| Luis Mandel. The Semantics of the Untyped Constrained Lambda Calculus. Technical Report Number 9319, Ludwig-Maximilians-Universitt, Leopoldstrae 11b, 80802 Mnchen, Germany, 1993. |
....and M an arbitrary (possibly constrained) term. The operational semantics of the calculus is given by an extension of the usual reduction rules of calculus. Additional rules describe the interaction between constraints and terms. The denotational semantics of this calculus is given (see [647]) and the semantic correctness of the reduction rules is demonstrated. In [248] the calculus is further extended with existential quantifiers. Existentially quantified variables are only computed by the constraint solver whereas the variables under the scope of a abstractor are computed inside ....
L. Mandel. The Semantics of the Untyped Constrained Lambda Calculus. Technical Report Number 9319, Ludwig-Maximilians-Universitat Munchen, Oct. 1993. \Phi.
....n, and in this way the term t which originally appeared meaningless acquires a meaning. Of course, since we are dealing with an untyped calculus it is still possible to define terms which have infinite reductions and so do not compute. The complete semantics of the calculus is presented in [Man93] 13 6 Examples In the following example we show how to calculate the area of a triangle. We fix the set of real numbers as the constraint domain. As function letters we have , Delta 2 (for square) As predicate letters we have the usual equality and the usual relation symbols , ....
Luis Mandel. The Semantics of the Untyped Constrained Lambda Calculus. Technical Report Number 9319, Ludwig-Maximilians-Universitt, Leopoldstrae 11b, 80802 Mnchen, Germany, 1993.
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