<!DOCTYPE html><html><head><title></title><style type="text/css">p.MsoNormal,p.MsoNoSpacing{margin:0}</style></head><body><div style="color:rgb(31, 31, 31);font-family:"Proxima Nova", system-ui, -apple-system, "Segoe UI", Arial, sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;orphans:2;text-align:start;text-indent:0px;text-transform:none;white-space:normal;widows:2;word-spacing:0px;-webkit-text-stroke-width:0px;background-color:rgb(255, 255, 255);text-decoration-style:initial;text-decoration-color:initial;">I'm writing a type checker with type classes and for some reason thought<br></div><div style="color:rgb(31, 31, 31);font-family:"Proxima Nova", system-ui, -apple-system, "Segoe UI", Arial, sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;orphans:2;text-align:start;text-indent:0px;text-transform:none;white-space:normal;widows:2;word-spacing:0px;-webkit-text-stroke-width:0px;background-color:rgb(255, 255, 255);text-decoration-style:initial;text-decoration-color:initial;">that the below program should be inferred and generalized automatically. I<br></div><div style="color:rgb(31, 31, 31);font-family:"Proxima Nova", system-ui, -apple-system, "Segoe UI", Arial, sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;orphans:2;text-align:start;text-indent:0px;text-transform:none;white-space:normal;widows:2;word-spacing:0px;-webkit-text-stroke-width:0px;background-color:rgb(255, 255, 255);text-decoration-style:initial;text-decoration-color:initial;">wasn't sure whether or not GHC would actually accept this or not, so I had to test.<br></div><div style="color:rgb(31, 31, 31);font-family:"Proxima Nova", system-ui, -apple-system, "Segoe UI", Arial, sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;orphans:2;text-align:start;text-indent:0px;text-transform:none;white-space:normal;widows:2;word-spacing:0px;-webkit-text-stroke-width:0px;background-color:rgb(255, 255, 255);text-decoration-style:initial;text-decoration-color:initial;"><br></div><div style="color:rgb(31, 31, 31);font-family:"Proxima Nova", system-ui, -apple-system, "Segoe UI", Arial, sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;orphans:2;text-align:start;text-indent:0px;text-transform:none;white-space:normal;widows:2;word-spacing:0px;-webkit-text-stroke-width:0px;background-color:rgb(255, 255, 255);text-decoration-style:initial;text-decoration-color:initial;">For both Hugs and GHC, a recursive definition's type is not generalized<br></div><div style="color:rgb(31, 31, 31);font-family:"Proxima Nova", system-ui, -apple-system, "Segoe UI", Arial, sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;orphans:2;text-align:start;text-indent:0px;text-transform:none;white-space:normal;widows:2;word-spacing:0px;-webkit-text-stroke-width:0px;background-color:rgb(255, 255, 255);text-decoration-style:initial;text-decoration-color:initial;">by the inferer. You need a type signature. See below. I checked with<br></div><div style="color:rgb(31, 31, 31);font-family:"Proxima Nova", system-ui, -apple-system, "Segoe UI", Arial, sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;orphans:2;text-align:start;text-indent:0px;text-transform:none;white-space:normal;widows:2;word-spacing:0px;-webkit-text-stroke-width:0px;background-color:rgb(255, 255, 255);text-decoration-style:initial;text-decoration-color:initial;">Hugs just in case there was a generalization limit in GHC due to its more exotic<br></div><div style="color:rgb(31, 31, 31);font-family:"Proxima Nova", system-ui, -apple-system, "Segoe UI", Arial, sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;orphans:2;text-align:start;text-indent:0px;text-transform:none;white-space:normal;widows:2;word-spacing:0px;-webkit-text-stroke-width:0px;background-color:rgb(255, 255, 255);text-decoration-style:initial;text-decoration-color:initial;">capabilities (like how let generalization is disabled by type families).<br></div><div style="color:rgb(31, 31, 31);font-family:"Proxima Nova", system-ui, -apple-system, "Segoe UI", Arial, sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;orphans:2;text-align:start;text-indent:0px;text-transform:none;white-space:normal;widows:2;word-spacing:0px;-webkit-text-stroke-width:0px;background-color:rgb(255, 255, 255);text-decoration-style:initial;text-decoration-color:initial;"><br></div><div style="color:rgb(31, 31, 31);font-family:"Proxima Nova", system-ui, -apple-system, "Segoe UI", Arial, sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;orphans:2;text-align:start;text-indent:0px;text-transform:none;white-space:normal;widows:2;word-spacing:0px;-webkit-text-stroke-width:0px;background-color:rgb(255, 255, 255);text-decoration-style:initial;text-decoration-color:initial;">I wonder: is it in general impossible or super hard to infer the most<br></div><div style="color:rgb(31, 31, 31);font-family:"Proxima Nova", system-ui, -apple-system, "Segoe UI", Arial, sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;orphans:2;text-align:start;text-indent:0px;text-transform:none;white-space:normal;widows:2;word-spacing:0px;-webkit-text-stroke-width:0px;background-color:rgb(255, 255, 255);text-decoration-style:initial;text-decoration-color:initial;">general type for all cases like this without a type signature? Or is it just considered a <br></div><div style="color:rgb(31, 31, 31);font-family:"Proxima Nova", system-ui, -apple-system, "Segoe UI", Arial, sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;orphans:2;text-align:start;text-indent:0px;text-transform:none;white-space:normal;widows:2;word-spacing:0px;-webkit-text-stroke-width:0px;background-color:rgb(255, 255, 255);text-decoration-style:initial;text-decoration-color:initial;">rare case that we don't care about? Perhaps it has subtler downsides? <br></div><div style="color:rgb(31, 31, 31);font-family:"Proxima Nova", system-ui, -apple-system, "Segoe UI", Arial, sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;orphans:2;text-align:start;text-indent:0px;text-transform:none;white-space:normal;widows:2;word-spacing:0px;-webkit-text-stroke-width:0px;background-color:rgb(255, 255, 255);text-decoration-style:initial;text-decoration-color:initial;"><br></div><div style="color:rgb(31, 31, 31);font-family:"Proxima Nova", system-ui, -apple-system, "Segoe UI", Arial, sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;orphans:2;text-align:start;text-indent:0px;text-transform:none;white-space:normal;widows:2;word-spacing:0px;-webkit-text-stroke-width:0px;background-color:rgb(255, 255, 255);text-decoration-style:initial;text-decoration-color:initial;">It any case, I'm happy to just copy GHC and Hugs as it makes my life<br></div><div style="color:rgb(31, 31, 31);font-family:"Proxima Nova", system-ui, -apple-system, "Segoe UI", Arial, sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;orphans:2;text-align:start;text-indent:0px;text-transform:none;white-space:normal;widows:2;word-spacing:0px;-webkit-text-stroke-width:0px;background-color:rgb(255, 255, 255);text-decoration-style:initial;text-decoration-color:initial;">easier to just require an explicit signature in this case.<br></div><div style="color:rgb(31, 31, 31);font-family:"Proxima Nova", system-ui, -apple-system, "Segoe UI", Arial, sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;orphans:2;text-align:start;text-indent:0px;text-transform:none;white-space:normal;widows:2;word-spacing:0px;-webkit-text-stroke-width:0px;background-color:rgb(255, 255, 255);text-decoration-style:initial;text-decoration-color:initial;"><br></div><div style="color:rgb(31, 31, 31);font-family:"Proxima Nova", system-ui, -apple-system, "Segoe UI", Arial, sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;orphans:2;text-align:start;text-indent:0px;text-transform:none;white-space:normal;widows:2;word-spacing:0px;-webkit-text-stroke-width:0px;background-color:rgb(255, 255, 255);text-decoration-style:initial;text-decoration-color:initial;">Cheers<br></div><div style="color:rgb(31, 31, 31);font-family:"Proxima Nova", system-ui, -apple-system, "Segoe UI", Arial, sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;orphans:2;text-align:start;text-indent:0px;text-transform:none;white-space:normal;widows:2;word-spacing:0px;-webkit-text-stroke-width:0px;background-color:rgb(255, 255, 255);text-decoration-style:initial;text-decoration-color:initial;"><br></div><div style="color:rgb(31, 31, 31);font-family:"Proxima Nova", system-ui, -apple-system, "Segoe UI", Arial, sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;orphans:2;text-align:start;text-indent:0px;text-transform:none;white-space:normal;widows:2;word-spacing:0px;-webkit-text-stroke-width:0px;background-color:rgb(255, 255, 255);text-decoration-style:initial;text-decoration-color:initial;">-- ERROR "Q.hs":4 - Type error in application<br></div><div style="color:rgb(31, 31, 31);font-family:"Proxima Nova", system-ui, -apple-system, "Segoe UI", Arial, sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;orphans:2;text-align:start;text-indent:0px;text-transform:none;white-space:normal;widows:2;word-spacing:0px;-webkit-text-stroke-width:0px;background-color:rgb(255, 255, 255);text-decoration-style:initial;text-decoration-color:initial;">-- *** Expression : f (n - 1) 'a'<br></div><div style="color:rgb(31, 31, 31);font-family:"Proxima Nova", system-ui, -apple-system, "Segoe UI", Arial, sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;orphans:2;text-align:start;text-indent:0px;text-transform:none;white-space:normal;widows:2;word-spacing:0px;-webkit-text-stroke-width:0px;background-color:rgb(255, 255, 255);text-decoration-style:initial;text-decoration-color:initial;">-- *** Term : 'a'<br></div><div style="color:rgb(31, 31, 31);font-family:"Proxima Nova", system-ui, -apple-system, "Segoe UI", Arial, sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;orphans:2;text-align:start;text-indent:0px;text-transform:none;white-space:normal;widows:2;word-spacing:0px;-webkit-text-stroke-width:0px;background-color:rgb(255, 255, 255);text-decoration-style:initial;text-decoration-color:initial;">-- *** Type : Char<br></div><div style="color:rgb(31, 31, 31);font-family:"Proxima Nova", system-ui, -apple-system, "Segoe UI", Arial, sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;orphans:2;text-align:start;text-indent:0px;text-transform:none;white-space:normal;widows:2;word-spacing:0px;-webkit-text-stroke-width:0px;background-color:rgb(255, 255, 255);text-decoration-style:initial;text-decoration-color:initial;">-- *** Does not match : ()<br></div><div style="color:rgb(31, 31, 31);font-family:"Proxima Nova", system-ui, -apple-system, "Segoe UI", Arial, sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;orphans:2;text-align:start;text-indent:0px;text-transform:none;white-space:normal;widows:2;word-spacing:0px;-webkit-text-stroke-width:0px;background-color:rgb(255, 255, 255);text-decoration-style:initial;text-decoration-color:initial;"><br></div><div style="color:rgb(31, 31, 31);font-family:"Proxima Nova", system-ui, -apple-system, "Segoe UI", Arial, sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;orphans:2;text-align:start;text-indent:0px;text-transform:none;white-space:normal;widows:2;word-spacing:0px;-webkit-text-stroke-width:0px;background-color:rgb(255, 255, 255);text-decoration-style:initial;text-decoration-color:initial;">-- • Couldn't match expected type ‘()’ with actual type ‘Char’<br></div><div style="color:rgb(31, 31, 31);font-family:"Proxima Nova", system-ui, -apple-system, "Segoe UI", Arial, sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;orphans:2;text-align:start;text-indent:0px;text-transform:none;white-space:normal;widows:2;word-spacing:0px;-webkit-text-stroke-width:0px;background-color:rgb(255, 255, 255);text-decoration-style:initial;text-decoration-color:initial;">-- • In the second argument of ‘f’, namely ‘'a'’<br></div><div style="color:rgb(31, 31, 31);font-family:"Proxima Nova", system-ui, -apple-system, "Segoe UI", Arial, sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;orphans:2;text-align:start;text-indent:0px;text-transform:none;white-space:normal;widows:2;word-spacing:0px;-webkit-text-stroke-width:0px;background-color:rgb(255, 255, 255);text-decoration-style:initial;text-decoration-color:initial;">-- In the expression: f (n - 1) 'a'<br></div><div style="color:rgb(31, 31, 31);font-family:"Proxima Nova", system-ui, -apple-system, "Segoe UI", Arial, sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;orphans:2;text-align:start;text-indent:0px;text-transform:none;white-space:normal;widows:2;word-spacing:0px;-webkit-text-stroke-width:0px;background-color:rgb(255, 255, 255);text-decoration-style:initial;text-decoration-color:initial;"><br></div><div style="color:rgb(31, 31, 31);font-family:"Proxima Nova", system-ui, -apple-system, "Segoe UI", Arial, sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;orphans:2;text-align:start;text-indent:0px;text-transform:none;white-space:normal;widows:2;word-spacing:0px;-webkit-text-stroke-width:0px;background-color:rgb(255, 255, 255);text-decoration-style:initial;text-decoration-color:initial;">-- f :: Int -> a -> Int<br></div><div style="color:rgb(31, 31, 31);font-family:"Proxima Nova", system-ui, -apple-system, "Segoe UI", Arial, sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;orphans:2;text-align:start;text-indent:0px;text-transform:none;white-space:normal;widows:2;word-spacing:0px;-webkit-text-stroke-width:0px;background-color:rgb(255, 255, 255);text-decoration-style:initial;text-decoration-color:initial;">f 0 x = 0<br></div><div style="color:rgb(31, 31, 31);font-family:"Proxima Nova", system-ui, -apple-system, "Segoe UI", Arial, sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;orphans:2;text-align:start;text-indent:0px;text-transform:none;white-space:normal;widows:2;word-spacing:0px;-webkit-text-stroke-width:0px;background-color:rgb(255, 255, 255);text-decoration-style:initial;text-decoration-color:initial;">f 1 x = f 0 ()<br></div><div style="color:rgb(31, 31, 31);font-family:"Proxima Nova", system-ui, -apple-system, "Segoe UI", Arial, sans-serif;font-size:14px;font-style:normal;font-variant-ligatures:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;orphans:2;text-align:start;text-indent:0px;text-transform:none;white-space:normal;widows:2;word-spacing:0px;-webkit-text-stroke-width:0px;background-color:rgb(255, 255, 255);text-decoration-style:initial;text-decoration-color:initial;">f n x = f (n-1) 'a'<br></div></body></html>