User interface:Julian/MIU system

MIU system, naïve approach:

 kind (miu) term (miu (M)) term (miu (I)) term (miu (U)) term (miu (+ miu miu))

kind (validmiu) term (validmiu (|- miu))

var (miu x y z)

stmt (assoc1 ( (|- ( (x + y) + z ) ) )  (|- ( x + (y + z) ) ) )

stmt (assoc2 ( (|- ( x + (y + z) ) ) )  (|- ( (x + y) + z ) ) )

stmt (initial (

)  (|- ( (M) + (I) ) ) )

stmt (rule1 ( (|- ( x + (I) ) ) )  (|- ( ( x  + (I) ) + (U) ) ) )

stmt (rule2 ( (|- ( (M) + x ) ) )  (|- ( ( (M) + x ) + x ) ) )

stmt (rule3 ( (|- ( ( ( ( x + (I) ) + (I) ) + (I) ) + y ) ) )  (|- ( ( x + (U) ) + y ) ) )

stmt (rule3' ( (|- ( ( ( x + (I) ) + (I) ) + (I) ) ) )  (|- ( x + (U) ) ) )

stmt (rule4 ( (|- ( ( ( x + (U) ) + (U) ) + y ) ) )  (|- ( x + y ) ) )

stmt (rule4' ( (|- ( ( x + (U) ) + (U) ) ) )  (|- x ) )

