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POUnintuitive type signature in Haskell
 

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    <p>I made this (what I thought to be) fairly straightforward code to calculate the third side of a triangle:</p> <pre><code>toRadians :: Int -&gt; Double toRadians d = let deg = mod d 360 in deg/180 * pi lawOfCosines :: Int -&gt; Int -&gt; Int -&gt; Double lawOfCosines a b gamma = sqrt $ a*a + b*b - 2*a*b*(cos (toRadians gamma)) </code></pre> <p>However, when I tried to load it into GHCi, I got the following errors:</p> <pre><code>[1 of 1] Compiling Main ( law_of_cosines.hs, interpreted ) law_of_cosines.hs:3:18: Couldn't match expected type `Double' with actual type `Int' In the first argument of `(/)', namely `deg' In the first argument of `(*)', namely `deg / 180' In the expression: deg / 180 * pi law_of_cosines.hs:6:26: No instance for (Floating Int) arising from a use of `sqrt' Possible fix: add an instance declaration for (Floating Int) In the expression: sqrt In the expression: sqrt $ a * a + b * b - 2 * a * b * (cos (toRadians gamma)) In an equation for `lawOfCosines': lawOfCosines a b gamma = sqrt $ a * a + b * b - 2 * a * b * (cos (toRadians gamma)) law_of_cosines.hs:6:57: Couldn't match expected type `Int' with actual type `Double' In the return type of a call of `toRadians' In the first argument of `cos', namely `(toRadians gamma)' In the second argument of `(*)', namely `(cos (toRadians gamma))' </code></pre> <p>It turns out the fix was to remove my type signatures, upon which it worked fine.</p> <pre><code>toRadians d = let deg = mod d 360 in deg/180 * pi lawOfCosines a b gamma = sqrt $ a*a + b*b - 2*a*b*(cos (toRadians gamma)) </code></pre> <p>And when I query the type of <code>toRadians</code> and <code>lawOfCosines</code>:</p> <pre><code>*Main&gt; :t toRadians toRadians :: (Floating a, Integral a) =&gt; a -&gt; a *Main&gt; :t lawOfCosines lawOfCosines :: (Floating a, Integral a) =&gt; a -&gt; a -&gt; a -&gt; a *Main&gt; </code></pre> <p>Can someone explain to me what's going on here? Why the "intuitive" type signatures I had written were in fact incorrect?</p>
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    1. COdeg is an int mod has type int -> int -> int. You have to use fromInteger or fromIntegral to convert to a floating point in the first function
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