The simply typed lambda calculus (with β η \beta \eta -equivalence) is the internal language of Cartesian closed categories (CCCs), as was first observed by Joachim Lambek.(λAbs.(λApp.(λVar.(λlength.(λhead.(λmap.(λtake.(λfilter.(λconcat.(λnot.(λdelete.(λdelete.(λelem.(λfresh.(λfreeVars.(λsubst.(λlazyEval.lazyEval) Additionally, the strong normalization property described below implies that any evaluation strategy will terminate on all simply typed terms. As for any typed language, type safety is a fundamental property of all of these evaluation strategies.
Likewise, the operational semantics of simply typed lambda calculus can be fixed as for the untyped lambda calculus, using call by name, call by value, or other evaluation strategies.
#Haskell lambda calculus interpreter free
Holds whenever Γ ⊢ t : σ → τ \Gamma \vdash t\!:\sigma \to \tau and x x does not appear free in t t. The simply typed lambda calculus ( λ → \lambda ^t
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