The Fortress Language Specification - CiteSeerX

trait RationalQuantityunit U absorbs unit,bool ninf ,bool lt,bool eq,bool gt,bool pinf ,bool nan
extends { RationalQuantityU,ninf ′ ,lt ′ ,eq ′ ,gt ′ ,pinf ′ ,nan ′
where {bool ninf ′ ,bool lt ′ ,bool eq ′ ,bool gt ′ ,bool pinf ′ ,bool nan ′ ,
ninf → ninf ′ ,lt → lt ′ ,eq → eq ′ ,gt → gt ′ ,pinf → pinf ′ ,nan → nan ′ },
Field RationalQuantityU,ninf ,lt,eq,gt,pinf ,nan,
RationalQuantityU,ninf ,lt,false,gt,pinf ,nan, +, −, ·, /
where {lt ∧ eq ∧ gt ∧ ¬ninf ∧ ¬pinf ∧ ¬nan, U = dimensionless },
Field RationalQuantityU,ninf ,lt,eq,gt,pinf ,nan,
RationalQuantityU,ninf ,lt,false,gt,pinf ,nan, +, −, ×, /
where {lt ∧ eq ∧ gt ∧ ¬ninf ∧ ¬pinf ∧ ¬nan, U = dimensionless },
Field RationalQuantityU,ninf ,lt,eq,gt,pinf ,nan,
RationalQuantityU,ninf ,lt,false,gt,pinf ,nan, +, −,juxtaposition, /
where {lt ∧ eq ∧ gt ∧ ¬ninf ∧ ¬pinf ∧ ¬nan, U = dimensionless },
AbelianGroupRationalQuantityU,ninf ,lt,eq,gt,pinf ,nan, +, −,
TotalOrderOperatorsRationalQuantityU,ninf ,lt,eq,gt,pinf ,nan, ,CMP
where { ¬nan } }
where {ninf ∨ lt ∨ eq ∨ gt ∨ pinf ∨ nan }
coercion ( : Identity+) = 0
coercion ( : Identity·) = 1
coercion ( : Identity×) = 1
coercion ( : Identityjuxtaposition) = 1
coercion ( : Zero×) = 0
coercion (x:IntegerQuantityU,ninf ,lt,eq,gt,pinf ,nan)
opr juxtaposition unit U ′ ,bool ninf ′ ,bool lt ′ ,bool eq ′ ,bool gt ′ ,bool pinf ′ ,bool nan ′
(self,other:RationalQuantityU ′ ,ninf ′ ,lt ′ ,eq ′ ,gt ′ ,pinf ′ ,nan ′ ) :
RationalQuantity U U ′ ,
ninf ∧ pinf ′ ∨ ninf ∧ gt ′ ∨ lt ∧ pinf ′ ∨ pinf ∧ ninf ′ ∨ pinf ∧ lt ′ ∨ gt ∧ ninf ′ ,
lt ∧ gt ′ ∨ gt ∧ lt ′ ,
eq ∧ (lt ′ ∨ eq ′ ∨ gt ′ ) ∨ (lt ∨ eq ∨ gt) ∧ eq ′ ,
lt ∧ lt ′ ∨ gt ∧ gt ′ ,
ninf ∧ ninf ′ ∨ ninf ∧ lt ′ ∨ lt ∧ ninf ′ ∨ pinf ∧ pinf ′ ∨ pinf ∧ gt ′ ∨ gt ∧ pinf ′ ,
nan ∨ nan ′ ∨ ninf ∧ eq ′ ∨ pinf ∧ eq ′ ∨ eq ∧ ninf ′ ∨ eq ∧ pinf ′
opr +(self): RationalQuantityU,ninf ,lt,eq,gt,pinf ,nan
opr +bool ninf ′ ,bool lt ′ ,bool eq ′ ,bool gt ′ ,bool inf ′ ,bool nan ′
(self,other:RationalQuantityU,ninf ′ ,lt ′ ,eq ′ ,gt ′ ,pinf ′ ,nan ′ ) :
RationalQuantity U,
ninf ∧ (ninf ′ ∨ lt ′ ∨ eq ′ ∨ gt ′ ) ∨ (ninf ∨ lt ∨ eq ∨ gt) ∧ ninf ′ ,
lt ∧ (lt ′ ∨ eq ′ ∨ gt ′ ) ∨ (lt ∨ eq ∨ gt) ∧ lt ′ ,
lt ∧ gt ′ ∨ eq ∧ eq ′ ∨ gt ∧ lt ′ ,
gt ∧ (lt ′ ∨ eq ′ ∨ gt ′ ) ∨ (lt ∨ eq ∨ gt) ∧ gt ′ ,
pinf ∧ (lt ′ ∨ eq ′ ∨ gt ′ ∨ pinf ′ ) ∨ (lt ∨ eq ∨ gt ∨ pinf ) ∧ pinf ′ ,
nan ∨ nan ′ ∨ ninf ∧ pinf ′ ∨ pinf ∧ ninf ′
opr −(self): RationalQuantityU,pinf ,gt,eq,lt,ninf ,nan
opr −bool ninf ′ ,bool lt ′ ,bool eq ′ ,bool gt ′ ,bool pinf ′ ,bool nan ′
(self,other:RationalQuantityU,ninf ′ ,lt ′ ,eq ′ ,gt ′ ,pinf ′ ,nan ′ ) :
RationalQuantity U,
ninf ∧ (lt ′ ∨ eq ′ ∨ gt ′ ∨ pinf ′ ) ∨ (ninf ∨ lt ∨ eq ∨ gt) ∧ pinf ′ ,
lt ∧ (lt ′ ∨ eq ′ ∨ gt ′ ) ∨ (lt ∨ eq ∨ gt) ∧ gt ′ ,
lt ∧ lt ′ ∨ eq ∧ eq ′ ∨ gt ∧ gt ′ ,
gt ∧ (lt ′ ∨ eq ′ ∨ gt ′ ) ∨ (lt ∨ eq ∨ gt) ∧ lt ′ ,
pinf ∧ (ninf ′ ∨ lt ′ ∨ eq ′ ∨ gt ′ ) ∨ (lt ∨ eq ∨ gt ∨ pinf ) ∧ ninf ′ ,
nan ∨ nan ′ ∨ ninf ∧ ninf ′ ∨ pinf ∧ pinf ′
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