Prolog and Automatic Language Implementation Systems

syntax n ∈ Num x ∈ Var a ∈ Aexp a ::= n | x | a1 + a2 | a1 * a2 | a1 a2 Semantic domains Integer = {... -3, -2, -1, 0, 1, 2, 3 ...} Truth-Value = {true, false} State = Var → Integer Semantic valuation functions N: Num → Integer A: Aexp → State → Integer A [[n]] = λs. N [[n]] A [[x]] = λs. s x A [[a1 + a2]] = λs. A [[a1]] s + A [[a2]] s A [[a1 * a2]] = λs. A [[a1]] s * A [[a2]] s 6 Prolog and Automatic Language Implementation Systems ISSN 1335-8243 © 2005 Faculty of Electrical Engineering and Informatics, Technical University of Košice, Slovak Republic A [[a1 a2]] = λs. A [[a1]] s A [[a2]] s /* A : Aexp -> State -> Integer */ a(X,State,apply(lambda(_,X),State)) :integer(X). a(X,State,apply(lambda(_,Val),State):atom(X), lookup(X, State, Val). a(+(A1,A2),State,add(A1_den,A2_den)) :a(A1, State, A1_den), a(A2, State, A2_den). a(*(A1,A2),State,mull(A1_den,A2_den)):a(A1, State, A1_den), a(A2, State, A2_den). a(-(A1,A2),State,sub(A1_den,A2_den)) :a(A1, State, A1_den), a(A2, State, A2_den). lookup(X,[X,Y|_],Y). lookup(X,[_,_|Rest],Y) :lookup(X, Rest, Y). evaluate(Program, State, Integer) :a(Program, State, Lambda_code), lambda_machine(Lambda_code,Integer). Fig. 7 Prolog interpreter of While language Again, rapid language implementation is obtained and language can be tested by writing simple programs such as: ?a(+(7, 9),[],R). R = add(apply(lambda(_288,7),[]), apply(lambda(_318,9),[])) ?evaluate(+(7, 9), [], R). R = 16 ?evaluate(+(7, i), [I, 1], R). R = 8