Parsing LANG1

In this section we will investigate the parsing of LANG1, that is, we will construct a function that will go from the concrete syntax of LANG1 to the abstract syntax of LANG1. Loosely speaking, this function, call it doparse, will be an inverse to the function given by the homomorphism h_syn = aitch(alg_LANG1Syn, __ ) . However, since the context-free grammar for LANG1 is ambiguous (i.e., h_synis not injective), what we will get is h_syndoparse = 1 but doparse

h_syn

1. The ambiguity is not be a problem since we will get h_sem doparse

h_syn= h_sem , where h_sem = aitch(alg_LANG1Sem, __ )
It follows then that the function h_sem doparse is a compiler for LANG1, that is, it is a function taking expressions written in the concrete syntax to their meanings.

The Programs

We offer the user three programs

doparse(prog) which takes a concrete program, prog, as argument and returns the corresponding abstract program.
compLANG1(prog) which takes a concrete program, prog, as argument and returns the corresponding function on states -- more accurately speaking, it returns a JavaScript program that computes that function. Thus compLANG1 can be viewed as a compiler from LANG1 to JavaScript. However, the result of applying compLANG1 to a LANG1 program, prog, is a JavaScript program implementing a function SttStt rather than a direct translation of prog into JavaScript.
runLANG1(prog, stt) which takes a concrete program, prog, and a state, stt, as arguments and returns the state resulting from applying the function corresponding to prog to the state stt.

There is a built-in sample state, called samplestt, with initial value [["a", 10], ["b", 3], ["c", 77]] that can be used to test the following examples. Note that performing the examples will modify the value of samplestt. Of course, you can also input states of your own choosing.

Here are some sample concrete LANG1 programs which you can parse, compile or run:

"b:=1; While (1<=a) do b:=(a*b); a:=(a+(-1)) od" -- the familiar program for the factorial

"If (a<=b) then c:=1 else c:=2 fi"

"If (a<=b) then c:=(c+(-1)) else c:=(c+1) fi"