YEAH

[proglang.git] / formalsemantics

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+INTERPOL - ANTICS
++++++++++++++++++
+
+
+
+<e,o> |> v  means that e evaluates to v in the state o.
+
+
+
+
+basic arithmetic operations.
+
+(PLUS)
+<e1 + e2, o> |> v   <=   <e1,o> |> v1  &  <e2,o> |> v2  &  v is the sum of v1 and v2
+
+
+(MINUS)
+<e1 - e2, o> |> v   <=   <e1,o> |> v1  &  <e2,o> |> v2  &  v is v1 subtracted from v2
+
+
+(MULT)
+<e1 * e2, o> |> v   <=   <e1,o> |> v1  &  <e2,o> |> v2  &  v is the product of v1 and v2
+
+
+(DIV)
+<e1 / e2, o> |> v   <=   <e1,o> |> v1  &  <e2,o> |> v2  &  v is v1 divided by v2
+
+
+
+basic comparative operations.
+
+
+(Less Than)
+
+<e1 < e2, o> |> true   <=  <e1,o> |> v1  & <e2,o> |> v2  &  v1 is smaller than v2
+<e1 < e2, o> |> false  <=  <e1,o> |> v1  & <e2,o> |> v2  &  v1 is larger than or as large as v2
+
+<e1 <= e2, o> |> true   <=  <e1,o> |> v1  & <e2,o> |> v2  &  v1 is smaller than or as small as v2
+<e1 <= e2, o> |> false  <=  <e1,o> |> v1  & <e2,o> |> v2  &  v1 is larger than v2
+
++similar rules apply for greater than+
+
+
+(Equal, Not Equal)
+
+<e1 == e2, o> |> true   <=  <e1,o> |> v1  & <e2,o> |> v2  &  v1 is equal to v2
+<e1 == e2, o> |> false  <=  <e1,o> |> v1  & <e2,o> |> v2  &  v1 is not equal to v2
+
+<e1 != e2, o> |> true   <=  <e1,o> |> v1  & <e2,o> |> v2  &  v1 is not equal to to v2
+<e1 != e2, o> |> false  <=  <e1,o> |> v1  & <e2,o> |> v2  &  v1 is equal to v2
+
+
+
+(Not, Neg)
+
+<!e, o> |> false  <=  <e,o> |> true
+<!e, o> |> true   <=  <e,o> |> false
+
+<-e, o> |> v2  <=  <e,o> |> v1  &  v2 is the negative value of v1
+
+
+
+
+(Int)
+<n,o> |> n  <=
+
+(Bool)
+<b,o> |> b  <=
+
+
+
+
+
+(If)
+<if e s1 else s2, o> |> o'   <=   <e,o> |> true  &  <s1, o> |> o'
+<if e s1 else s2, o> |> o'   <=   <e,o> |> false  &  <s2, o> |> o'
+
+(While)
+<while e s, o> |> o'' <=   <e,o> |> true  &  <s,o> |> o'  &  <while e s, o'> |> o''
+<while e s, o> |> o   <=   <e,o> |> false
+
+(Assign)
+<x = e, o> |> o[x->v]   <=   <e,o> |> v
+
+(Seq)
+<s1; s2, o> |> o''   <=   <s1,o> |> o'  &  <s2, o'> |> o''