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Fix right shifting of negative numbers: -1 >>Int 1 ==K -1
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pykwasm/src/pykwasm/kdist/wasm-semantics/kwasm-lemmas.md

Lines changed: 7 additions & 2 deletions
Original file line numberDiff line numberDiff line change
@@ -187,6 +187,7 @@ We want K to understand what a bit-shift is.
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rule (X >>Int N) => 0
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requires 0 <=Int N
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andBool 0 <=Int X
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andBool X <Int 2 ^Int N
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[simplification]
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rule (_X <<Int N) modInt M => 0
@@ -212,9 +213,11 @@ We want K to understand what a bit-shift is.
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```k
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rule ((X <<Int M) +Int Y) >>Int N => (X <<Int (M -Int N)) +Int (Y >>Int N)
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requires M >=Int N andBool N >=Int 0
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andBool 0 <=Int X andBool 0 <=Int Y
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[simplification]
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rule (Y +Int (X <<Int M)) >>Int N => (X <<Int (M -Int N)) +Int (Y >>Int N)
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requires M >=Int N andBool N >=Int 0
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andBool 0 <=Int X andBool 0 <=Int Y
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[simplification]
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```
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@@ -241,6 +244,7 @@ The following rules decrease the modulus by rearranging it around a shift.
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requires N >=Int 0
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andBool POW >Int 0
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andBool POW modInt (2 ^Int N) ==Int 0
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andBool 0 <=Int X
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[simplification]
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rule (X <<Int N) modInt POW => (X modInt (POW /Int (2 ^Int N))) <<Int N
@@ -310,8 +314,9 @@ Bounds on `#getRange`:
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rule 0 <=Int VAL1 +Int VAL2 => true requires 0 <=Int VAL1 andBool 0 <=Int VAL2 [simplification]
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rule #getRange(_, _, WIDTH) <Int MAX => true requires 2 ^Int (8 *Int WIDTH) <=Int MAX [simplification]
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rule #getRange(_, _, WIDTH) <<Int SHIFT <Int MAX => true requires 2 ^Int ((8 *Int WIDTH) +Int SHIFT) <=Int MAX
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requires 0 <=Int SHIFT
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rule #getRange(_, _, WIDTH) <<Int SHIFT <Int MAX => true
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requires 2 ^Int ((8 *Int WIDTH) +Int SHIFT) <=Int MAX
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andBool 0 <=Int SHIFT
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[simplification]
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rule (#getRange(_, _, WIDTH1) #as VAL1) +Int ((#getRange(_, _, WIDTH2) <<Int SHIFT) #as VAL2) <Int MAX => true
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requires VAL1 <Int MAX

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