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| <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><meta name="viewport" content="width=device-width, initial-scale=1" /><title>HelVM.HelTC.HelTC</title><link href="linuwial.css" rel="stylesheet" type="text/css" title="Linuwial" /><link rel="stylesheet" type="text/css" href="quick-jump.css" /><link rel="stylesheet" type="text/css" href="https://fonts.googleapis.com/css?family=PT+Sans:400,400i,700" /><script src="haddock-bundle.min.js" async="async" type="text/javascript"></script><script type="text/x-mathjax-config">MathJax.Hub.Config({ tex2jax: { processClass: "mathjax", ignoreClass: ".*" } });</script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-AMS-MML_HTMLorMML" type="text/javascript"></script></head><body><div id="package-header"><span class="caption">heltc-0.1.0.1: HELCT - Heavenly Esoteric Little C Transpiler to Esoteric Languages</span><ul class="links" id="page-menu"><li><a href="index.html">Contents</a></li><li><a href="doc-index.html">Index</a></li></ul></div><div id="content"><div id="module-header"><table class="info"><tr><th>Safe Haskell</th><td>None</td></tr><tr><th>Language</th><td>Haskell2010</td></tr></table><p class="caption">HelVM.HelTC.HelTC</p></div><div id="interface"></div></div><div id="footer"><p>Produced by <a href="http://www.haskell.org/haddock/">Haddock</a> version 2.24.2</p></div></body></html> | ||
| <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><meta name="viewport" content="width=device-width, initial-scale=1" /><title>HelVM.HelTC.HelTC</title><link href="linuwial.css" rel="stylesheet" type="text/css" title="Linuwial" /><link rel="stylesheet" type="text/css" href="quick-jump.css" /><link rel="stylesheet" type="text/css" href="https://fonts.googleapis.com/css?family=PT+Sans:400,400i,700" /><script src="haddock-bundle.min.js" async="async" type="text/javascript"></script><script type="text/x-mathjax-config">MathJax.Hub.Config({ tex2jax: { processClass: "mathjax", ignoreClass: ".*" } });</script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-AMS-MML_HTMLorMML" type="text/javascript"></script></head><body><div id="package-header"><span class="caption">heltc-0.1.0.2: HELCT - Heavenly Esoteric Little C Transpiler to Esoteric Languages</span><ul class="links" id="page-menu"><li><a href="index.html">Contents</a></li><li><a href="doc-index.html">Index</a></li></ul></div><div id="content"><div id="module-header"><table class="info"><tr><th>Safe Haskell</th><td>None</td></tr><tr><th>Language</th><td>Haskell2010</td></tr></table><p class="caption">HelVM.HelTC.HelTC</p></div><div id="interface"></div></div><div id="footer"><p>Produced by <a href="http://www.haskell.org/haddock/">Haddock</a> version 2.24.2</p></div></body></html> |
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| <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><meta name="viewport" content="width=device-width, initial-scale=1" /><title>heltc-0.1.0.1: HELCT - Heavenly Esoteric Little C Transpiler to Esoteric Languages (Index)</title><link href="linuwial.css" rel="stylesheet" type="text/css" title="Linuwial" /><link rel="stylesheet" type="text/css" href="quick-jump.css" /><link rel="stylesheet" type="text/css" href="https://fonts.googleapis.com/css?family=PT+Sans:400,400i,700" /><script src="haddock-bundle.min.js" async="async" type="text/javascript"></script><script type="text/x-mathjax-config">MathJax.Hub.Config({ tex2jax: { processClass: "mathjax", ignoreClass: ".*" } });</script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-AMS-MML_HTMLorMML" type="text/javascript"></script></head><body><div id="package-header"><span class="caption">heltc-0.1.0.1: HELCT - Heavenly Esoteric Little C Transpiler to Esoteric Languages</span><ul class="links" id="page-menu"><li><a href="index.html">Contents</a></li><li><a href="doc-index.html">Index</a></li></ul></div><div id="content"></div><div id="footer"><p>Produced by <a href="http://www.haskell.org/haddock/">Haddock</a> version 2.24.2</p></div></body></html> | ||
| <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><meta name="viewport" content="width=device-width, initial-scale=1" /><title>heltc-0.1.0.2: HELCT - Heavenly Esoteric Little C Transpiler to Esoteric Languages (Index)</title><link href="linuwial.css" rel="stylesheet" type="text/css" title="Linuwial" /><link rel="stylesheet" type="text/css" href="quick-jump.css" /><link rel="stylesheet" type="text/css" href="https://fonts.googleapis.com/css?family=PT+Sans:400,400i,700" /><script src="haddock-bundle.min.js" async="async" type="text/javascript"></script><script type="text/x-mathjax-config">MathJax.Hub.Config({ tex2jax: { processClass: "mathjax", ignoreClass: ".*" } });</script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-AMS-MML_HTMLorMML" type="text/javascript"></script></head><body><div id="package-header"><span class="caption">heltc-0.1.0.2: HELCT - Heavenly Esoteric Little C Transpiler to Esoteric Languages</span><ul class="links" id="page-menu"><li><a href="index.html">Contents</a></li><li><a href="doc-index.html">Index</a></li></ul></div><div id="content"></div><div id="footer"><p>Produced by <a href="http://www.haskell.org/haddock/">Haddock</a> version 2.24.2</p></div></body></html> |
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| <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><meta name="viewport" content="width=device-width, initial-scale=1" /><title>heltc-0.1.0.1: HELCT - Heavenly Esoteric Little C Transpiler to Esoteric Languages</title><link href="linuwial.css" rel="stylesheet" type="text/css" title="Linuwial" /><link rel="stylesheet" type="text/css" href="quick-jump.css" /><link rel="stylesheet" type="text/css" href="https://fonts.googleapis.com/css?family=PT+Sans:400,400i,700" /><script src="haddock-bundle.min.js" async="async" type="text/javascript"></script><script type="text/x-mathjax-config">MathJax.Hub.Config({ tex2jax: { processClass: "mathjax", ignoreClass: ".*" } });</script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-AMS-MML_HTMLorMML" type="text/javascript"></script></head><body><div id="package-header"><span class="caption">heltc-0.1.0.1: HELCT - Heavenly Esoteric Little C Transpiler to Esoteric Languages</span><ul class="links" id="page-menu"><li><a href="index.html">Contents</a></li><li><a href="doc-index.html">Index</a></li></ul></div><div id="content"><div id="description"><h1>heltc-0.1.0.1: HELCT - Heavenly Esoteric Little C Transpiler to Esoteric Languages</h1><div class="doc"><p>Please see the README on GitHub at <a href="https://github.com/helvm/heltc#readme">https://github.com/helvm/heltc#readme</a></p></div></div><div id="module-list"><p class="caption">Modules</p><ul><li><span class="module details-toggle-control details-toggle" data-details-id="n.1">HelVM</span><details id="n.1" open="open"><summary class="hide-when-js-enabled">Submodules</summary><ul><li><span class="module details-toggle-control details-toggle" data-details-id="n.1.1">HelTC</span><details id="n.1.1" open="open"><summary class="hide-when-js-enabled">Submodules</summary><ul><li><span class="module"><span class="noexpander"> </span><a href="HelVM-HelTC-HelTC.html">HelVM.HelTC.HelTC</a></span></li></ul></details></li></ul></details></li></ul></div></div><div id="footer"><p>Produced by <a href="http://www.haskell.org/haddock/">Haddock</a> version 2.24.2</p></div></body></html> | ||
| <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><meta name="viewport" content="width=device-width, initial-scale=1" /><title>heltc-0.1.0.2: HELCT - Heavenly Esoteric Little C Transpiler to Esoteric Languages</title><link href="linuwial.css" rel="stylesheet" type="text/css" title="Linuwial" /><link rel="stylesheet" type="text/css" href="quick-jump.css" /><link rel="stylesheet" type="text/css" href="https://fonts.googleapis.com/css?family=PT+Sans:400,400i,700" /><script src="haddock-bundle.min.js" async="async" type="text/javascript"></script><script type="text/x-mathjax-config">MathJax.Hub.Config({ tex2jax: { processClass: "mathjax", ignoreClass: ".*" } });</script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-AMS-MML_HTMLorMML" type="text/javascript"></script></head><body><div id="package-header"><span class="caption">heltc-0.1.0.2: HELCT - Heavenly Esoteric Little C Transpiler to Esoteric Languages</span><ul class="links" id="page-menu"><li><a href="index.html">Contents</a></li><li><a href="doc-index.html">Index</a></li></ul></div><div id="content"><div id="description"><h1>heltc-0.1.0.2: HELCT - Heavenly Esoteric Little C Transpiler to Esoteric Languages</h1><div class="doc"><p>Please see the README on GitHub at <a href="https://github.com/helvm/heltc#readme">https://github.com/helvm/heltc#readme</a></p></div></div><div id="module-list"><p class="caption">Modules</p><ul><li><span class="module details-toggle-control details-toggle" data-details-id="n.1">HelVM</span><details id="n.1" open="open"><summary class="hide-when-js-enabled">Submodules</summary><ul><li><span class="module details-toggle-control details-toggle" data-details-id="n.1.1">HelTC</span><details id="n.1.1" open="open"><summary class="hide-when-js-enabled">Submodules</summary><ul><li><span class="module"><span class="noexpander"> </span><a href="HelVM-HelTC-HelTC.html">HelVM.HelTC.HelTC</a></span></li></ul></details></li></ul></details></li></ul></div></div><div id="footer"><p>Produced by <a href="http://www.haskell.org/haddock/">Haddock</a> version 2.24.2</p></div></body></html> |
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| ; Based on https://crypto.stanford.edu/~blynn/lambda/ | ||
|
|
||
| : T \ x \ y y | ||
| : F \ x \ y x | ||
| : , \ x \ y \ f f x y | ||
| : . \ x T | ||
| : @ \ n \ f \ x f (n f x) | ||
|
|
||
| ; 2 \ f \ x f (f x) | ||
| ; 3 \ f \ x f (f (f x)) | ||
| : exp \ m \ n n m | ||
|
|
||
| exp 2 3; Compute 2^ 3. |
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| ; Based on https://crypto.stanford.edu/~blynn/lambda/ | ||
|
|
||
| : T \ x \ y y | ||
| : F \ x \ y x | ||
| : , \ x \ y \ f f x y | ||
| : . \ x T | ||
| : @ \ n \ f \ x f (n f x) | ||
|
|
||
| : pred \ n \ f \ x n (\ g \ h h (g f)) (\ u x) (\ u u) | ||
| : mul \ m \ n \ f m (n f) | ||
| : is0 \ n n (\ _ F) T | ||
| : Y \ f (\ x x x) (\ x f (x x)) | ||
| : fact Y (\ f \ n (is0 n) 1 (mul n (f (pred n)))) | ||
|
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||
| fact 4; Compute 4! |
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| ; https://crypto.stanford.edu/~blynn/lambda/ | ||
|
|
||
| : var \ m \ a \ b \ c a m | ||
| : app \ m \ n \ a \ b \ c b m n | ||
| : abs \ f \ a \ b \ c c f | ||
|
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||
| ; Our `quote` primitive lies outside lambda calculus: | ||
| ; quote ((\ y y) x) | ||
|
|
||
| ; Encoding terms in lambda calculus (without typing the raw encoding): | ||
| ; app (abs (\ y var y)) (var x) |
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| ; https://crypto.stanford.edu/~blynn/lambda/ | ||
|
|
||
| ; Shallow encoding. | ||
| : var \ x \ i x | ||
| : app \ m \ n \ i i (m i) (n i) | ||
| : abs \ f \ i \ x f x i | ||
| : E \ q q (\ x x); A self-interpreter. | ||
|
|
||
| : qsucc abs (\ n abs(\ f abs(\ x app (var f) (app (app (var n) (var f)) (var x))))) | ||
| : q0 abs (\ f abs(\ x var x)) | ||
|
|
||
| E (app qsucc (app qsucc q0)); Compute succ (succ 0). |
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| ; Based on https://crypto.stanford.edu/~blynn/lambda/ | ||
|
|
||
| ; See Mogensen, "Efficient Self-Interpretation in Lambda Calculus". | ||
| : Y \ f (\ x f(x x))(\ x f(x x)) | ||
| : E Y (\ e \ m m (\ x x) (\ m \ n (e m)(e n)) (\ m \ v e (m v))) | ||
| : P Y (\ p \ m (\ x x(\ v p(\ a \ b \ c b m(v (\ a \ b b)))) m )) | ||
| : RR Y (\ r \ m m (\ x x) (\ m \ n (r m) (\ a \ b a) (r n)) (\ m (\ g \ x x g (\ a \ b \ c c (\ w g (P (\ a \ b \ c a w))(\ a \ b b)))) (\ v r (m v)))) | ||
| : R \ m RR m (\ a \ b b) | ||
| ; 1 \ f \ x f x | ||
| : succ \ n \ f \ x f (n f x) | ||
|
|
||
| ; E (quote (succ (succ (succ 1)))); Self-interpreter demo. |
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| ; Based on https://crypto.stanford.edu/~blynn/lambda/ | ||
|
|
||
| ; See Mogensen, "Efficient Self-Interpretation in Lambda Calculus". | ||
| : Y \ f (\ x f(x x))(\ x f(x x)) | ||
| : E Y (\ e \ m m (\ x x) (\ m \ n (e m)(e n)) (\ m \ v e (m v))) | ||
| : P Y (\ p \ m (\ x x(\ v p(\ a \ b \ c b m(v (\ a \ b b)))) m )) | ||
| : RR Y (\ r \ m m (\ x x) (\ m \ n (r m) (\ a \ b a) (r n)) (\ m (\ g \ x x g (\ a \ b \ c c (\ w g (P (\ a \ b \ c a w))(\ a \ b b)))) (\ v r (m v)))) | ||
| : R \ m RR m (\ a \ b b) | ||
| ; 1 \ f \ x f x | ||
| : succ \ n \ f \ x f (n f x) | ||
|
|
||
| ; R (quote (succ (succ (succ 1)))); Self-reducer demo. |
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| ; https://justine.lol/lambda/ | ||
|
|
||
| : if # 0 | ||
| : omega # (0 0) | ||
| : pair ### ((0 2) 1) | ||
| : car # (0 $true) | ||
| : cdr # (0 $false) | ||
| : or ## ((0 0) 1) | ||
| : and ## ((0 1) 0) | ||
| : not ### ((2 0) 1) | ||
| : xor ## ((1 ## ((2 0) 1)) 0) | ||
| : bitxor ## ((1 0) ## ((2 0) 1)) | ||
| : iszero ### ((2 # 1) 1) | ||
| : Y # (# (0 0) # (1 (0 0))) | ||
|
|
||
| : zero ## 0 | ||
| : one ## (1 0) | ||
| : two ## (1 (1 0)) | ||
| : three ## (1 (1 (1 0))) | ||
| : four ## (1 (1 (1 (1 0)))) | ||
| : five ## (1 (1 (1 (1 (1 0))))) | ||
| : six ## (1 (1 (1 (1 (1 (1 0)))))) | ||
| : seven ## (1 (1 (1 (1 (1 (1 (1 0))))))) | ||
| : eight ## (1 (1 (1 (1 (1 (1 (1 (1 0)))))))) | ||
| : nine ## (1 (1 (1 (1 (1 (1 (1 (1 (1 0))))))))) | ||
|
|
||
| : pow ## (0 1) | ||
| : mul ### (2 (1 0)) | ||
| : dec ### (((2 ## (0 (1 3))) # 1) # 0) | ||
| : sub ## ((0 $dec) 1) | ||
| : inc ### (1 ((2 1) 0)) | ||
| : add #### ((3 1) ((2 1) 0)) | ||
| : fac ## (((1 ## (0 (1 ## ((2 1) (1 0))))) #1) #0) | ||
| : min #### (((3 ## (0 1)) #1) ((2 ## (3 (0 1))) #1)) | ||
| : div #### (((3 ## (0 1)) # 1) ((3 # (((3 ## (0 1)) # (3 (0 1))) #0)) 0)) | ||
| : mod #### (((3 $cdr) ((3 # (((3 ### ((0 (2 (5 1))) 1)) #1) 1)) #1)) ##0) | ||
|
|
||
| : eq ## ((((1 # ((0 #0) #0)) ((0 ### (1 2)) ##0)) ###0) ##1) | ||
| : le ## (((1 ## (0 1)) ###1) ((0 ## (0 1)) ###0)) | ||
| : lt ## (((0 ## (0 1)) ###0) ((1 ## (0 1)) ###1)) | ||
| : odd # (# (0 0) ## ((0 ## 1) # ((0 ## 0) (2 2)))) | ||
| : divides ## (((1 $cdr) ($omega #(((1 ### ((0 (2 ##0)) 1)) #(1 1)) ##1))) ##0) |
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| @@ -0,0 +1,7 @@ | ||
| : T \ x \ y y | ||
| : F \ x \ y x | ||
| : , \ x \ y \ f f x y | ||
| : . \ x T | ||
| : @ \ n \ f \ x f (n f x) | ||
|
|
||
| , 'h , 'e , 'l , 'l , 'o . |
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| @@ -0,0 +1,7 @@ | ||
| : T \ x \ y y | ||
| : F \ x \ y x | ||
| : , \ x \ y \ f f x y | ||
| : . \ x T | ||
| : @ \ n \ f \ x f (n f x) | ||
|
|
||
| , -1 , +2 , -3 , +4 . |
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| : T \ x \ y y | ||
| : F \ x \ y x | ||
| : , \ x \ y \ f f x y | ||
| : . \ x T | ||
| : @ \ n \ f \ x f (n f x) | ||
|
|
||
| , 0 , 1 , 2 , 3 , 4 . |
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| @@ -0,0 +1,7 @@ | ||
| : T \ x \ y y | ||
| : F \ x \ y x | ||
| : , \ x \ y \ f f x y | ||
| : . \ x T | ||
| : @ \ n \ f \ x f (n f x) | ||
|
|
||
| , . , . , . , . . |
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| : T \ x \ y y | ||
| : F \ x \ y x | ||
| : , \ x \ y \ f f x y | ||
| : . \ x T | ||
| : @ \ n \ f \ x f (n f x) | ||
|
|
||
| , (, true 1) , (, false 2) , (, true 3) , (, false 4) . |
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| @@ -0,0 +1,8 @@ | ||
| : T \ x \ y y | ||
| : F \ x \ y x | ||
| : , \ x \ y \ f f x y | ||
| : . \ x T | ||
| : @ \ n \ f \ x f (n f x) | ||
|
|
||
| : hello "hello" | ||
| hello |
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| : T \ x \ y y | ||
| : F \ x \ y x | ||
| : , \ x \ y \ f f x y | ||
| : . \ x T | ||
| : @ \ n \ f \ x f (n f x) | ||
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||
| "hello" |
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| ; https://users $monash $edu/~lloyd/tildeFP/Lambda/Examples/ | ||
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| : TRUE \ a \ b a | ||
| : FALSE \ a \ b b | ||
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| : AND \ p \ q p q FALSE | ||
| : OR \ p \ q p TRUE q | ||
| : NOT \ p \ a \ b p b a | ||
| : IF \ p \ a \ b p a b | ||
| ; EQ \ x \ y if x = y then TRUE else FALSE ; Are you kidding? |
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| : | \ guard \ body \ tail \ expression ? (guard expression) body (tail expression) |
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| ; Constants | ||
| : id \ x x | ||
| : T \ x \ y x | ||
| : F \ x \ y y | ||
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| ; Logic | ||
| : and \ p \ q p q p | ||
| : or \ p \ q p p q | ||
| : not \ p p F T | ||
| : nand \ p \ q not (and p q) | ||
| : nor \ p \ q not (or p q) | ||
| : if \ p \ a \ b p a b | ||
| : if \ p \ x \ y p x y | ||
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| : compose \ f \ g \ x f (g x) | ||
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| : pair \ x \ y \ f f x y | ||
| : , pair | ||
| : fst \ p p T | ||
| : snd \ p p F | ||
| : car fst | ||
| : cdr snd | ||
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| ; List | ||
| : cons \ x \ y \ f \ init f x (y f init) | ||
| ; nil \ x \ init init | ||
| : nil F | ||
| ; . nil | ||
| : null \ p p (\ x \ y F) | ||
| : repeat \ n \ x n (pair x) nil | ||
| : uncons \ xs \ f \ z xs (\ a \ b \ _ f a b) z | ||
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| : fold \ f \ l \ init l f init | ||
| : map \ f \ l \ g \ init l (compose g f) init | ||
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| : nilmap \ f \ a if (null a) (f a) nil | ||
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| ; Arithmetic add | ||
| : succ \ n \ f \ x f (n f x) | ||
| ; add \ m \ n \ f \ x m f (n f x) | ||
| : add \ m \ n m succ n | ||
| ; mul \ m \ n \ f m (n f) | ||
| : mul \ m \ n m (add n) 0 | ||
| : pow \ b \ e e b | ||
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| ; 0 \ f \ x x | ||
| ; 1 \ f \ x f x | ||
| ; 2 \ f \ x f (f x) | ||
| ; 3 \ f \ x f (f (f x)) | ||
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| ; Arithmetic minus | ||
| : is0 \ n n (\ x F) T | ||
| : eq0 is0 | ||
| : phi \ x cons (cdr x) (succ (cdr x)) | ||
| : Φ phi | ||
| ; pred \ n \ f \ x n (\ g \ h h (g f)) (\ u x) (\ u u) | ||
| ; pred \ n n (\ g \ k is0 (g 1) k (add (g k) 1)) (\ v 0) 0 | ||
| : pred \ n car (n Φ (cons 0 0)) | ||
| : sub \ m \ n n pred m | ||
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| ; Compare | ||
| : leq \ m \ n is0 (sub m n) | ||
| : geq \ m \ n leq n m | ||
| : eq \ m \ n and (leq n m) (geq n m) | ||
| : neq \ m \ n nand (leq n m) (geq n m) | ||
| : lt \ m \ n and (leq n m) (not (geq n m)) | ||
| : gt \ m \ n and (not (leq n m)) (geq n m) | ||
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| ; Other | ||
| : Y \ rec (\ x rec (x x)) (\ x rec (x x)) | ||
| : fix Y | ||
| ; I id | ||
| ; S \ x \ y \ z x z (y z) | ||
| ; K T | ||
| : B \ x \ y \ z x (y z) | ||
| : C \ x \ y \ z x z y | ||
| : W \ x \ y x y y | ||
| : ω \ x x x | ||
| : Δ \ x x x | ||
| : Ω ω ω | ||
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| ; List recursive | ||
| : reverse Y (\ rec \ ys \ xs uncons xs (\ x \ xs rec (cons x ys) xs) ys) nil | ||
| : fact Y (\ rec \ n (is0 n) 1 (mul n (rec (pred n)))) |
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| : Y \ f (\ x f (x x)) (\ x f (x x)) | ||
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| : cons \ a \ b \ f f a b | ||
| : nil \ x \ y y | ||
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| : uncons \ xs \ f \ z xs (\ a \ b \ _ f a b) z | ||
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| : reverse Y (\ c \ ys \ xs uncons xs (\ x \ xs c (cons x ys) xs) ys) nil |
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| ; https://www.cl.cam.ac.uk/~rmk35/lambda_calculus/lambda_calculus.html | ||
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| : Y \ f (\ x f (x x)) (\ x f (x x)) | ||
| : id \ x x | ||
| : compose \ f \ g \ x f (g x) | ||
| : T \ x \ y x | ||
| : F \ x \ y y | ||
| : if \ p \ x \ y p x y | ||
| : pair \ x \ y \ f f x y | ||
| : fst \ p p (\ x \ y x) | ||
| : snd \ p p (\ x \ y y) | ||
| : cons \ x \ y \ f \ init f x (y f init) | ||
| : nil \ f \ init init | ||
| : fold \ f \ l \ init l f init | ||
| : map \ f \ l \ g \ init l (compose g f) init | ||
| : succ \ n \ f \ x f (n f x) | ||
| : add \ n \ m \ f \ x n f (m f x) | ||
| : mul \ n \ m \ f \ x n (m f) x | ||
| : pow \ n \ m m n | ||
| : pred \ n \ f \ x n (\ g \ h h (g f)) (\ u x) (\ u u) | ||
| : eq0 \ n n (\ x F) T |
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