src/HOL/IMP/ASM.thy
 author huffman Thu Aug 11 09:11:15 2011 -0700 (2011-08-11) changeset 44165 d26a45f3c835 parent 44036 d03f9f28d01d child 45015 fdac1e9880eb permissions -rw-r--r--
remove lemma stupid_ext
     1 header "Arithmetic Stack Machine and Compilation"

     2

     3 theory ASM imports AExp begin

     4

     5 subsection "Arithmetic Stack Machine"

     6

     7 datatype ainstr = LOADI val | LOAD string | ADD

     8

     9 type_synonym stack = "val list"

    10

    11 abbreviation "hd2 xs == hd(tl xs)"

    12 abbreviation "tl2 xs == tl(tl xs)"

    13

    14 text{* \noindent Abbreviations are transparent: they are unfolded after

    15 parsing and folded back again before printing. Internally, they do not

    16 exist. *}

    17

    18 fun aexec1 :: "ainstr \<Rightarrow> state \<Rightarrow> stack \<Rightarrow> stack" where

    19 "aexec1 (LOADI n) _ stk  =  n # stk" |

    20 "aexec1 (LOAD n) s stk  =  s(n) # stk" |

    21 "aexec1  ADD _ stk  =  (hd2 stk + hd stk) # tl2 stk"

    22

    23 fun aexec :: "ainstr list \<Rightarrow> state \<Rightarrow> stack \<Rightarrow> stack" where

    24 "aexec [] _ stk = stk" |

    25 "aexec (i#is) s stk = aexec is s (aexec1 i s stk)"

    26

    27 value "aexec [LOADI 5, LOAD ''y'', ADD]

    28  <''x'' := 42, ''y'' := 43> [50]"

    29

    30 lemma aexec_append[simp]:

    31   "aexec (is1@is2) s stk = aexec is2 s (aexec is1 s stk)"

    32 apply(induct is1 arbitrary: stk)

    33 apply (auto)

    34 done

    35

    36

    37 subsection "Compilation"

    38

    39 fun acomp :: "aexp \<Rightarrow> ainstr list" where

    40 "acomp (N n) = [LOADI n]" |

    41 "acomp (V x) = [LOAD x]" |

    42 "acomp (Plus e1 e2) = acomp e1 @ acomp e2 @ [ADD]"

    43

    44 value "acomp (Plus (Plus (V ''x'') (N 1)) (V ''z''))"

    45

    46 theorem aexec_acomp[simp]: "aexec (acomp a) s stk = aval a s # stk"

    47 apply(induct a arbitrary: stk)

    48 apply (auto)

    49 done

    50

    51 end