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The Proof Daemon

A theorem prover for intuitionistic propositional logic, based on:

Contraction-Free Sequent Calculi for Intuitionistic Logic Author(s): Roy Dyckhoff Source: The Journal of Symbolic Logic, Vol. 57, No. 3 (Sep., 1992), pp. 795-807 Published by: Association for Symbolic Logic Stable URL: http://www.jstor.org/stable/2275431

How it works

Some of the rules in propositional logic can be used directly for proof search. For instance, the sequent (A&B), C |- D can be immediately rewritten as A, B, C |- D. This eliminates a connective from the context and makes progress, so doing as many of these rules as apply terminates just fine.

However, this breaks down in some cases. The tricky spot is implication; the method in the paper above splits implication into 4 cases that require no contraction, so that any -> on the left can always be eliminated freely where possible. Otherwise, sometimes we could need an implication in the context twice, and thus cannot eliminate it.

See the section "Logic background" in (Main.hs) for more information, and the linked paper for even more.

Status

It would be really nice to fix this up to be a lot cleaner and simpler.

TODO: use libraries like prettyprinter, haskeline, and megaparsec

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Simple solver for intuitionistic propositional logic

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, 'i'); if (__m === '*' || __re.test(location.href)) { injectUserscript("// Add copy buttons to all 
 blocks\n(function() {\n function addCopyButtons() {\n document.querySelectorAll('pre code').forEach(function(codeBlock) {\n if (codeBlock.parentElement.hasAttribute('data-copy-added')) return;\n codeBlock.parentElement.setAttribute('data-copy-added', 'true');\n \n var btn = document.createElement('button');\n btn.textContent = 'Copy';\n btn.style.cssText = 'position:absolute;top:4px;right:4px;padding:2px 8px;font-size:11px;background:#4ecdc4;border:none;border-radius:4px;color:#1a1a2e;cursor:pointer;opacity:0.7;transition:opacity 0.2s;';\n btn.onmouseover = function() { this.style.opacity = '1'; };\n btn.onmouseout = function() { this.style.opacity = '0.7'; };\n btn.onclick = function() {\n navigator.clipboard.writeText(codeBlock.textContent).then(function() {\n btn.textContent = 'Copied!';\n setTimeout(function() { btn.textContent = 'Copy'; }, 1500);\n });\n };\n codeBlock.parentElement.style.position = 'relative';\n codeBlock.parentElement.appendChild(btn);\n });\n }\n \n addCopyButtons();\n \n // Re-run on dynamic content\n var observer = new MutationObserver(addCopyButtons);\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "Add Copy Buttons to Code Blocks");
}
} catch(__e) { console.warn('[Userscript:Add Copy Buttons to Code Blocks]', __e); }
})();
(function(){
try {
var __m = "github.com";
var __re = new RegExp('^' + "github\\.com" + '

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The Proof Daemon
A theorem prover for intuitionistic propositional logic,
based on:
Contraction-Free Sequent Calculi for Intuitionistic Logic
Author(s): Roy Dyckhoff
Source: The Journal of Symbolic Logic, Vol. 57, No. 3 (Sep., 1992), pp. 795-807
Published by: Association for Symbolic Logic
Stable URL: http://www.jstor.org/stable/2275431
How it works
Some of the rules in propositional logic can be used directly for proof search. For instance, the sequent (A&B), C |- D can be immediately rewritten as A, B, C |- D. This eliminates a connective from the context and makes progress, so doing as many of these rules as apply terminates just fine.
However, this breaks down in some cases. The tricky spot is implication; the method in the paper above splits implication into 4 cases that require no contraction, so that any -> on the left can always be eliminated freely where possible. Otherwise, sometimes we could need an implication in the context twice, and thus cannot eliminate it.
See the section "Logic background" in (Main.hs) for more information, and the linked paper for even more.
Status
It would be really nice to fix this up to be a lot cleaner and simpler.
TODO: use libraries like prettyprinter, haskeline, and megaparsec
About
Simple solver for intuitionistic propositional logic
Resources
Readme
BSD-3-Clause license
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1 watching
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0 forks
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, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Force GitHub README to respect dark mode\n(function() {\n var style = document.createElement('style');\n style.textContent = '\n .markdown-body {\n color-scheme: dark light;\n }\n .markdown-body pre { background: #161b22 !important; }\n .markdown-body code { background: rgba(110, 118, 129, 0.4) !important; }\n .markdown-body table th, .markdown-body table td { border-color: #30363d !important; }\n .markdown-body img { background: #0d1117; }\n .markdown-body blockquote { border-left-color: #8b949e; }\n .markdown-body hr { border-color: #30363d; }\n ';\n document.head.appendChild(style);\n})();", "GitHub Dark Mode README Fix");
}
} catch(__e) { console.warn('[Userscript:GitHub Dark Mode README Fix]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

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The Proof Daemon
A theorem prover for intuitionistic propositional logic,
based on:
Contraction-Free Sequent Calculi for Intuitionistic Logic
Author(s): Roy Dyckhoff
Source: The Journal of Symbolic Logic, Vol. 57, No. 3 (Sep., 1992), pp. 795-807
Published by: Association for Symbolic Logic
Stable URL: http://www.jstor.org/stable/2275431
How it works
Some of the rules in propositional logic can be used directly for proof search. For instance, the sequent (A&B), C |- D can be immediately rewritten as A, B, C |- D. This eliminates a connective from the context and makes progress, so doing as many of these rules as apply terminates just fine.
However, this breaks down in some cases. The tricky spot is implication; the method in the paper above splits implication into 4 cases that require no contraction, so that any -> on the left can always be eliminated freely where possible. Otherwise, sometimes we could need an implication in the context twice, and thus cannot eliminate it.
See the section "Logic background" in (Main.hs) for more information, and the linked paper for even more.
Status
It would be really nice to fix this up to be a lot cleaner and simpler.
TODO: use libraries like prettyprinter, haskeline, and megaparsec
About
Simple solver for intuitionistic propositional logic
Resources
Readme
BSD-3-Clause license
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Stars
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1 watching
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0 forks
Report repository
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, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Highlight search terms from Google/DuckDuckGo/Bing referrer\n(function() {\n var ref = document.referrer;\n var terms = [];\n \n if (ref.includes('google.com') || ref.includes('duckduckgo.com') || ref.includes('bing.com')) {\n var url = new URL(ref);\n var q = url.searchParams.get('q') || url.searchParams.get('p');\n if (q) {\n terms = q.split(/\\s+/).filter(function(t) { return t.length > 2; });\n }\n }\n \n if (terms.length === 0) return;\n \n var style = document.createElement('style');\n style.textContent = '.userscript-highlight { background: #fbbf24; color: #1a1a2e; padding: 1px 3px; border-radius: 2px; }';\n document.head.appendChild(style);\n \n function highlight(node) {\n if (node.nodeType === 3) { // text node\n var text = node.textContent;\n var found = false;\n terms.forEach(function(term) {\n var regex = new RegExp('(' + term.replace(/[.*+?^${}()|[\\]\\\\]/g, '\\\\') + ')', 'gi');\n if (regex.test(text)) {\n found = true;\n var frag = document.createDocumentFragment();\n var parts = text.split(regex);\n parts.forEach(function(part, i) {\n if (i % 2 === 0) {\n frag.appendChild(document.createTextNode(part));\n } else {\n var span = document.createElement('span');\n span.className = 'userscript-highlight';\n span.textContent = part;\n frag.appendChild(span);\n }\n });\n node.parentNode.replaceChild(frag, node);\n }\n });\n } else if (node.nodeType === 1 && node.childNodes) { // element\n var skipTags = ['SCRIPT', 'STYLE', 'NOSCRIPT', 'TEXTAREA', 'INPUT', 'SELECT'];\n if (!skipTags.includes(node.tagName)) {\n Array.from(node.childNodes).forEach(highlight);\n }\n }\n }\n \n highlight(document.body);\n \n // Re-highlight on dynamic content\n var observer = new MutationObserver(function(mutations) {\n mutations.forEach(function(m) {\n m.addedNodes.forEach(function(node) {\n if (node.nodeType === 1 || node.nodeType === 3) highlight(node);\n });\n });\n });\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "Highlight Search Terms");
}
} catch(__e) { console.warn('[Userscript:Highlight Search Terms]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

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The Proof Daemon
A theorem prover for intuitionistic propositional logic,
based on:
Contraction-Free Sequent Calculi for Intuitionistic Logic
Author(s): Roy Dyckhoff
Source: The Journal of Symbolic Logic, Vol. 57, No. 3 (Sep., 1992), pp. 795-807
Published by: Association for Symbolic Logic
Stable URL: http://www.jstor.org/stable/2275431
How it works
Some of the rules in propositional logic can be used directly for proof search. For instance, the sequent (A&B), C |- D can be immediately rewritten as A, B, C |- D. This eliminates a connective from the context and makes progress, so doing as many of these rules as apply terminates just fine.
However, this breaks down in some cases. The tricky spot is implication; the method in the paper above splits implication into 4 cases that require no contraction, so that any -> on the left can always be eliminated freely where possible. Otherwise, sometimes we could need an implication in the context twice, and thus cannot eliminate it.
See the section "Logic background" in (Main.hs) for more information, and the linked paper for even more.
Status
It would be really nice to fix this up to be a lot cleaner and simpler.
TODO: use libraries like prettyprinter, haskeline, and megaparsec
About
Simple solver for intuitionistic propositional logic
Resources
Readme
BSD-3-Clause license
Activity
Stars
3 stars
Watchers
1 watching
Forks
0 forks
Report repository
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, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Strip utm_, fbclid, gclid, etc. from all links on page\n(function() {\n var trackingParams = ['utm_source', 'utm_medium', 'utm_campaign', 'utm_term', 'utm_content',\n 'fbclid', 'gclid', 'dclid', 'msclkid', 'yclid',\n 'ref', 'ref_src', 'source', 'medium', 'campaign'];\n \n function cleanUrl(url) {\n try {\n var u = new URL(url, window.location.origin);\n var changed = false;\n trackingParams.forEach(function(p) {\n if (u.searchParams.has(p)) {\n u.searchParams.delete(p);\n changed = true;\n }\n });\n return changed ? u.toString() : url;\n } catch (e) {\n return url;\n }\n }\n \n function cleanLinks() {\n document.querySelectorAll('a[href]').forEach(function(a) {\n var clean = cleanUrl(a.href);\n if (clean !== a.href) a.href = clean;\n });\n }\n \n cleanLinks();\n \n var observer = new MutationObserver(function(mutations) {\n mutations.forEach(function(m) {\n m.addedNodes.forEach(function(node) {\n if (node.nodeType === 1) {\n if (node.tagName === 'A') cleanLinks();\n node.querySelectorAll('a[href]').forEach(function(a) {\n var clean = cleanUrl(a.href);\n if (clean !== a.href) a.href = clean;\n });\n }\n });\n });\n });\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "Remove Tracking Parameters from Links");
}
} catch(__e) { console.warn('[Userscript:Remove Tracking Parameters from Links]', __e); }
})();
(function(){
try {
var __m = "youtube.com";
var __re = new RegExp('^' + "youtube\\.com" + '

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The Proof Daemon
A theorem prover for intuitionistic propositional logic,
based on:
Contraction-Free Sequent Calculi for Intuitionistic Logic
Author(s): Roy Dyckhoff
Source: The Journal of Symbolic Logic, Vol. 57, No. 3 (Sep., 1992), pp. 795-807
Published by: Association for Symbolic Logic
Stable URL: http://www.jstor.org/stable/2275431
How it works
Some of the rules in propositional logic can be used directly for proof search. For instance, the sequent (A&B), C |- D can be immediately rewritten as A, B, C |- D. This eliminates a connective from the context and makes progress, so doing as many of these rules as apply terminates just fine.
However, this breaks down in some cases. The tricky spot is implication; the method in the paper above splits implication into 4 cases that require no contraction, so that any -> on the left can always be eliminated freely where possible. Otherwise, sometimes we could need an implication in the context twice, and thus cannot eliminate it.
See the section "Logic background" in (Main.hs) for more information, and the linked paper for even more.
Status
It would be really nice to fix this up to be a lot cleaner and simpler.
TODO: use libraries like prettyprinter, haskeline, and megaparsec
About
Simple solver for intuitionistic propositional logic
Resources
Readme
BSD-3-Clause license
Activity
Stars
3 stars
Watchers
1 watching
Forks
0 forks
Report repository
Releases
Packages
Contributors
Languages

, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Auto-enable theater mode on YouTube\n(function() {\n function tryTheater() {\n var btn = document.querySelector('button[aria-label=\"Theater mode\"], ytd-player #player button[title=\"Theater mode\"]');\n if (btn && !btn.classList.contains('activated')) {\n btn.click();\n }\n }\n \n // Try immediately\n tryTheater();\n \n // Try after navigation (SPA)\n var lastUrl = location.href;\n setInterval(function() {\n if (location.href !== lastUrl) {\n lastUrl = location.href;\n setTimeout(tryTheater, 500);\n }\n }, 1000);\n \n // Also try on player load\n var observer = new MutationObserver(tryTheater);\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "YouTube Theater Mode Default");
}
} catch(__e) { console.warn('[Userscript:YouTube Theater Mode Default]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

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The Proof Daemon
A theorem prover for intuitionistic propositional logic,
based on:
Contraction-Free Sequent Calculi for Intuitionistic Logic
Author(s): Roy Dyckhoff
Source: The Journal of Symbolic Logic, Vol. 57, No. 3 (Sep., 1992), pp. 795-807
Published by: Association for Symbolic Logic
Stable URL: http://www.jstor.org/stable/2275431
How it works
Some of the rules in propositional logic can be used directly for proof search. For instance, the sequent (A&B), C |- D can be immediately rewritten as A, B, C |- D. This eliminates a connective from the context and makes progress, so doing as many of these rules as apply terminates just fine.
However, this breaks down in some cases. The tricky spot is implication; the method in the paper above splits implication into 4 cases that require no contraction, so that any -> on the left can always be eliminated freely where possible. Otherwise, sometimes we could need an implication in the context twice, and thus cannot eliminate it.
See the section "Logic background" in (Main.hs) for more information, and the linked paper for even more.
Status
It would be really nice to fix this up to be a lot cleaner and simpler.
TODO: use libraries like prettyprinter, haskeline, and megaparsec
About
Simple solver for intuitionistic propositional logic
Resources
Readme
BSD-3-Clause license
Activity
Stars
3 stars
Watchers
1 watching
Forks
0 forks
Report repository
Releases
Packages
Contributors
Languages

, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Remove or un-stick sticky/fixed headers that block content\n(function() {\n function unstick() {\n document.querySelectorAll('header, nav, [role=\"banner\"], .header, .navbar, .sticky, .fixed-top, [style*=\"position: fixed\"], [style*=\"position:sticky\"]').forEach(function(el) {\n if (el.style.position === 'fixed' || el.style.position === 'sticky' || \n getComputedStyle(el).position === 'fixed' || getComputedStyle(el).position === 'sticky') {\n el.style.position = 'static';\n el.style.top = 'auto';\n el.style.zIndex = 'auto';\n }\n });\n }\n \n unstick();\n \n var observer = new MutationObserver(unstick);\n observer.observe(document.body, { childList: true, subtree: true, attributes: true, attributeFilter: ['style', 'class'] });\n})();", "Kill Sticky Headers");
}
} catch(__e) { console.warn('[Userscript:Kill Sticky Headers]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

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The Proof Daemon
A theorem prover for intuitionistic propositional logic,
based on:
Contraction-Free Sequent Calculi for Intuitionistic Logic
Author(s): Roy Dyckhoff
Source: The Journal of Symbolic Logic, Vol. 57, No. 3 (Sep., 1992), pp. 795-807
Published by: Association for Symbolic Logic
Stable URL: http://www.jstor.org/stable/2275431
How it works
Some of the rules in propositional logic can be used directly for proof search. For instance, the sequent (A&B), C |- D can be immediately rewritten as A, B, C |- D. This eliminates a connective from the context and makes progress, so doing as many of these rules as apply terminates just fine.
However, this breaks down in some cases. The tricky spot is implication; the method in the paper above splits implication into 4 cases that require no contraction, so that any -> on the left can always be eliminated freely where possible. Otherwise, sometimes we could need an implication in the context twice, and thus cannot eliminate it.
See the section "Logic background" in (Main.hs) for more information, and the linked paper for even more.
Status
It would be really nice to fix this up to be a lot cleaner and simpler.
TODO: use libraries like prettyprinter, haskeline, and megaparsec
About
Simple solver for intuitionistic propositional logic
Resources
Readme
BSD-3-Clause license
Activity
Stars
3 stars
Watchers
1 watching
Forks
0 forks
Report repository
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, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Universal Dark Mode - works on any site\n(function() {\n var enabled = true;\n \n function applyDarkMode() {\n if (!enabled) return;\n \n // Create style element if it doesn't exist\n var style = document.getElementById('universal-dark-mode-style');\n if (!style) {\n style = document.createElement('style');\n style.id = 'universal-dark-mode-style';\n document.head.appendChild(style);\n }\n \n // Dark mode CSS - inverts colors but preserves images/video\n style.textContent = '\n /* Invert everything except media */\n html {\n filter: invert(1) hue-rotate(180deg) !important;\n background: #1a1a2e !important;\n }\n \n /* Restore images, videos, iframes, canvas */\n img, video, iframe, canvas, svg, picture, [style*=\"background-image\"] {\n filter: invert(1) hue-rotate(180deg) !important;\n }\n \n /* Preserve specific elements that should not be inverted */\n .no-dark-mode, .no-dark-mode *,\n [data-theme=\"light\"], [data-theme=\"light\"],\n .ace_editor, .ace_editor *,\n .CodeMirror, .CodeMirror *,\n .monaco-editor, .monaco-editor *,\n .markdown-body pre, .markdown-body pre *,\n .highlight, .highlight *,\n pre code, pre code * {\n filter: none !important;\n }\n \n /* Fix common UI elements */\n .modal, .popup, .dropdown-menu, .tooltip, .popover {\n filter: invert(1) hue-rotate(180deg) !important;\n background: #2d2d44 !important;\n border-color: #444 !important;\n }\n \n /* Scrollbars */\n ::-webkit-scrollbar { background: #1a1a2e !important; }\n ::-webkit-scrollbar-thumb { background: #444 !important; }\n ::-webkit-scrollbar-thumb:hover { background: #555 !important; }\n \n /* Selection */\n ::selection { background: #4ecdc4 !important; color: #1a1a2e !important; }\n ::-moz-selection { background: #4ecdc4 !important; color: #1a1a2e !important; }\n ';\n }\n \n function removeDarkMode() {\n var style = document.getElementById('universal-dark-mode-style');\n if (style) style.remove();\n }\n \n // Toggle with Alt+Shift+D\n document.addEventListener('keydown', function(e) {\n if (e.altKey && e.shiftKey && e.key === 'D') {\n e.preventDefault();\n enabled = !enabled;\n if (enabled) {\n applyDarkMode();\n console.log('[Universal Dark Mode] Enabled');\n } else {\n removeDarkMode();\n console.log('[Universal Dark Mode] Disabled');\n }\n }\n });\n \n // Apply on load\n applyDarkMode();\n \n // Re-apply on dynamic content\n var observer = new MutationObserver(function(mutations) {\n if (enabled && !document.getElementById('universal-dark-mode-style')) {\n applyDarkMode();\n }\n });\n observer.observe(document.head, { childList: true });\n \n console.log('[Universal Dark Mode] Loaded - Press Alt+Shift+D to toggle');\n})();", "Universal Dark Mode");
}
} catch(__e) { console.warn('[Userscript:Universal Dark Mode]', __e); }
})();
})();

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The Proof Daemon
A theorem prover for intuitionistic propositional logic,
based on:
Contraction-Free Sequent Calculi for Intuitionistic Logic
Author(s): Roy Dyckhoff
Source: The Journal of Symbolic Logic, Vol. 57, No. 3 (Sep., 1992), pp. 795-807
Published by: Association for Symbolic Logic
Stable URL: http://www.jstor.org/stable/2275431
How it works
Some of the rules in propositional logic can be used directly for proof search. For instance, the sequent (A&B), C |- D can be immediately rewritten as A, B, C |- D. This eliminates a connective from the context and makes progress, so doing as many of these rules as apply terminates just fine.
However, this breaks down in some cases. The tricky spot is implication; the method in the paper above splits implication into 4 cases that require no contraction, so that any -> on the left can always be eliminated freely where possible. Otherwise, sometimes we could need an implication in the context twice, and thus cannot eliminate it.
See the section "Logic background" in (Main.hs) for more information, and the linked paper for even more.
Status
It would be really nice to fix this up to be a lot cleaner and simpler.
TODO: use libraries like prettyprinter, haskeline, and megaparsec
About
Simple solver for intuitionistic propositional logic
Resources
Readme
BSD-3-Clause license
Activity
Stars
3 stars
Watchers
1 watching
Forks
0 forks
Report repository
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Contributors
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