From 220afb51d70a59f33221315293387554220b7761 Mon Sep 17 00:00:00 2001 From: Brian Huffman Date: Mon, 25 Jun 2018 10:32:27 -0700 Subject: [PATCH] Update CryptolPrims.md for prims with changed types and new instances. --- docs/CryptolPrims.md | 73 +++++++++++++++++++++++------------------- docs/CryptolPrims.pdf | Bin 88512 -> 90132 bytes 2 files changed, 40 insertions(+), 33 deletions(-) diff --git a/docs/CryptolPrims.md b/docs/CryptolPrims.md index f7e49ab0..1134b147 100644 --- a/docs/CryptolPrims.md +++ b/docs/CryptolPrims.md @@ -17,8 +17,9 @@ Comparisons and Ordering instance Cmp Bit // No instance for functions. instance (Cmp a, fin n) => Cmp [n]a - instance (Cmp a, Cmp b) => Cmp (a,b) + instance (Cmp a, Cmp b) => Cmp (a, b) instance (Cmp a, Cmp b) => Cmp { x : a, y : b } + instance Cmp Integer Signed Comparisons --------------------- @@ -33,7 +34,7 @@ Signed Comparisons instance (fin n, n >= 1) => SignedCmp [n] instance (SignedCmp a, fin n) => SignedCmp [n]a // (for [n]a, where a is other than Bit) - instance (SignedCmp a, SignedCmp b) => SignedCmp (a,b) + instance (SignedCmp a, SignedCmp b) => SignedCmp (a, b) instance (SignedCmp a, SignedCmp b) => SignedCmp { x : a, y : b } @@ -48,39 +49,49 @@ Arithmetic (^^) : {a} (Arith a) => a -> a -> a (/$) : {a} (Arith a) => a -> a -> a (%$) : {a} (Arith a) => a -> a -> a + lg2 : {a} (Arith a) => a -> a + negate : {a} (Arith a) => a -> a + +The prefix notation `- x` is syntactic sugar for `negate x`. // No instance for `Bit`. - instance (fin n) => Arith ( [n] Bit) - instance (Arith a) => Arith ( [n] a) + instance (fin n) => Arith ([n]Bit) + instance (Arith a) => Arith ([n]a) instance (Arith b) => Arith (a -> b) - instance (Arith a, Arith b) => Arith (a,b) + instance (Arith a, Arith b) => Arith (a, b) instance (Arith a, Arith b) => Arith { x : a, y : b } + instance Arith Integer -Note that because there is no instances for `Arith Bit` +Note that because there is no instance for `Arith Bit` the top two instances do not actually overlap. Boolean ------- - False : Bit - True : Bit + False : Bit + True : Bit - zero : a - (&&) : a -> a -> a - (||) : a -> a -> a - (^) : a -> a -> a - (~) : a -> a + zero : {a} (Zero a) => a + (&&) : {a} (Logic a) => a -> a -> a + (||) : {a} (Logic a) => a -> a -> a + (^) : {a} (Logic a) => a -> a -> a + complement : {a} (Logic a) => a -> a - (==>) : Bit -> Bit -> Bit - (/\) : Bit -> Bit -> Bit - (\/) : Bit -> Bit -> Bit + (==>) : Bit -> Bit -> Bit + (/\) : Bit -> Bit -> Bit + (\/) : Bit -> Bit -> Bit + + instance Logic Bit + instance (Logic a) => Logic ([n]a) + instance (Logic b) => Logic (a -> b) + instance (Logic a, Logic b) => Logic (a, b) + instance (Logic a, Logic b) => Logic { x : a, y : b } + // No instance for `Logic Integer`. Sequences --------- - length : {n,a,m} (m >= width n) => [n]a -> [m] - - join : {parts,ench,a} (fin each) => [parts][each]a -> [parts * each]a + join : {parts,each,a} (fin each) => [parts][each]a -> [parts * each]a split : {parts,each,a} (fin each) => [parts * each]a -> [parts][each]a (#) : {front,back,a} (fin front) => [front]a -> [back]a -> [front + back]a @@ -98,25 +109,22 @@ Sequences updates : {n,a,m,d} (fin m, fin d) => [n]a -> [d][m] -> [d]a -> [n]a updatesEnd : {n,a,m,d} (fin n, fin m, fin d) => [n]a -> [d][m] -> [d]a -> [n]a - // Abbreviations - groupBy n = split`{each = n} - tail n = splitAt`{front = 1}.1 - take n = splitAt`{front = n}.0 - drop n = splitAt`{front = n}.1 + take : {front,back,elem} (fin front) => [front + back]elem -> [front]elem + drop : {front,back,elem} (fin front) => [front + back]elem -> [back]elem + head : {a, b} [1 + a]b -> b + tail : {a, b} [1 + a]b -> [a]b + last : {a, b} [1 + a]b -> b - /* Also, `length` is not really needed: - length : {n,a,m} (m >= width n) => [n]a -> [m] - length _ = `n - */ + groupBy : {each,parts,elem} (fin each) => [parts * each]elem -> [parts][each]elem +Function `groupBy` is the same as `split` but with its type arguments +in a different order. Shift And Rotate ---------------- -New types: - - (<<) : {n,a,m} (fin n) => [n]a -> [m] -> [n]a - (>>) : {n,a,m} (fin n) => [n]a -> [m] -> [n]a + (<<) : {n,a,m} (fin n, Zero a) => [n]a -> [m] -> [n]a + (>>) : {n,a,m} (fin n, Zero a) => [n]a -> [m] -> [n]a (<<<) : {n,a,m} (fin n) => [n]a -> [m] -> [n]a (>>>) : {n,a,m} (fin n) => [n]a -> [m] -> [n]a @@ -135,4 +143,3 @@ Debugging error : {n a} [n][8] -> a trace : {n, a, b} (fin n) => [n][8] -> a -> b -> b traceVal : {n, a} (fin n) => [n][8] -> a -> a - \ No newline at end of file diff --git a/docs/CryptolPrims.pdf b/docs/CryptolPrims.pdf index 98404f1bd19b04126ab893553f9122feebf7573e..e6e84af0c54ae370a79808753fa10640f2b8f997 100644 GIT binary patch delta 65551 zcmZU%LwGI>u&o)}wr$(CZQDE67biQmZQHhObH}!m{!e$`!F^5*>Zw81Xbs*~tG@|6 zxgR{943vqRC=FQwm=d>bb)2Y6RkhLt)<;ou)QY_P8Od|l>?&PC7a9aFW7r}Iu{2gnX}8@%)YNRPOOAG!xj*KjG{=o-a<6E zX;ry%uF1@bG`}Pi5$Y`XvDyV8R)j$w|Ia&C9AA=^xSmhTN*ti*kHTQm$|M&Of74Wf 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