trees is beyond the scope of this text howeverfor some simple expressionslike prefix expressionsit is relatively easy to build parser ourselves in middle school we learned when checking to see if sentence is properly formed we should use the english grammar grammar is set of rules that dictate how sentence in language can be put together in computer science we have many different languages and each language has its own grammar prefix expressions make up language we call them the language of prefix expressions and they have their own grammarcalled context-free grammar context-free grammar for prefix expressions is given in sect the prefix expression grammar ( ,ewhere {et {identifiernumber+* is defined by the set of productions number grammargconsists of three setsa set of non-terminals symbols denoted by na set of terminals or tokens called and setpof productions one of the nonterminals is designated the start symbol of the grammar for this grammarthe special symbol is the start symbol and only non-terminal of the grammar the symbol stands for any prefix expression in this grammar there are three productions that provide the rules for how prefix expressions can be constructed the productions state that any prefix expression is composed of (you can read as is composed of plus sign followed by two prefix expressionsa multiplication symbol followed by two prefix expressionsor just number the grammar is recursive so every time you see in the grammarit can be replaced by another prefix expression this grammar is very easy to convert to function that given queue of tokens will build an abstract syntax tree of prefix expression functionlike the function in sect that reads tokens and returns an abstract syntax tree is called parser since the grammar is recursivethe parsing function is recursive as well it has base case firstfollowed by the recursive cases the code in sect provides that function prefix expression parser import queue def ( )if isempty()raise valueerror("invalid prefix expression" token dequeue( this copy belongs to 'acha