Ad-lib function (concept feature request -- verbose lambda syntax)
Expression 19: left angle-bracket, left angle-bracket, sin "k" "x" plus cos "k" "x" | "x" , right angle-bracket | "k" , right angle-bracket left parenthesis, pi , right parenthesis equals left angle-bracket, sin pi "x" plus cos pi "x" | "x" , right angle-bracket Sorry, I don't understand the 'langle' symbol.sinkx+coskx|x|kπ=sinπx+cosπx|x
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Expression 20: left parenthesis, left angle-bracket, left angle-bracket, sin "k" "x" plus cos "k" "x" | "x" , right angle-bracket | "k" , right angle-bracket left parenthesis, pi , right parenthesis , right parenthesis left parenthesis, 1 quarter , right parenthesis equals StartRoot, 2 , EndRoot Sorry, I don't understand the 'langle' symbol.sinkx+coskx|x|kπ14=2
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Higher order function: Functional (take function and output value)
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Expression 22: left angle-bracket, "f" left parenthesis, 1 , right parenthesis plus "f" left parenthesis, negative 2 , right parenthesis plus "f" left parenthesis, 3 , right parenthesis | "f" , right angle-bracket Sorry, I don't understand the 'langle' symbol.f1+f−2+f3|f
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Expression 23: left angle-bracket, "f" left parenthesis, 1 , right parenthesis plus "f" left parenthesis, negative 2 , right parenthesis plus "f" left parenthesis, 3 , right parenthesis | "f" , right angle-bracket left parenthesis, , right parenthesis equals 6 Sorry, I don't understand the 'langle' symbol.f1+f−2+f3|fabs=6
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Expression 24: left angle-bracket, "f" left parenthesis, 1 , right parenthesis plus "f" left parenthesis, negative 2 , right parenthesis plus "f" left parenthesis, 3 , right parenthesis | "f" , right angle-bracket left parenthesis, left angle-bracket, 2 "x" plus 1 | "x" , right angle-bracket , right parenthesis equals 5 Sorry, I don't understand the 'langle' symbol.f1+f−2+f3|f2x+1|x=5
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Higher order function: Operator (take function and output function with same domain)
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Expression 26: left angle-bracket, left angle-bracket, "f" left parenthesis, "x" , right parenthesis plus "f" left parenthesis, "x" plus 2 , right parenthesis | "x" , right angle-bracket | "f" , right angle-bracket Sorry, I don't understand the 'langle' symbol.fx+fx+2|x|f
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Expression 27: left angle-bracket, left angle-bracket, "f" left parenthesis, "x" , right parenthesis plus "f" left parenthesis, "x" plus 2 , right parenthesis | "x" , right angle-bracket | "f" , right angle-bracket left parenthesis, , right parenthesis equals left angle-bracket, ln "x" plus ln left parenthesis, "x" plus 2 , right parenthesis | "x" , right angle-bracket Sorry, I don't understand the 'langle' symbol.fx+fx+2|x|fln=lnx+lnx+2|x
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Higher order function: Transform (take function and output function with different domain)
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Expression 29: left angle-bracket, left angle-bracket, "f" left parenthesis, "x" , right parenthesis minus "f" left parenthesis, "y" , right parenthesis | "x" , "y" , right angle-bracket | "f" , right angle-bracket Sorry, I don't understand the 'langle' symbol.fx−fy|x,y|f
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Expression 30: left angle-bracket, left angle-bracket, "f" left parenthesis, "x" , right parenthesis minus "f" left parenthesis, "y" , right parenthesis | "x" , "y" , right angle-bracket | "f" , right angle-bracket left parenthesis, left angle-bracket, StartRoot, "x" , EndRoot | "x" , right angle-bracket , right parenthesis equals left angle-bracket, StartRoot, "x" , EndRoot minus StartRoot, "y" , EndRoot | "x" , "y" , right angle-bracket Sorry, I don't understand the 'langle' symbol.fx−fy|x,y|fx|x=x−y|x,y
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Currying
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Expression 32: left angle-bracket, "a" plus "b" StartRoot, "c" , EndRoot | "a" , "b" , "c" , right angle-bracket equals left angle-bracket, left angle-bracket, left angle-bracket, "a" plus "b" StartRoot, "c" , EndRoot | "c" , right angle-bracket | "b" , right angle-bracket | "a" , right angle-bracket equals left angle-bracket, left angle-bracket, "a" positive "f" | "f" , right angle-bracket ∘ left angle-bracket, left angle-bracket, "b" times "f" | "f" , right angle-bracket ∘ left angle-bracket, StartRoot, "c" , EndRoot | "c" , right angle-bracket | "b" , right angle-bracket | "a" , right angle-bracket Sorry, I don't understand the 'langle' symbol.a+bc|a,b,c=a+bc|c|b|a=a+f|f∘b·f|f∘c|c|b|a
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Lambda syntax should also be supported
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Expression 34: forall left parenthesis, "a" , "b" , "c" , right parenthesis : left parenthesis, "a" plus "b" StartRoot, "c" , EndRoot , right parenthesis equals forall "a" : forall "b" : forall "c" : left parenthesis, "a" plus "b" StartRoot, "c" , EndRoot , right parenthesis equals forall "a" : left parenthesis, left parenthesis, forall "f" : "a" plus "f" , right parenthesis left parenthesis, forall "b" : left parenthesis, left parenthesis, forall "f" : "b" "f" , right parenthesis left parenthesis, forall "c" : StartRoot, "c" , EndRoot , right parenthesis , right parenthesis , right parenthesis , right parenthesis Sorry, I don't understand the way that ':' is used here.∀a,b,c:a+bc=∀a:∀b:∀c:a+bc=∀a:∀f:a+f∀b:∀f:bf∀c:c
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Y-Combinator
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Expression 36: left angle-bracket, left angle-bracket, "f" ∘ "x" ∘ "x" | "x" , right angle-bracket ∘ left angle-bracket, "f" ∘ "x" ∘ "x" | "x" , right angle-bracket | "f" , right angle-bracket Sorry, I don't understand the 'langle' symbol.f∘x∘x|x∘f∘x∘x|x|f
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Expression 37: forall "f" : left parenthesis, left parenthesis, forall "x" : "f" ∘ "x" ∘ "x" , right parenthesis left parenthesis, forall "x" : "f" ∘ "x" ∘ "x" , right parenthesis , right parenthesis Sorry, I don't understand the '∘' symbol.∀f:∀x:f∘x∘x∀x:f∘x∘x