Concepts and Semantics of Programming Languages 1. Therese Hardin

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The evaluation function is obtained directly as follows:

      Python def eval_exp1(env,mem,e): if isinstance(e,Cste1): return VCste1(CInt1(e.cste)) if isinstance(e,Var1): x = valeur_de(env,e.symb) if isinstance(x,CInt1) or isinstance(x,CRef1): return VCste1(x) return Erreur1() if isinstance(e,Plus1): ev1 = eval_exp1(env,mem,e.exp1) if isinstance(ev1,Erreur1): return Erreur1() v1 = ev1.cste ev2 = eval_exp1(env,mem,e.exp2) if isinstance(ev2,Erreur1): return Erreur1() v2 = ev2.cste if isinstance(v1,CInt1) and isinstance(v2,CInt1): return VCste1(CInt1(v1.cst_int + v2.cst_int)) return Erreur1() if isinstance(e,Bang1): x = valeur_de(env,e.symb) if isinstance(x,CRef1): y = valeur_ref(mem,x.cst_adr) if y is None: return Erreur1() return VCste1(y) return Erreur1() raise ValueErrorOCaml let rec eval_exp1 env mem e = match e with | Cste1 n -> VCste1 (CInt1 n) | Var1 x -> (match valeur_de env x with Some v -> VCste1 v | _ -> Erreur1) | Plus1 (e1, e2) -> ( match ((eval_exp1 env mem e1), (eval_exp1 env mem e2)) with | (VCste1 (CInt1 n1), VCste1 (CInt1 n2)) -> VCste1 (CInt1 (n1 + n2)) | _ -> Erreur1) | Bang1 x -> (match valeur_de env x with | Some (CRef1 a) -> (match valeur_ref mem a with Some v -> VCste1 v | _ -> Erreur1) | _ -> Erreur1) val eval_exp1 : (’a * ’b const1) list -> (’b * ’b const1) list -> ’a exp1 -> ’b valeurs1

      Considering example 2.2, we obtain:

      Python ex_env1 = [(“x”,CRef1(“rx”)),(“y”,CInt1(2))] ex_mem1 = [(“rx”,CInt1(3))] >>> (eval_exp1(ex_env1,ex_mem1,ex_exp1)).cste.cst_int 5OCaml let ex_env1 = [ (“x”, CRefl (“rx”)); (“y”, CIntl (2)) ] val ex_env1 : (string * string constl) list let ex_mem1 = [ (“rx”, CIntl (3)) ] val ex_mem1 : (string * ‘a constl) list # (eval_exp1 ex_env1 ex_mem1 ex_exp1) ;; - : string valeursl = VCstel (CIntl 5)

2.3. Definition and assignment

      2.3.1. Defining an identifier

      The language Def ₁ extends Exp₁ by adding definitions of identifiers. There are two constructs that make it possible to introduce an identifier naming a mutable or non-mutable variable (as defined in section 2.1.3). Note that, in both cases, the initial value must be provided. This value corresponds to a constant or to the result of a computation specified by an expression e ∈ Exp₁. These constructs modify the current state of the system; after computing , the next step in evaluating let x = e; is to add the binding (x, ) to the environment, while the evaluation of var x = e; adds a binding (x, r_x) to the environment and writes the value to the reference rx. In this case, we assume that the location denoted by the reference rx is computed by an external mechanism responsible for memory allocation.

Table 2.3. Language Def 1 of definitions

      The evaluation of a definition is expressed as follows:

      (2.1)

      This evaluation →_{Def 1} defines a relation between a state, a definition and a resulting state, or, in formal terms:

      Starting with a finite sequence of definitions d = [d₁; . . . d_n] and an initial state (Env₀, Mem₀), this relation produces the state (Env_n, Mem_n):

This sequence of transitions may, more simply, be noted (Env_n, Mem_n).

      EXAMPLE 2.3.– Starting with a memory with no accessible references and an “empty” environment, the sequence [var y = 2; let x = !y + 3;] builds the following state:

      In the environment Env = [(x, 5), (y, ry)], we obtain = {y} and = {x}.

      NOTE.– In the definition of the two transitions in [2.1], we presume that the result of the evaluation of the expression e, denoted as , is not an error result. In the case of an error, no state will be produced and the evaluation stops.

      The abstract syntax of language Def ₁ may be defined as follows:

       Python class Let_def1: def __init__(self,var,exp): self.var = var self.exp = exp class Var_def1: def __init__(self,var,exp): self.var = var self.exp СКАЧАТЬ