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theory Buffer(* File: Buffer.thy ID: $Id: Buffer.thy,v 1.3 2005/09/07 18:22:40 wenzelm Exp $ Author: Stephan Merz Copyright: 1997 University of Munich Theory Name: Buffer Logic Image: TLA *) header {* A simple FIFO buffer (synchronous communication, interleaving) *} theory Buffer imports TLA begin consts (* actions *) BInit :: "'a stfun => 'a list stfun => 'a stfun => stpred" Enq :: "'a stfun => 'a list stfun => 'a stfun => action" Deq :: "'a stfun => 'a list stfun => 'a stfun => action" Next :: "'a stfun => 'a list stfun => 'a stfun => action" (* temporal formulas *) IBuffer :: "'a stfun => 'a list stfun => 'a stfun => temporal" Buffer :: "'a stfun => 'a stfun => temporal" defs BInit_def: "BInit ic q oc == PRED q = #[]" Enq_def: "Enq ic q oc == ACT (ic$ ~= $ic) & (q$ = $q @ [ ic$ ]) & (oc$ = $oc)" Deq_def: "Deq ic q oc == ACT ($q ~= #[]) & (oc$ = hd< $q >) & (q$ = tl< $q >) & (ic$ = $ic)" Next_def: "Next ic q oc == ACT (Enq ic q oc | Deq ic q oc)" IBuffer_def: "IBuffer ic q oc == TEMP Init (BInit ic q oc) & [][Next ic q oc]_(ic,q,oc) & WF(Deq ic q oc)_(ic,q,oc)" Buffer_def: "Buffer ic oc == TEMP (EEX q. IBuffer ic q oc)" ML {* use_legacy_bindings (the_context ()) *} end
theorem tl_not_self:
xs ≠ [] ==> tl xs ≠ xs
theorem Deq_visible:
|- <Deq ic q oc>_(ic, q, oc) = Deq ic q oc
theorem Deq_enabled:
basevars (ic, q, oc) ==> |- Enabled (<Deq ic q oc>_(ic, q, oc)) = (q ≠ #[])
theorem Deq_enabledE:
|- Enabled (<Deq ic q oc>_(ic, q, oc)) --> q ≠ #[]