Chapter 4: Language Semantics The need for language semantics: a. for the programmer - to know how to use language constructs b. for the implementor - to know how to implement the language

Semantics Semantics: the study or analysis of the relationships between linguistic symbols and their meanings

Semantic descriptions Informal descriptions of language semantics - provided in verbal form in the language manuals. May be ambiguous. Formal description: studied theoretically, no satisfactory models have been produced so far.

Formal semantic models Grammatical models Operational (imperative) models Axiomatic models Applicative (functional) models Specification models

Grammatical models  grammar rules are paired with semantic rules. Resulting grammars are called attribute grammars RuleAttribute E  E + Tvalue (E1) = value (E2) + value(T) E  Tvalue (E) = value (T) T  T * Pvalue (T1) = value (T2) * value (P) T  Pvalue (T) = value (P) P  Ivalue (P) = value of number I P  (E)value (P) = value (E)

Operational models Describe the meaning of the language constructs in terms of machine states, i.e. memory and register contents. Operational semantics – describes what has to be done.

Applicative models Treat programs as functions. Denotational semantics (functional semantics) Lambda calculus

Denotational semantics Specifies the meaning of expressions by their denotation The domain of interpretation defines the denotation of composite expressions in terms of the denotations of their components. -> Compositional semantics

Lambda calculus Formal mathematical system devised by Alonzo Church to investigate functions, function application and recursion

Example illustrating lambda calculus A function accepts input and produces an output. Suppose we have a "chocolate-covering" function that produces the following outputs for the corresponding inputs: INPUTOUTPUT peanuts->chocolate-covered peanuts raisins->chocolate-covered raisins ants->chocolate-covered ants

Lambda functions We can use Lambda-calculus to describe such a function: Lx. chocolate - covered x If we want to apply the function to an argument, we use the following syntax: (Lx.chocolate-covered x)peanuts -> chocolate-covered peanuts

Using Lambda expressions to get new functions Functions can also be the result of applying a lambda-expression Ly.Lx. y - covered x We can use this to create a caramel-covering function: (Ly.Lx.y-covered x) caramel -> Lx. caramel-covered x

Functions as inputs Functions can also be the inputs to other functions, as with this "apply-to-ants" function: Lf.(f) ants We can feed the chocolate-covering function to the "apply-to-ants" function: (Lf.(f)ants)Lx.chocolate-covered x -> (Lx.chocolate-covered x)ants -> chocolate-covered ants

Axiomatic models Describe the meaning as pre- conditions and post-conditions Used in program verifications

Specification models Describe the relationship among various functions that implement a program. Example of a specification model: Algebraic data types - describe the meaning in terms of algebraic operations, e.g. pop(push(S,x)) = S