Curry: An Integrated Functional Logic Language

Eval [ei ] ⇒ D
Eval [e1=:=e2 ] ⇒ replace(e1=:=e2, i, D) if ei = f(t1, . . . , tn), i ∈ {1, 2}
Eval [c(e1, . . . , en)=:=c(e ′ 1 , . . . , e′ n)] ⇒ {id e1=:=e ′ 1 & . . . & en=:=e ′ n}
Eval [c(e1, . . . , en)=:=d(e ′ 1 , . . . , e′ m)] ⇒ ∅
Eval [x=:=e] ⇒ D
Eval [e=:=x] ⇒ D
if e is not a variable
Eval [x=:=y ] ⇒ {{x ↦→ y} success}
if c �= d or n �= m
Eval [x=:=c(e1, . . . , en)] ⇒ {σ y1=:=σ(e1) & . . . & yn=:=σ(en)}
Eval [x=:=c(e1, . . . , en)] ⇒ ∅ if x ∈ cv(c(e1, . . . , en))
Figure 4: Solving equational constraints
if x �∈ cv(c(e1, . . . , en)),
σ = {x ↦→ c(y1, . . . , yn)},
y1, . . . , yn fresh variables
lazy evaluation of the expressions and binding of variables to constructor terms. The evaluation
steps implementing this method are shown in Figure 4, where we consider the symbol =:= is a
binary infix function symbol. The last two rules implements an occur check where the critical
variables (cv) are only those variables occurring outside a function call:
cv(x) = {x}
cv(c(e1, . . . , en)) = cv(e1) ∪ . . . ∪ cv(en)
cv(f(e1, . . . , en)) = ∅
However, Curry implementations can also provide other methods to solve equational constraints
or other types of constraints with appropriate constraint solvers. The only property, which is
important for the operational semantics, is the fact that a solved constraint has the form success,
i.e., a solvable constraint c is reducible to the answer expression σ success where σ is a solution
of c.
D.5 Higher-Order Features
Warren [49] has shown for the case of logic programming that the higher-order features of functional
programming can be implemented by providing a (first-order) definition of the application function.
Since Curry supports the higher-order features of current functional languages but excludes the
guessing of higher-order objects by higher-order unification (as, e.g., in [24, 38, 43]), the operational
semantics specified in Figure 2 can be simply extended to cover Curry’s higher-order features by
adding the following axiom (here we denote by the infix operator “@” the application of a function
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