29 B_not_def "B(noti(b)) == (%sigma. not(B(b,sigma)))" |
29 B_not_def "B(noti(b)) == (%sigma. not(B(b,sigma)))" |
30 B_and_def "B(b0 andi b1) == (%sigma. B(b0,sigma) and B(b1,sigma))" |
30 B_and_def "B(b0 andi b1) == (%sigma. B(b0,sigma) and B(b1,sigma))" |
31 B_or_def "B(b0 ori b1) == (%sigma. B(b0,sigma) or B(b1,sigma))" |
31 B_or_def "B(b0 ori b1) == (%sigma. B(b0,sigma) or B(b1,sigma))" |
32 |
32 |
33 C_skip_def "C(skip) == id(loc->nat)" |
33 C_skip_def "C(skip) == id(loc->nat)" |
34 C_assign_def "C(x := a) == {io:(loc->nat)*(loc->nat). \ |
34 C_assign_def "C(x := a) == {io:(loc->nat)*(loc->nat). |
35 \ snd(io) = fst(io)[A(a,fst(io))/x]}" |
35 snd(io) = fst(io)[A(a,fst(io))/x]}" |
36 |
36 |
37 C_comp_def "C(c0 ; c1) == C(c1) O C(c0)" |
37 C_comp_def "C(c0 ; c1) == C(c1) O C(c0)" |
38 C_if_def "C(ifc b then c0 else c1) == {io:C(c0). B(b,fst(io))=1} Un \ |
38 C_if_def "C(ifc b then c0 else c1) == {io:C(c0). B(b,fst(io))=1} Un |
39 \ {io:C(c1). B(b,fst(io))=0}" |
39 {io:C(c1). B(b,fst(io))=0}" |
40 |
40 |
41 Gamma_def "Gamma(b,c) == (%phi.{io : (phi O C(c)). B(b,fst(io))=1} Un \ |
41 Gamma_def "Gamma(b,c) == (%phi.{io : (phi O C(c)). B(b,fst(io))=1} Un |
42 \ {io : id(loc->nat). B(b,fst(io))=0})" |
42 {io : id(loc->nat). B(b,fst(io))=0})" |
43 |
43 |
44 C_while_def "C(while b do c) == lfp((loc->nat)*(loc->nat), Gamma(b,c))" |
44 C_while_def "C(while b do c) == lfp((loc->nat)*(loc->nat), Gamma(b,c))" |
45 |
45 |
46 end |
46 end |