2 edition of Formal systems and recursive functions found in the catalog.
Includes bibliographical references.Description based on print version record.
|The Physical Object|
|Pagination||xvi, 57 p. :|
|Number of Pages||55|
|2||Studies in logic and the foundations of mathematics -- v. 40.|
|3||Studies in Logic and the Foundations of Mathematics -- v. 40|
|Some modal calculi based on IC / R.A. Bull Logic of interrogatives / M.J. Cresswell Some generalizations and applications of a relativization procedure for propositional calculi / Ronald Harrop Method for producing reduction types in the restricted lower predicate calculus / H. Hermes, D. Ro dding Distributive normal forms in first-order logic / Jaakko Hintikka Semantical analysis of intuitionistic logic I / Saul A. Kripke Set theory and higher-order logic / Richard Montague Existence in Lesniewski and in Russell / A.N. Prior Functions and rogators / A. Sloman Infinitely long terms of transfinite type / W.W. Tait Constructive order types, I / John N. Crossley Multiple successor arithmetics / R.L. Goodstein Unsolvable problems in the theory of computable numbers / B.H. Mayoh Predicative well-orderings / Kurt Schu tte Remarks on machines, sets, and the decision problem / Hao Wang.|
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Another useful abbreviation is to write list for. This predicate is true if the S-expression occurs among the elements of the list. In the case the expressionitself, is taken. Finally, the evaluation of is accomplished by evaluating with the list of pairs put on the front of the previous list. If and are S-expressions, so is. Examples of S-expressions are Here is an atomic symbol used to terminate lists.
The symbols are atomic in the sense that any substructure they may have as sequences of characters is ignored. In the case of the 's have to be evaluated in order until a true is found, and then the corresponding must be evaluated.
They are formed by using the special characters There is a twofold reason for departing from the usual mathematical practice of using single letters for atomic symbols. We shall now define the S-expressions S stands for symbolic. cdr [x] is also defined when x is not atomic.
car[x] is defined if and only if x is not atomic.
The expressions representing these functions are written in a conventional functional notation.
We shall then show how these functions themselves can be expressed as symbolic expressions, and we shall define a universal function that allows us to compute from the expression for a given function its value for given arguments.