src/HOL/Induct/Com.thy
author nipkow
Mon, 06 Aug 2001 13:43:24 +0200
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turned translation for 1::nat into def. introduced 1' and replaced most occurrences of 1 by 1'.
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(*  Title:      HOL/Induct/Com
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    ID:         $Id$
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Copyright   1997  University of Cambridge
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Example of Mutual Induction via Iteratived Inductive Definitions: Commands
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*)
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Com = Main +
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types loc
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      state = "loc => nat"
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      n2n2n = "nat => nat => nat"
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arities loc :: term
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datatype
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  exp = N nat
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      | X loc
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      | Op n2n2n exp exp
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      | valOf com exp          ("VALOF _ RESULTIS _"  60)
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and
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  com = SKIP
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      | ":="  loc exp          (infixl  60)
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      | Semi  com com          ("_;;_"  [60, 60] 60)
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      | Cond  exp com com      ("IF _ THEN _ ELSE _"  60)
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      | While exp com          ("WHILE _ DO _"  60)
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(** Execution of commands **)
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consts  exec    :: "((exp*state) * (nat*state)) set => ((com*state)*state)set"
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       "@exec"  :: "((exp*state) * (nat*state)) set => 
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                    [com*state,state] => bool"     ("_/ -[_]-> _" [50,0,50] 50)
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translations  "csig -[eval]-> s" == "(csig,s) : exec eval"
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syntax  eval'   :: "[exp*state,nat*state] => 
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		    ((exp*state) * (nat*state)) set => bool"
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						   ("_/ -|[_]-> _" [50,0,50] 50)
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translations
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    "esig -|[eval]-> ns" => "(esig,ns) : eval"
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(*Command execution.  Natural numbers represent Booleans: 0=True, 1=False*)
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inductive "exec eval"
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  intrs
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    Skip    "(SKIP,s) -[eval]-> s"
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    Assign  "(e,s) -|[eval]-> (v,s') ==> (x := e, s) -[eval]-> s'(x:=v)"
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    Semi    "[| (c0,s) -[eval]-> s2; (c1,s2) -[eval]-> s1 |] 
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            ==> (c0 ;; c1, s) -[eval]-> s1"
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    IfTrue "[| (e,s) -|[eval]-> (0,s');  (c0,s') -[eval]-> s1 |] 
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            ==> (IF e THEN c0 ELSE c1, s) -[eval]-> s1"
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    IfFalse "[| (e,s) -|[eval]->  (1',s');  (c1,s') -[eval]-> s1 |] 
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             ==> (IF e THEN c0 ELSE c1, s) -[eval]-> s1"
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    WhileFalse "(e,s) -|[eval]-> (1',s1) ==> (WHILE e DO c, s) -[eval]-> s1"
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    WhileTrue  "[| (e,s) -|[eval]-> (0,s1);
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                (c,s1) -[eval]-> s2;  (WHILE e DO c, s2) -[eval]-> s3 |] 
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                ==> (WHILE e DO c, s) -[eval]-> s3"
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end