33 | font-size: 22px;
34 | }
35 |
36 | @media(min-width: 768px) {
37 | flex-direction: row;
38 |
39 | &__logo {
40 | width: 160px;
41 | margin-right: 10px;
42 | }
43 |
44 | &__title {
45 | font-size: 60px;
46 | }
47 |
48 | &__subtitle {
49 | font-size: 30px;
50 | }
51 | }
52 |
53 | }
54 |
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/styles/_index.scss:
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1 | .index {
2 | max-width: 900px;
3 | margin: auto;
4 | padding: 20px 0;
5 | display: flex;
6 | flex-wrap: wrap;
7 | justify-content: center;
8 |
9 | &__col {
10 | white-space: nowrap;
11 | padding: 15px 25px;
12 | margin: 15px;
13 | background: #fefefe;
14 | box-shadow: 0 1px 4px rgba(0, 0, 100, 0.1), inset 0 0 0 1px rgba(0, 0, 0, 0.1);
15 | transition: box-shadow 0.5s cubic-bezier(0.23, 1, 0.32, 1);
16 |
17 | &:hover {
18 | box-shadow: 0 8px 40px rgba(0, 0, 100, 0.15), inset 0 0 0 1px rgba(0, 0, 0, 0.1);
19 | }
20 | }
21 |
22 | a {
23 | line-height: 1.5;
24 | color: #888;
25 | font-size: 24px;
26 | }
27 |
28 | a[href^="#"] {
29 | color: #BBBBBB;
30 | }
31 |
32 | a:hover {
33 | color: #3A98C8;
34 | }
35 |
36 | a[href^="#"]:hover {
37 | color: #BBBBBB;
38 | }
39 |
40 | h2 {
41 | font-size: 24px;
42 | text-align: left;
43 | color: #707070;
44 | margin: 0 0 10px;
45 | text-transform: uppercase;
46 | }
47 | }
48 |
--------------------------------------------------------------------------------
/src/lexer.mll:
--------------------------------------------------------------------------------
1 | {
2 | open Parser
3 | open Lexing
4 |
5 | let nextLine lexbuf =
6 | let pos = lexbuf.lex_curr_p in
7 | lexbuf.lex_curr_p <- { pos with pos_bol = pos.pos_cnum; pos_lnum = pos.pos_lnum + 1 }
8 |
9 | }
10 |
11 | let nl = "\r\n"|"\r"|"\n"
12 | let inlineComment = "--" [^ '\n' '\r']* (nl|eof)
13 |
14 | let ws = ['\t' ' ']
15 | let latin1 = [^ '\t' ' ' '\r' '\n' '(' ')' ':' ','] # '-'
16 | let bytes2 = ['\192'-'\223']['\128'-'\191']
17 | let bytes3 = ['\224'-'\239']['\128'-'\191']['\128'-'\191']
18 | let bytes4 = ['\240'-'\247']['\128'-'\191']['\128'-'\191']['\128'-'\191']
19 | let utf8 = latin1|bytes2|bytes3|bytes4
20 | let ident = utf8*
21 |
22 | let defeq = ":=" | "\xE2\x89\x94"
23 | let arrow = "->" | "\xE2\x86\x92"
24 | let lam = "\\" | "\xCE\xBB"
25 |
26 | rule read = parse
27 | | nl { nextLine lexbuf; read lexbuf }
28 | | inlineComment { nextLine lexbuf; read lexbuf }
29 | | ws+ { read lexbuf }
30 | | '(' { LPARENS }
31 | | ')' { RPARENS }
32 | | lam { LAM }
33 | | arrow { ARROW }
34 | | ':' { COLON }
35 | | ',' { COMMA }
36 | | "def" { DEF }
37 | | "abbrev" { ABBREV }
38 | | defeq { DEFEQ }
39 | | "#eval" { EVAL }
40 | | ident as s { IDENT s }
41 | | eof { EOF }
42 |
--------------------------------------------------------------------------------
/styles/mathjax.js:
--------------------------------------------------------------------------------
1 | (function () {
2 | var newMathJax = 'https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js';
3 | var oldMathJax = 'cdn.mathjax.org/mathjax/latest/MathJax.js';
4 | var replaceScript = function (script, src) {
5 | var newScript = document.createElement('script');
6 | newScript.src = newMathJax + src.replace(/.*?(\?|$)/, '$1');
7 | newScript.onload = script.onload;
8 | newScript.onerror = script.onerror;
9 | script.onload = script.onerror = null;
10 | while (script.firstChild) newScript.appendChild(script.firstChild);
11 | if (script.id != null) newScript.id = script.id;
12 | script.parentNode.replaceChild(newScript, script);
13 | console.info('MathJax: 2.7.1.');
14 | }
15 |
16 | if (document.currentScript) {
17 | var script = document.currentScript;
18 | replaceScript(script, script.src);
19 | } else {
20 | var n = oldMathJax.length;
21 | var scripts = document.getElementsByTagName('script');
22 | for (var i = 0; i < scripts.length; i++) {
23 | var script = scripts[i];
24 | var src = (script.src || '').replace(/.*?:\/\//,'');
25 | if (src.substr(0, n) === oldMathJax) {
26 | replaceScript(script, src);
27 | break;
28 | }
29 | }
30 | }
31 | })();
32 |
--------------------------------------------------------------------------------
/styles/_stack.scss:
--------------------------------------------------------------------------------
1 | .stack {
2 | margin: auto;
3 | max-width: 100%;
4 | border-spacing: 10px;
5 | color: #282828;
6 | font-size: 20px;
7 |
8 | td {
9 | background-color:#fff9a6;
10 | // width: 80px;
11 | padding: 4px;
12 | outline: 1px solid rgba(0, 0, 0, .3);
13 | }
14 |
15 | th {
16 | padding: 4px;
17 | text-align: left;
18 | font-weight: normal;
19 | }
20 |
21 | .empty {
22 | background-color: inherit;
23 | outline: inherit;
24 |
25 | }
26 |
27 | }
28 |
29 |
30 |
31 |
32 | @media(max-width: 600px) {
33 | .stack {
34 | font-size: 16px;
35 | display: inline-block;
36 | border-spacing: 0;
37 | tbody {
38 | display: block;
39 | }
40 |
41 | tr {
42 | display: block;
43 | text-align: left;
44 | vertical-align: top;
45 | position: relative;
46 | }
47 |
48 | td {
49 | margin: 30px 0 10px;
50 | text-align: center;
51 | padding: 4px;
52 | display: inline-block;
53 | width: 90px;
54 | }
55 |
56 | td[colspan="4"] {
57 | width: 360px;
58 | }
59 |
60 | td[colspan="2"] {
61 | width: 180px;
62 | }
63 |
64 | th {
65 | position: absolute;
66 | top: 0;
67 | width: 100%;
68 | }
69 | }
70 | }
71 |
72 |
73 |
74 | @media(max-width: 320px) {
75 | .stack {
76 | font-size: 12px;
77 | td {
78 | margin: 20px 0 5px;
79 | width: 80px;
80 | }
81 |
82 | td[colspan="4"] {
83 | width: 320px;
84 | }
85 |
86 | td[colspan="2"] {
87 | width: 160px;
88 | }
89 | }
90 | }
91 |
92 |
93 |
94 |
--------------------------------------------------------------------------------
/styles/_exe.scss:
--------------------------------------------------------------------------------
1 | .exe {
2 |
3 | figure {
4 | max-width: inherit;
5 | }
6 |
7 | h1 {
8 | color: #7D8A96;
9 | font-size: 32px;
10 | text-transform: uppercase;
11 | border-bottom: 1px solid rgba(0, 0 , 0,0.3);
12 | display: inline-block;
13 | margin: 42px 0 10px;
14 | @media(min-width: 768px) {
15 | font-size: 40px;
16 | }
17 | }
18 |
19 | h1 + h2 {
20 | margin-top: 0px;
21 | }
22 | }
23 |
24 | .macro {
25 | margin: 0 auto;
26 | display: flex;
27 | justify-content: space-around;
28 | max-width: 600px;
29 | flex-wrap: wrap;
30 | width: 100%;
31 | &__col {
32 | h3 {
33 | padding: 0;
34 | width: initial;
35 | }
36 | padding-left: 24px;
37 | line-height: 1.5;
38 | font-size: 14px;
39 | @media(min-width: 768px) {
40 | font-size: 22px;
41 | }
42 | }
43 | }
44 |
45 | .langf {
46 | @media(min-width: 920px) {
47 | display: flex;
48 | flex-direction: row;
49 | justify-content: center;
50 | }
51 |
52 | ol {
53 | display: inline-block;
54 | max-width: 650px;
55 | margin: auto;
56 | font-size: 20px;
57 | padding-left: 36px;
58 | }
59 |
60 | &__col {
61 | @media(min-width: 920px) {
62 | .langf-col:last-child {
63 | white-space: pre;
64 | margin-left: 20px;
65 | }
66 |
67 | }
68 | }
69 | }
--------------------------------------------------------------------------------
/styles/_types.scss:
--------------------------------------------------------------------------------
1 | .types {
2 | display: inline-block;
3 | text-align: left;
4 | max-width: 100%;
5 | padding: 0 8px;
6 | h1 {
7 | color: #7D8A96;
8 | font-size: 32px;
9 | text-transform: uppercase;
10 | border-bottom: 1px solid rgba(0, 0 , 0,0.3);
11 | display: inline-block;
12 | margin: 42px 0 10px;
13 | @media(min-width: 768px) {
14 | font-size: 40px;
15 | }
16 | }
17 |
18 | section {
19 | max-width: 100%;
20 | }
21 |
22 | p {
23 | margin: 0;
24 | padding-left: 0;
25 | }
26 |
27 |
28 |
29 | h1 + h2 {
30 | margin-top: 0px;
31 | }
32 |
33 |
34 | .type {
35 | max-width: 660px;
36 | display: flex;
37 | flex-flow: row wrap;
38 | &__col {
39 | padding-left: 22px;
40 | flex: 1 0 15%;
41 | h3 {
42 | width: initial;
43 | padding: 0;
44 | margin: 0;
45 | }
46 | @media(min-width: 600px) {
47 | padding-right: 22px;
48 | flex: 1 0 15%;
49 | font-size: 20px;
50 | }
51 | }
52 | }
53 |
54 | .legend {
55 | margin: 20px auto 0;
56 | display: inline-block;
57 | padding: 10px 20px;
58 | font-size: 24px;
59 | background: #FDF6E3;
60 | border-radius: 4px;
61 | box-shadow: 0 4px 6px rgba(50,50,93,.11),
62 | 0 1px 3px rgba(0, 0, 0,.08);
63 | }
64 | }
--------------------------------------------------------------------------------
/LICENSE:
--------------------------------------------------------------------------------
1 | DHARMA License
2 |
3 | Copyright (c) 2016—2022 Groupoid Infinity
4 |
5 | Permission to use, copy, modify, and/or distribute this software for any
6 | purpose with or without fee is hereby granted, provided that the above
7 | copyright notice and this permission notice appear in all copies.
8 |
9 | YOU CANNOT USE THIS SOFTWARE IN ANY (PROVABLE BY MONEY TRACE)
10 | PROCESS CHAIN OF EXTERMINATING UKRAINIANS BY ANY MEANS OF FASCIST
11 | ACTIONS AGAINST OUR TERRITORIAL INTEGRITY, CULTURAL DIVERSITY BY
12 | APPLYING MILITARY INVASIONS, ECONOMICAL WARS, HUMANITARIAN DISASTERS,
13 | ARTFICIAL HOLODOMORS, GENOCIDE, RAPING, LOOTING, ROBBERIES, SPREADING
14 | FAKE INFORMATION, AND OTHER CONTEMPORARY WEAPONS OF WAR AT SCALE
15 | OR IN INVIDIVUAL MANNER.
16 |
17 | YOU CANNOT USE THIS SOFTWARE BY ANY MEANS IN INTEREST OF LEGAL
18 | ENTITIES OR INDIVIDUALS WHO IS SUPPORTING NOW OR WAS SUPPORTING
19 | BACK THEN FASCISM, RUSCISM, COMMUNISM, CHAUVINISM, HUMILIATION,
20 | AND OTHER SUPPRESSIVE IDEOLOGIES IN DIFFERENT EXPRESSIONS.
21 |
22 | STOP KILLING UKRAINIANS,
23 | THE COUNTER RENDERS TENS OF MILLIONS.
24 |
25 | THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
26 | WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
27 | MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
28 | ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
29 | WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
30 | ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
31 | OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
32 |
--------------------------------------------------------------------------------
/src/alonzo.ml:
--------------------------------------------------------------------------------
1 | open Error
2 |
3 | module ENV = Map.Make (String)
4 | let decls : (Expr.exp ENV.t) ref = ref ENV.empty
5 | let abbrs : (Expr.typexp ENV.t) ref = ref ENV.empty
6 |
7 | let rec unabbr (texp: Expr.typexp) : Expr.typexp =
8 | match texp with
9 | | TVar n -> Option.value (ENV.find_opt n !abbrs) ~default:texp
10 | | TFun (t1, t2) -> TFun (unabbr t1, unabbr t2)
11 |
12 | let rec teval (params: Expr.param list): Expr.exp -> Expr.typexp = function
13 | | EVar n -> begin
14 | let param = List.find_opt (function Expr.PVar(pn, _) -> pn = n) params in
15 | match param with
16 | | None -> begin match ENV.find_opt n !decls with
17 | | Some v -> teval [] v
18 | | None -> raise (UnboundVariable n)
19 | end
20 | | Some PVar (_, t) -> unabbr t
21 | end
22 | | ELam (PVar (n, t), e) -> TFun (unabbr t, teval (List.append params [PVar (n,t)]) e)
23 | | EApp (e1, e2) ->
24 | let te1 = teval params e1 in
25 | let te2 = teval params e2 in
26 | begin match te1 with
27 | | TFun (t1, t2) when t1 = te2 -> unabbr t2
28 | | _ -> raise (Application (e1, te1, e2, te2))
29 | end
30 |
31 | let rec subst (x: Expr.name) (sub: Expr.exp): Expr.exp -> Expr.exp = function
32 | | EVar n -> if n = x then sub else EVar n
33 | | ELam (p, e) -> ELam(p, subst x sub e)
34 | | EApp (e1, e2) -> EApp (subst x sub e1, subst x sub e2)
35 |
36 | let rec reduce (exp : Expr.exp): Expr.exp =
37 | match exp with
38 | | EVar n -> begin match ENV.find_opt n !decls with
39 | | Some v -> v
40 | | None -> EVar n
41 | end
42 | | ELam (p, e) -> ELam (p, reduce e)
43 | | EApp (e1, e2) ->
44 | let re1 = reduce e1 in
45 | let re2 = reduce e2 in
46 | begin match re1 with
47 | | ELam (PVar (n, _), e) -> reduce (subst n re2 e)
48 | | _ -> EApp (re1, re2)
49 | end
50 |
51 | let run (commands : Expr.command list): unit =
52 | let checker (expected: Expr.typexp) (e: Expr.exp) (f: unit -> unit) =
53 | let actual = teval [] e in
54 | if actual = unabbr expected then f () else raise (Type (expected, actual)) in
55 |
56 | let runner = function
57 | | Expr.Decl (n, t, e) -> checker t e (fun () -> decls := ENV.add n (reduce e) !decls);
58 | | Expr.Abbr (n, t) -> abbrs := ENV.add n (unabbr t) !abbrs;
59 | | Expr.Eval (e, t) -> checker t e (fun () -> print_endline (reduce e |> Expr.e_to_s)); in
60 |
61 | List.iter runner commands
62 |
63 | let evalFile path : unit =
64 | let chan = open_in path in
65 | let lexbuf = Lexing.from_channel chan in
66 | try
67 | let commands = Parser.main Lexer.read lexbuf in
68 | handle_errors run commands;
69 | close_in chan;
70 | flush_all ()
71 | with Parser.Error ->
72 | Parser (Lexing.lexeme_start lexbuf, Lexing.lexeme_end lexbuf, Lexing.lexeme lexbuf)
73 | |> raise
74 |
75 | let main () =
76 | Array.sub Sys.argv 1 (Array.length Sys.argv - 1) |> Array.iter evalFile;
77 | ()
78 |
79 | let () = main ()
80 |
--------------------------------------------------------------------------------
/framework.js:
--------------------------------------------------------------------------------
1 | // Mixin usages in PUG:
2 |
3 | // +tex(false, false).
4 | // $\mathbf{Definition}$ (Space of Sections). Let $\mathbf{H}$ be
5 | // a $(\infty,1)$-topos, and let $E \rightarrow B : \mathbf{H}_{/B}$ a bundle in
6 | // $\mathbf{H}$, object in the slice topos. Then the space of sections $\Gamma_\Sigma(E)$
7 | // of this bundle is the Dependent Product.
8 |
9 | // +tex(true, false).
10 | // $$
11 | // \Gamma_\Sigma(E) = \Pi_\Sigma (E) \in \mathbf{H}.
12 | // $$
13 |
14 | // +code.
15 | // def Pi (A : U) (B : A → U) : U := Π (x : A), B x
16 |
17 | const {mathjax} = require('mathjax-full/js/mathjax.js');
18 | const {TeX} = require('mathjax-full/js/input/tex.js');
19 | const {SVG} = require('mathjax-full/js/output/svg.js');
20 | const {liteAdaptor} = require('mathjax-full/js/adaptors/liteAdaptor.js');
21 | const {RegisterHTMLHandler} = require('mathjax-full/js/handlers/html.js');
22 | const {AssistiveMmlHandler} = require('mathjax-full/js/a11y/assistive-mml.js');
23 | const {AllPackages} = require('mathjax-full/js/input/tex/AllPackages.js');
24 |
25 | const adaptor = liteAdaptor();
26 | const handler = RegisterHTMLHandler(adaptor);
27 |
28 | const tex = new TeX({
29 | packages: ['base', 'autoload', 'require', 'ams', 'amscd', 'newcommand', 'configmacros'],
30 | inlineMath: [ ["$", "$"] ],
31 | macros: { // Plug your Glyphs here
32 | llparenthesis: '\\mathopen{\u2987}',
33 | rrparenthesis: '\\mathclose{\u2988}',
34 | llbracket: '\\mathopen{\u27E6}',
35 | rrbracket: '\\mathclose{\u27E7}',
36 | incmap: '\\mathclose{\u21AA}',
37 | meet: '\\mathopen{\u2227}',
38 | map: '\\mathopen{\u21A6}',
39 | join: '\\mathopen{\u2228}',
40 | trans: '\\, \\mathbin{\\vcenter{\\rule{.3ex}{.3ex}}} \\,',
41 | mapright: ['\\xrightarrow{{#1}}', 1],
42 | mapdown: ['\\Big\\downarrow\\rlap{\\raise2pt{\\scriptstyle{#1}}}', 1],
43 | mapdiagl: ['\\vcenter{\\searrow}\\rlap{\\raise2pt{\\scriptstyle{#1}}}', 1],
44 | mapdiagr: ['\\vcenter{\\swarrow}\\rlap{\\raise2pt{\\scriptstyle{#1}}}', 1],
45 | }
46 | });
47 |
48 | tex.postFilters.add(({math, data}) => {
49 | if (!data.error) return;
50 | data.root.walkTree((node) => {
51 | if (node.isKind('merror')) {
52 | console.log('TeX error:\n ' + node.attributes.get('data-mjx-error'));
53 | }
54 | });
55 | });
56 |
57 | const svg = new SVG({fontCache: 'local'});
58 |
59 | function renderPug(block) {
60 | var recv; with({pug_html: ""}){
61 | eval(`(${block})();`); recv = pug_html;
62 | }; return recv
63 | }
64 |
65 | function renderTeX(formulae) {
66 | return adaptor.innerHTML(mathjax.document(formulae, {
67 | InputJax: tex, OutputJax: svg
68 | }).render().document.body);
69 | }
70 |
71 | exports.tex = function (block) {
72 | return renderTeX(renderPug(block));
73 | }
74 |
75 | exports.highlight = function (block) {
76 | return renderPug(block)
77 | .replace(/([(){}→=]+|:|:=)/g,
78 | '$1')
79 | .replace(/\b(∀|Π|Σ|W|λ|glue|unglue|Glue|transp|hcomp|where|def|begin|end|module|import|option|false|true|indᵂ|sup|.1|.2|𝟎|𝟏|𝟐|ind₂|ind₁|ind₀|★|0₂|1₂|PathP|PartialP|inc|ouc|axiom|theorem|lemdata|ma|U|V)\b(?!:)/g,
80 | '$1');
81 | }
82 |
--------------------------------------------------------------------------------
/styles/main.scss:
--------------------------------------------------------------------------------
1 | @font-face {
2 | font-family: 'local';
3 | src: url('https://groupoid.space/Geometria-Light.otf');
4 | font-weight: normal;
5 | font-style: normal;
6 | }
7 |
8 | .MathJax_Display {
9 | overflow-x: auto;
10 | overflow-y: hidden;
11 | }
12 |
13 | nav a {
14 | font-size: 18px;
15 | border: 2px solid #dedede;
16 | background-color: white;
17 | color: lightblue;
18 | text-decoration: none;
19 | margin: 5px 5px;
20 | padding: 7px 12px;
21 | min-width: 150px;
22 | text-align: center;
23 | }
24 |
25 | nav a:visited {
26 | color: lightblue;
27 | }
28 |
29 | nav a:hover {
30 | border-bottom: 2px solid #00b8cf;
31 | }
32 |
33 |
34 | nav {
35 | display: flex;
36 | background-color: #FBFBFB;
37 | flex-direction: row;
38 | justify-content: center;
39 | }
40 |
41 | nav a {
42 | font-size: 18px;
43 | min-width: initial;
44 | }
45 |
46 |
47 | * {
48 | margin: 0;
49 | padding: 0;
50 | box-sizing: border-box;
51 | }
52 |
53 | sub,
54 | sup {
55 | font-size: 80%;
56 | line-height: 0;
57 | position: relative;
58 | vertical-align: baseline;
59 | }
60 |
61 | sub {
62 | bottom: -0.25em;
63 | }
64 |
65 | sup {
66 | top: -0.5em;
67 | }
68 |
69 | html {
70 | height: 100%;
71 | }
72 |
73 | body {
74 | min-height: 100%;
75 | text-rendering: optimizeLegibility;
76 | -webkit-font-smoothing: antialiased;
77 | }
78 |
79 | h1, h2, h3, h4 {
80 | font-weight: normal;
81 | }
82 |
83 | ul {
84 | list-style-type: none;
85 | }
86 |
87 | ol,
88 | ul {
89 | text-align: left;
90 | line-height: 1.5;
91 | }
92 |
93 | img, figure {
94 | vertical-align: middle;
95 | }
96 |
97 | img { margin-left:20px; }
98 |
99 | .content {
100 | min-height: 100%;
101 | font-family: local;
102 | display: flex; // sticky footer
103 | flex-direction: column;
104 | position: relative;
105 | }
106 |
107 | .main {
108 | color: #586E75;
109 | background: #FBFBFB;
110 | padding: 50px 0px;
111 | text-align: center;
112 | box-shadow: 0 3px 10px rgba(0,0,0,0);
113 | // 0 -3px 10px rgba(0,0,0,0.3);
114 | z-index: 5;
115 | flex: 1 1 auto; // sticky footer
116 |
117 | }
118 |
119 | figure {
120 | min-width: 300px;
121 | overflow-x: auto;
122 | padding: 10px 2px;
123 | font-size: 18px;
124 | display: block;
125 | }
126 |
127 | figure::after {
128 | content: "\A";
129 | white-space: pre;
130 | }
131 |
132 | h2 {
133 | font-size: 24px;
134 | color: #268BD2;
135 | @media(min-width: 768px) {
136 | font-size: 32px;
137 | }
138 | margin: 34px 0 8px;
139 | }
140 |
141 | h3 {
142 | max-width: 100%;
143 | margin: 16px auto 0;
144 | // width: 650px;
145 | padding: 0 0 0 8px;
146 | text-transform: uppercase;
147 | text-align: left;
148 | font-size: 22px;
149 | }
150 |
151 | p {
152 | max-width: 100%;
153 | width: 650px;
154 | margin: auto;
155 | padding: 8px;
156 | text-align: left;
157 | font-size: 18px;
158 | line-height: 1.4;
159 | @media(min-width: 768px) {
160 | font-size: 22px;
161 | }
162 | }
163 |
164 | p:hover {
165 | background: white;
166 | }
167 |
168 | mark {
169 | background: #FDF6E3;
170 | padding: 0px 2px;
171 | border-radius: 2px;
172 | color: #586E75;
173 | }
174 |
175 | a {
176 | color: #3A98C8;
177 | text-decoration: none;
178 | &:visited {
179 | color: #3A98C8;
180 | }
181 |
182 | &:hover {
183 | color: #D33682;
184 | }
185 |
186 | &:active {
187 | color: #D33682;
188 | }
189 | }
190 |
191 |
192 | @import '_aside';
193 | @import '_header';
194 | @import '_footer';
195 | @import '_semantics';
196 | @import '_intro';
197 | @import '_status';
198 | @import '_resources';
199 | @import '_index';
200 | @import '_om';
201 | @import '_exe';
202 | @import '_types';
203 | @import '_list';
204 | @import '_code';
205 | @import '_canvas';
206 | @import '_stack';
207 |
208 |
--------------------------------------------------------------------------------
/header.pug:
--------------------------------------------------------------------------------
1 | mixin tex(center=false, paragraph=true)
2 | if paragraph
3 | p(style=center ? {'text-align': 'center' } : null)!= tex(`${block}`)
4 | else
5 | span(style=center ? {
6 | 'text-align': 'center',
7 | 'display': 'block',
8 | 'padding-top': '8px',
9 | 'padding-bottom': '8px',
10 | } : null)!= tex(`${block}`)
11 |
12 | mixin tex2(center=false, paragraph=true)
13 | p(style=center ? {
14 | 'text-align': 'center',
15 | 'display': 'block',
16 | 'padding-top': '8px',
17 | 'padding-bottom': '8px',
18 | } : null)!= tex(`${block}`)
19 |
20 | mixin code
21 | code!= highlight(`${block}`)
22 |
23 | mixin header(logo, title, subtitle)
24 | header.header
25 | .header__titles
26 | h1.header__title!= title
27 | h4.header__subtitle!= subtitle
28 |
29 | doctype html
30 | html
31 | head
32 | meta(charset='utf-8')
33 | meta(http-equiv='x-ua-compatible' content='ie=edge')
34 | meta(property='fb:app_id' content='118554188236439')
35 | meta(name='viewport' content='width=device-width, initial-scale=1')
36 | meta(name='author' content='Maxim Sokhatsky')
37 | meta(name='twitter:site' content='@5HT')
38 | meta(name='twitter:creator' content='@5HT')
39 | meta(property='og:type' content='website')
40 | meta(property='og:image' content='https://avatars.githubusercontent.com/u/17128096?s=400&u=66a63d4cdd9625b2b4b37d724cc00fe6401e5bd8&v=4')
41 | meta(name='msapplication-TileColor' content='#ffffff')
42 | meta(name='msapplication-TileImage' content='https://anders.groupoid.space/images/ms-icon-144x144.png')
43 | meta(name='theme-color' content='#ffffff')
44 |
45 | link(rel='stylesheet' href='https://anders.groupoid.space/main.css?v=1')
46 | link(rel='apple-touch-icon' sizes='57x57' href='https://anders.groupoid.space/images/apple-icon-57x57.png')
47 | link(rel='apple-touch-icon' sizes='60x60' href='https://anders.groupoid.space/images/apple-icon-60x60.png')
48 | link(rel='apple-touch-icon' sizes='72x72' href='https://anders.groupoid.space/images/apple-icon-72x72.png')
49 | link(rel='apple-touch-icon' sizes='76x76' href='https://anders.groupoid.space/images/apple-icon-76x76.png')
50 | link(rel='apple-touch-icon' sizes='114x114' href='https://anders.groupoid.space/images/apple-icon-114x114.png')
51 | link(rel='apple-touch-icon' sizes='120x120' href='https://anders.groupoid.space/images/apple-icon-120x120.png')
52 | link(rel='apple-touch-icon' sizes='144x144' href='https://anders.groupoid.space/images/apple-icon-144x144.png')
53 | link(rel='apple-touch-icon' sizes='152x152' href='https://anders.groupoid.space/images/apple-icon-152x152.png')
54 | link(rel='apple-touch-icon' sizes='180x180' href='https://anders.groupoid.space/images//apple-icon-180x180.png')
55 | link(rel='icon' type='image/png' sizes='192x192' href='https://anders.groupoid.space/images/android-icon-192x192.png')
56 | link(rel='icon' type='image/png' sizes='32x32' href='https://anders.groupoid.space/images/favicon-32x32.png')
57 | link(rel='icon' type='image/png' sizes='96x96' href='https://anders.groupoid.space/images/favicon-96x96.png')
58 | link(rel='icon' type='image/png' sizes='16x16' href='https://anders.groupoid.space/images/favicon-16x16.png')
59 | link(rel='manifest' href='https://anders.groupoid.space/images/manifest.json')
60 |
61 | style.
62 | svg a{fill:blue;stroke:blue}
63 | [data-mml-node="merror"]>g{fill:red;stroke:red}
64 | [data-mml-node="merror"]>rect[data-background]{fill:yellow;stroke:none}
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67 | .mjx-dotted{stroke-linecap:round;stroke-dasharray:0,140}
68 | use[data-c]{stroke-width:3px}
69 |
70 | body.content
71 | block vars
72 | block content
73 |
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/src/stlc.ml:
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1 | (* Alonzo (c) 2025 5HT $ ocamlc -o alonzo stlc.ml *)
2 |
3 | type term =
4 | | Var of string
5 | | Star
6 | | Arrow of term * term
7 | | Lam of string * term * term
8 | | App of term * term
9 | | Unit
10 | | Prod of term * term
11 | | Pair of term * term
12 | | Pr1 of term
13 | | Pr2 of term
14 |
15 | let rec string_of_term = function
16 | | Var x -> x
17 | | Star -> "*"
18 | | Arrow (a, b) -> "(" ^ string_of_term a ^ " -> " ^ string_of_term b ^ ")"
19 | | Lam (x, a, t) -> "λ (" ^ x ^ " : " ^ string_of_term a ^ "), " ^ string_of_term t
20 | | App (t1, t2) -> "(" ^ string_of_term t1 ^ " " ^ string_of_term t2 ^ ")"
21 | | Unit -> "unit"
22 | | Prod (a, b) -> "(" ^ string_of_term a ^ " * " ^ string_of_term b ^ ")"
23 | | Pair (t1, t2) -> "<" ^ string_of_term t1 ^ ", " ^ string_of_term t2 ^ ">"
24 | | Pr1 t -> "π1(" ^ string_of_term t ^ ")"
25 | | Pr2 t -> "π2(" ^ string_of_term t ^ ")"
26 |
27 | type context = (string * term) list
28 |
29 | let rec subst x s = function
30 | | Var y -> if x = y then s else Var y
31 | | Arrow (a, b) -> Arrow (subst x s a, subst x s b)
32 | | Lam (y, a, b) when x <> y -> Lam (y, subst x s a, subst x s b)
33 | | App (f, a) -> App (subst x s f, subst x s a)
34 | | Prod (a, b) -> Prod (subst x s a, subst x s b)
35 | | Pair (t1, t2) -> Pair (subst x s t1, subst x s t2)
36 | | Pr1 t -> Pr1 (subst x s t)
37 | | Pr2 t -> Pr2 (subst x s t)
38 | | t -> t
39 |
40 | let rec lookup x = function
41 | | [] -> raise (Failure ("Unbound variable: " ^ x))
42 | | (y, typ) :: rest -> if x = y then typ else lookup x rest
43 |
44 | let rec equal ctx t1 t2 = match t1, t2 with
45 | | Var x, Var y -> x = y
46 | | Star, Star -> true
47 | | Arrow (a, b), Arrow (a', b') -> equal ctx a a' && equal ctx b b'
48 | | Lam (x, a, b), Lam (y, a', b') -> equal ctx a a' && equal ((x, a) :: ctx) b (subst y (Var x) b')
49 | | App (f, a), App (f', a') -> equal ctx f f' && equal ctx a a'
50 | | Unit, Unit -> true
51 | | Prod (a, b), Prod (a', b') -> equal ctx a a' && equal ctx b b'
52 | | Pair (t1, t2), Pair (t1', t2') -> equal ctx t1 t1' && equal ctx t2 t2'
53 | | Pr1 t, Pr1 t' -> equal ctx t t'
54 | | Pr2 t, Pr2 t' -> equal ctx t t'
55 | | Lam (x, _, b), t -> equal ctx b (App (t, Var x))
56 | | t, Lam (x, _, b) -> equal ctx (App (t, Var x)) b
57 | | _ -> false
58 |
59 | and reduce ctx t = match t with
60 | | App (Lam (x, _, b), a) -> subst x a b
61 | | App (f, a) -> App (reduce ctx f, reduce ctx a)
62 | | Pr1 (Pair (t1, _)) -> t1
63 | | Pr2 (Pair (_, t2)) -> t2
64 | | Pr1 t -> Pr1 (reduce ctx t)
65 | | Pr2 t -> Pr2 (reduce ctx t)
66 | | _ -> t
67 |
68 | and normalize ctx t =
69 | let t' = reduce ctx t in
70 | if equal ctx t t' then t else normalize ctx t'
71 |
72 | and infer ctx t = let res = match t with
73 | | Var x -> lookup x ctx
74 | | Star -> Star
75 | | Arrow (a, b) ->
76 | let _ = infer ctx a in
77 | let _ = infer ctx b in
78 | if equal ctx (infer ctx a) Star && equal ctx (infer ctx b) Star then Star
79 | else raise (Failure "Arrow type components must be of type *")
80 | | Lam (x, a, b) ->
81 | let _ = infer ctx a in
82 | if not (equal ctx (infer ctx a) Star) then raise (Failure "Lambda annotation must be a type");
83 | Arrow (a, infer ((x, a) :: ctx) b)
84 | | App (f, a) ->
85 | let f_type = infer ctx f in
86 | (match f_type with
87 | | Arrow (a', b) ->
88 | let a_type = infer ctx a in
89 | if equal ctx a_type a' then b
90 | else raise (Failure "Argument type mismatch")
91 | | _ -> raise (Failure "Application requires an arrow type"))
92 | | Unit -> Star
93 | | Prod (a, b) ->
94 | let _ = infer ctx a in
95 | let _ = infer ctx b in
96 | if equal ctx (infer ctx a) Star && equal ctx (infer ctx b) Star then Star
97 | else raise (Failure "Product type components must be of type *")
98 | | Pair (t1, t2) ->
99 | let t1_type = infer ctx t1 in
100 | let t2_type = infer ctx t2 in
101 | Prod (t1_type, t2_type)
102 | | Pr1 t ->
103 | let t_type = infer ctx t in
104 | (match t_type with
105 | | Prod (a, _) -> a
106 | | _ -> raise (Failure "First projection requires a product type"))
107 | | Pr2 t ->
108 | let t_type = infer ctx t in
109 | (match t_type with
110 | | Prod (_, b) -> b
111 | | _ -> raise (Failure "Second projection requires a product type"))
112 | in normalize ctx res
113 |
114 | (* Test Suite *)
115 |
116 | let id_type = Arrow (Star, Star)
117 | let id = Lam ("x", Star, Var "x")
118 | let unit_type = Star
119 | let pair_type = Prod (Star, Star)
120 | let pair_test = Pair (Unit, Unit)
121 | let pr1_test = Pr1 pair_test
122 | let pr2_test = Pr2 pair_test
123 |
124 | let beta = (App (Lam ("x", Star, Var "x"), Unit), Unit)
125 | let eta = (Lam ("x", Star, App (Var "f", Var "x")), Var "f")
126 | let pair_beta = (Pr1 (Pair (Unit, Unit)), Unit)
127 |
128 | let rec test_equal ctx t1 t2 =
129 | let t1' = normalize ctx t1 in
130 | let t2' = normalize ctx t2 in
131 | equal ctx t1' t2'
132 |
133 | let run_type_test name term expected_type =
134 | let ctx = [] in
135 | try
136 | let inferred = infer ctx term in
137 | let norm_inferred = normalize ctx inferred in
138 | let norm_expected = normalize ctx expected_type in
139 | Printf.printf "Test %s:\n- Term: %s\n- Inferred: %s\n- Expected: %s\n- Result: %s\n\n"
140 | name
141 | (string_of_term term)
142 | (string_of_term norm_inferred)
143 | (string_of_term norm_expected)
144 | (if test_equal [] norm_inferred norm_expected then "PASS" else "FAIL")
145 | with
146 | | Failure msg -> Printf.printf "Test %s: Failed with error: %s\n\n" name msg
147 |
148 | let run_equality_test ctx name (t1, t2) =
149 | let result = test_equal ctx t1 t2 in
150 | Printf.printf "Equality Test %s:\n- Term1: %s\n- Term2: %s\n- Result: %s\n\n"
151 | name
152 | (string_of_term t1)
153 | (string_of_term t2)
154 | (if result then "PASS" else "FAIL")
155 |
156 | let () =
157 | let ctx = [("f", Arrow (Star, Star)); ("u", Star)] in
158 | run_type_test "Identity" id id_type;
159 | run_type_test "Unit" Unit unit_type;
160 | run_type_test "Pair" pair_test pair_type;
161 | run_type_test "First Projection" pr1_test Star;
162 | run_type_test "Second Projection" pr2_test Star;
163 | run_equality_test ctx "Beta Reduction" beta;
164 | run_equality_test ctx "Eta Equivalence" eta;
165 | run_equality_test [] "Pair Beta" pair_beta;
166 |
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/index.pug:
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1 | include header
2 |
3 | html
4 | head
5 | meta(property='og:title' content='ALONZO')
6 | meta(property='og:description' content='Внутрішня мова декартово замкнених категорій')
7 | meta(property='og:url' content='https://alonzo.groupoid.space/')
8 |
9 | block title
10 | title ALONZO
11 |
12 | block content
13 | +header('', 'Alonzo', 'Мінімальна мова для функціональних обчислень у декартово-замкнених категоріях')
14 | article.main
15 | .exe
16 | section
17 | h1 Анотація
18 | aside Намдак Тонпа
19 | time ДАТА: 2 ЧЕРВНЯ 2025
20 | section
21 | +tex.
22 | Мова програмування $\mathbf{Alonzo}$ — це внутрішня мова декартово-замкнених категорій,
23 | що реалізує функціональні обчислення через лямбда-абстракцію, аплікацію, стрілкові типи,
24 | одиничний тип та добутки. Вона забезпечує строгу типізацію та відповідає структурі CCC.
25 |
26 | .semantics
27 | section
28 | h2#ast Синтаксис
29 | +tex.
30 | Терми $\mathbf{Alonzo}$ складаються зі змінних, зірки (тип типів), стрілкових типів,
31 | лямбда-абстракцій, аплікацій, одиничного типу, добутків, пар та їх проекцій.
32 | Мова підтримує строгі типи, забезпечуючи типобезпеку.
33 | code.
34 | I = #identifier
35 | STLC = I | Star | Arrow (STLC, STLC) | Lam (I, STLC, STLC)
36 | | App (STLC, STLC) | Unit | Prod (STLC, STLC)
37 | | Pair (STLC, STLC) | Pr1 STLC | Pr2 STLC
38 | br.
39 | code('OCaml').
40 | type term =
41 | | Var of string
42 | | Star
43 | | Arrow of term * term
44 | | Lam of string * term * term
45 | | App of term * term
46 | | Unit
47 | | Prod of term * term
48 | | Pair of term * term
49 | | Pr1 of term
50 | | Pr2 of term
51 | br.
52 |
53 | h2#rules Правила обчислень
54 | +tex.
55 | Обчислення в $\mathbf{Alonzo}$ базуються на бета-редукції для аплікацій
56 | та редукції для проекцій пар, з підтримкою eta-рівності.
57 | code.
58 | App (Lam (x, A, t), u) → subst x u t (* β-редукція *)
59 | Pr1 (Pair (t,unofficial, u)) → t (* π1-редукція *)
60 | Pr2 (Pair (t, u)) → u (* π2-редукція *)
61 | Lam (x, A, App (t, Var x)) → t (* η-рівність *)
62 | br.
63 | +tex(true).
64 | $$
65 | \begin{equation}
66 | \tag{β-reduction}
67 | \dfrac
68 | {(\lambda x : A . t) \, u}
69 | {t[x \mapsto u]}
70 | \end{equation}
71 | $$
72 | +tex(true).
73 | $$
74 | \begin{equation}
75 | \tag{π1-reduction}
76 | \dfrac
77 | {\pi_1 \langle t, u \rangle}
78 | {t}
79 | \end{equation}
80 | $$
81 | +tex(true).
82 | $$
83 | \begin{equation}
84 | \tag{π2-reduction}
85 | \dfrac
86 | {\pi_2 \langle t, u \rangle}
87 | {u}
88 | \end{equation}
89 | $$
90 |
91 | h2#typing Правила типізації
92 | +tex.
93 | Типізація в $\mathbf{Alonzo}$ забезпечує, що кожен терм має коректний тип.
94 | Основні правила включають:
95 | code.
96 | (* Контекст: Γ = список пар (x : A) *)
97 | Var x : A (* якщо (x : A) ∈ Γ *)
98 | Star : Star (* тип типів *)
99 | Arrow (A, B) : Star (* якщо A : Star, B : Star *)
100 | Lam (x, A, t) : Arrow (A, B) (* якщо Γ ⊢ A : Star, Γ, x : A ⊢ t : B *)
101 | App (t, u) : B (* якщо t : Arrow (A, B), u : A *)
102 | Unit : Star (* одиничний тип *)
103 | Prod (A, B) : Star (* якщо A : Star, B : Star *)
104 | Pair (t, u) : Prod (A, B) (* якщо t : A, u : B *)
105 | Pr1 t : A (* якщо t : Prod (A, B) *)
106 | Pr2 t : B (* якщо t : Prod (A, B) *)
107 | br.
108 |
109 | h2 Підстановка
110 | +tex.
111 | Підстановка в $\mathbf{Alonzo}$ замінює змінну на терм, зберігаючи типобезпеку.
112 | code('OCaml').
113 | let rec subst x s = function
114 | | Var y -> if x = y then s else Var y
115 | | Arrow (a, b) -> Arrow (subst x s a, subst x s b)
116 | | Lam (y, a, b) when x <> y -> Lam (y, subst x s a, subst x s b)
117 | | App (f, a) -> App (subst x s f, subst x s a)
118 | | Prod (a, b) -> Prod (subst x s a, subst x s b)
119 | | Pair (t1, t2) -> Pair (subst x s t1, subst x s t2)
120 | | Pr1 t -> Pr1 (subst x s t)
121 | | Pr2 t -> Pr2 (subst x s t)
122 | | t -> t
123 | br.
124 |
125 | h2 Редукція
126 | +tex.
127 | Редукція виконує бета-редукцію та редукцію проекцій для активних пар.
128 | code('OCaml').
129 | let rec reduce ctx t = match t with
130 | | App (Lam (x, _, b), a) -> subst x a b
131 | | App (f, a) -> App (reduce ctx f, reduce ctx a)
132 | | Pr1 (Pair (t1, _)) -> t1
133 | | Pr2 (Pair (_, t2)) -> t2
134 | | Pr1 t -> Pr1 (reduce ctx t)
135 | | Pr2 t -> Pr2 (reduce ctx t)
136 | | _ -> t
137 | br.
138 |
139 | h2 Нормалізація
140 | +tex.
141 | Нормалізація повторює редукцію до досягнення нормальної форми.
142 | code('OCaml').
143 | let rec normalize ctx t =
144 | let t' = reduce ctx t in
145 | if equal ctx t t' then t else normalize ctx t'
146 | br.
147 |
148 | h2 Внутрішня мова CCC
149 | +tex.
150 | Доведення, що $\mathbf{Alonzo}$ є внутрішньою мовою декартово-замкнених категорій:
151 | +tex(true).
152 | $$
153 | \begin{cases}
154 | \mathrm{Var} : A, \\
155 | \mathrm{Star} : \mathrm{Type}, \\
156 | \mathrm{Arrow} : A \to B \to \mathrm{Type}, \\
157 | \mathrm{Lam} : (A \to B) \to (A \implies B), \\
158 | \mathrm{App} : (A \implies B) \to A \to B, \\
159 | \mathrm{Unit} : \mathbf{1}, \\
160 | \mathrm{Prod} : A \to B \to \mathrm{Type}, \\
161 | \mathrm{Pair} : A \to B \to A \times B, \\
162 | \mathrm{Pr1} : A \times B \to A, \\
163 | \mathrm{Pr2} : A \times B \to B.
164 | \end{cases}
165 | $$
166 | +tex.
167 | Ці конструктори відповідають аксіомам CCC:
168 | +tex.
169 | $\mathrm{Star}$ позначає об'єкти категорії (типи),
170 | $\mathrm{Arrow}$ моделює експоненціальний об'єкт $B^A$,
171 | $\mathrm{Lam}$ відповідає морфізму $\lambda: (A \to B) \to (A \implies B)$,
172 | $\mathrm{App}$ реалізує оцінку $ev: (A \implies B) \times A \to B$,
173 | $\mathrm{Unit}$ є термінальним об'єктом $\mathbf{1}$, для якого $A \to \mathbf{1}$ є унікальним,
174 | $\mathrm{Prod}$ моделює декартовий добуток $A \times B$,
175 | $\mathrm{Pair}$ створює пару $\langle t, u \rangle: A \to B \to A \times B$,
176 | $\mathrm{Pr1}$ і $\mathrm{Pr2}$ є проекціями $\pi_1: A \times B \to A$ та $\pi_2: A \times B \to B$,
177 | $\mathrm{Var}$ позначає об'єкти категорії.
178 | +tex.
179 | Лямбда-абстракція та аплікація відповідають структурі CCC:
180 | +tex(true).
181 | $$
182 | \begin{cases}
183 | \lambda x.t \vdash \mathrm{Lam}(x, A, t): A \implies B, \\
184 | t \, u \mapsto \mathrm{App}(t, u): B.
185 | \end{cases}
186 | $$
187 |
188 | section
189 | h1 Бібліографія
190 | p(style="font-size:16px;").
191 | [1]. Church, A. A Formulation of the Simple Theory of Types. 1940
192 | [2]. Guallart, N. An Overview of Type Theories. 2014
193 | [3]. García, M. Category Theory and Lambda Calculus. 2020
194 |
195 | include footer
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3 | src: url("https://groupoid.space/Geometria-Light.otf");
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220 | .semantics figure {
221 | display: inline-block;
222 | max-width: min-content;
223 | font-size: 13px; }
224 | @media (min-width: 800px) {
225 | .semantics figure {
226 | font-size: 16px; } }
227 | .semantics h1 {
228 | color: #7D8A96;
229 | font-size: 32px;
230 | text-transform: uppercase;
231 | border-bottom: 1px solid rgba(0, 0, 0, 0.3);
232 | display: inline-block;
233 | margin-bottom: 8px; }
234 | .semantics section {
235 | margin-top: 40px; }
236 |
237 | .intro {
238 | width: 650px;
239 | max-width: 100%;
240 | margin: auto; }
241 |
242 | .status {
243 | text-align: left;
244 | display: inline-block;
245 | padding-left: 32px; }
246 | .status ol {
247 | line-height: 1.5;
248 | font-size: 18px; }
249 | @media (min-width: 768px) {
250 | .status ol {
251 | font-size: 22px; } }
252 |
253 | .resources {
254 | max-width: 650px;
255 | margin: 32px auto 0;
256 | text-align: left;
257 | padding: 8px; }
258 | .resources__title {
259 | display: inline-block;
260 | margin-bottom: 10px;
261 | color: #7D8A96;
262 | font-size: 32px;
263 | text-transform: uppercase;
264 | border-bottom: 1px solid rgba(0, 0, 0, 0.3); }
265 | @media (min-width: 768px) {
266 | .resources__title {
267 | font-size: 40px; } }
268 | .resources__list {
269 | padding-left: 32px;
270 | line-height: 1.5;
271 | font-size: 18px; }
272 | @media (min-width: 768px) {
273 | .resources__list {
274 | font-size: 22px; } }
275 |
276 | .index {
277 | max-width: 900px;
278 | margin: auto;
279 | padding: 20px 0;
280 | display: flex;
281 | flex-wrap: wrap;
282 | justify-content: center; }
283 | .index__col {
284 | white-space: nowrap;
285 | padding: 15px 25px;
286 | margin: 15px;
287 | background: #fefefe;
288 | box-shadow: 0 1px 4px rgba(0, 0, 100, 0.1), inset 0 0 0 1px rgba(0, 0, 0, 0.1);
289 | transition: box-shadow 0.5s cubic-bezier(0.23, 1, 0.32, 1); }
290 | .index__col:hover {
291 | box-shadow: 0 8px 40px rgba(0, 0, 100, 0.15), inset 0 0 0 1px rgba(0, 0, 0, 0.1); }
292 | .index a {
293 | line-height: 1.5;
294 | color: #888;
295 | font-size: 24px; }
296 | .index a[href^="#"] {
297 | color: #BBBBBB; }
298 | .index a:hover {
299 | color: #3A98C8; }
300 | .index a[href^="#"]:hover {
301 | color: #BBBBBB; }
302 | .index h2 {
303 | font-size: 24px;
304 | text-align: left;
305 | color: #707070;
306 | margin: 0 0 10px;
307 | text-transform: uppercase; }
308 |
309 | .om figure {
310 | max-width: inherit; }
311 |
312 | .om section h1 {
313 | margin-top: 50px; }
314 |
315 | .om h1 {
316 | color: #7D8A96;
317 | font-size: 32px;
318 | text-transform: uppercase;
319 | border-bottom: 1px solid rgba(0, 0, 0, 0.3);
320 | display: inline-block;
321 | margin-bottom: 32px; }
322 | @media (min-width: 768px) {
323 | .om h1 {
324 | font-size: 40px; } }
325 |
326 | .om h1 + h2 {
327 | margin-top: 20px; }
328 |
329 | .om h3 {
330 | max-width: 100%;
331 | margin: auto;
332 | width: 600px;
333 | padding: 16px 8px 0; }
334 |
335 | .exe figure {
336 | max-width: inherit; }
337 |
338 | .exe h1 {
339 | color: #7D8A96;
340 | font-size: 32px;
341 | text-transform: uppercase;
342 | border-bottom: 1px solid rgba(0, 0, 0, 0.3);
343 | display: inline-block;
344 | margin: 42px 0 10px; }
345 | @media (min-width: 768px) {
346 | .exe h1 {
347 | font-size: 40px; } }
348 |
349 | .exe h1 + h2 {
350 | margin-top: 0px; }
351 |
352 | .macro {
353 | margin: 0 auto;
354 | display: flex;
355 | justify-content: space-around;
356 | max-width: 600px;
357 | flex-wrap: wrap;
358 | width: 100%; }
359 | .macro__col {
360 | padding-left: 24px;
361 | line-height: 1.5;
362 | font-size: 14px; }
363 | .macro__col h3 {
364 | padding: 0;
365 | width: initial; }
366 | @media (min-width: 768px) {
367 | .macro__col {
368 | font-size: 22px; } }
369 |
370 | @media (min-width: 920px) {
371 | .langf {
372 | display: flex;
373 | flex-direction: row;
374 | justify-content: center; } }
375 |
376 | .langf ol {
377 | display: inline-block;
378 | max-width: 650px;
379 | margin: auto;
380 | font-size: 20px;
381 | padding-left: 36px; }
382 |
383 | @media (min-width: 920px) {
384 | .langf__col .langf-col:last-child {
385 | white-space: pre;
386 | margin-left: 20px; } }
387 |
388 | .types {
389 | display: inline-block;
390 | text-align: left;
391 | max-width: 100%;
392 | padding: 0 8px; }
393 | .types h1 {
394 | color: #7D8A96;
395 | font-size: 32px;
396 | text-transform: uppercase;
397 | border-bottom: 1px solid rgba(0, 0, 0, 0.3);
398 | display: inline-block;
399 | margin: 42px 0 10px; }
400 | @media (min-width: 768px) {
401 | .types h1 {
402 | font-size: 40px; } }
403 | .types section {
404 | max-width: 100%; }
405 | .types p {
406 | margin: 0;
407 | padding-left: 0; }
408 | .types h1 + h2 {
409 | margin-top: 0px; }
410 | .types .type {
411 | max-width: 660px;
412 | display: flex;
413 | flex-flow: row wrap; }
414 | .types .type__col {
415 | padding-left: 22px;
416 | flex: 1 0 15%; }
417 | .types .type__col h3 {
418 | width: initial;
419 | padding: 0;
420 | margin: 0; }
421 | @media (min-width: 600px) {
422 | .types .type__col {
423 | padding-right: 22px;
424 | flex: 1 0 15%;
425 | font-size: 20px; } }
426 | .types .legend {
427 | margin: 20px auto 0;
428 | display: inline-block;
429 | padding: 10px 20px;
430 | font-size: 24px;
431 | background: #FDF6E3;
432 | border-radius: 4px;
433 | box-shadow: 0 4px 6px rgba(50, 50, 93, 0.11), 0 1px 3px rgba(0, 0, 0, 0.08); }
434 |
435 | .list h1 {
436 | color: #7D8A96;
437 | font-size: 32px;
438 | text-transform: uppercase;
439 | border-bottom: 1px solid rgba(0, 0, 0, 0.3);
440 | display: inline-block;
441 | margin: 42px 8px 10px; }
442 | @media (min-width: 768px) {
443 | .list h1 {
444 | font-size: 40px; } }
445 |
446 | code {
447 | display: inline-block;
448 | overflow-x: auto;
449 | max-width: 100%;
450 | padding: 12px;
451 | margin: 8px 0;
452 | white-space: pre;
453 | text-align: left;
454 | border-radius: 4px;
455 | font-size: 14px;
456 | color: #00259c;
457 | background: white;
458 | box-shadow: 0 1px 4px #f1f0f0, inset 0 0 0 1px #e7e6e5; }
459 | @media (min-width: 768px) {
460 | code {
461 | font-size: 17px; } }
462 |
463 | pre {
464 | white-space: normal;
465 | max-width: 100%;
466 | width: 650px;
467 | padding: 12px;
468 | margin: 8px auto;
469 | text-align: left;
470 | border-radius: 4px;
471 | font-size: 14px;
472 | color: #00259c;
473 | background: white;
474 | box-shadow: 0 1px 4px #f1f0f0, inset 0 0 0 1px #e7e6e5; }
475 | @media (min-width: 768px) {
476 | pre {
477 | font-size: 17px; } }
478 |
479 | .h__name {
480 | color: #00259c;
481 | font-weight: bold; }
482 |
483 | .h__keyword {
484 | color: #ca30d4; }
485 |
486 | .h__symbol {
487 | color: #9f9fa3; }
488 |
489 | canvas {
490 | max-width: 100%;
491 | position: absolute;
492 | z-index: -10; }
493 |
494 | .stack {
495 | margin: auto;
496 | max-width: 100%;
497 | border-spacing: 10px;
498 | color: #282828;
499 | font-size: 20px; }
500 | .stack td {
501 | background-color: #fff9a6;
502 | padding: 4px;
503 | outline: 1px solid rgba(0, 0, 0, 0.3); }
504 | .stack th {
505 | padding: 4px;
506 | text-align: left;
507 | font-weight: normal; }
508 | .stack .empty {
509 | background-color: inherit;
510 | outline: inherit; }
511 |
512 | @media (max-width: 600px) {
513 | .stack {
514 | font-size: 16px;
515 | display: inline-block;
516 | border-spacing: 0; }
517 | .stack tbody {
518 | display: block; }
519 | .stack tr {
520 | display: block;
521 | text-align: left;
522 | vertical-align: top;
523 | position: relative; }
524 | .stack td {
525 | margin: 30px 0 10px;
526 | text-align: center;
527 | padding: 4px;
528 | display: inline-block;
529 | width: 90px; }
530 | .stack td[colspan="4"] {
531 | width: 360px; }
532 | .stack td[colspan="2"] {
533 | width: 180px; }
534 | .stack th {
535 | position: absolute;
536 | top: 0;
537 | width: 100%; } }
538 |
539 | @media (max-width: 320px) {
540 | .stack {
541 | font-size: 12px; }
542 | .stack td {
543 | margin: 20px 0 5px;
544 | width: 80px; }
545 | .stack td[colspan="4"] {
546 | width: 320px; }
547 | .stack td[colspan="2"] {
548 | width: 160px; } }
549 |
--------------------------------------------------------------------------------
/bundle.js:
--------------------------------------------------------------------------------
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e[0]=f*(m*b-d*v)-l*(u*b-s*v)+h*(u*d-s*m),e[1]=-(r*(m*b-d*v)-l*(a*b-i*v)+h*(a*d-i*m)),e[2]=r*(u*b-s*v)-f*(a*b-i*v)+h*(a*s-i*u),e[3]=-(r*(u*d-s*m)-f*(a*d-i*m)+l*(a*s-i*u)),e[4]=-(o*(m*b-d*v)-c*(u*b-s*v)+p*(u*d-s*m)),e[5]=n*(m*b-d*v)-c*(a*b-i*v)+p*(a*d-i*m),e[6]=-(n*(u*b-s*v)-o*(a*b-i*v)+p*(a*s-i*u)),e[7]=n*(u*d-s*m)-o*(a*d-i*m)+c*(a*s-i*u),e[8]=o*(l*b-d*h)-c*(f*b-s*h)+p*(f*d-s*l),e[9]=-(n*(l*b-d*h)-c*(r*b-i*h)+p*(r*d-i*l)),e[10]=n*(f*b-s*h)-o*(r*b-i*h)+p*(r*s-i*f),e[11]=-(n*(f*d-s*l)-o*(r*d-i*l)+c*(r*s-i*f)),e[12]=-(o*(l*v-m*h)-c*(f*v-u*h)+p*(f*m-u*l)),e[13]=n*(l*v-m*h)-c*(r*v-a*h)+p*(r*m-a*l),e[14]=-(n*(f*v-u*h)-o*(r*v-a*h)+p*(r*u-a*f)),e[15]=n*(f*m-u*l)-o*(r*m-a*l)+c*(r*u-a*f),e}t.exports=r},{}],6:[function(e,t,n){function r(e){var t=new Float32Array(16);return t[0]=e[0],t[1]=e[1],t[2]=e[2],t[3]=e[3],t[4]=e[4],t[5]=e[5],t[6]=e[6],t[7]=e[7],t[8]=e[8],t[9]=e[9],t[10]=e[10],t[11]=e[11],t[12]=e[12],t[13]=e[13],t[14]=e[14],t[15]=e[15],t}t.exports=r},{}],7:[function(e,t,n){function 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a=e(13);t.exports=r},{13:13}],17:[function(e,t,n){function r(e,t,n){var r=t[0],a=t[1],i=t[2],o=t[3],f=t[4],u=t[5],s=t[6],c=t[7],l=t[8],m=t[9],d=t[10],p=t[11],h=t[12],v=t[13],b=t[14],g=t[15],y=n[0],x=n[1],w=n[2],k=n[3];return e[0]=y*r+x*f+w*l+k*h,e[1]=y*a+x*u+w*m+k*v,e[2]=y*i+x*s+w*d+k*b,e[3]=y*o+x*c+w*p+k*g,y=n[4],x=n[5],w=n[6],k=n[7],e[4]=y*r+x*f+w*l+k*h,e[5]=y*a+x*u+w*m+k*v,e[6]=y*i+x*s+w*d+k*b,e[7]=y*o+x*c+w*p+k*g,y=n[8],x=n[9],w=n[10],k=n[11],e[8]=y*r+x*f+w*l+k*h,e[9]=y*a+x*u+w*m+k*v,e[10]=y*i+x*s+w*d+k*b,e[11]=y*o+x*c+w*p+k*g,y=n[12],x=n[13],w=n[14],k=n[15],e[12]=y*r+x*f+w*l+k*h,e[13]=y*a+x*u+w*m+k*v,e[14]=y*i+x*s+w*d+k*b,e[15]=y*o+x*c+w*p+k*g,e}t.exports=r},{}],18:[function(e,t,n){function r(e,t,n,r,a,i,o){var f=1/(t-n),u=1/(r-a),s=1/(i-o);return e[0]=-2*f,e[1]=0,e[2]=0,e[3]=0,e[4]=0,e[5]=-2*u,e[6]=0,e[7]=0,e[8]=0,e[9]=0,e[10]=2*s,e[11]=0,e[12]=(t+n)*f,e[13]=(a+r)*u,e[14]=(o+i)*s,e[15]=1,e}t.exports=r},{}],19:[function(e,t,n){function r(e,t,n,r,a){var i=1/Math.tan(t/2),o=1/(r-a);return e[0]=i/n,e[1]=0,e[2]=0,e[3]=0,e[4]=0,e[5]=i,e[6]=0,e[7]=0,e[8]=0,e[9]=0,e[10]=(a+r)*o,e[11]=-1,e[12]=0,e[13]=0,e[14]=2*a*r*o,e[15]=0,e}t.exports=r},{}],20:[function(e,t,n){function r(e,t,n,r){var a=Math.tan(t.upDegrees*Math.PI/180),i=Math.tan(t.downDegrees*Math.PI/180),o=Math.tan(t.leftDegrees*Math.PI/180),f=Math.tan(t.rightDegrees*Math.PI/180),u=2/(o+f),s=2/(a+i);return e[0]=u,e[1]=0,e[2]=0,e[3]=0,e[4]=0,e[5]=s,e[6]=0,e[7]=0,e[8]=-((o-f)*u*.5),e[9]=(a-i)*s*.5,e[10]=r/(n-r),e[11]=-1,e[12]=0,e[13]=0,e[14]=r*n/(n-r),e[15]=0,e}t.exports=r},{}],21:[function(e,t,n){function r(e,t,n,r){var a,i,o,f,u,s,c,l,m,d,p,h,v,b,g,y,x,w,k,S,_,A,E,D,T=r[0],j=r[1],C=r[2],O=Math.sqrt(T*T+j*j+C*C);return Math.abs(O)<1e-6?null:(O=1/O,T*=O,j*=O,C*=O,a=Math.sin(n),i=Math.cos(n),o=1-i,f=t[0],u=t[1],s=t[2],c=t[3],l=t[4],m=t[5],d=t[6],p=t[7],h=t[8],v=t[9],b=t[10],g=t[11],y=T*T*o+i,x=j*T*o+C*a,w=C*T*o-j*a,k=T*j*o-C*a,S=j*j*o+i,_=C*j*o+T*a,A=T*C*o+j*a,E=j*C*o-T*a,D=C*C*o+i,e[0]=f*y+l*x+h*w,e[1]=u*y+m*x+v*w,e[2]=s*y+d*x+b*w,e[3]=c*y+p*x+g*w,e[4]=f*k+l*S+h*_,e[5]=u*k+m*S+v*_,e[6]=s*k+d*S+b*_,e[7]=c*k+p*S+g*_,e[8]=f*A+l*E+h*D,e[9]=u*A+m*E+v*D,e[10]=s*A+d*E+b*D,e[11]=c*A+p*E+g*D,t!==e&&(e[12]=t[12],e[13]=t[13],e[14]=t[14],e[15]=t[15]),e)}t.exports=r},{}],22:[function(e,t,n){function r(e,t,n){var r=Math.sin(n),a=Math.cos(n),i=t[4],o=t[5],f=t[6],u=t[7],s=t[8],c=t[9],l=t[10],m=t[11];return t!==e&&(e[0]=t[0],e[1]=t[1],e[2]=t[2],e[3]=t[3],e[12]=t[12],e[13]=t[13],e[14]=t[14],e[15]=t[15]),e[4]=i*a+s*r,e[5]=o*a+c*r,e[6]=f*a+l*r,e[7]=u*a+m*r,e[8]=s*a-i*r,e[9]=c*a-o*r,e[10]=l*a-f*r,e[11]=m*a-u*r,e}t.exports=r},{}],23:[function(e,t,n){function r(e,t,n){var r=Math.sin(n),a=Math.cos(n),i=t[0],o=t[1],f=t[2],u=t[3],s=t[8],c=t[9],l=t[10],m=t[11];return t!==e&&(e[4]=t[4],e[5]=t[5],e[6]=t[6],e[7]=t[7],e[12]=t[12],e[13]=t[13],e[14]=t[14],e[15]=t[15]),e[0]=i*a-s*r,e[1]=o*a-c*r,e[2]=f*a-l*r,e[3]=u*a-m*r,e[8]=i*r+s*a,e[9]=o*r+c*a,e[10]=f*r+l*a,e[11]=u*r+m*a,e}t.exports=r},{}],24:[function(e,t,n){function r(e,t,n){var r=Math.sin(n),a=Math.cos(n),i=t[0],o=t[1],f=t[2],u=t[3],s=t[4],c=t[5],l=t[6],m=t[7];return t!==e&&(e[8]=t[8],e[9]=t[9],e[10]=t[10],e[11]=t[11],e[12]=t[12],e[13]=t[13],e[14]=t[14],e[15]=t[15]),e[0]=i*a+s*r,e[1]=o*a+c*r,e[2]=f*a+l*r,e[3]=u*a+m*r,e[4]=s*a-i*r,e[5]=c*a-o*r,e[6]=l*a-f*r,e[7]=m*a-u*r,e}t.exports=r},{}],25:[function(e,t,n){function r(e,t,n){var r=n[0],a=n[1],i=n[2];return e[0]=t[0]*r,e[1]=t[1]*r,e[2]=t[2]*r,e[3]=t[3]*r,e[4]=t[4]*a,e[5]=t[5]*a,e[6]=t[6]*a,e[7]=t[7]*a,e[8]=t[8]*i,e[9]=t[9]*i,e[10]=t[10]*i,e[11]=t[11]*i,e[12]=t[12],e[13]=t[13],e[14]=t[14],e[15]=t[15],e}t.exports=r},{}],26:[function(e,t,n){function 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