src/ZF/IMP/Denotation.thy
author clasohm
Sat Dec 09 13:36:11 1995 +0100 (1995-12-09 ago)
changeset 1401 0c439768f45c
parent 1155 928a16e02f9f
child 1478 2b8c2a7547ab
permissions -rw-r--r--
removed quotes from consts and syntax sections
     1 (*  Title: 	ZF/IMP/Denotation.thy
     2     ID:         $Id$
     3     Author: 	Heiko Loetzbeyer & Robert Sandner, TUM
     4     Copyright   1994 TUM
     5 
     6 Denotational semantics of expressions & commands
     7 *)
     8 
     9 Denotation = Com + 
    10 
    11 consts
    12   A     :: i => i => i
    13   B     :: i => i => i
    14   C     :: i => i
    15   Gamma :: [i,i,i] => i
    16 
    17 rules	(*NOT definitional*)
    18   A_nat_def	"A(N(n)) == (%sigma. n)"
    19   A_loc_def	"A(X(x)) == (%sigma. sigma`x)" 
    20   A_op1_def	"A(Op1(f,a)) == (%sigma. f`A(a,sigma))"
    21   A_op2_def	"A(Op2(f,a0,a1)) == (%sigma. f`<A(a0,sigma),A(a1,sigma)>)"
    22 
    23 
    24   B_true_def	"B(true) == (%sigma. 1)"
    25   B_false_def	"B(false) == (%sigma. 0)"
    26   B_op_def	"B(ROp(f,a0,a1)) == (%sigma. f`<A(a0,sigma),A(a1,sigma)>)" 
    27 
    28 
    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))"
    31   B_or_def	"B(b0 ori b1) == (%sigma. B(b0,sigma) or B(b1,sigma))"
    32 
    33   C_skip_def	"C(skip) == id(loc->nat)"
    34   C_assign_def	"C(x := a) == {io:(loc->nat)*(loc->nat). 
    35 			       snd(io) = fst(io)[A(a,fst(io))/x]}"
    36 
    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 
    39 			 	             {io:C(c1). B(b,fst(io))=0}"
    40 
    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})"
    43 
    44   C_while_def	"C(while b do c) == lfp((loc->nat)*(loc->nat), Gamma(b,c))"
    45 
    46 end