This tool is meant to transform Lean files to other documents. Currently what is implemented turns a Lean file with comments into a HTML page. For instance, this webpage was generated from this Lean file.
25 | 26 | 31 |-- begin header
16 |
17 | -- Everything in the header will be hidden in the HTML file.
18 | import data.real.basic
19 |
20 | notation `|` x `|` := abs x
21 |
22 | @[user_attribute]
23 | meta def ineq_rules : user_attribute :=
24 | { name := `ineq_rules,
25 | descr := "lemmas usable to prove inequalities" }
26 |
27 | attribute [ineq_rules] add_lt_add le_max_left le_max_right
28 |
29 | meta def obvious_ineq := `[linarith <|> apply_rules ineq_rules]
30 | run_cmd add_interactive [`obvious_ineq]
31 | -- end header
32 |
33 | /-
34 | # The sandwich theorem
35 |
36 | In this demo file, we define limits of sequences of real numbers and prove the sandwich theorem.
37 | -/
38 |
39 | /- Definition
40 | A sequence of real numbers $a_n$ tends to $l$ if
41 | $\forall \varepsilon > 0, \exists N, \forall n \geq N, |a_n - l | \leq \varepsilon$.
42 | -/
43 | definition is_limit (a : ℕ → ℝ) (l : ℝ) :=
44 | ∀ ε > 0, ∃ N, ∀ n ≥ N, | a n - l | < ε
45 |
46 | /- Theorem
47 | If $(a_n)$, $(b_n)$, and $(c_n)$ are three real-valued sequences satisfying $a_n ≤ b_n ≤ c_n$ for all $n$, and if furthermore $a_n→ℓ$ and $c_n→ℓ$, then $b_n→ℓ$.
48 | -/
49 | theorem sandwich (a b c : ℕ → ℝ)
50 | (l : ℝ) (ha : is_limit a l) (hc : is_limit c l)
51 | (hab : ∀ n, a n ≤ b n) (hbc : ∀ n, b n ≤ c n) : is_limit b l :=
52 | begin
53 | -- We need to show that for all $ε>0$ there exists $N$ such that $n≥N$ implies $|b_n-ℓ|<ε$. So choose ε > 0.
54 | intros ε Hε,
55 | -- we now need an $N$. As usual it is the max of two other N's, one coming from $(a_n)$ and one from $(c_n)$. Choose $N_a$ and $N_c$ such that $|aₙ - l| < ε$ for $n ≥ Na$ and $|cₙ - l| < ε$ for $n ≥ Nc$.
56 | cases ha ε Hε with Na Ha,
57 | cases hc ε Hε with Nc Hc,
58 | -- Now let $N$ be the max of $N_a$ and $N_c$; we claim that this works.
59 | let N := max Na Nc,
60 | use N,
61 | -- Note that N ≥ Na and N ≥ Nc,
62 | have HNa : Na ≤ N := by obvious_ineq,
63 | have HNc : Nc ≤ N := by obvious_ineq,
64 | -- so for all n ≥ N,
65 | intros n Hn,
66 | -- we have $n≥ N_a$ and $n\geq N_c$, so $aₙ ≤ bₙ ≤ cₙ$, and $|aₙ - l|, |bₙ - l|$ are both less than $\epsilon$.
67 | have h1 : a n ≤ b n := hab n,
68 | have h2 : b n ≤ c n := hbc n,
69 | have h3 : |a n - l| < ε := Ha n (le_trans HNa Hn),
70 | have h4 : |c n - l| < ε := Hc n (le_trans HNc Hn),
71 | -- The result now follows easily from these inequalities (as $l-ε<a_n≤b_n≤c_n<l+ε$).
72 | revert h3,revert h4,
73 | unfold abs,unfold max,
74 | split_ifs;intros;linarith,
75 | end
76 | This tool is meant to transform Lean files to other documents. Currently what is implemented turns a Lean file with comments into a HTML page. For instance, this webpage was generated from this Lean file.
25 | 26 | 31 |and
48 | rendered = self.markdown_renderer.render(Document(prepare(text))) 49 | return rendered if par else rendered[3:-5] 50 | 51 | def transform_text(self, text): 52 | return Text(paragraphs=[ 53 | Paragraph(content=self.render_markdown(par.content)) 54 | for par in text.paragraphs]) 55 | 56 | def transform_theorem(self, theorem): 57 | theorem.text = self.render_markdown(theorem.text) 58 | for proof_item in theorem.proof.items: 59 | proof_item.text = self.render_markdown(proof_item.text, par=False) 60 | for proof_line in proof_item.lines: 61 | for r, s in self.ts_filters: 62 | proof_line.tactic_state_left = r.sub( 63 | s, proof_line.tactic_state_left) 64 | proof_line.tactic_state_right = r.sub( 65 | s, proof_line.tactic_state_right) 66 | return theorem 67 | 68 | transform_example = transform_theorem 69 | transform_lemma = transform_theorem 70 | 71 | def transform_trad(self, theorem): 72 | theorem.content = self.render_markdown(theorem.content) 73 | return theorem 74 | 75 | def render(self, objects, out_path, page_context=None, title=None): 76 | """ 77 | Renders objects to path 78 | """ 79 | objects = [getattr(self, f'transform_{obj.name}', lambda x: x)(obj) 80 | for obj in objects] 81 | page_context = page_context or dict() 82 | page_context['title'] = page_context.get('title', title or 'Lean') 83 | res = '\n'.join([ 84 | self.env.get_template(obj.name).render(obj=color(obj), 85 | lang=page_context['lang']) for obj in objects]) 86 | page_context['content'] = res 87 | self.env.get_template('page').stream(page_context).dump(out_path) 88 | 89 | @classmethod 90 | def from_file(cls, path, ts_filters=None): 91 | return cls( 92 | env=Environment(loader=FileSystemLoader(path)), 93 | ts_filters=ts_filters or []) 94 | 95 | -------------------------------------------------------------------------------- /src/format_lean/server.py: -------------------------------------------------------------------------------- 1 | import os, subprocess, json 2 | 3 | class LeanError(Exception): 4 | pass 5 | 6 | class Server: 7 | """ 8 | Very rough interface around the Lean server. Will work only if nothing bad 9 | happens/ 10 | """ 11 | def __init__(self, lean_exec_path, lean_path): 12 | self.proc = subprocess.Popen([lean_exec_path, "-j0", "--server"], 13 | stdin=subprocess.PIPE, stdout=subprocess.PIPE, 14 | universal_newlines=True, bufsize=1, 15 | env={'LEAN_PATH': lean_path}) 16 | self.seq_num = 0 17 | 18 | def sync(self, filename): 19 | self.seq_num += 1 20 | s = f'{{"seq_num": {self.seq_num}, "command": "sync", "file_name": "{filename}"}}\n' 21 | self.proc.stdin.write(s) 22 | self.proc.stdout.readline() 23 | 24 | def info(self, filename, line, col): 25 | self.seq_num += 1 26 | s = f'{{"seq_num": {self.seq_num}, "command":"info", ' \ 27 | f'"file_name": "{filename}", ' \ 28 | f'"line": {line},"column":{col}}}\n' 29 | self.proc.stdin.write(s) 30 | ret = json.loads(self.proc.stdout.readline().rstrip()) 31 | if 'record' in ret: 32 | return ret['record']['state'] 33 | else: 34 | raise LeanError(ret) 35 | -------------------------------------------------------------------------------- /src/format_lean/teach_lean.css: -------------------------------------------------------------------------------- 1 | code { 2 | font-size: 1.2rem; 3 | font-weight: bold; 4 | } 5 | 6 | div#content { 7 | width: 100%; 8 | } 9 | 10 | div#content > p { 11 | width: 80%; 12 | } 13 | 14 | @media (max-width: 760px) { 15 | div#content { 16 | width: 100%; 17 | } 18 | } 19 | div.definition_wrapper { 20 | margin-top: 1rem; 21 | } 22 | 23 | span.definition_label { 24 | font-weight: bold; 25 | } 26 | 27 | div.definition_content { 28 | margin-left: 0.5rem; 29 | padding-left: 0.5rem; 30 | border-left: 0.15rem solid black; 31 | } 32 | 33 | div.definition_text:hover { 34 | transition: all 0.2s ease; 35 | background: #ffffc5; 36 | } 37 | 38 | div.definition_lean { 39 | display: block; 40 | } 41 | 42 | div.example_wrapper { 43 | margin-top: 1rem; 44 | } 45 | 46 | span.example_label { 47 | font-weight: bold; 48 | } 49 | 50 | div.example_content { 51 | margin-left: 0.5rem; 52 | padding-left: 0.5rem; 53 | border-left: 0.25rem solid black; 54 | } 55 | 56 | div.example_text:hover { 57 | transition: all 0.2s ease; 58 | background: #ffffc5; 59 | } 60 | 61 | div.example_lean { 62 | display: block; 63 | } 64 | 65 | div.lemma_wrapper { 66 | margin-top: 1rem; 67 | } 68 | 69 | span.lemma_label { 70 | font-weight: bold; 71 | } 72 | 73 | div.lemma_content { 74 | margin-left: 0.5rem; 75 | padding-left: 0.5rem; 76 | border-left: 0.15rem solid black; 77 | } 78 | 79 | div.lemma_text:hover { 80 | transition: all 0.2s ease; 81 | background: #ffffc5; 82 | } 83 | 84 | div.lemma_lean { 85 | display: none; 86 | } 87 | 88 | div.theorem_wrapper { 89 | margin-top: 1rem; 90 | } 91 | 92 | span.theorem_label { 93 | font-weight: bold; 94 | } 95 | 96 | div.theorem_content { 97 | margin-left: 0.5rem; 98 | padding-left: 0.5rem; 99 | border-left: 0.25rem solid black; 100 | } 101 | 102 | div.theorem_text:hover { 103 | transition: all 0.2s ease; 104 | background: #ffffc5; 105 | } 106 | 107 | div.theorem_lean { 108 | display: block; 109 | } 110 | 111 | div.proof_wrapper { 112 | margin-top: 1rem; 113 | width: 100%; 114 | } 115 | 116 | div.proof_wrapper::after { 117 | content: ""; 118 | clear: both; 119 | display: table; 120 | } 121 | 122 | span.proof_label { 123 | font-weight: bold; 124 | display: block; 125 | } 126 | 127 | span.proof_qed { 128 | font-weight: bold; 129 | display: block; 130 | } 131 | 132 | div.proof_content { 133 | padding-left: 0.5rem; 134 | } 135 | 136 | div.small_proof_content { 137 | padding-left: 0.5rem; 138 | width: 49%; 139 | float: left; 140 | } 141 | 142 | div.small_tactic_state { 143 | padding-left: 0.5rem; 144 | width: 49%; 145 | float: left; 146 | } 147 | 148 | span.proof_item_text:hover { 149 | transition: all 0.2s ease; 150 | background: #ffffc5; 151 | } 152 | 153 | div.proof_item_lean { 154 | display: block; 155 | } 156 | 157 | div.proof_line { 158 | display: flex; 159 | } 160 | 161 | div.inline_proof_item { 162 | display: inline; 163 | } 164 | 165 | span.tactic_left:hover { 166 | transition: all 0.2s ease; 167 | background: #ffffc5; 168 | } 169 | 170 | span.tactic_left { 171 | width: 3rem; 172 | background: #ffffdf; 173 | } 174 | 175 | span.tactic_right { 176 | margin-left: 2rem; 177 | width: 3rem; 178 | background: #ffffdf; 179 | } 180 | 181 | span.tactic_right:hover { 182 | transition: all 0.2s ease; 183 | background: #ffffc5; 184 | } 185 | 186 | span[class^=tactic_state_] { 187 | display: none; 188 | } 189 | 190 | div.example_wrapper { 191 | font-size: 1.4rem; 192 | } 193 | 194 | div.lemma_wrapper { 195 | font-size: 1.4rem; 196 | } 197 | 198 | div.theorem_wrapper { 199 | font-size: 1.4rem; 200 | } 201 | 202 | div.definition_wrapper { 203 | font-size: 1.4rem; 204 | } 205 | 206 | pre { 207 | margin-top: 0.2rem; 208 | margin-bottom: 0.2rem; 209 | } 210 | 211 | span.tactic_left { 212 | width: 3rem; 213 | background: #dddddd; 214 | } 215 | 216 | span.tactic_left:hover { 217 | transition: all 0.2s ease; 218 | background: #c4c4c4; 219 | } 220 | 221 | span.tactic_right { 222 | margin-left: 2rem; 223 | width: 3rem; 224 | background: #dddddd; 225 | } 226 | 227 | span.tactic_right:hover { 228 | transition: all 0.2s ease; 229 | background: #c4c4c4; 230 | } 231 | 232 | pre { 233 | white-space: pre-wrap; 234 | word-break: keep-all; 235 | } 236 | 237 | div.tikzcd { 238 | display: block; 239 | margin: 0.5rem auto; 240 | overflow: auto; 241 | text-align: center; 242 | } 243 | 244 | /*# sourceMappingURL=teach_lean.css.map */ 245 | -------------------------------------------------------------------------------- /src/format_lean/teach_lean.css.map: -------------------------------------------------------------------------------- 1 | {"version":3,"sourceRoot":"","sources":["../../sass/teach_lean.scss","../../sass/_definitions.scss","../../sass/_examples.scss","../../sass/_lemmas.scss","../../sass/_theorems.scss","../../sass/_proofs.scss","../../sass/_tikzcd.scss"],"names":[],"mappings":"AAGA;EACC;EACA;;;AAED;EACC;;;AAGD;EACC;;;AAED;EACA;IACC;;;ACbD;EAEI;;;AAGJ;EAEI;;;AAGJ;EAEI;EACA;EACA;;;AAGJ;EAEE;EAEA;;;AAGF;EAGC;;;AC5BD;EAEI;;;AAGJ;EAEI;;;AAGJ;EAEI;EACA;EACA;;;AAGJ;EAEE;EAEA;;;AAGF;EAGC;;;AC3BD;EAEI;;;AAGJ;EAEI;;;AAGJ;EAEI;EACA;EACA;;;AAGJ;EAEE;EAEA;;;AAGF;EAEE;;;AC1BF;EAEI;;;AAGJ;EAEI;;;AAGJ;EAEI;EACA;EACA;;;AAIJ;EAEE;EAEA;;;AAIF;EAGC;;;AC/BD;EAEI;EACF;;;AAEF;EACE;EACA;EACA;;;AAGF;EAEI;EACF;;;AAGF;EAEI;EACF;;;AAIF;EAEI;;;AAGJ;EAEI;EACF;EACA;;;AAGF;EAEI;EACF;EACA;;;AAIF;EAEE;EAEA;;;AAIF;EAEC;;;AAKD;EACE;;;AAIF;EAEC;;;AAGD;EACE;EACA;;;AAEF;EACE;EACA;;;AACF;EACE;EACA;EACA;;;AACF;EACE;EACA;;;AACF;EACE;;;ALhEF;EACC;;;AAED;EACC;;;AAED;EACC;;;AAED;EACC;;;AAGD;EACC;EACA;;;AAKD;EACE;EACA,YAJO;;;AAKT;EACE;EACA;;;AAED;EACC;EACA;EACA,YAZO;;;AAcT;EACE;EACA;;;AAED;EACA;EACC;;;AM1DF;EACC;EACA;EACA;EACA","file":"teach_lean.css"} -------------------------------------------------------------------------------- /src/format_lean/templates/definition: -------------------------------------------------------------------------------- 1 |\n' + token.content + '
\n' 136 | 137 | 138 | -------------------------------------------------------------------------------- /src/format_lean/with_tufte.css: -------------------------------------------------------------------------------- 1 | body { 2 | width: 100%; 3 | max-width: 100%; 4 | } 5 | 6 | code { 7 | font-size: 1.2rem; 8 | font-weight: bold; 9 | } 10 | 11 | div#content { 12 | width: 70%; 13 | } 14 | 15 | @media (max-width: 760px) { 16 | div#content { 17 | width: 100%; 18 | } 19 | } 20 | #dragbar { 21 | background-color: #111; 22 | } 23 | 24 | h1#tactic_state_header { 25 | font-size: 2rem; 26 | line-height: 2rem; 27 | margin: 1rem 0; 28 | color: #111; 29 | } 30 | 31 | div.definition_wrapper { 32 | margin-top: 1rem; 33 | } 34 | 35 | span.definition_label { 36 | font-weight: bold; 37 | } 38 | 39 | div.definition_content { 40 | margin-left: 0.5rem; 41 | padding-left: 0.5rem; 42 | border-left: 0.15rem solid black; 43 | } 44 | 45 | div.definition_text:hover { 46 | transition: all 0.2s ease; 47 | background: #ffffc5; 48 | } 49 | 50 | div.definition_lean { 51 | display: none; 52 | } 53 | 54 | div.example_wrapper { 55 | margin-top: 1rem; 56 | } 57 | 58 | span.example_label { 59 | font-weight: bold; 60 | } 61 | 62 | div.example_content { 63 | margin-left: 0.5rem; 64 | padding-left: 0.5rem; 65 | border-left: 0.25rem solid black; 66 | } 67 | 68 | div.example_text:hover { 69 | transition: all 0.2s ease; 70 | background: #ffffc5; 71 | } 72 | 73 | div.example_lean { 74 | display: none; 75 | } 76 | 77 | div.lemma_wrapper { 78 | margin-top: 1rem; 79 | } 80 | 81 | span.lemma_label { 82 | font-weight: bold; 83 | } 84 | 85 | div.lemma_content { 86 | margin-left: 0.5rem; 87 | padding-left: 0.5rem; 88 | border-left: 0.15rem solid black; 89 | } 90 | 91 | div.lemma_text:hover { 92 | transition: all 0.2s ease; 93 | background: #ffffc5; 94 | } 95 | 96 | div.lemma_lean { 97 | display: none; 98 | } 99 | 100 | div.theorem_wrapper { 101 | margin-top: 1rem; 102 | } 103 | 104 | span.theorem_label { 105 | font-weight: bold; 106 | } 107 | 108 | div.theorem_content { 109 | margin-left: 0.5rem; 110 | padding-left: 0.5rem; 111 | border-left: 0.25rem solid black; 112 | } 113 | 114 | div.theorem_lean { 115 | display: none; 116 | } 117 | 118 | div.proof_wrapper { 119 | margin-top: 1rem; 120 | width: 100%; 121 | } 122 | 123 | div.proof_wrapper::after { 124 | content: ""; 125 | clear: both; 126 | display: table; 127 | } 128 | 129 | span.proof_label { 130 | font-weight: bold; 131 | display: block; 132 | } 133 | 134 | span.proof_qed { 135 | font-weight: bold; 136 | display: block; 137 | } 138 | 139 | div.proof_content { 140 | padding-left: 0.5rem; 141 | } 142 | 143 | div.small_proof_content { 144 | padding-left: 0.5rem; 145 | width: 49%; 146 | float: left; 147 | } 148 | 149 | div.small_tactic_state { 150 | padding-left: 0.5rem; 151 | width: 49%; 152 | float: left; 153 | } 154 | 155 | div.proof_item_lean { 156 | display: none; 157 | } 158 | 159 | div.proof_line { 160 | display: flex; 161 | } 162 | 163 | div.inline_proof_item { 164 | display: inline; 165 | } 166 | 167 | span.tactic_left:hover { 168 | transition: all 0.2s ease; 169 | background: #ffffc5; 170 | } 171 | 172 | span.tactic_left { 173 | width: 3rem; 174 | background: #ffffdf; 175 | } 176 | 177 | span.tactic_right { 178 | margin-left: 2rem; 179 | width: 3rem; 180 | background: #ffffdf; 181 | } 182 | 183 | span.tactic_right:hover { 184 | transition: all 0.2s ease; 185 | background: #ffffc5; 186 | } 187 | 188 | span[class^=tactic_state_] { 189 | display: none; 190 | } 191 | 192 | div.example_wrapper { 193 | font-size: 1.4rem; 194 | } 195 | 196 | div.lemma_wrapper { 197 | font-size: 1.4rem; 198 | } 199 | 200 | div.theorem_wrapper { 201 | font-size: 1.4rem; 202 | } 203 | 204 | pre { 205 | margin-top: 0.2rem; 206 | margin-bottom: 0.2rem; 207 | } 208 | 209 | span.tactic_left { 210 | display: inline-block; 211 | width: 1rem; 212 | height: 1rem; 213 | background: #dddddd; 214 | } 215 | 216 | span.tactic_left:hover { 217 | transition: all 0.2s ease; 218 | background: #c4c4c4; 219 | } 220 | 221 | span.tactic_right { 222 | display: inline-block; 223 | width: 1rem; 224 | height: 1rem; 225 | margin-left: 0; 226 | background: #dddddd; 227 | } 228 | 229 | span.tactic_right:hover { 230 | transition: all 0.2s ease; 231 | background: #c4c4c4; 232 | } 233 | 234 | html { 235 | position: relative; 236 | } 237 | 238 | body { 239 | margin: 0; 240 | } 241 | 242 | div#wrapper { 243 | width: 100%; 244 | min-height: 100%; 245 | } 246 | 247 | div#content { 248 | padding: 1rem; 249 | width: 70%; 250 | } 251 | 252 | #dragbar { 253 | position: absolute; 254 | top: 0; 255 | min-height: 100%; 256 | left: 70%; 257 | width: 3px; 258 | cursor: col-resize; 259 | } 260 | 261 | div#tactic_state_wrapper { 262 | position: fixed; 263 | margin-left: 70%; 264 | top: 0px; 265 | padding: 1rem; 266 | } 267 | 268 | div#content { 269 | margin: 0; 270 | padding-left: 30px; 271 | } 272 | 273 | body { 274 | padding: 0; 275 | } 276 | 277 | /*# sourceMappingURL=with_tufte.css.map */ 278 | -------------------------------------------------------------------------------- /src/format_lean/with_tufte.css.map: -------------------------------------------------------------------------------- 1 | {"version":3,"sourceRoot":"","sources":["../../sass/with_tufte.scss","../../sass/_definitions.scss","../../sass/_examples.scss","../../sass/_lemmas.scss","../../sass/_theorems.scss","../../sass/_proofs.scss","../../sass/_big_tactic_state_layout.scss"],"names":[],"mappings":"AAGA;EACI;EACA;;;AAGJ;EACC;EACA;;;AAED;EACC;;;AAED;EACA;IACC;;;AAGD;EACG;;;AAGH;EACE;EACA;EACA;EACA;;;ACzBF;EAEI;;;AAGJ;EAEI;;;AAGJ;EAEI;EACA;EACA;;;AAGJ;EAEE;EAEA;;;AAGF;EAKC;;;AC9BD;EAEI;;;AAGJ;EAEI;;;AAGJ;EAEI;EACA;EACA;;;AAGJ;EAEE;EAEA;;;AAGF;EAKC;;;AC7BD;EAEI;;;AAGJ;EAEI;;;AAGJ;EAEI;EACA;EACA;;;AAGJ;EAEE;EAEA;;;AAGF;EAEE;;;AC1BF;EAEI;;;AAGJ;EAEI;;;AAGJ;EAEI;EACA;EACA;;;AAYJ;EAKC;;;ACjCD;EAEI;EACF;;;AAEF;EACE;EACA;EACA;;;AAGF;EAEI;EACF;;;AAGF;EAEI;EACF;;;AAIF;EAEI;;;AAGJ;EAEI;EACF;EACA;;;AAGF;EAEI;EACF;EACA;;;AAYF;EAIC;;;AAGD;EACE;;;AAIF;EAEC;;;AAGD;EACE;EACA;;;AAEF;EACE;EACA;;;AACF;EACE;EACA;EACA;;;AACF;EACE;EACA;;;AACF;EACE;;;ALrDF;EACC;;;AAED;EACC;;;AAED;EACC;;;AAGD;EACC;EACA;;;AAKD;EACE;EACA;EACA;EACA,YANO;;;AAQT;EACE;EACA;;;AAGF;EACE;EACA;EACA;EACA;EACA,YAlBO;;;AAoBT;EACE;EACA;;;AMpEF;EACC;;;AAGD;EACI;;;AASJ;EACE;EACA;;;AAGF;EAEE;EACA,OAVW;;;AAab;EACG;EACA;EACA;EACA,MAjBU;EAkBV;EACA;;;AAGH;EAEE;EACA,aAzBW;EA0BX;EACA;;;ANiCF;EACC;EACA;;;AAGD;EACC","file":"with_tufte.css"} --------------------------------------------------------------------------------